The effect of resonant magnetic perturbations on the impurity

Transcription

The effect of resonant magnetic
perturbations on the impurity transport
in TEXTOR-DED plasmas
Dissertation
zur
Erlangung des Grades eines
Doktors der Naturwissenschaften
an der Fakultät Physik und Astronomie
der Ruhr-Universität Bochum
von
Albert Josef Greiche
aus
Darmstadt
Bochum 2009
a
1. Gutachter: Prof. Dr. R. C. Wolf
2. Gutachter: Prof. Dr. H. Soltwisch
Datum der Disputation: 14. Mai 2009
Abstract
Thermonuclear fusion provides a new mechanism for the generation of
electrical power which has the perspective to serve humanity for several
millions of years. One possibility to implement fusion on earth is to magnetically confine hot deuterium tritium plasmas in so called tokamaks. The
fusion reactions take place in the hot plasma core. Each of the fusion reactions between deuterium and tritium yields 17.6 MeV which can be used
in the process of generating electrical power.
Impurities contaminate the plasma which then is cooled down and diluted. This leads to a reduction of the fusion reactions and in consequence
the energy yield. The transport behaviour of the impurities in the plasma
is not fully understood up to now. Nevertheless, experiments have shown
that the application of resonant magnetic perturbations (RMP) can control
the impurity content in the plasma.
The dynamic ergodic divertor (DED) on the tokamak Textor is able to
induce static and dynamic RMPs. During the application of RMPs transient impurity transport experiments with argon have been performed and
the time evolution of the impurity concentrations have been monitored.
The line emission intensity of the impurities in the plasma is measured
in the vacuum ultraviolet (VUV) and in the soft x-ray (SXR) with the
absolutely calibrated VUV spectrometer Hexos and SXR PIN diodes, respectively.
The analysis of the transient impurity transport experiments is performed with the help of the transport code Strahl. The impurity flows
in Strahl are described by a combination of a diffusive and a convective
flow. In the computing process the code solves the coupled set of continuity equations of each of the ionization stages of an impurity. With this
method the time evolution of the impurity ion densities and the line emission intensities of the ionization stages can be computed. The adaption to
the experimental measurements is performed with the help of the diffusion
coefficient and the drift velocity which influence the fluxes in the continuity
equations.
When no detectable tearing modes are excited in the plasma, the transient impurity transport experiments with argon do not show a change of
the impurity transport in the plasma core during the application of neither
static nor dynamic RMPs. As soon as a tearing mode is excited, the diffusion coefficient is increased in the vicinity of the mode. The excitation of
an m/n = 2/1 tearing mode leads to a vanishing of the internal sawteeth
oscillation and the excitation of an m/n = 1/1 internal kink mode. Both
modes lead to an additional local increase of the diffusive transport. It is
also observed, that in the presence of a high concentration of argon, the
rotation frequency of the m/n = 2/1 tearing mode reduces and the island
width increases. A possible reason can be an increase of the resistivity of
the plasma which can lead to a braking and growing of the island.
In steady state L-mode plasmas which have been heated with neutral
beam injection a change of the intensity ratio of different iron ionization
stages during the application of a static RMP implies a change of the iron
transport. Neither a reduction of the iron sources at the wall nor fluctuations of the background plasma can explain the change of the intensity
i
ratio.
The application of dynamic RMPs in ohmic-heated plasmas shows a
dependence of the total reduction of the iron concentration on the applied
rotation frequency of the RMP. The measurement with three different RMP
frequencies shows that the highest reduction of the iron concentration in
the plasma core occurs when the slip between the electron fluid in the
plasma and the RMP is lowest.
ii
Contents
1 Introduction
1
2 Background
2.1 Resonant magnetic perturbations . . . . . . . . . . . . . . . . . .
2.2 Transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3 Transport experiments . . . . . . . . . . . . . . . . . . . . . . . .
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4
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3 Experimental tools
3.1 Dynamic Ergodic Divertor on Textor . .
3.2 Hexos . . . . . . . . . . . . . . . . . . . .
3.3 Absolute intensity calibration . . . . . . .
3.4 Diagnostics and heating methods applied
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4 Method of analysis
4.1 Strahl code . . . . . . . . . . . .
4.2 Impurity particle source function .
4.3 Changes due to NBI . . . . . . . .
4.4 Errors of the transport coefficients
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5 Experimental results
5.1 dc DED in steady state plasma . . . . . . . . . . . . . .
5.2 Impurity transport with tearing modes . . . . . . . . . .
5.3 Plasmas with density pump out . . . . . . . . . . . . . .
5.4 Influence of dynamic RMP fields on impurity transport
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6 Summary and Outlook
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iii
List of Figures
iv
1.1
The tokamak . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1
2.2
2.3
2.4
2.5
2.6
Magnetic island . . . . . . . . . . . . . . . . .
Stochastic magnetic field lines . . . . . . . . .
Banana orbit . . . . . . . . . . . . . . . . . .
Transport regimes . . . . . . . . . . . . . . .
Radiative transition . . . . . . . . . . . . . .
Corona equilibrium vs. plasma with transport
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
3.10
3.11
Top view of the tokamak Textor. . . . .
Currents in DED coils . . . . . . . . . . .
Poincaré plot of 3/1 DED . . . . . . . . .
Reflectivity of Ni and Au . . . . . . . . .
Setup of Hexos . . . . . . . . . . . . . .
MCP saturation . . . . . . . . . . . . . .
Calibration of Hexos . . . . . . . . . . .
Voltage correction factors of the signals .
The determination process of the impurity
Fitted oxygen spectra . . . . . . . . . . .
Correction of the central SXR channel . .
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5
6
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4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
4.10
4.11
4.12
4.13
ne and Te of v/D variation test . . . . . . . . . . . . .
Influence of v/D ratio . . . . . . . . . . . . . . . . . .
Recycling fluxes of Strahl. . . . . . . . . . . . . . . .
Te in the SOL . . . . . . . . . . . . . . . . . . . . . . .
Estimated safety factor . . . . . . . . . . . . . . . . . .
Contributions to the neutral hydrogen density. . . . .
NBI cross section in the model . . . . . . . . . . . . .
Charge exchange recombination rates of Ar XVII . . .
Relative changes of the normalized emissivity . . . . .
Change of Ar XVI intensity time evolution due to NBI
Error determination for ne . . . . . . . . . . . . . . . .
Error determination for Te . . . . . . . . . . . . . . . .
Error determination for nH . . . . . . . . . . . . . . .
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5.1
5.2
The coilsets of the m/n = 3/1 DED base mode . . . . . . . . . .
Plasma scenario dc DED . . . . . . . . . . . . . . . . . . . . . . .
61
62
List of Figures
5.3
5.4
5.5
5.6
5.7
5.8
5.9
5.10
5.11
5.12
5.13
5.14
5.15
5.16
5.17
5.18
5.19
5.20
5.21
5.22
5.23
5.24
5.25
5.26
5.27
5.28
5.29
5.30
Fe XXIII, 13.3 nm and Fe XV, 28.4 nm . . . . . . . . . . . . . .
Reduction of central impurities and ω vs. IDED . . . . . . . . . .
Argon time traces in the VUV and SXR . . . . . . . . . . . . . .
Experimental and fitted argon time traces, dc DED, 2.4 kA . . .
Transport coefficients, dc DED, 2.4 kA . . . . . . . . . . . . . . .
Estimated shear . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Iron ratios and emissivities, dc DED, 2.4 kA . . . . . . . . . . . .
Fractional abundances if argon and iron . . . . . . . . . . . . . .
Plasma scenario with tearing modes . . . . . . . . . . . . . . . .
3/1 island in temperature profile . . . . . . . . . . . . . . . . . .
Reduction of impurities and rotation with tearing mode . . . . .
Ar in the VUV and SXR during tearing modes . . . . . . . . . .
Experimental and fitted argon time traces, locked tearing mode .
Diffusion coefficient, locked m/n = 3/1 tearing mode . . . . . . .
Experimental and fitted argon time traces, rotating tearing mode
Transport coefficients, rotating m/n = 2/1 tearing mode . . . . .
MHD frequency during argon puff . . . . . . . . . . . . . . . . .
Plasma scenarios with pump out . . . . . . . . . . . . . . . . . .
Reduction of central impurities and ne vs. IDED . . . . . . . . .
Argon time traces in plasmas with density pump out . . . . . . .
Experimental and fitted argon time traces, density pump out . .
Transport coefficients pumped out discharge . . . . . . . . . . . .
Plasma scenario ac DED . . . . . . . . . . . . . . . . . . . . . . .
Reduction of impurities during ac DED . . . . . . . . . . . . . .
Argon time traces during ac DED . . . . . . . . . . . . . . . . . .
Experimental and fitted argon time traces, ac discharges . . . . .
Transport coefficients, ac DED . . . . . . . . . . . . . . . . . . .
Reduction of Fe XXIII with respect to fslip . . . . . . . . . . . .
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v
vi
Glossary
~
∇
α
αI,Z
β
γ
Γ
ε
η
ϑ
λ
λAr,D
λD
µ0
ν
τ
τeq
ϕ
ΦW
χ
ω
Ω
a
Aik
~
B
B0
Bϑ
Bϕ
c
cF e
CXRS
D
DAM
DED
DRB
e
~
E
gradient
drift parameter
effective recombination rate coefficient
plasma beta (plasma pressure over magnetic pressure)
coefficient determined by thermal forces
particle flow
emissivity
resistivity
poloidal angle
wavelength
Coulomb logarithm for collisions between Ar and D
Debye shielding radius
permeability of free space
collision frequency
optical depth
thermal equilibration time
toroidal angle
particle flow to the wall
angular coordinate ϑ − (n/m)ϕ
toroidal angular rotation
solid angle
plasma radius
transition probability from level i to level k
magnetic field vector
magnetic field on the magnetic axis
poloidal magnetic field
toroidal magnetic field
vacuum speed of light
concentration of iron in the plasma
charge exchange recombination spectroscopy
diffusion coefficient
drift Alfvén mode
dynamic ergodic divertor
drift resistive ballooning mode
electron charge
electrical field vector
vii
Eϕ
EN BI
Er
ECE
ECRH
ETG
f
fϕ
fik
fslip
ft
fM HD
fRM P
fe∗
gi
Hexos
HFS
I
IDED
Ip
ITG
Jet
L
LC
Lm
Ln
LT
LBO
LCFS
LFS
m
me
mp
mI
MCP
MHD
n
ne
nH
ni
nI
nN BI
nZ
viii
toroidal magnetic field
energy of the neutral beam particles
radial electric field
electron cyclotron emission
electron cyclotron resonance heating
electron temperature gradient
frequency
frequency of toroidal plasma rotation
oscillator strength
slip frequency
fraction of trapped particles
MHD frequency, e.g. rotation frequency of a tearing mode
frequency of rotating magnetic field
diamagnetic drift frequency
statistical weight of level i
high efficiency XUV overview spectrometer system
high field side
intensity
effective current in the DED perturbation coils
plasma current
ion temperature gradient
joint european torus
length along the diameter of the absorbing ion density in the plasma
connection length
mean etendue
decay length of the density profile
decay length of the temperature profile
laser blow-off
last closed magnetic flux surface
low field side
poloidal mode number
electron mass
proton mass
impurity mass
multi channel plate
resonant magnetic perturbation
toroidal mode number
electron density
neutral hydrogen density
ion density
impurity density
neutral hydrogen density introduced by NBI
density of ionization stage with charge number Z
nli
N
NBI
p
p−1
P
r
rL
rmix
rs
R
R0
RMP
s
Sa
Sf
SI,Z
SOL
Spred
SXR
t
Te
Ti
TEM
Textor
TM
q
q0
qa
qs
~v
vD
vT
VUV
XUV
z
Z
Zef f
absorbing ion density
number of photons
neutral beam injection
pressure
inverse sensitivity
power
minor radius
Larmor radius
mixing radius due to sawteeth oscillation
radius of rational magnetic flux surface
major radius
major radius of the tokamak
resonant magnetic perturbation
shear
signal of detector at working voltage a
magnetic field screening factor
effective ionization rate coefficient
scrape off layer
survey poor resolution extended domain
soft x-ray
time
electron temperature
ion temperature
trapped electron mode
tokamak experiment for technology oriented research
tearing mode
safety factor
safety factor on the magnetic axis
edge safety factor in the cylindrical approximation
rational q = m/n of rational magnetic flux surface
velocity vector
drift velocity
thermal velocity
vacuum ultraviolet
extreme ultraviolet
r − rs , distance from O-point of an island
ion charge number
effective charge number in the plasma
ix
1 Introduction
The energy which is emitted by the sun is provided by thermonuclear reactions
[1] - [4] which take place in the hot and dense core of the star. In these reactions
four protons are fused to one helium nucleus. The mass of the generated helium
nucleus is lower than the sum of the four proton masses. According to E = mc2
with the energy E, the mass m, and the speed of light in free space c, the missing
mass is converted into energy.
This energy conversion can yield a large amount of energy such that a very
low amount of fuel is needed for the generation of electrical power. With today’s
total energy consumption the world wide resources on earth which are necessary
for fusion will last for several millions of years.
Fusion research aims at using fusion reactions in electrical power plants. Since
the conditions of the sun’s core, in particular the pressure of more than 2×1016
Pa, cannot be stationary provided on earth, it is not feasible to use the same
reaction as in the sun for the energy production.
One possibility to implement fusion power plants on earth is to magnetically
confine plasmas in which the fusion reactions take place. In the hot plasma the
particles are ionized and according to the Lorentz force they gyrate around the
magnetic field lines such that their movement perpendicular to the field lines is
reduced.
In the so called Tokamak (russian acronym for Toroidal’naya Kamera s Magnitnymi Katushkami - toroidal chamber in magnetic coils) the combination of
an external toroidal magnetic field Bt and a poloidal magnetic field Bp which
is generated by an induced plasma current, confine the plasma (figure 1.1 [5]).
A transformer, in which the plasma is the secondary coil, induces the plasma
current of several hundred kA to MA. Due to the plasma current and with the
help of additional heating devices the plasma reaches the temperatures which
are necessary for the fusion reaction to start
D+ + T+ → He2+ + n
In this reaction, the nuclei of the hydrogen isotopes deuterium (D) and tritium
(T) are fused into a helium nucleus (He) and a neutron (n) [6]. The energy
yield of this reaction is 17.6 MeV. The energy is used in the power generation
process of future tokamaks. The energy of the He nucleus will be stored in the
plasma core which will provide a constant heating. The maximum relative power
density of the fusion reaction between deuterium and tritium is at a temperature
of about 1 - 2×108 K.
1
1 Introduction
Figure 1.1: The tokamak principle.
During the operation of the fusion plasma, impurities contaminate the plasma.
They either originate from solid surfaces in the plasma chamber or in the case
of helium are produced by the fusion reaction. They dilute and cool down the
plasma which leads to a reduction of the cross section and the energy yield
becomes less efficient. Therefore, it is necessary to develop and study methods
which allow for a reduction of the impurity contamination. Up to now the transport processes of particles in the plasma are not fully understood. Nevertheless,
resonant magnetic perturbations (RMP) have turned out to be able to control
the impurity contamination. RMPs ergodize the confining magnetic field near
the resonant magnetic flux surfaces in the plasma. In former experiments on the
tokamak Tore Supra it has been observed, that the impurity contamination
could be reduced during the application of an RMP [7]. The reduction of the
impurity contamination has not been fully understood, yet, and is one of the
questions which are discussed in this thesis.
The application of an RMP also causes a variety of magneto-hydrodynamic
(MHD) phenomena like the excitation of tearing modes. A decrease of the
impurity transport has been diagnosed in former impurity transport experiments
on Textor in the presence of a locked m/n = 2/1 tearing mode [8], with
the poloidal and toroidal mode number m and n, respectively. This decrease
contradicts to theoretical predictions of an increasing effect on the transport
due to tearing modes [9] and is also a subject of this thesis.
The dynamic ergodic divertor (DED), a set of perturbation coils on the toka-
2
mak Textor, provides world wide unique possibilities for the study of rotating
resonant magnetic perturbations. With the help of the reduction of the impurity
contamination the dependence of the magnetic field screening on the relative slip
between the electron fluid in the plasma and the resonant magnetic perturbation
is studied.
We begin with a presentation of the theoretical background in chapter 2. The
3rd and 4th chapter describe the experimental methods and the analysis method
with the impurity transport code Strahl. The results of the impurity transport
experiments are presented in chapter 5. The last chapter provides a summary
of this thesis and a short discussion about further interesting topics which could
be studied in the future.
3
2 Background
This chapter presents the background which is relevant for the understanding of
the subject discussed in this thesis. It begins with a discussion about resonant
magnetic perturbations and its consequences on the magnetic field and the magnetic instabilities. Then different theories of transport are presented. It starts
with the collisional and anomalous transport. It is followed by an overview of
typical measurement techniques and the results of former impurity transport experiments. In the end theoretical studies about transport mechanisms induced
by resonant magnetic perturbations are presented.
2.1 Resonant magnetic perturbations
This section presents the consequences of the application of resonant magnetic
perturbations (RMP) on the magnetic field of a tokamak plasma. The first part
discusses the superposition of an RMP with the equilibrium magnetic field in
the vacuum approximation. In the second subsection the consequences on a
tokamak plasma are given.
2.1.1 Magnetic islands and stochasticity
In order to confine a plasma the kinetic pressure p of the hot plasma has to
be balanced by an external force [6]. In magnetic confinement fusion devices
~ The efficiency of the
this is performed by the equilibrium magnetic field B.
2
~
confinement due to B is represented by β = 2pµ0 /B with the permeability of
the free space µ0 .
~ consists of a toroidal and poloidal component. Toroidal
The magnetic field B
~ ϕ . The poloidal component B
~ϑ
field coils generate the toroidal component B
results from a combination of the magentic field of the plasma current Ip , the
poloidal field coils and in the case of divertor devices from the divertor coils.
The plasma current Ip is induced by a transformer. The poloidal field coils are
~ ϕ and B
~ ϑ in equilibrium
used for plasma positioning. The superposition of the B
with the plasma pressure yields the helical magnetic field of nested magnetic
flux surfaces of a tokamak.
In the poloidal plane (ϑ plane) the magnetic field lines perform one complete
rotation after a certain number of toroidal circulations ∆ϕ. This is reflected by
the safety factor q
q=
4
∆ϕ
2π
(2.1)
Figure 2.1: The comparison between the nested magnetic flux surfaces with and
without a magnetic island in the (z, χ) plane. According to [6].
Magnetic field lines with the same safety factor form toroidal surfaces in tokamaks with an axisymmetric magnetic equilibrium. In typical tokamak plasmas
q increases from the plasma core towards the plasma edge.
At Textor the safety factor at the plasma edge qa can be expressed in the
cylindrical geometry
Bϕ
qa = 5 × 106 a2 ·
(2.2)
R0 Ip
with the plasma radius a, the major radius of the tokamak R0 and the plasma
current Ip .
The topology of the magnetic field can be changed by a magnetic perturbation
which is resonant to a magnetic flux surface s at r = rs with a rational q = qs =
m/n with the poloidal and toroidal mode number m and n, respectively. We
will first neglect the plasma response, i. e. we discuss the magnetic fields in the
vacuum approximation.
The superposition of a resonant magnetic perturbation (RMP) with the helical
magnetic field lines of a tokamak can lead to the formation of so called magnetic
islands. Figure 2.1 shows the magnetic flux surfaces with and without a magnetic
island. The flux surfaces are plotted against the angular coordinate χ = ϑ −
(n/m) · ϕ, which is orthogonal to the helical magnetic field line, with z = r − rs .
Inside of those islands the field lines build nested helical magnetic surfaces with
a new magnetic axis in the region of the so called O-point of the island. The edge
of the island is determined by two parts of a separatrix. The maximum radial
distance between the two parts determines the island width. The intersection
point of the two parts is the so called X-point of the island. On the separatrix
5
2 Background
Figure 2.2: Poincaré plot of the stochastic magnetic field lines in a toroidal
configuration.
of a magnetic island the magnetic field lines connect points with different radii
such that a charged test particle can cross this radial distance by a propagation
along the magnetic field line.
Resonant magnetic perturbations which are resonant to more than one magnetic flux surface with rational q induce several chains of magnetic islands. As
long as the width of each of the islands is smaller than the radial distance between the island chains all of the magnetic field lines lie within the magnetic flux
surfaces [6]. When the island widths grow above this separating distance, the
islands overlap. The trajectories of the magnetic field lines become stochastic,
i.e. the magnetic flux surfaces are destroyed and the field lines fill a stochastic
volume (figure 2.2). This property is called stochasticity. The behaviour of the
magnetic field lines in a stochastic plasma can be described with the help of
magnetic field line diffusion.
2.1.2 Tearing modes
On a magnetic flux surface s with a rational qs = m/n in a tokamak plasma
an RMP destabilizes the tearing instability by modifying the current density
profile. If the destabilization is above a certain threshold the magnetic field
lines on the resonant magnetic flux surface are teared. The reconnection of the
magnetic field lines leads to tearing modes in form of magnetic islands [6].
Charged particles can propagate very fast along the magnetic field lines compared to their propagation perpendicular to the field line. On the separatrix of
the tearing mode this leads to an equilibration of the pressure between points
with different radii. This equilibration leads to a flattening of the radial density and temperature profile at the location of the magnetic island, i. e. the
gradients of the radial profiles vanish around the tearing mode location.
6
Usually the m = 2 tearing modes are the most unstable ones and therefore,
they are destabilized most frequently in comparison with other mode numbers.
If the tearing mode is excited by an external resonant magnetic perturbation
the rotation of the mode can be phase locked to the perturbation and the mode
is then called ”locked”. A mode which is not phase locked to a magnetic perturbation rotates with its MHD frequency fM HD .
2.1.3 Magnetic field screening
In order to excite a tearing mode, the resonant magnetic perturbation has to
exceed a critical perturbation strength before the mode is excited [10]. This
process of mode excitation is the so called mode penetration. When penetrating
the plasma the RMP induces screening currents which are driven around the
resonant magnetic flux sufaces [11]. The magnetic field which results from the
vacuum approximation is altered due to the presence of the plasma.
On the tokamak Textor experimental and theoretical studies have shown
that the threshold current of an external perturbation coil which is needed for
the excitation of the m/n = 2/1 tearing mode depends on the relative rotation
between the plasma and the RMP [12] - [14]. If there is no relative rotation the
threshold current of the external perturbation coil is the lowest. A high relative
rotation increases the threshold current. In particular, in order to achieve the
minimum threshold current, it has been found that the frequency of the RMP
fRM P has to match the MHD frequency of the tearing mode fRM P = fM HD =
fϕ + fe∗ with the toroidal plasma rotation frequency fϕ and the electron diamagnetic drift frequency fe∗ . An approximation of fe∗ can be calculated according
to [15]
− 7
3
2mTe (0) qa
q
∗
fe =
−
1
(2.3)
πBϕ a2
q0
q0
with the central electron temperature Te (0). When sawteeth are present in the
plasma, the central safety factor q0 can be expressed by q0 = qa /(qa + 1) [15].
The electron diamagnetic drift frequency is the rotation frequency of the electron fluid in the plasma. Without plasma rotation the MHD frequency equals
the electron diamagnetic drift frequency. Therefore, the lowest threshold current for the excitation of the m/n = 2/1 tearing mode is achieved with fRM P
= fe∗ . This condition indicates that the relative rotation between the RMP and
the electron fluid inhibits mode penetration.
2.1.4 Sawteeth
During the operation of a tokamak plasma the central plasma inside the q = 1
magnetic flux surface oscillates sawtooth-like, which can be observed e. g. in the
electron temperature and the plasma pressure [6]. The oscillation starts with a
slow ramp phase in which e.g. the electron temperature increases steadily. The
ramp phase ends with a fast relaxation of the plasma parameters, the so called
7
2 Background
sawtooth crash, to the values in the beginning of the ramp phase. Outside√of the
q = 1 shell inverted sawteeth are observed up to a radius of about rmix = 2rq=1
with the radius rq=1 of the q = 1 surface. This indicates that due to the sudden
relaxation of the core plasma parameters the thermal energy of the plasma core
is released to the region outside the q = 1 surface as a heat pulse.
The mechanism of the sawtooth oscillation is not fully understood up to now.
But it is assumed that as soon as the central q becomes smaller than one the
ramping of the core plasma parameters leads to a destabilization of an m/n =
1/1 instability, i. e. an internal kink mode on the q = 1 magnetic flux surface
[16]. This mode causes reconnections of the magnetic field lines and a flattening
of the central q profile. This leads to a sawtooth crash and starts a new sawtooth
cycle.
If impurities are present in the tokamak plasma, the sawtooth crashes expel
them from the plasma core [17]. Inside rmix the impurity density profile becomes
hollow, i. e. the maximum of the impurity density is not located on the axis
anymore but on a shell around the axis.
In the presence of an m/n = 2/1 tearing mode it has been observed that the
sawtooth oscillations either vanish or their frequency is changed. The reason
for the stabilization of the sawtooth oscillation is not fully understood up to
now. The large size of the m/n = 2/1 tearing mode leads to a distortion of the
magnetic flux surfaces further inside the plasma [18]. It has also been observed
that the m/n = 1/1 internal kink mode couples to the m/n = 2/1 tearing
mode. Since the m/n = 1/1 internal kink mode is assumed to be related to the
sawtooth oscillations [19], the coupling to the m/n = 2/1 tearing mode can be
a reason for the stabilization of the sawtooth oscillations.
2.2 Transport
The propagation of charged particles in the confined plasma causes fluctuations
of the local electric and magnetic fields [16]. The forces which result from
those fluctuations interact with the charged particles and induce transport. The
definition of the transport due to these fluctuations is governed by the Debye
shielding length λD .
The Debye shielding length determines the length scale below which quasineutrality cannot be assumed anymore. In typical tokamak plasmas the charge
density is such that charge separation does only occur on small length scales
and the plasma is quasi-neutral [6].
If the length scale of those fluctuations is below or equal λD the fluctuations
cause Coulomb collisions and collisional transport, respectively. Fluctuations
which have length scales much larger than λD are the cause of the anomalous and turbulent transport, respectively. The radial displacements which are
caused by Coulomb collisions between different species are subject of the classical
and neoclassical transport which describe the transport in a cylinder and torus
8
2.2 Transport
geometry. The transport which is induced by turbulences is called anomalous
transport.
Since in this thesis the neoclassical transport is not considered in the analysis,
we only briefly discuss the classical and neoclassical case. The anomalous case
discussed in the end of this section.
2.2.1 Classical transport
The classical transport is caused by the friction forces due to collisions in the
~ and the
cylindrical geometry which are perpendicular to the magnetic field B
~
pressure gradient ∇p [6]. In the fluid description the classical diffusion coefficient
Dcl is determined by Dcl = ηpB −2 with the resistivity η. The classical diffusion
2 with the collisionality of the electrons ν and
coefficient is proportional to νrL
the electron Larmor radius rL .
Diffusion can also be described by a random walk of a particle. The step
length is then determined by the average displacement of the particle due to a
collision. The step time is the average time between the collisions. Since charged
particles gyrate around magnetic field lines the average displacement due to a
collision is the gyration radius, i. e. the Larmor radius. Therefore, an ansatz
with the help of a random walk model yields the same proportionality for the
classical transport as the fluid description. In such an ansatz the step length is
rL and the step time is ν −1 .
2.2.2 Neoclassical transport
The neoclassical transport is caused by the friction forces in the toroidal geom~ and the pressure gradient ∇p
~
etry which are parallel to the magnetic field B,
[16]. The neoclassical transport can be distinguished in three regimes which are
determined by the collisionality of the plasma. We speak of high collisionality if
the mean free path of the particles is shorter than the connection length along
a magnetic field line between the inside and outside of the torus. If the mean
free path is longer than the connection length the plasma is collisionless. In a
collisional plasma the neoclassical transport is in the Pfirsch-Schlüter regime, in
the collisionless case in the banana regime. The transition between the latter
two cases is the plateau regime. A very detailed description of the neoclassical
transport is presented in [20].
Pfirsch-Schlüter transport
We start with the discussion of the Pfirsch-Schlüter transport [6]. The toroidal
geometry of the plasma gives rise to a force which is directed to the outer side
of the torus, i. e. the hoop force. In order to confine the plasma the magnetic
field has to balance this force. The balancing force results from the so called
Pfirsch-Schlüter current which flows along the magnetic field lines. This current
induces a diffusive radial flow due to resistive dissipation.
9
2 Background
Figure 2.3: Exemplary banana orbit of a trapped particle in the ϑ plane
By first neglecting the inductive toroidal electric field Eϕ the contribution of
2 with η bethe Pfirsch-Schlüter transport to the diffusion is DP S = 2q 2 ηk p/Bϕ,0
k
ing the parallel component of the resistivity, the safety factor q = rB0 /R0 Bϑ for
a large aspect-ratio torus with circular cross-section, and the magnetic field B0
at the major radius R0 . The parallel resistivity shows that the Pfirsch-Schlüter
contribution is caused by the parallel friction forces in the toroidal geometry.
In addition, the Pfirsch-Schlüter diffusion coefficient exceeds the classical diffusion coefficient by 2ηk q 2 /η⊥ with η⊥ being the perpendicular component of the
resistivity.
By considering an additional electric field Eϕ which is generated by induction,
a radial flow velocity v = −Eϕ Bϑ /B 2 yields an additional convective term to
the radial transport. In the presence of thermal forces further terms appear
which are proportional to dT /dr.
Banana regime transport
Having discussed the transport in a high collisionality regime we now focus
on the transport in the low collisionality regime. In order to give a heuristic
estimate of the diffusion coefficient in this regime, we analyze the dependences
of the particle trajectories [6]. Due to the toroidal configuration of the magnetic
field, Bϕ is proportional 1/R with R being the distance from the main axis of
the torus. Therefore, near the main axis of the torus the vacuum magnetic field
is higher than far away from the main axis. This determines the high field side
(HFS) and the low field side (LFS) of the torus. Due to the inhomogeneous
magnetic field, the particles flowing with a low parallel velocity vk,0 along the
magnetic field lines at the LFS are reflected due to the magnetic mirror effect
at the HFS (figure 2.3).
Due to the shape of the orbits in the ϑ plane they are called banana or~
bits. When vp
⊥,0 is the velocity perpendicular to B at the LFS and the relation
vk,0 /v⊥,0 < 2a/R0 holds, the particles are trapped in banana orbits. The
particles complete the banana orbits only in plasmas with a low collisionality
10
2.2 Transport
ν < (a/R0 )3/2 vT /(Rq)
p with ν being the frequency for 90° collisions, the thermal velocity vT = T /m, the temperature T (eV) of the particle and its mass
m. In order to detrap the particles due to collisions the effective collision frequency νef f = νR0 /a has to fulfill νef f < ωbf with the trapped particle bounce
frequency ωbf .
p
The√width of the banana orbits is wbo ∝ qrL R0 /a with the Larmor radius
rL = 2mT /(ZeB), the charge state Z and the elementary charge e.
The diffusion process of a particle can be simulated by a random walk. The
random walk is determined by the step length wbo and step frequency νef f
2 ν
which results in a diffusion coefficient wbo
ef f . Since only the trapped particles
contribute to this diffusive transport, the diffusion coefficient of the banana
transport regime is given by
DB ∝
r
a
2
νef f wbo
∝
R0
R0
a
3
2
q
2
2
νrL
=
R0
a
3
2
2ηk q 2
Dcl
η⊥
p
with the fraction of trapped particles a/R0 .In this estimate the proportionality
ηk ∝ mν/(e2 n) is used with the particle density n.
Plateau transport
The transport in the collisionality regime between the Pfirsch-Schlüter and Banana transport regime in
a
R0
3
2
vT
vT
<ν<
Rq
Rq
(2.4)
is driven by particles with a low vk . These particles circulate very slowly in
the torus and during the toroidal circulation they collide with small angles with
∆vk /vk . We can calculate vk by comparing the toroidal circulation frequency
which is ∝ vk /(Rq) with the effective small angle collision frequency ν(vT /vk )2 .
This comparison yields the resonant velocity
vk
∝
vT
νRq
vT
1
3
(2.5)
Using the boundaries from relation (2.4) in (2.5) we get the boundaries of vk for
this collisionality regime
r
a
vk ∝
·v
and vk ∝ vT .
(2.6)
R0 T
In order to estimate the corresponding diffusion we perform a heuristic random
walk approach. By taking into account the magnetic drift with the drift velocity
vD = rL ∇⊥ B/(v⊥ B) the step length is d ∝ vD t with the transit time t ∝ Rq/vk
11
2 Background
Figure 2.4: The variation of the diffusion coefficient in the different collisional
regimes.
which determines the collision frequency of the particles. The fraction of the
particles with a resonant velocity is vk /vT
DP ∝
vk 2 Rq
v q 2
v
∝ T rL
vT D vk
R
(2.7)
which does not depend on the resistivity and therefore is independent of collisions. Figure 2.4 shows the development of the diffusion coefficient with respect
to the collisionality. Since the diffusion coefficient DP does not depend on the
collisionality the transport regime which is described with this diffusion coefficent is called Plateau transport.
2.2.3 Anomalous transport
The neoclassical transport theory is not able to explain the particle transport in
many experimental conditions. The observed diffusive and convective processes
exceed the neoclassical processes typically by about one order of magnitude.
The transport has been considered to be anomalousy high and therefore it has
been called anomalous transport. Since fluctuations with a length scale which
is much larger than the Debye length are often the predominant mechanism for
the radial transport this transport regime is also called turbulent transport [16].
Drift instabilities which are micro instabilities are thought to cause the anomalous transport [21] - [23]. Drift instabilities are generated by the dissipative
effects which occur due to the destabilization of electrostatic waves, the drift
waves, in a low-β plasma. In the fluid description of the plasma the drift waves
12
2.2 Transport
are caused by diamagnetic drifts which occur due to the gradients in temperature
and density [16].
It is assumed [16] that the most probable explanation of the anomalous transport is caused by a drift instability, the ion temperature gradient (ITG) mode.
The ITG modes occur due to the 1/R dependence and the toroidal geometry
of the magnetic field Bϑ in a tokamak. If the ratio between the radial decay
~ ln n|−1 )r and the radial decay length of the ion
length of the density Ln = (|∇
−1
~ ln Ti | )r rises above a critical threshold, the ITG mode
temperature LTi = (|∇
is destabilized [16], [24].
ITG modes play a significant role in the ion heat transport whereas electron
temperature gradients (ETG) modes and trapped electron modes (TEM) play
a significant role in the electron heat transport. The particle transport can be
influenced by the interaction of the ITG and TEM.
In order to analyze the contributions of the anomalous transport
p TEM have
to be taken into account. A significant fraction of electrons ft = 2r/(R0 + r)
is trapped in a low collisionality plasma [6], [25] and therefore the destabilization
of the TEM can contribute to the anomalous transport.
Other drift instabilities, which are important for the anomalous transport, are
the drift resistive ballooning mode (DRB) and the drift Alfvén mode (DAM).
The DRB is destabilized due to the curvature in the tokamak [6], [26]. At the
HFS the curvature is away from the plasma which stabilizes the DRB but at
the LFS with a curvature pointing towards the plasma the DRB is destabilized
due to resistive effects. Unstable DRBs tend to expand analogue to a balloon
which is pumped up, i.e. they have a ballooning character [24]. A model of the
anomalous transport which is driven by the DRB is presented in [26].
The DAM is a combination of magnetic fluctuations and drift modes. They
are destabilized by resistive effects and can lead to micro-tearing instabilities
which contribute to the anomalous transport.
However, since the anomalous transport is still not fully understood, in this
thesis the diffusive and convective contribution of the anomalous and neoclassical transport are determined by a simple plasma fluid description. In this
description the particle flows consist of a diffusive and convective part and are
computed with the help of the continuity equation. For a more detailed description see chapter 4.
2.2.4 Impurity transport
Experiments have shown that the impurity transport in a tokamak plasma is a
combination of a neoclassical and an anomalous contribution [6], [27] - [29].
The neoclassical contribution of the impurity transport is caused by the collisions between unlike particles, i. e. plasma ions and impurities. These collisions
lead to friction forces which change the density profile of the impurities nZ . The
frictional forces disappear when
13
2 Background
1 dnZ
Z dni
γ dT
=
+
nZ dr
ni r
T dr
(2.8)
with the coefficient γ depending on the thermal forces. Without thermal
forces (2.8) becomes
nZ (r)
=
nZ (0)
ni (r)
ni (0)
Z
(2.9)
For tokamaks this means that in the absence of thermal forces the neoclassical component of the impurity transport causes high impurity densities in the
plasma core which implicates a serious dilution of the plasma and a high energy
loss due to radiation. In the presence of thermal forces, γ can become negative
which reduces the consequences of (2.9). This temperature screening effect is
changed with the transport regime of the plasma ions and the impurities.
Due to the higher mass and the higher charge of the impurities, they usually
have high collisionalities such that their neoclassical transport is governed by the
Pfirsch-Schlüter transport. In order to analyze the temperature screening effect,
we divide the Pfirsch-Schlüter transport in two subdivisions, the intermediate
Pfirsch-Schlüter regime and the extreme Pfirsch-Schlüter regime. The particles
are in the intermediate Pfirsch-Schlüter regime when the collisionality is too low
to cause a Maxwellian plasma ion distribution. The non-Maxwellian plasma
ion distribution can also arise in the Pfirsch-Schlüter regime when the plasma
is contaminated with impurities. Due to the impurities the relaxation time
to get a Maxwellian plasma ion distribution can be higher than the time for
90° collisions. It has been shown that temperature screening happens in the
intermediate Pfirsch-Schlüter regime [6]. If the collisionality is high enough the
particles are in the extreme Pfirsch-Schlüter regime in which no temperature
screening takes place. The extreme Pfirsch-Schlüter regime usually appears
only near the plasma edge whereas the central plasma is in the intermediate
Pfirsch-Schlüter regime. Therefore the temperature screening effect screens the
impurities from the plasma core.
Although the anomalous contribution of the impurity transport is not completely understood up to now, the radial particle flux Γ with charge state Z,
averaged over a magnetic flux surface can be adequately described by an empirical formula
Γ = −D
dnZ
2r
+ α 2 nZ
dr
a
(2.10)
with the diffusion coefficient D and the drift parameter α. Usually α ∝ v/D
with the inward drift velocity v. The inward drift velocity has a neoclassical contribution which results from the neoclassical inward pinch effect and an
anomalous contribution which is not fully understood up to now. The peakedness of the impurity concentration profile, which is the ratio nZ (0)/nZ (r), is
14
2.3 Transport experiments
represented by the drift parameter α since according to (2.10) and assuming
nZ (0)/nZ (r) > 1 the diffusion leads to an outward flow whereas the inward
drift velocity leads to an inward flow. The balance between those flows determines the peakedness nZ (0)/nZ (r) of the impurity concentration. In typical
tokamak plasmas v is usually directed inward such that the concentration profile
of the plasma ions and the impurities is peaked in the center.
There are different experimental methods which can be applied for the study of
the impurity transport in toroidal plasmas. All of those experimental methods
need informations about the impurity ion density distribution. One method for
the analysis of the impurity transport is to measure the ion density profile of
intrinsic impurities which contaminate the plasma due to plasma wall interaction processes [7], [30] – [32]. The shape of the impurity ion density profile is
determined by the ratio of the inward pinch velocity and the diffusion coefficient.
A change of the ion density profile is thus caused by a change of the impurity
transport.
The injection of extrinsic impurities can be performed in perturbative studies
with several methods which we now briefly discuss.
Non gaseous elements can be injected by laser blow-off (LBO) and laser ablation [33] – [38]. LBO and laser ablation require a short (< 1 ms) pulse laser
system (< 1 ms). The laser irradiates the frontside of a target from which the
element is injected into the plasma. In LBO the injected material originates
from the backside of a thin target and is detached due to a shockwave induced
by the laser pulse. In laser ablation the material on the frontside of the target
is heated such that a laser plasma is generated from which the particles are
entering the tokamak plasma.
Another method to inject solid elements is pellet injection [39]. With the help
of a special injection system frozen hydrogenic pellets which can be seeded with
impurities are accelerated and ejected into the plasma. With this method it is
possible to either inject the impurities directly into the core plasma or to use
the perturbation induced by the pellet for transport studies.
Transient impurity transport experiments with gas injection experiments are
performed with a fast injection valve [28], [29], [40] – [43]. The valve is opened
for about 1 ms and introduces the gaseous impurity atoms into the plasma.
With the help of sinusoidally modulated gas injection in long pulsed plasmas
the transport can be analyzed with the help of a harmonic analysis of the impurity radiation [44]. After the injection the time development of the impurity ion
density distribution in the plasma is monitored and analyzed with a transport
code in order to determine the diffusion coefficient and the drift velocity.
The impurity transport experiments on the tokamak Textor have been performed with the transient injection of the gaseous impurity argon. The tem-
15
2 Background
perature in typical Textor plasmas is such that the different ionization stages
of argon are present from the edge to the central plasma. With the highest
ionization stage being Ar16+ (Ar XVII) the emission from the ionization stages
of argon allow for a transport analysis over most of the minor radius.
The measurement of the impurity ion density nI,Z can be performed by active
and passive spectroscopy. Active spectroscopy can be performed with the help
of laser induced fluorescence or fast neutral particle beams which enables charge
exchange recombination spectroscopy (CXRS) [16], [29]. In CXRS an impurity
I with charge state Z recombines into an excited level due to a collision with
the fast neutral particles, e. g. hydrogen H
I+Z + H → I+(Z−1) (n, l) + H+
(2.11)
with the principal and orbital quantum number n and l of the excited level.
The ion density can be derived from the measured intensity with the help of the
0
emission coefficient cx
n→n0 for the transition from the excited state n to state n
cx
n→n0 =
1
n n X cx 0 (λ)
4π I,Z H n→n
(2.12)
with the product of the effective rate coefficient for charge exchange recombinacx
tion with the photon energy Xn→n
0 (λ) and the density of the neutral particles
nH . In (2.12) only particles with full beam energy are taken into account.
Charge exchange reactions with neutral particles with less than the full beam
energy have to be added to (2.12).
In passive spectroscopy the characteristic line emission intensity of resonance
lines is measured. The upper levels of the resonance lines are excited due to
collisions with the electrons since the plasmas in a tokamak usually are optically
thin. Therefore, in order to calculate the line emission due to radiative decay,
the population density of the ions in the excited level is needed. In the limit of
a low density plasma as in the solar corona with ne ≈ 1015 m−3 , the so called
coronal limit [45], the time constants of the radiative decay of the excited levels
are usually much shorter than the characteristic transport time. In addition only
two body collisions between ions and electrons have to be taken into account
since the collision rates of three body collsions are very small so that they can
be neglected.
The electron density for which the coronal limit is applicable is proportional
to (Z + 1)7 with the charge of the ion Z [45]. For Z = 0 and Z = 9 the electron density has to be smaller than 1022 m−3 and 1029 m−3 , respectively. The
coronal limit can be applied for the allowed radiative decays into the ground
state for highly ionized impurity ions in typical tokamak plasmas. The equilibrium between the ground state and the excited states is the so called coronal
equilibrium.
In the case of non-resonant line emission a collisional radiative approach has
to be applied in order to determine the equilibrium between the states. This
16
Figure 2.5: Radiative transition from level i to the levels k and j, respectively,
with the photon energy hc/λ.
approach takes into account the excitation due to electron collisions from the
ground state and other excited states, the de-excitation from higher states, and
charge exchange with neutral particles. In tokamak plasmas the contribution of
the electron collisions is the dominating excitation mechanism.
In order to obtain the measured intensity from the transition of level i to level
k, the emissivity of the impurity ion density distribution is needed
=
1
ne nI,Z XI,Z (λik )
4π
(2.13)
with the electron density ne and the effective emission rate coefficient XI,Z (λik )
which is the product of the excitation rate coefficient and the photon energy.
The emissivity is integrated along the line-of-sight (los)
Z
1
Aik
P
Li→k =
f n ne XI,Z (λik )dl
(2.14)
4π j<i Aij los Z I
with the transition probabilities from level i to level k and j, Aik and Aij ,
respectively, and the fractional abundance fZ = nI,Z /nI . Usually there is more
than one level below the energy level i in which the electron can decay (figure
2.5). Therefore, only a fraction of all of the decays P
happen from level i to level
k. This fraction is determined by the factor Aik / j<i Aij which reflects the
branching ratios of the transition probabilities.
17
2 Background
100
100
90
80
90
Ar IX
Ar V
80
60
fraction nI,Z/nI (%)
fraction nI,Z/nI (%)
Ar VII
70 Ar IV
Ar VI
50
40
Ar X
30
60
Ar IX
Ar II
Ar VII
50
40
Ar V
Ar III
Ar IV
Ar VIII
Ar VI
30
Ar VIII
20
20
Ar XI
10
10
0
10
70
20
30
40
Te (eV)
50 60 70 80
0
10
100
(a) Corona equilibrium
20
30
40
Te (eV)
50 60 70 80
100
(b) Plasma with transport
Figure 2.6: The ionization stage distribution for argon in the corona equilibrium
(a) and in a plasma with transport (b).
In plasmas in the corona equilibrium the radial distribution of each of the
impurity ionization stages in the plasma is determined by the radial electron
temperature distribution (figure 2.6(a)). If the highest temperature is not sufficient to completely ionize the element, the radial distribution of the ionization
stages provides information about the complete line-of-sight. In plasmas with
radial transport the distribution of the ionization stages is shifted towards higher
temperatures and is broadened (figure 2.6(b)).
Former studies of the impurity transport have shown that in the central plasmas of the tokamaks Aug [28], Pbx [30], Atc [33], and Textor [46] the transport coefficients are very low in the order of 10−1 - 10−2 m2 s−1 . At Aug and at
the Atc tokamak the transport coefficients derived by the neoclassical theory
can reproduce the experimental findings in the plasma core.
Between the plasma core and the plasma edge a transition from low diffusion to high diffusion has been found at Aug [28], Alcator C-Mod [34], Tore
Supra [35], Tftr [36], Textor [40], Nstx [41] and Jet [47]. During the transition the diffusion coefficient increases from about 10−1 m2 s−1 to a few m2 s−1
which is about one order of magnitude higher than the neoclassical diffusion
coefficient. This shows that towards the plasma edge the impurity transport
becomes anomalous.
At AUG [28], Tore Supra [35] and Jet [47] the transition region has been
located at a magnetic shear
s=
r dq
q dr
(2.15)
of about 0.5. Below a shear of 0.5 the diffusion coefficient has been low and
above 0.5 the diffusion coefficient has been high.
18
At Textor the anomalous diffusion coefficient has been compared with computed diffusion coefficients from an ITG transport model and from a gyro-Bohm
transport model, respectively [40]. The modelled diffusion coefficients have fitted to the experimental diffusion coefficient.
Indications of a Z-dependent impurity transport between low-Z and mid-Z
impurities are reported from Aug [28], Tftr [36] and Pbx [30] whereas studies
with low-Z impurities at Jet [29] do not show a Z-dependence.
Experimental transport studies with argon in plasmas with excited tearing
modes have concluded that the impurity transport is decreased due to the island
[8]. In contradiction to this conclusion theoretical studies have shown, that
the deviation from the symmetry of the equilibrium magnetic field which is
introduced by the tearing mode leads to a significant increase of the plasma
transport in the vicinity of the island [9].
This thesis discusses the consequences of stochastic magnetic fields on the
impurity transport. Although it is difficult to observe the stochasticity of a
plasma it is assumed that stochastic plasma volumes decrease the confinement
of the plasma [6]. On Tore Supra the stochastic magnetic field has been
applied with the ergodic divertor (ED). Impurity transport experiments have
shown that the impurity contamination has been reduced during the activation
of the ED [7], [32].
In [7] transient impurity transport experiments on Tore Supra with laser
blow-off injected nickel do not show a screening of nickel during the activation of
the ED. The confinement of the injected impurities has always been increased.
Therefore, a transport barrier near the edge has been introduced in order to
simulate the experiment. Measurements of the intrinsic carbon emission lines
have indicated an increase of the diffusive transport during ED activation. It
has not been possible to find transport coefficients which satisfactory model the
injected nickel and the intrinsic carbon behaviour.
The production and circulation of carbon in Tore Supra edge plasmas has
been studied in [32]. The sources of carbon at the wall have been monitored with
cameras and optical fibres. With the help of a simplified 3D test particle model
the fraction of carbon which penetrates the plasma core, i. e. the screening
efficiency has been computed. The model tracks the motion of impurity ions
at a certain radius in the vicinity of the wall until the ions are neutralized or
penetrate the core plasma. With the help of the screening efficiency this paper
has shown that the reduction of the carbon contamination during the activation
of the ED is caused by an increase of the screening efficiency, i. e. the fraction
of carbon particles penetrating the core plasma has decreased.
There are also several theoretical studies about the consequences of stochastic
magnetic fields on the transport properties of the plasma [48], [49], [50]. All
of them state an increase of the transport due to the stochastization and a
reduction of the impurity contamination. In [48] and [49] an increase of the
diffusive transport is expected.
A study of the diffusive transport in a stochastic plasma edge is performed in
19
2 Background
[48]. The edge diffusion coefficient in this model is coupled to the magnetic field
line diffusion coefficient via the thermal speed of the protons. The neoclassical
transport is neglected. With the help of an purely diffusive ansatz for the
anomalous transport, the edge diffusion coefficient is increased due to magnetic
field line diffusion in the stochastic plasma. It is assumed that all of the particles
in the plasma have the same diffusion coefficient. The stochastization has then
to lead to a convection parallel to the magnetic field lines with the thermal speed
vp of the protons. Due to the viscosity of the plasma all of the heavier particles
are flowing with vp . This leads to an increase of the diffusion in the stochastic
edge plasma by a factor of 3. This increase causes a reduction of the particle
confinement time and reduces the impurity contamination of the plasma.
A stochastic edge layer induced by the ripples of the toroidal field is studied
in [49]. The impurities are driven out of the plasma by an anomalous outward
flow along the stochastic field lines. Inward flows due to thermal forces drive
impurities into the plasma. The balance between the inward and outward flow
determines the impurity content in the plasma. The averaged flows of the impurities and the plasma are expressed with the help of magnetic field line diffusion
coefficients. For large tokamaks the stochastic plasma edge reduces the impurity
content. It is noted that the model uses a simple model for impurity penetration into the plasma. Therefore, the application of a more realistic impurity
penetration model will yield more correct results [49].
Reference [50] predicts an increase of the convective outward transport in
a stochastic edge plasma. This convection drives out the particles which are
introduced into the plasma, e.g. by recycling processes. Frictions with the
plasma ions are the cause of the outward convection which enhances the impurity
exhaust. The model computes the diffusive and convective flow in the trace
impurity limit in which the interactions between the impurity particles can be
neglected. This analysis shows that the increase of the diffusivity due to the
stochastic plasma cannot explain the reduction of the impurity contamination.
Due to the high mass of the impurities the thermal motion is too slow and yields
only a neglectable contribution to the radial transport. The convective transport
is computed by considering the heat and background particle transport. The
background particles flow towards the wall and due to collisions an outward
convection of the impurities is driven. This convection leads to the reduction of
the impurity contamination of the plasma.
20
The experiments which are discussed in this thesis are performed with plasmas
from the limiter tokamak Textor with a major radius R = 1.75 m and a minor
radius ra = 0.47 m. Sixteen copper coils generate a maximum toroidal magnetic
field of BΦ = 3 T and a transformer with an iron core induces a maximum current
of I = 800 kA responsible for the poloidal magnetic field in the plasma.
The studies which are presented in this thesis need a variety of diagnostic tools
which are already described in several papers and doctoral theses. This chapter
only presents the details of the most important diagnostics which have been used
to perform the experiments. The first section describes the Dynamic Ergodic
Divertor on Textor. The newly developed vacuum ultraviolet spectrometer
Hexos and its absolute calibration is presented in the second and third sections.
The last section contains a brief description of the diagnostics used.
3.1 Dynamic Ergodic Divertor on Textor
In Textor [51] resonant magnetic perturbations are excited with the Dynamic
Ergodic Divertor (DED) [52], [53]. The main aims of the DED on Textor
are to study the change of the particle confinement in the edge plasma and to
homogeneously distribute the heat loads generated by the plasma onto the wall
of the vacuum vessel. It also has turned out that resonant magnetic perturbations (RMP) like those created by the DED are an excellent tool to influence
the MHD behaviour at the edge such as edge-localized modes (ELMs) [54], [55].
This thesis discusses the change of the impurity particle confinement induced
by the DED.
The DED consists of 16 + 2 helical coils which are mounted on the high
field side (HFS) around the center column of Textor. Sixteen of these coils
generate the perturbation field and the two outermost coils compensate the field
errors introduced by the feedthroughs of the coils connecting them to the power
supplies [56]. In total, a current of up to 15 kA per conductor can be applied.
The application of an ac current leads to a rotating perturbation field. The
applicable ac frequency ranges from 1 kHz up to 10 kHz and also 50 Hz. A
positive rotation direction of the RMP induced by the ac current is defined to
toroidally rotate clockwise in the top view of Textor which is in the direction
of the toroidal magnetic field BΦ (figure 3.1). The poloidal rotation of this case
is downwards at the high field side (HFS) and upwards at the low field side
(LFS) which corresponds to the electron diamagnetic drift direction.
21
Figure 3.1: Top view of the tokamak Textor.
The interconnection of the coils defines the base mode of the DED. Possible
base modes are m/n = 12/4, 6/2 and 3/1 with m and n being the poloidal and
toroidal mode number, respectively. In case of the m/n = 12/4 DED base mode
with dc current the direction of the current in the DED coils changes with two
adjacent coils. Each of the coils is fed separately such that 15 kA per coil are
applied. The m/n = 6/2 and 3/1 base mode are generated by an alternation
of the current direction of 4 adjacent and 8 adjacent coils, respectively (figure
3.2). In the ac current case adjacent coil sets have a phase shift of 90°. In the
m/n = 6/2 and 3/1 base mode 2 and 4 neighbouring coils, respectively´, are
grouped together. Therefore, the maximum current per coil in the m/n = 6/2
base mode is 7.5 kA per coil and in the 3/1 base mode it is 3.75 kA per coil.
The maximum current is 15 kA per coil group. The lower the poloidal mode
number m the deeper penetrates the perturbing field into the plasma.
In the vacuum approximation the resonant magnetic perturbation generated
22
3.2 Hexos
(a) 12/4
(b) 6/2
(c) 3/1
Figure 3.2: A poloidal cut of Textor showing the 16+2 coils of the DED
mounted at the high field side of Textor. In dc operation the coil sets of
the same colour have the same current direction. In ac operation there is a
phase shift of 90° between the coil sets. The green coils are the compensation
coils.
by the DED creates magnetic island chains on the resonant surfaces of the
confining magnetic field. As soon as the island chains overlap the magnetic
field becomes stochastic such that a single field line toroidally connects to every
spatial point in the island overlap region. The approximation of the resulting
field shows three different regions which can be distinguished. They differ in the
connection lengths of the magnetic field lines to the wall. The so called laminar
zone with very short connection lengths and open field lines onto the wall is the
outermost region which also forms a helical SOL [57]. With the help of heat
deposition patterns on the divertor target plates which strongly depend on the
collisionality of the plasma [58], the strike points of the open field lines can be
observed.
The second region is the stochastic zone with remanent islands and long connection lengths to the wall. The island chains overlap and ergodize the field so
a single magnetic field line is connected to every point in space in this volume.
The innermost region contains island chains which do not overlap. Figure 3.3
shows a Poincaré plot of the vacuum approximation of the resonant magnetic
perturbation in the m/n = 3/1 DED base mode with a coil current of 1 kA.
The plot is a poloidal cross section of the edge of the Textor volume plotted
over the poloidal angle ϑ in which ϑ = 0 is in the equatorial plane at the LFS.
Each dot represents the intersection of a magnetic field line with the ϑ plane.
3.2 High-efficiency extreme ultraviolet overview
spectrometer system Hexos
The High-Efficiency XUV Overview Spectrometer system (Hexos) has been
developed for the stellarator Wendelstein 7-X (W7-X) [59], [60], [61]. In
23
Figure 3.3: Poincaré with overlayed laminar plot of a vacuum approximation of
a perturbation field of an m/n = 3/1 DED base mode with a coil current of
1 kA. The laminar plot shows the connection lengths LC of the magnetic field
lines at the plasma edge (r/a > 0.95). The poloidal angle ϑ starts at the low
field side of the equatorial plane of the torus.
24
3.2 Hexos
1
Reflectivity @ α = 86°
0.9
Ni
Au
0.8
0.7
0.6
0.5
0.4
0.3
0.2
2
4
6
λ (nm)
8
10
Figure 3.4: Reflectivity of nickel and gold with an incidence angle α = 86° [64]
(grazing incidence). The wavelength range of Hexos 1 is 2.5 to 10.5 nm.
comparison to the Survey Poor Resolution Extended Domain (Spred) spectrometer [62], [63] it provides a larger etendue, a broader wavelength range and
a better spectral resolution. It consists of two double flat field spectrometers
which observe the spectral range from 2.5 nm to 160 nm with overlap (see table 3.1). This range is sufficient to monitor the emission lines of all important
intrinsic impurities in a fusion plasma like the intense Mg-like, Na-like, Be-like,
and Li-like emission lines of all elements in the periodic table up to Mo. The
emission lines of high-Z metals (Wo, Ta) are very numerous and cannot be resolved in the spectra because they overlap. They take the form of quasi-continua
around 5 – 6 nm and are located in the wavelength range of Hexos. In order
to perform impurity transport experiments with injected impurities VUV spectrometers like Hexos are used to monitor the line emission intensities of the
impurity ionization stages.
The most important element of Hexos are newly developed holographic
toroidal diffraction gratings with about 2000 ion etched grooves per mm. The
gratings are numerically optimized for a high throughput with good spectral
resolution. The toroidal shape of the diffraction gratings practically avoids a
Hexos no.
λ (nm)
∆λ (nm)
Incidence angle α (°)
Angle of first order β (°)
Etendue (10−4 mm2 sr)
Width of entrance slit (µm)
Standard MCP voltage at Textor (V)
1
2.5 – 10.5
0.03
86
78.1 – 83.2
0.3
220
880
2
9 – 24
0.05
76
67.0 – 72.1
1.0
120
960
3
20 – 66
0.13
65
55.2 – 61.7
2.1
60
870
4
60 – 160
0.26
45
34.5 – 40.9
2.1
60
810
Table 3.1: Technical data of the Hexos spectrometers.
25
Figure 3.5: Setup of Hexos. The toroidal holographic diffraction grating is the
only optical and dispersive element. It images the entrance slit onto the focal
plane where the detector is located [60].
loss of light caused by astigmatism. The holographic grating recording technique allows to place the spectrometer and the detectors in a geometry which
differs from the Rowland geometry. This technique also greatly reduces optical abberations. Due to the optimization of the shape of the gratings the even
orders of the diffraction are mitigated. Since all materials absorb vacuum ultra violet (VUV) emission very strongly the number of reflecting surfaces has
to be minimized. Therefore, these gratings are the only optical and diffractive
element in the optical paths of Hexos. To optimize the reflectivity the coating
of the grating of Hexos 1 consists of nickel and the coating of the remaining
spectrometers consist of gold (figure 3.4) [64]. Hexos uses the first order of the
diffraction for the spectral analysis (figure 3.5).
The detectors are single stage high current open microchannel-plates (MCP)
from Burle Industries Inc. (channel length/channel diameter = 60:1, pore
size = 10 µm, total diameter = 40 mm, longitudinal resistance < 8 MΩ). A
CsI coating is used as photocathode material at the entrance [65]. Due to the
photoelectrical [66] the photocathode material converts an incoming photon into
one or more electrons. Those electrons are accelerated into the microchannels.
In an avalanche process each of the accelerated primary electrons releases δ
secondary electrons due to collisions with the channel walls. The secondary
electrons are then accelerated as well and by hitting the wall they release δ 2
electrons. This avalanche process depends nonlinearly on the applied MCP
voltage because the probability to release a secondary electron from the wall
increases by increasing the velocity of the electrons. The gain G of the MCP is
δ c with c being the total number of collisions with the wall [67].
After amplifying the signal with the MCP the electrons are accelerated onto
a P47-phosphor-screen which converts the electric signal to visible light. The
image of the screen propagates through a taper consisting of numerous conical
glas fibers. The larger end pieces of the fibers are grouped at the entrace of the
taper and the smaller end pieces on the exit. Therefore, the taper is mounted
such that the image size is reduced. A linear array of photo diodes with 1024
26
3.2 Hexos
1
normalized signal
0.8
0.6
0.4
0.2
0
10
12
14
16
18
λ (nm)
20
22
24
Figure 3.6: Continuous: non saturated spectrum, dotted: saturated spectrum
due to space charge effects on the MCP. The detector saturation effects in a
nitrogen spectrum are recorded with a laboratory pinch light source. The measured intensity ratios between the emission lines are wrong due to the saturation.
rectangular pixels records the spectra with a time resolution of 1 ms and a
dynamic range of 10 bit. The working voltages of the phosphor screen and the
detectors can vary from 7000 to 8000 V and 700 to 1200 V, respectively. The
actual voltage which is used for the operation of Hexos has to take into account
the saturation limit of the detectors. One possible effect which causes detector
saturation can appear when too many electrons enter the MCP channel. Due
to space charge effects the accelerating electric field along the MCP channel
is disturbed. As consequence, during the time interval of the read-out of the
pixels the contribution of those electrons to the measured signal is reduced. An
example for this case is presented in figure 3.6. A second possible effect for
detector saturation appears when the pixels of the linear array are saturated.
The electrons from the saturated photodiode can spill over to the neighbouring
non-saturated pixels. As consequence the FWHM of the measures emission line
intensity becomes broader than without the electron spill over. In the cameras of
Hexos the saturation threshold of the MCP limits the capacity of the pixels such
that they do not reach their full capacity [65]. Therefore, electron spill over does
not occur in the used cameras. The above mentioned working voltages avoid
detector saturation in typical Textor plasmas.
The voltages used in the detectors to accelerate the photo and secondary
electrons within a distance of < 1 mm are in the order of ≈ 1 kV. This is
the reason why ultra high vacuum < 10−4 Pa is needed at the location of the
MCPs to avoid arcing. Since there are no materials which can be used as
window between the spectrometer and the tokamak plasma (p ≈ 10−2 Pa) the
spectrometer is pumped differentially. A pumping aperture is located between
the entrance slit and the detector so the spectrometer consists of two volumes
27
(chambers) which are separated. Each chamber is evacuated by a separate
turbomolecular pump.
3.3 Absolute intensity calibration
In order to quantify the impurity concentration in the experiments performed in
the course of this thesis it is necessary to absolutely calibrate the VUV spectrometers. The knowledge of the impurity concentrations, i. e. the concentrations of
the main intrinsic impurities helium, boron, carbon, and oxygen is needed for
the determination of the effective charge Zef f . The effective charge influences
the profile of the neutral hydrogen density which is important for the correct
determination of the impurity transport coefficients (see also section 4.3). The
results of the calibration have been published in [68].
The intensity calibration of a VUV spectrometer is very challenging because
there are only a few primary or secondary standards of intensity in the VUV
which are suitable for performing a calibration. A synchrotron, for example,
as a primary standard emits known photon fluxes for a very wide wavelength
range. But for a calibration of the Hexos system it is not suitable since the
synchrotron radiation is highly collimated [69]. Furthermore the VUV spectrometers would need to be carefully aligned to the synchrotron. The alignment
procedure would need an additional expensive mounting of the spectrometers
which allows for a translation in the plane perpendicular to the synchrotron
radiation and a rotation around the axes in this plane. Therefore, it has been
decided to perform the calibration with laboratory light sources and non collimated radiation from Textor, respectively. The calibration procedure with
the help of the secondary standard has been performed during the laboratory
testing phase of the spectrometers [70].
The calibration includes three steps. Before the intensity calibration a spectral calibration has to be performed. With the help of a laboratory light source
a set of emission lines with known wavelengths in the VUV is recorded by consecutively using different working gases. The pixels of the linear array can thus
be associated with the known wavelengths. These obtained spectral calibration
points are used to interpolate the wavelengths in between the calibrated pixels.
The second step is the intensity calibration from 147 nm down to 16 nm with
a secondary standard, a hollow cathode with different working gases [71] which
has been calibrated at the electron synchrotron Bessy [72]. The spectral region
below 16 nm is inaccessible with the hollow cathode. The region down to 2.8 nm
is calibrated in a third step with the branching ratio technique [73], [74]. This
technique uses emission line pairs which originate from the same upper energy
level with known intensity ratios. One emission line has to be in the spectral
region already calibrated the other one in the uncalibrated region. We used line
pairs from a pinch light source from Aixuv [75] and from Textor plasmas.
28
Hexos
2
2
3
3
3
3
3
3
3
3
3
3
4
4
4
4
4
4
4
4
4
4
4
4
4
Ion
Al IV, He
He II
He II
He II
He II
Ne II
Ne II
Ne III
Ar II
Ar II
He I
Ar II
Ne I
Ne I
Ar III
Kr II
Kr II
Ar II
Ar II
Kr II
Ar I
Ar I
Kr I
Kr I
Xe I
λ (nm)
IHC (A)
W
I ( µsr
)
16.10
24.30
24.30
25.60
30.40
40.65
46.10
49.00
54.30
54.75
58.40
61.24
73.59
74.37
76.92
88.63
91.74
91.98
93.21
96.50
104.82
106.62
116.49
123.58
146.96
2
2
2
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1.53
46.5
46.5
147
676
149
1025
99
28.3
32.9
1530
7.5
577
381
15.6
96.9
182
388
238
201
211
176
49.5
136
82.8
P (pW)
S ( counts
)
ms
0.18
5.50
5.50
17.39
79.96
17.63
121.25
11.71
3.35
3.89
180.98
0.89
68.25
45.07
1.85
11.46
21.53
45.90
28.15
23.78
24.96
20.82
5.86
16.09
9.79
1
31
12
49
242
49
339
33
9
10
486
2
528
391
17
79
160
372
223
234
286
281
72
184
89
7
10 photons
p−1 ( counts·cm
2 sr )
1.5
2.1
2.6
2.2
2.4
3.5
4.0
4.3
4.9
5.2
5.3
5.6
2.3
2.1
2.1
3.1
2.9
2.7
2.8
2.3
2.2
1.9
2.3
2.6
3.9
Table 3.2: The calibrated emission lines of the hollow cathode [71], [76], [77]
used for the calibration of Hexos. The intensity at the entrance slit and the
calibration factors for Hexos are also presented. The counts of the signal are
determined by the voltage measured for the pixel. The working voltage of the
MCP and the phosphor screen are 1150 V and 7500 V, respectively.
3.3.1 Calibration with the hollow cathode
The calibration of Hexos 3 and 4 has been completely performed with the tabulated calibrated emission lines of the hollow cathode [71], [76], [77] (table 3.2).
Hexos 2 is partially calibrated with the hollow cathode. For the determination
of the inverse sensitivity p−1 from the hollow cathode spectra with different
working gases (table 3.2) we need the number of photons N per second passing
the entrance slit of the spectrometer. The number of the photons is proportional
to the wavelength dependent intensity of the hollow cathode I(λ) (power per
solid angle), the solid angle of the entrance slit Ω = A/d2ls with the area of the
entrance slit A and the distance dls between the slit and the aperture of the
hollow cathode. N is inversly proportional to the energy of the photon hc/λ
with the Planck constant h and the vacuum speed of light c.
N=
I ·Ω·λ
h·c
(3.1)
29
7
7
x 10
x 10
9
p−1 (photons/(counts cm2 sr))
10
8
7
6
5
4
3
2
3
4
5
6
7
λ (nm)
8
9
2.5
2
1.5
1
10
10
12
(a) Hexos 1
6
20
22
24
7
x 10
6
5
4
3
2
20
16
18
λ (nm)
(b) Hexos 2
7
7
14
30
40
λ (nm)
50
(c) Hexos 3
60
x 10
5.5
5
4.5
4
3.5
3
2.5
2
1.5
60
80
100
120
λ (nm)
140
160
(d) Hexos 4
Figure 3.7: The intensity calibration curves of Hexos. The blue diamonds and
the red squares are the calibration points derived from the hollow cathode and
the branching ratio technique, respectively. The continuous lines in figures 3.7(c)
and 3.7(d) are the calculated inverse sensitvities. The dashed curves are an
interpolation of the calibration in between the data points. The structure of the
calibration curve in 3.7(d) is discussed in section 3.3.1.
30
The ratio of the number of photons N and the background corrected signal S
integrated over the width of the line, measured in the time ∆t = 1 ms multiplied with the mean etendue Lm after the entrance slit determines the inverse
sensitivity
p−1 =
N · ∆t
Lm · S
(3.2)
The calibration factors (table 3.2) are calculated with a solid angle which results
from the area A of the entrance slit with a height of 3.8 mm and a width of
30 µm and the distance dls from light source to entrance slit of 98 cm. The
calibration curves of Hexos 2 - 4 are presented in figures 3.7(b) - 3.7(d).
The laboratory light sources are point-like light sources whereas the tokamak
or stellarator plasma illuminates the full viewing angle of the spectrometer.
Therefore, it is necessary to determine whether the calibration depends on the
incidence angle of the radiation on the grating. In order to change the incidence angle the position of the point-like laboratory light sources is changed
with respect to the grating. The plane in which the light sources are moved is
perpendicular to the optical path in the spectrometer. The calibration does not
change due to the change of the incidence angle.
To validate the calibration performed with the hollow cathode we compared
it to a calculated detector sensitivity. The calculated sensitivity is the product
of the grating efficiency simulated with the software PCGrate from International Intellectual Group Inc. [78] and the angle dependent quantum
efficiency of the detector. Since there are no data for the utilized model of the
detector we used data from similar detectors [65], [79], [80]. Taking into account
the error of the calibration factors of ±20% (square root sum of the accuracy of
the hollow cathode voltage (5%), its long term stability (10%), the accuracy of
the line width integration (10%), and the error of the tabulated emission lines
of the hollow cathode (10% - 13%)) the calibration fits well to the calculated
sensitivity. Due to this agreement the shape of the spline is a good interpolation
for the calibration between the data points.
The errors of the calibration can only influence the determination of the transport coefficients due to the determination of the neutral hydrogen density profile.
As will be shown in section 4.4 the error of the intensity calibration does not
contribute to the error of the determined transport coefficients.
The maximum of the inverse sensitivity around 90 nm (figure 3.7(d)) is a
consequence of the transition from the excitation of one photo electron to two
photo electrons [80]. Since the excitation of two electrons results in lower kinetic
energies compared to the excitation of one electron, the escaping probability
from the photo cathode material drops and the inverse sensitivity rises. The
further increase of the energy of the photon increases the energy of both of the
photo electrons such that the escaping probability rises again and the inverse
sensitivity drops.
31
3.3.2 Calibration with branching ratios
The shortest visible tabulated wavelengths of the hollow cathode are used for
calibrating Hexos 2 down to 16 nm. To calibrate the spectral region inaccessible
by the tabulated emission lines we used branching line pairs of a pinch light
source from Aixuv [75]. We derived intensity ratios with the help of transition
probabilities of line pairs with the same upper excitation level [74]. In a system
with two energy levels i and k with i > k the transition probability Aik gives the
probability of a sponateous transition from the upper level i to the lower level
k. The transition probability is the Einstein coefficient of spontaneous emission.
The emission line at the longer wavelength is already calibrated and the emission line at the shorter wavelength emits in an uncalibrated spectral region.
Furthermore, it is important that blending is compensated or avoided and that
the light sources are optically thin for the utilized emission lines. If all of the
components of a measured line are known the compensation of blending can be
performed by a fit of the spectrum. See the section 3.3.4 for a discussion of the
optical depth of the light sources.
The intensity Iik of the shorter wavelength λik is proportional to the intensity
Iij of the longer wavelengths λij
Iik =
Aik λij
· Iij
Aij λik
(3.3)
Aik and Aij are the transition probabilities of the shorter and longer wavelength, respectively. The calibration of Iij can be transferred to Iik with (3.7),
(3.8) and (3.3).
We used the line pairs O VI 12.9/49.8 nm, Ar VIII 15.9/33.7 nm and N V
18.6/71.4 nm to calibrate Hexos 2 (table 3.3). The calibration points derived
with the branching ratio technique using the transition probabilities from [74]
and [81] fit well to the calibration points obtained with the hollow cathode
(figure 3.7(b)).
The calibration of Hexos 1 is performed with emission lines from Textor
plasmas. The transition probabilities of the utilized line C VI 2.8/18.2 nm, B
IV 5.2/38.1 nm and B V 4.1/26.2 nm are taken from [81], [82] and [83]. Since
the Textor plasma illuminates the full field of view of the spectrometer the
existing calibration of the longer wavelengh can be transferred very easily to the
shorter wavelength with the help of (3.2), (3.8) and (3.3).
p−1
ik =
Aik Sij −1
·p
Aij Sik ij
(3.4)
Sij and Sik are the voltage corrected signals. More information about the voltage
correction is given in section 3.3.3. We list the calibration points in table 3.3.
In comparison with the error of the calibration with the hollow cathode the
additional used signal has to be taken into account. The error of the calibration
32
Ion
C VI
BV
B IV
O VI
Ar VIII
NV
λik
(nm)
2.85
4.09
5.26
12.98
15.90
18.61
Aik
(s−1 )
2.17×1011
1.05×1011
1.08×1011
2.90×1010
1.10×1010
1.40×1010
Sik
( counts
)
ms
1204
1076
534
86
152
56
λij
(nm)
18.21
26.23
38.12
49.84
33.77
71.38
Aij
(s−1 )
2.91×1010
1.41×1010
5.10×1009
8.90×1009
1.10×1010
4.30×1009
Sij
( counts
)
ms
2321
563
75
4
42
3
p−1
photons
( counts·cm
2 sr )
1.33×1008
8.61×1007
9.81×1007
1.48×1007
1.62×1007
9.12×1006
Ref.
[82],[83]
[82],[83]
[81]
[74],[81]
[81]
[74],[81]
Table 3.3: Transition probabilities of the line pairs used with the branching ratio
technique ([74], [81] - [83]).
2
(S/S800 V) (a.u)
10
1
10
0
10
800
850
900
950 1000 1050
MCP voltage (V)
1100
1150
Figure 3.8: Fitted factors for the voltage correction of the signal to a MCP
voltage of 1150 V. Four datasets from two different spectrometers are used to
derive these factor. The factors are normalized to an MCP voltage of 800 V.
factor is 23 % which is similar to error of the calibration factor derived with the
hollow cathode.
All spectrometers are calibrated for a MCP voltage of 1150 V and a screen
voltage of 7500 V.
3.3.3 Application of the calibration
In order to calculate the optical depth of the emission lines in Textor we
have to estimate the ion densities in the plasma. Those densities are derived
with the help of the absolute intensities of the spectrometers already calibrated.
Therefore, we first describe the application of the calibration.
Since the calibration is performed with an MCP voltage of 1150 and on Textor the MCP voltage is set between 810 and 960 V (table 3.1) the line width
integrated signal has to be corrected. With the help of laboratory measurements in which the MCP voltage is varied we analyze the dependency of the
signal change on the MCP voltage. Since the gain of the MCPs is strongly non-
33
linear (see section 3.2) the fitting of the signal is performed with an exponential
function with a polynomial as exponent (figure 3.8)
S/S800 = K ∗ exp(a + bx + cx2 + dx3 + ex4 )
(3.5)
with x being the MCP voltage.
The signal conversion factor from voltage a to voltage b is the ratio between
the factor of voltage b and the factor of voltage a
Sb =
fb
Sa .
fa
(3.6)
The power at the entrance slit P reads
P =
Sb
hc
· p−1 · Lm ·
∆t
λ
(3.7)
with the extrapolated (voltage corrected) signal Sb measured in ∆t =R1Rms the
inverse sensitivity p−1 , the mean etendue of the spectrometer Lm =
dAΩs
with the solid angle Ωs from which light can be detected by the spectrometer,
and the energy of one photon hc/λ of the observed wavelength λ.
In case of a pointlike light source the intensity I is the ratio of P and the area
of the entrance slit. The intensity (W/m2 ) of a spatially extended light source
(like a tokamak plasma) is
4π
I=
P
(3.8)
Lm
Figure 3.9 shows the determination process of the impurity density. In order
to calculate the impurity ion density in Textor plasmas a transport equilibrium
calculation with Strahl has to be performed. The transport equilibrium calculation is performed by setting all parameters to temporal constant values and
by calculating the ion density distributions until they do not change anymore.
Initial profiles of the electron density, the electron temperature and the neutral
hydrogen distribution of the time point of the discharge to be analyzed have to
be provided as input parameters. These profiles and the transport coefficients
determine the radial position of the ion densities. The line integrated emission
intensity from those ion densities is measured with spectrometers and/or cameras, respectively. For a more detailed description how local information from
line integrated signals is extracted see section 4.1. The transport coefficients
which are used to derive the ion density distribution are obtained by impurity
transport experiments. If the transport coefficients are unknown, a reasonable
assumption for the transport coefficients has to be performed, e.g. with the help
of discharges with similar plasma parameters. In a manual fitting process of the
simulated to the experimental intensities the impurity ion density can be derived
with an error of ≈ 34 %. This error is derived by the square root of the total
sum of squared errors from the calibration factor 23 %, voltage interpolation
34
Figure 3.9: The determination process of the impurity density.
35
10 %, measured signal 10 %, atomic data 15 %, transport coefficients 15 %, and
experimental input data 5 %.
The local concentration is calculated with the help of the local impurity ion
density. The absolute emission line intensity determines the local impurity ion
density of an ionization stage at the position of the emissivity shell. The local
impurity ion density is determined by the local concentration and therefore the
local concentration results from the modelling. With a set of ionization stages it
is possible to derive the radial impurity density distribution and concentration,
respectively. The knowledge of the concentration profiles of the most abundant
impurities results in a rough estimate for Zef f .
3.3.4 The optical depth
The estimation of the applicability of the branching ratio technique is performed
by calculating the optical depths of the utilized emission lines. If induced emission is considered the optical depth τ (in SI units) for a Doppler-broadened line
[84] is
s
mc2
hc
−15
l
τ = 3.52 · 10 fik λni
· L 1 − exp −
(3.9)
kB Te
λkB Te
and the absorbing oscillator strength
fik = 1.5 · 10−4 (gk /gi )λ2 Aki
(3.10)
with the statistical weights gk and gi [85], the density of the absorbing ions
the mass of the ion m, the Boltzmann-constant kB , and the length L of the
absorbing ion density line-of-sight in the plasma. The statistical weights are
taken from [81, 83].
The optical depth τ is determined by estimating the density of the absorbing
ions nli with the Flychk code [86]. In order to calculate the ion density in a
certain excitation state, the program considers collisional and radiative atomic
processes and solves the rate equations for the population distribution of the
energy levels. To calculate the optical depth we calculated the absorbing ion
densities for the pinch light source (oxygen, argon and nitrogen). Assuming
a plasma density which results from the compression of an ideal gas in the
original cylindrical volume the total ion density becomes ni ≈ 5 × 1022 m−3 .
The assumed pinch plasma diameter is compressed from ≈ 4 mm to 0.5 mm at
an initial pressure of ≈ 40 Pa and initial gas temperature of ≈ 380 K.
The pinch plasma is not homogeneous and due to the compression it changes
in time. The energy distribution of the particles is a combination between a
Maxwellian and non-Maxwellian energy distribution. Therefore, a temperature
in the common definition of an thermal equilibrium does not exist. Since a
temperature is essentially needed for the calculation of the optical depth, we
estimate the temperature for the Maxwellian part of the energy distribution by
nli ,
36
O VI
O VI
1.2
OV
normalized intensity (a.u.)
1.2
O IV
1
0.8
0.6
0.4
0.2
0
10
12
14
16
18
λ (nm)
20
22
O IV
1
0.8
0.6
0.4
0.2
0
24
OV
10
12
14
(a) Te = 10 eV
1
0.8
0.6
0.4
0.2
10
12
14
16
18
λ (nm)
20
22
22
24
0.6
0.4
0.2
10
12
14
16
18
λ (nm)
20
(d) Te = 75 eV
O VI
1.2
24
0.8
0
24
OV
O IV
1
0.8
0.6
0.4
0.2
10
22
O IV
1
O VI
0
24
OV
(c) Te = 50 eV
1.2
22
O VI
1.2
OV
O IV
0
20
(b) Te = 25 eV
O VI
1.2
16
18
λ (nm)
12
14
16
18
λ (nm)
20
(e) Te = 100 eV
22
24
OV
O IV
1
0.8
0.6
0.4
0.2
0
10
12
14
16
18
λ (nm)
20
(f) Te = 150 eV
Figure 3.10: The calibrated normalized oxygen spectrum (continuous and black)
recorded from pinch light source is the same figures 3.10(a) - 3.10(f). It is
compared to oxygen spectra (dashed and red) computed with Flychk with
different electron temperatures. The fitted spectra are used to estimate the
electron temperature in the pinch plasma. We note that the O VI, 17.3 nm,
emission line in the experimental spectrum is corrected for saturation.
37
Ion
C VI
C VI
BV
BV
B IV
B IV
O VI
O VI
Ar VIII
Ar VIII
NV
NV
λ
(nm)
2.85
18.2
4.09
26.2
5.26
38.10
12.98
49.8
15.9
33.7
18.6
71.4
ne
(m−3 )
2.6×1019
2.6×1019
1.7×1019
1.7×1019
0.8×1019
0.8×1019
3.0×1023
3.0×1023
4.0×1023
4.0×1023
2.5×1023
2.5×1023
Te
(eV)
392
392
259
259
120
120
35
35
35
35
35
35
nli
(m−3 )
5.3×1015
2.0×1007
8.7×1014
7.5×1006
2.9×1013
4.1×1011
4.5×1020
2.3×1018
6.5×1018
4.5×1018
4.8×1019
5.9×1017
L
(cm)
35
35
35
35
25
25
0.6
0.6
0.6
0.6
0.6
0.6
τ
light source
5.3×10−06
5.4×10−14
1.6×10−06
8.8×10−14
2.0×10−07
1.0×10−08
2.6×10−01
1.3×10−02
5.3×10−03
8.5×10−03
3.4×10−02
3.4×10−03
Textor
Textor
Textor
Textor
Textor
Textor
Aixuv
Aixuv
Aixuv
Aixuv
Aixuv
Aixuv
Table 3.4: The optical depths τ and the parameters used for the calculation.
The width of the absorbing density L of carbon and boron is the FWHM of the
emissivity shell in the plasma and in the case of oxygen, argon and nitrogen L is
the length of the pinch plasma. The maximum of the emissivity shell of boron
and carbon in the Textor plasma determine the electron temperatures Te . We
have calculated the absorbing ion density with Flychk.
comparing the a recorded calibrated oxygen spectrum to computed oxygen spectra calculated with the Flychk code in a plasma in local thermal equilibrium
(figure 3.10). In the experimental spectrum the emission lines of the ionization
stages of O IV to O VI are visible. None of the computed spectra can reproduce
the experimental one. In addition, in the spectra of plasmas with an electron
temperature of 100 eV or larger additional emission lines appear which are not
visible in the experimental spectrum. On the base of the computed spectra of
figure 3.10, we roughly estimate the electron temperature Te to be between 30 –
40 eV.We note that in nitrogen spectra from this light source, the emission line
of N VI, 2.5 nm, is visible. In plasmas with a Maxwellian energy distribution the
excitation of this emission line needs a temperature of about 100 eV. Therefore,
we assume that this emission line is excited by the non-Maxwellian component
of the energy distribution.
In [75] an average temperature Te = 35 eV is derived by a corona plasma
approximation. We use this value for the following calculations.By using the
calibrated spectral ranges of Hexos we estimate the impurity densities nli of
carbon and boron in the Textor plasma with transport equilibrium calculations
of the transport code Strahl. At the position of the emissivity shell maxima of
C VI, B V and B IV the Strahl calculation determines the impurity densities to
5.5×1017 , 1.7×1017 and 1.6×1017 m−3 , respectively. The electron temperatures
and densities at the maxima are used to calculate nli with Flychk. Table 3.4
lists the optical depths calculated with (3.9) and the parameters used for the
determination. The emission lines used with the braching ratio technique are
optically thin with the exception of O VI 12.98 nm. The optical depth of the O
VI 12.98 nm emission line is around 0.3. This means that the inverse sensitivity
38
normalized signal (a.u.)
2
1.5
original signal
artificial bg.
bg. corr. signal
Ar injection
1
0.5
0
2.95
Fitted sawtooth
3
3.05
time (s)
3.1
3.15
Figure 3.11: Subtraction of the sawtooth background from the central SXR
channels. The blue line is the original signal, the red dotted line is the artificial sawtooth and the black line is the difference between the original and
artificial signal. For the determination of the artificial signal, the rising signal
of the first sawtooth (indicated) of the original signal has been fitted. All of the
following sawteeth of the artifical signal are interpolated with the help of the
fit. The signal before t = 3 s shows how the complete signal would look like
without an argon injection.
p−1 of the calibration point is overestimated. This introduces a systematic
error for this calibration point which increases the lower part of the error bar
in figure 3.7. Since the electron temperature of the pinch light source plasma
which is crucial for the determination of the optical depth is not well known,
the magnitude of the overestimation cannot be determined. We would like to
note that this specific calibration point should be used with care. In this thesis
this calibration point is not used.
In this section we list the diagnostics which have been applied in the evaluation of
the experiments for this thesis. If no reference is given for a particular diagnostic
which are mentioned below, a more detailed description is given in [87].
Hexos is located in Textor section 4 – 5 and is used for impurity transport
experiments. The argon in the impurity injection experiments is puffed into
the tokamak plasma within the time ∆t ≈ 1 ms which corresponds to ≈ 1018
particles. The puffing is performed by a piezo electric valve in section 13 – 14
at a poloidal angle of ϑ ≈ 30° from the equatorial plane on the low field side.
The pressure in the vessel rises within 0.2 ms after the opening of the valve and
decays with 1/t2 after the closing of the valve
39
The determination of the central line integrated electron density profiles and
electron temperature profiles is performed with an HCN laser interferometer
system and the monitoring of electron cyclotron emission (ECE) with an ECE
diagnostic, respectively. Additionally a Thomson scattering diagnostic is used
to determine the temperature.The electron densities and electron temperatures
at the last closed magnetic flux surface (LCFS) are obtained via a He-Beam
diagnostic [88] Tearing modes are detected via an ECE imaging camera [89].
The toroidal angular frequencies of the plasma are obtained with core and edge
versions of charge exchange spectroscopy systems (CXRS) [87], [90], [91]. The
detection of magnetic islands is performed with the help of the ECE imaging
cameras and soft x-ray (SXR) PIN diodes. Soft x-ray radiation is emitted from
the nearly fully ionized hydrogen and helium ions and partially ionized impurities in plasma the hot plasma core of Textor. The emission of the soft x-rays
depends on the impurity density according to equation (2.13).
In typical Textor plasmas the signals of the diagnostics measuring the
central density or temperature are modulated by sawtooth oscillations (section 2.1.4). Therefore, the central SXR signals which measure the emission of
Ar XVII are modulated by sawtooth oscillations as well. In some plasma scenarios the amplitude of this modulation is of the order of the changes which are
introduced by Ar XVII on the SXR signal which complicates the analysis. For
these scenarios a background subtraction of the sawteeth has been performed in
order to obtain unmodulated Ar XVII intensities (figure 3.11). The background
sawteeth are constructed in three steps. At first the shape of the rising signal
of one SXR sawtooth before the argon injection is fitted. The fit is performed
with a polynomial of 10th up to 19th order depending on the shape of the rising
signal. In a second step the crash times of the sawteeth before and during the
presence of argon in the plasma are obtained from the central ECE channels. In
the last step the artificial background is produced by interpolating a sawtooth
in between of all of the crash times with the help of the fitting parameters of
the first step. The background is then substracted from the SXR signal and the
result is the contribution of Ar XVII. The construction procedure is only applicable if all of the sawteeth have a similar amplitude. As soon as the amplitude
varies with every sawtooth, a background subtraction with this procedure is not
feasible anymore.
The line emission of the impurities according to (2.14) is monitored in the
VUV and in the SXR. The monitoring is performed with Hexos and with SXR
PIN diodes which are installed in four cameras with 80 µm Be filters. The
Be filters are edge filters for radiation with λ > 0.7 nm. These SXR PIN
diodes cover the poloidal cross section with approximately 15 line-of-sights per
camera which results in a spatial resolution of 3 cm. The time evolution of the
emission lines in the VUV and SXR results in time traces. Due to the gradient
in the electron density and electron temperature towards the plasma center the
impurities which are injected at the edge are ionized successively. With the help
of the time evolution of the different ionization stages the transport parameters
40
can be derived with impurity transport code calculations.
In addition to Hexos a Spred spectrometer is available at Textor [92].
This second VUV spectrometer is located in section 8 – 9 and therefore provides
information at another toroidal angle.
The DED base mode of the experiments is m/n = 3/1 with dc currents of up
to 3.75 kA per coil, and ac currents of 1 kA per coil with frequencies of 1, -1,
and -5 kHz. In the m/n = 6/2 DED base we have worked with dc currents up
to 15 kA per 2 coils. The heating of some of the experiments is performed with
the help of neutral beam injectors (NBI) [93] and electron cyclotron resonance
heating (ECRH) [94].
41
The analysis of the impurity transport experiments is performed with the one
dimensional impurity transport code Strahl. The code calculates the radial
impurity ion density distribution by solving the coupled set of continuity equations. This is performed for all of the ionization stages of an impurity species
with the help of the radial transport coefficients. The transport coefficients
represent the sum of the neoclassical and anomalous transport. In the plasma
core the transport coefficients are averaged over the sawtooth crashes, i.e. they
are significantly higher than the transport coefficients in between the sawtooth
crashes. Therefore, neoclassical contributions to the transport in the plasma
core do not play a role and are not discussed in this thesis. The detailed numerical scheme is presented in [95] and [96]. This chapter presents the model
used by Strahl, a discussion about the applicability of an experimental impurity particle source function, the changes of the core impurity transport due
to neutral beam injection and the errors of the analysis method. In all of the
equations we use SI units except for the temperatures which are given in eV.
4.1 Strahl code
The transport code Strahl calculates the radial ion density distribution nI,Z
for each ionization stage Z of an ionized impurity species I. It solves the set
of coupled continuity equations for each point of time, each radial position and
each ionization stage.
∂nI,Z
∂t
∂nI,Z
1 ∂
=
r D
− vnI,Z +QI,Z
r ∂r
∂r
|
{z
}
(4.1)
−Γ
The transport coefficients are derived in a manual fitting procedure. In the
course of this procedure the flux Γ, which is determined by the radial profile
of the diffusion coefficient D and the radial profile of the pinch velocity v, is
adapted until the emission line intensities of the calculated radial ion density
distribution fit to the experimental intensities. The quality of the determined
transport coefficients improves with the number of ionization stages used in the
fitting process. In the applied model a positive pinch velocity points radially
outwards to the wall of the vessel. The source and sink terms QI,Z which couples
42
4.1 Strahl code
the different ionization stages via ionization and recombination reads
cx
QI,Z = − (ne SI,Z + ne αI,Z + nth
H αI,Z )nI,Z
(4.2a)
+ ne SI,Z−1 nI,Z−1
(4.2b)
cx
+ (ne αI,Z+1 + nth
H αI,Z+1 )nI,Z+1
(4.2c)
with the effective rate coefficients for ionization SI,Z , recombination αI,Z and
cx taken from the Atomic Data and Analysis
charge exchange recombination αI,Z
Structure database (ADAS) [97]. The term (4.2a) shows the losses of nI,Z due to
ionization ne nI,Z SI,Z , recombination ne nI,Z αI,Z and charge exchange recombicx
nation nth
H αI,Z . The terms (4.2b) and (4.2c) show the contributions to nI,Z due
to ionization and recombination from the lower and higher ionization stages, respectively. In the low density limit, the effective rate coefficients SI,Z , αI,Z and
cx depend on the electron temperature T . Additional essential input data are
αI,Z
e
the experimental radial ne profile, the Te profile, and a calculated radial thermal
neutral hydrogen density distribution nth
H taken from [98]. The ion temperatures
are not necessary for the determination of the transport coefficients with this
model [96]. Additionally, nth
H has to be corrected by the influence of a possible
neutral beam injection (discussed in section 4.3).
The impurity ion density distribution itself is not accessible for direct observations. The only possibility is the measurement of the line emission from the
ionization stages. In order to acquire the line emission intensity the code calculates the emissivity of the impurity ion density with the help of the background
plasma parameters and the temperature dependent emission rates due to electron collisions (equation 2.13). This yields the radial emissivity distribution of
the ionization stages in the plasma. The line integral along the line-of-sight of
a diagnostic yields the observable intensity for each of the emission lines.
In order to determine the ratio v/D, the simulated intensity ratios of the
emission lines of different ionization stages are compared with the experimental
intensity ratios. In the case of intrinsic impurities in flow equilibrium conditions
(net flow = 0) this is the only method to acquire information about the transport
properties. An example of the consequences of a varied ratio of v/D on the iron
ionization balance with an unchanged background plasma (figure 4.1) is given
in figure 4.2. In order to simplify the analysis of the v/D ratio variation, the
diffusion coefficient of this simulation is assumed to be radially constant at
1 m2 s−1 . We note that any shape of the radial diffusion coeffient profile could
be used to determine the consequences of a v/D ratio variation. The sources
and sinks at the wall are not changed. A 30 % variation of the ratio v/D (figure
4.2(a)) results in a change of the Fe XXIII and Fe XVI density of about 25 %
and 10 %, respectively (figure 4.2(b)). Therefore, a change of their ratio in the
same background plasma is a consequence of a changed ratio v/D.
In the case of transient impurity experiments, short impurity puffs introduce
neutral impurity atoms which are distributed and ionized in the plasma. The
simulated time evolutions of the emission lines of each ionization stage in the
43
19
x 10
1200
5
1000
4
800
3
600
2
400
1
200
0
0
0.2
0.4
0.6
0.8
Te (eV)
ne (m−3)
6
0
1
r/a
Figure 4.1: The electron density profile and the temperature profile which are
used for the determination of the influence of v/D. Their shape is typical for
the complete NBI heated L-mode discharge from which they are taken.
VUV and (if possible) in the SXR are compared to the experimental ones [40].
This method allows for the determination of absolute radial profiles of D and v.
The fitting procedure is performed by varying the profiles of D and v until the
simulated time evolution of the impurity emission line intensities is reproduced.
The emission line intensity of an ionization stage is determined by the respective ion density, the electron temperature and the electron density. A change of
the electron density or temperature would therefore change the time evolution
of the emission line intensity. Therefore, this method can only be applied if the
background plasma, i. e. the electron density and temperature, is in steady
state. The Strahl code calculates the time evolutions of the ion densities and
their emission line intensities with the help of equation (4.1). In order to determine absolute radial transport coefficients a dynamic process, i. e. transient
impurity transport experiment, is required. Directly after the injection of the
impurity, the gradients of all impurity ion densities are large compared to the ion
densities. Therefore, the diffusive transport is much larger than the convective
one and the radial profile of the diffusion coefficient can be determined. This is
also the reason why for intrinsic impurities the absolute transport coefficients
cannot be determined.
Since the extrinsic impurities are injected transiently, they are pumped out
of the plasma. In the pumping phase the maxima of the ion densities decrease
but the shape of the radial distribution is unchanged. In this phase the ratio of
v/D is determined by the shape of the radial impurity density profile and since
D is known from the injection phase, v can be derived.
In steady state the particle flows entering the plasma equal the particle flows
leaving the plasma. Recycling and sputtering processes at the wall are one of
the contributors to the inflowing particles.
44
4.1 Strahl code
0
1.4
1.01
1
0.99
1.2
normalized nFe (a.u.)
v/D (m−1)
−1
−2
−3
1
0.8
0.6
0.4
Fe XVI
0.2 Fe XXIII
−4
Fe X
0
−5
0
0.2
0.4
0.6
0.8
1
0
0.2
0.4
0.6
0.8
1
r/a
r/a
(a) Change of v/D
(b) Fe ion densities
Figure 4.2: The dependence of the simulated iron ion density on a 30 % change of
the ratio v/D with a radial constant diffusion of 1 m2 s−1 . Continuous: reference,
dashed: changed v/D.
Due to parallel transport, and the two or three dimensional recyling and sputtering processes a one dimensional transport model is not suitable to simulate
the edge plasma transport. Nevertheless, assumptions of the particle in- and
outflows have to be made in order to determine the boundary conditions of the
model. The recycling model which is used in Strahl is optimized for a divertor
tokamak like AUG [99] or JET [100] (figure 4.3). It consists of a valve which introduces the impurities, a wall, a plasma volume which is divided into a core and
scrape-off-layer region (SOL) containing Ncore + NSOL particles, and a divertor
volume with Ndiv particles which is connected to a pump. The SOL is connected
to the wall and the divertor with fluxes. The fluxes from and to the divertor
can be adjusted via transport times τdiv,SOL and τSOL,div , respectively. The flow
from the LCFS towards the wall ΦW is determined by the transport properties
and the impurity ion density at the LCFS. It is assumed to be constant
ΦW = DLCF S
nZ,LCF S
(4.3)
λ
with the impurity ion density nZ,LCF S and the diffusion coefficient at the
LCFS DLCF S , respectively, and the decay length λ. With the help of the decay
length λ and the diffusion at the LCFS, the particle outflow can be changed.
Since the transport in the edge plasma is not one dimensional, the diffusion
coefficient at the LCFS is not subject of the analysis with the Strahl code and
can be chosen such that the experimental and simulated intensity time evolution
of the lowest ionization stage fit. The linear decay length λ is estimated to be
about 1 to 3 cm in a SOL with a width of about 2 cm. The width of the SOL
is determined by the distance of the LCFS to the wall in the experiment.
An adjustable recycling coefficient R determines the ratio between the recycling fluxes and the fluxes to the wall. The neutral impurities are introduced
through the valve with an freely adjustable particle source function and by the
45
Figure 4.3: Recycling fluxes of Strahl.
recycling fluxes. Those particles which hit the wall or the pump are removed
from the plasma. The last boundary condition is at the magnetic axis where
the ion flows become zero.
Since TEXTOR as a limiter device does not use a poloidal divertor we set
τdiv,SOL and τSOL,div to very large values so the fluxes between divertor and SOL
vanish. This means that factually the divertor volume does not exist anymore
in the modelling. Since the recycling coefficient for argon is not well known
the recycling factor R in the recycling model is set to zero and the inflowing
recycling particles from the wall are replaced by the experimental time trace
of a low ionization stage. The validity of this procedure is shown in the next
section.
4.2 Impurity particle source function
The impurity particle source function introduces the impurity particles which are
flowing into the plasma from the wall. For argon the particle source function is a
combination of the time evolution of the short argon injection and the recycling
argon particles. The particle source function of argon is unknown. In order to
perform the analysis with the Strahl code we use the time evolution of the
Ar VIII, 70.0 nm, line emission intensity as time evolution of the argon particle
source function. Therefore, we have to ensure that the Ar VIII intensity time
evolution measures only inflowing particles. Additionally, the particles have to
be homogeneously distributed on the magnetic flux surfaces such that due to the
poloidal and toroidal symmetry the assumption of one dimensionality is fulfilled.
At first we estimate the recombination time of the high ionization stages using
atomic data from ADAS [97]. If the recombination time is longer than the time
the respective ion needs to diffuse towards the wall the ion cannot contribute to
46
50
Te (eV)
40
30
20
10
0
0.465
0.47
0.475
r (m)
0.48
0.485
Figure 4.4: Te in the SOL of a reference discharge measured with a He-Beam
diagnostic [88]. The LCFS is located at about 47 cm. The errorbar indicates
the average error of the signal.
the density of the lower ionization stages.
The recombination rate of Ar IX αAr,IX in a plasma with ne = 2×1019 m−3
and Te = 150 eV at r/a ≈ 0.8 is αAr,IX ≈ 2.37e-018 m3 s−1 (figure 4.1). This
results in a recombination time of tα ≈ 42 ms. The characteristic transport time
ttrans is
ttrans = l2 /D
(4.4)
With the squared distance l2 = 92 cm2 , which is equivalent to the distance
between r/a ≈ 0.8 and r/a = 1, and a diffusion coefficient of D = 5 m2 s−1
which is derived from impurity transport experiments the average transport time
towards the wall is about 1.6 ms. So the outflowing Ar IX ions do not recombine
before they hit the wall. Since the ionization times of the lower ionization stages
are < 1 ms all of their experimental intensity time traces represent only inflowing
particles.
Since argon is a noble gas it does not enter into chemical bonds with the
wall materials. Therefore, the particles which hit the wall are neutralized and
re-enter the plasma, i.e. they recycle. For a recycling species like argon this
means that the recycling particles from the wall which flow towards the plasma
center are measured by the experimental time evolution of a low ionization stage.
Since we have shown above that the Ar IX ion density does not contribute to
the density of the Ar VIII ions the time evolution of an Ar VIII emission line
represents all particles which are flowing from the LCFS towards the plasma
center. Therefore, the experimental intensity time evolution of a low ionization
stage in the edge plasma can be used as replacement of the recycling flows in
the STRAHL model.
47
In order to determine reliable radial transport coefficients, the one dimensional
STRAHL code requires a homogeneous impurity distribution on the magnetic
flux surfaces in a steady state plasma.
We estimate the time τhom for argon to be homogeneously distributed in
the edge plasma when injected by a gas valve (nD =ne,edge ≈ 5 × 1018 m−3 ,
TD =Te,edge ≈ 40 eV from a He-Beam diagnostic [88] figure 4.4). Three processes contribute to the time of the homogenization τhom . At first the neutral
argon particles have to be ionized and to be thermalized with the plasma. Afterwards we assume that parallel transport along the magnetic field lines and
poloidal diffusion perpendicular to the field lines distribute the argon ions on
the magnetic flux surface. In the beginning, we neglect radial transport and
stay on the separatrix.
We first analyze the injection process of the neutral argon at the wall. The
ionization time of neutral argon in the plasma is ≈ 1 µs. For this reason the cloud
of injected neutral argon with room temperature TAr ≈ 0.02 eV and a diameter
d = 0.3 m is ionized within 1 µs in the SOL with an electron temperature of
about 5 eV. We assume that the Ar II ions propagate to the separatrix where
they are thermalized with the background plasma.
In SI units with T in eV the thermal equilibration time of Ar II in a deuterium
plasma is [84]
τeq =1.75 × 1026 (mAr TD + mD TAr )3/2 . . .
√
2
2 −1
× ( mAr mD nD λAr,D ZAr
ZD
)
(4.5)
With mAr the mass of argon, mD the mass of Deuterium, ZD and ZAr the ionization stage of deuterium and argon, respectively, and the Coulomb logarithm
[84]
λAr,D
"
ZD ZAr (mD + mAr )
= 23 − ln
mD TAr + mAr TD
2
n Z2
nD ZD
+ Ar Ar
TD
TAr
0.5 #
(4.6)
with the density of argon nAr . With about 1018 injected argon atoms nAr
becomes about 1 × 1017 m−3 . With ZD = ZAr = 1 equation (4.5) yields ≈
0.8 ms. After the equilibration the thermal velocity of Ar II becomes [6]
q
(4.7)
vth = 9.77 × 103 Te,edge mp /mAr
With the proton mass mp the thermal velocity results to ≈ 10 km/s.
After the thermal equilibration the argon ions flow along the magnetic field
lines. In the rest frame of the plasma half of the particles flows in direction
of the magnetic field Bt and the other half flows in counter direction of the
magnetic field. The circumference of TEXTOR is 11 m, i.e. the ions perform
≈ 1 toroidal turn per ms in both of the directions along the magnetic field line.
48
5
safety factor
q (a.u.)
4
3
2
1
0
0
0.2
0.4
0.6
0.8
1
r/a
Figure 4.5: The estimated safety factor. For the estimate, the safety factor is
roughly determined by a fitted parabola. The boundary conditions for the fit are
1.) the locations of excited islands, 2.) the edge safety factor of 4.5 calculated
with equation (2.2) and 3.) an assumed axial safety factor of about 0.8.
Therefore, two toroidal turns per ms are performed by the argon cloud, fl =
2 ms−1 . With an edge safety factor of qa ≈ 4.5 more than one poloidal turn is
performed after n = 5 toroidal turns. An edge safety factor of qa ≈ 4.5 is used
in all of the performed experiments in the m/n = 3/1 DED base mode (see also
figure 4.5). The time τpol to perform n = 5 toroidal turns (about one poloidal
turn) after the argon injection becomes
τpol = τeq + qa /fl ≈ 3 ms.
(4.8)
Poloidal transport perpendicular to Bt additionally contributes to the distribution of the particles on the magnetic flux surface. In order to estimate the
magnitude of the poloidal perpendicular diffusion coefficient we estimate the
larmor radius of Ar II at a temperature Te,edge [6]
q
rL = 1.45 × 10−4 Te,edge mAr /mp · (Bt )−1
(4.9)
With the proton mass mp and the toroidal magnetic field Bt of about 2.25 T
the larmor radius is < 3 mm. Within this distance the background plasma
perpendicular to the magnetic field does not change significantly. Therefore, the
poloidal impurity transport is assumed to be in the order of the radial impurity
transport. In the θ plane the edges of the argon cloud poloidally diffuse away
from the center of the cloud. With D ≈ 5 m2 s−1 , which is derived from impurity
transport experiments, each side of the argon cloud diffuses the average distance
of
sl =
p
Dτpol
(4.10)
49
which is ≈ 12 cm. After the injection the argon cloud has an diameter of d ≈
0.3 m. After n = 5 toroidal turns the argon particles cover n(d + 2sl ) ≈ 2.7 m
of the poloidal circumference of L = 2πa ≈ 2.95 m.
In the discussiuon above the radial transport is negelected. Its influence is
taken into account in the following discussion. Due to radial transport processes
towards the plasma center the argon particles propagate into a denser and hotter
plasma. This leads to an increase of vth . With a higher thermal velocity the
particles perform more toroidal turns per ms than at the edge. Furthermore,
the distance to the magnetic axis and the safety factor q are smaller than at the
edge. The smaller safety factor increases the number of poloidal turns per ms fl
of the argon ions. Taking into account equation (4.8) the time to perform one
poloidal turn τpol is decreased.
Due to the smaller distance to the core the poloidal circumference L is reduced. Therefore, the argon particles cover a bigger fraction of the poloidal circumference than further outside of the plasma. Therefore, the homogenization
time tauhom decreases when taking into account radial transport. We assume
τhom < τpol = 3 ms so after a maximum of 3 ms the inflowing particles are
homogeneously distributed in the plasma.
The radius at which the Strahl code can be applied is estimated in the
following discussion. Taking into account the diffusive radial transport with
equation (4.10), the argon ions propagate a distance s = 12 cm. So after 3 ms
the ions arrive at a small radius of rx = 35 cm. Since at ry = 43 cm (r/a ≈ 0.9)
L already is 2.7 m, the cloud is homogeneously distributed between rx and ry .
Therefore, the STRAHL calculation is reliable in the shell of r = 39 cm (r/a ≤
0.8). The emissivity shell of Ar VIII, 70.0 nm is located near r/a = 0.9 and it
is suitable to be applied as particle source function for argon.
4.3 Changes due to NBI
The neutral hydrogen in the plasma changes the impurity balance due to charge
exchange recombination [101]. Since transport calculations are based on the
correct modelling of the impurity density distribution a change of the neutral
hydrogen density distribution can change the result of those calculations. The
thermal neutral hydrogen density distribution nth
H which is used to perform the
calculations in this thesis is taken from [98] (figure 4.6). It has been calculated for ohmic plasmas with the help of the code EIRENE [102]. Some of the
experiments are performed in NBI heated L-mode plasmas. The injection of
the neutral hydrogen changes the radial neutral hydrogen density distribution.
Therefore, the consequences of the changes have to be discussed.
In order to determine the additional density introduced by the NBI, a code
has been applied which uses a collisional radiative model [103], [104], [105].
The model of the neutral beam injection which is applied in the code is presented in figure 4.7. In a first step the code calculates the neutral hydrogen
50
4.3 Changes due to NBI
17
10
nth
H
16
nH (m−3)
10
NBI
nH
·
sum
q
E NBI
Ti
15
10
14
10
13
10
0
0.2
0.4
0.6
0.8
1
r/a
Figure 4.6: Contributions to the neutral hydrogen density.
flux density at the exit of the neutral beam injector via the applied acceleration
voltage, the dimensions of the input valve, and the profiles of the deposited
power which are taken from [93]. In a second step the mitigation of the flux
density due to charge exchange with the plasma and impurity ions is calculated
on the magnetic flux surfaces in the overlap volume of the NBI and the plasma
(figure 4.7). We note, that the impurity content, i. e. Zef f is important for
the determination of the beam mitigation. Charge exchange processes between
neutral hydrogen and plasma ions do not change the neutral hydrogen density
profile whereas charge exchange processes with an impurity reduce the neutral
hydrogen content. Therefore, a reduction of the impurity content increases the
neutral hydrogen density. In the last step the neutral particles introduced by
NBI are assumed to be homogeneously distributed on the magnetic flux surfaces by parallel transport. The result is a radial profile of the neutral hydrogen
BI .
density nN
H
In order to take into account the influence of the additional neutral hydrogen in the Strahl calculations we estimate the difference between the charge
exchange recombination rates at different temperatures. The charge exchange
cx is proportional to the square root of the temperature
recombination rate αI,Z
(figure 4.8). So the ratio of the charge exchange recombination rates between
BI with an energy of E
nN
H
p N BI and nH with a temperature of Ti (energy and
temperature in eV) is EN BI /Ti . This leads to the approximation
cx,N BI
BI
BI
nN
× αI,Z
≈ nN
×
H
H
s
EN BI
cx
× αI,Z
Ti
(4.11)
Taking into account the terms in (4.2a) and (4.2c), the radial neutral hydrogen
BI is multiplied with the temperature factor and added to the
distribution nN
H
neutral hydrogen distribution of the ohmic plasma (figure 4.6). The comparison
with the original distribution of the neutral hydrogen density is shown in figure
51
Figure 4.7: Courtesy of O. Marchuk. An example of the cross section of the neutral beam with the plasma (coloured region) in the top view of a tokamak used
in the model. The model applied for the calculations uses Textor geometry
with tangetial NBI. The width w of the neutral beam and the direction of the
plasma current are indicated.
4.6. The largest change of the neutral particle distribution by a factor > 20
occurs in the plasma core (r/a < 0.2). The changes of the emissivity in the
plasma core are shown in figure 4.9. The Ar XVI emissivity in the core changes
by a factor of ≈ 2. The variation on the time evolution of Ar XVI which results
due to the injection of neutral argon by a short puff (t ≈ 1 ms) at the edge
is presented in figure 4.10. The change of the ionization balance introduces a
change in the decay time. Since the decay time is used to determine the ratio
v/D it is inevitable to considers the additional amount of neutral hydrogen in
order to determine the correct transport coefficients for the plasma core.
A crucial question when applying transport codes for the analysis of impurity
transport experiments is the reliability of the calculated values. The fitting
procedure itself already has an error of ≈ 10 %. Additionally, we have to take
into account the sensitivity of the transport coefficients on the input data. The
influence of the input data errors on the calculation of the transport coefficients
is determined by changing the input data in the range of the measurement errors
and running the calculation. In the first section the errors of the radial profiles
of ne , Te and nH are discussed. The second section deals with the errors of
the atomic data and the last section determines the total error of the transport
coefficients.
52
−5
(cm3s−1)
αcx
Ar XVII
10
−6
10
−7
10
−8
10
0
10
1
10
2
10
3
10
Te (eV)
4
10
5
10
normalized emissivity (a.u.)
Figure 4.8: Charge exchange recombination rates of Ar XVII from ADAS [97].
Ar XII
Ar XIV
Ar XV
Ar XVI
Ar XVII
1
0.8
0.6
0.4
0.2
0
0
0.2
0.4
0.6
0.8
1
r/a
Figure 4.9: Relative changes of the normalized emissivity due to NBI. Dashed
and continuous lines are with and without NBI contribution, respectively.
53
1
Ar XVI with nNBI
H
Ar XVI w/o nNBI
H
0.8
0.6
0.4
0.2
0
3
3.02
3.04
3.06
time (s)
3.08
3.1
Figure 4.10: The change of the calculated Ar XVI, 35.4 nm, intensity time evolution due to NBI.
4.4.1 Influence of the plasma parameter profiles
Electron density profile
In the model used by Strahl the electron density plays two main roles. The first
one is during the determination of the sources and sinks of the ionization stages
with the help of the ionzation and recombination rates. Therefore, with a change
of ne the ion density distribution changes which influenced the determination of
the transport coefficients. The second role is the determination of the ionization
stage emissivity. Basically, the emissivity is used to compare the simulated ion
density distribution with the experiment because the integral over the emissivity
results in the simulated intensity of the emission lines. Therefore, a change of the
emissivity due to ne can change the simulated intensity ratios which influences
the determination of v/D for impurity density profiles in transport equilibrium.
The experimental error of the radial line integrated ne profiles is < 5 %. The
calculation of the radial ne profile from the line integrated profile is performed
with an Abel-inversion which increases the error. The profile of the evaluated
experiments have an error of about 15 %.
We perform two steps in order to estimate the influence of the error on the
transport coefficients. In a first step we simulate an impurity injection experiment with the original profile and an arbitrary chosen radial distribution of
transport coefficients. The result is a set of argon ion time traces. In a second
step we change the ne profile within an error of 15 %. Then we replace the
original ne profile and change the transport coefficients until the set of the time
traces fits to the original one.
The variation of the ne profile within the error of 5 % (figure 4.11(a)) influences
the transport coefficients (figures 4.11(b) and 4.11(c)) only in the edge plasma
in r/a > 0.8 (∆D ≈ 0.02 %, ∆v/D ≈ 8 %) whereas the center seems to be
54
normalized ne (a.u)
1
0.8
0.6
0.4
0.2
0
0
0.2
0.4
r/a
0.6
0.8
(a) Variation of ne
D (m2s−1)
10
1
0.1
0
0.2
0.4
r/a
0.6
0.8
(b) Changes in D
2
0
v/D (m−1)
−2
−4
−6
−8
−10
−12
0
0.2
0.4
r/a
0.6
0.8
(c) Changes in v/D
Figure 4.11: Changes of the transport coefficients due to a variation of the ne
profile within the error of 15 %.
55
normalized Te (a.u.)
1
0.8
0.6
0.4
0.2
0
0
0.2
0.4
r/a
0.6
0.8
(a) Variation of Te
D (m2s−1)
10
1
0.1
0
0.2
0.4
r/a
0.6
0.8
(b) Changes in D
2
0
v/D (m−1)
−2
−4
−6
−8
−10
−12
0
0.2
0.4
r/a
0.6
0.8
(c) Changes in v/D
Figure 4.12: Changes of the transport coefficients due to a change of the Te
profile within an error of ±10 %.
56
unaffected. Therefore, the error of the transport coefficients due to an error of
the ne profile is negligible in the plasma core.
Electron temperature profile
The electron temperature does not explicitly appear in the coupled set of the
continuity equations. But all the atomic data i.e. the effective rate coefficients
for ionization, recombination, charge exchange recombination, and emission depend on it non-linearly. So we expect that a variation of Te has more severe
consequences on the determination of the transport coefficients than a variation
of ne .
The determination process of the Te profile error on the transport coefficients
is the same as for ne . The experimental error of Te measured with an ECE
diagnostic is < 10 %. The variation of Te within the error is shown in figure
4.12(a). Strong changes up to a factor of 1.4 appear in the ratio v/D whereas
the changes of the diffusion coefficient D are within a 15 % range (figures 4.12(b)
and 4.12(c)). The change of the ionization balance due to the variation of the
temperature has a stronger influence on the transport coefficients. Especially
the v/D ratio seems to be sensitive to variations.
Neutral hydrogen density profile
The sources and sinks (4.2c) have a linear dependence on the neutral hydrogen
density. After the calculation of the ion density distribution i.e. during the
determination of the emissivity, the density does not have any influence.
The nH profile is known within a factor of 2 (figure 4.13(a)). A variation of
the nH profile leads to local changes of ±30 % for the diffusion coefficient (figure
4.13(b)). The v/D ratio locally changes up to a factor of 1.5 (figure 4.13(c)).
The dependence of the transport coefficients on the nH profile is weaker than
the dependence on the Te profile. This indicates that the influence of charge
exchange recombination processes on the transport coefficients is small. Only
large changes like the increase of the central nH profile by a factor of 20 (figure 4.6) due to the neutral beam injection influence the determination of the
transport coefficients.
Estimate of the total error of the background plasma
In order to determine a cumulative average error of the transport coefficients we
want to point out that the changes of the electron temperature yield the largest
errors. Additionally it is found that the error of the electron density profile on
the transport is negligible. The error of the neutral hydrogen profile results in
local variations of the transport coefficients. Taking into account these findings
we estimate the total error of the transport coefficients. The total average error
of the diffusion coefficient is estimated to be around 20 %. The average error of
the v/D ratio is around 30 %.
57
10
normalized nH
1
0.1
0.01
0.001
0
0.2
0.4
r/a
0.6
0.8
(a) Variation of nH
D (m2s−1)
10
1
0.1
0
0.2
0.4
r/a
0.6
0.8
(b) Changes in D
2
0
v/D (m−1)
−2
−4
−6
−8
−10
−12
0
0.2
0.4
r/a
0.6
0.8
(c) Changes in v/D
Figure 4.13: Changes of the transport coefficients due to a change of nH within
the factor of 2.
58
4.4.2 Atomic data
The atomic data for ionization, recombination, charge exchange recombination
and emission are provided from the ADAS database. The atomic data is used
to determine the ionization balance and the emissivity in the plasma. We first
discuss how a change of a certain rate influences the transport coefficients and
then we give an estimate of the errors on the transport coefficients which are
introduced by the atomic data.
The emission rates determine the radial emissivity of the radial impurity ion
distribution. The integrals of the plasma emissivity along the line-of-sight are
the simulated intensities which can be compared to the experimental intensities.
Therefore, the simulated intensities are used to compare the modelled ion density distribution with the experimental one. The ratios between the intensities
of different ionization stages are determined by the ionization balance in the
plasma. A change of the ratio of the emission rates between different ionization
stages will therefore change the intensity ratios although the ionization balance
remains the same. The estimate of the concentration is therefore changed if the
ratios between the emission rates are changed.
The determination of the transport coefficients with transient impurity transport experiments does not depend on the intensity ratios since only the normalized time evolutions are needed to determine the transport.
In the terms (4.2a) and (4.2c) the charge exchange recombination rates are
always coupled to the neutral hydrogen density. As presented above, the variation of nH by a factor of 2 shows relatively small changes. For this reason we
assume that a change of the charge exchange recombination rates within the
error of the atomic data of 15 % does not have a significant influence on the
transport coefficients.
The ionization and recombination rates determine the ionization balance via
the sources and sinks of the ion density. A change of these rates shifts the radial
position of the ion density shell and changes its shape. This changes the time
evolution of the emission lines and the transport coefficients have to compensate
these changes.
In order to assess the influence on the transport coefficients test calculations
with a 15 % change of the ionization and recombination rates of Ar IX (Ne-like)
have been performed. Ar IX has the broadest density distribution in the edge
plasma so a change of the rates will have the biggest effect for all of the low
ionization stages. The resulting changes on the transport coefficients are negligible (< 1 %). In order to study a simultaneous change of all of the ionization
and recombination rates, respectively, it is not sufficient to change the ne and
Te profiles because they also change the emission rates and furthermore do not
separately change the ionization and recombination rates.
Changing all of the effective ionization rates of argon at once within the error
of ±15 % leads to changes of the transport coefficients which also are around
15 %. The variation of the effective recombination rates within the error has
59
a smaller influence of approximately 7 % on the transport coefficients. The
cumulative effect of the variation of the ionization and recombination rates on
the error of transport coefficients is estimated to be approximately 16 %.
4.4.3 Total error
The total error of the transport coefficients is calculated via the square root of
the square sum of all of the errors. Additionally to the errors discussed above
the statistical errors of the impurity signals of ≈ 3 - 10 % have to be taken into
account. With the errors due to the plasma profiles (∆Dp ≈ 21 % and ∆(v/D)p
≈ 30 %), the atomic data of (∆Da ≈ 16 % and ∆(v/D)a ≈ 16 %) and the
fitting procedure (∆Df ≈ 10 % and ∆(v/D)f ≈ 10 %) the error of the diffusion
coefficient and the ratio v/D results to ∆Dtot ≈ 30 % and ∆(v/D)tot ≈ 37 %,
respectively.
60
This chapter presents findings of impurity transport experiments with static
and dynamic resonant magnetic perturbations.In order to evaluate, whether the
application of a resonant magnetic perturbation changes the impurity transport,
the perturbed discharge is compared to a reference discharge with the same
background plasma. The background plasma parameters are the electron density
and temperature in the core and at the edge. In most of the experiments two
methods are applied to analyze the impurity transport. One method is the
evaluation of transient impurity experiments which use a short (1 ms) local
argon puff at the edge and monitor the propagation of the argon particles into
the hot plasma center. With the help of Strahl the transport coefficients are
determined. The ionization stages which have been used in the fitting process
are Ar VIII, Ar X, Ar XII, Ar XIV - XVII. In order to improve the readability
we reduce the number of ionization stages we show. Within the error and under
the assumption of poloidal and toroidal symmetry the number of ionization
stages allows for the determination of an unambigious radial profile of transport
coefficients. The method for the determination of the transport coefficients
is used in all of the experiments discussed in this chapter. We not that the
neoclassical transport is not discussed in this thesis. The second method is the
monitoring of the emission line intensities of an intrinsic impurity, in particular
of iron, which represent the ion density distribution. The ion density distribution
of intrinsic impurities is determined by an equilibrium of in- and outflows, i.e.
the net flow is zero. As soon as a net-flow appears the ion density distribution
is modified which can be observed by a change of the measured intensities. The
first and second section discuss experiments with static RMP in m/n = 3/1
DED base mode which are in parts prepublished in [43]. The third section
Figure 5.1: The coilsets of the m/n = 3/1 DED base mode
61
ne (1019m−3)
Te (eV)
Te (eV)
IDED (kA)
ne (1019m−3)
6 r/a = 0
4
2
0
2 r/a = 1
Reference
RMP discharge
1
0
4
2
0
1000
500 r/a = 0
0
75
50
25 r/a = 1
0
1
1.5
2
2.5
3
time (s)
3.5
4
4.5
5
Figure 5.2: Plasma scenario of the dc DED experiment (105353) and the reference (105354). From top to bottom: central electron density, edge electron
density, DED current, central electron temperature and edge electron temperature. The argon injection of 1 ms duration is indicated at t = 3 s.
presents the analysis of experiments in the static m/n = 6/2 DED base mode
in so-called pumped out plasmas. The last section presents the results of the
worldwide first impurity transport experiments with a dynamic RMP.
5.1 dc DED in steady state plasma
5.1.1 Plasma scenario
In this section we analyze the impurity transport in the m/n = 3/1 DED base
mode configuration in the Textor discharges no.s 105347 to 105353. The reference discharge without DED application is 105354. In the discharges 105349 and
105350 only one of the 2 DED coil sets is applied (figure 5.1). The application
of only one coil set reduces the strength of the RMP by a factor of 2. Due to the
differenct locations of the coil sets their RMPs have a phase shift of 45° to each
other. This can be used to determine local impurity source effects which will not
be discussed in this thesis. In 105349 the coil set 1 is applied and in 105350 coil
set 2. The impurity transport experiments in steady state NBI-heated L-mode
plasmas are performed with an axial toroidal magnetic field BΦ,axis = 2.25 T,
a plasma current Ip = 310 kA, an edge safety factor qa ≈ 4.5, a central electron
density ne (0) = 6·1019 m−3 and a central electron temperature Te (0) = 1.2 keV.
Figure 5.2 shows the time evolutions of ne , Te and IDED from the reference dis-
62
charge 105354 and discharge 105353 with a maximum IDED of 2.4 kA per coil.
Neutral beam injection in co (0.35 MW) and counter (1.35 MW) direction of
the plasma current is applied from 1.3 to 4.8 s and 1.2 to 5.3 s, respectively. The
introduced plasma rotation in counter direction of the plasma current shifts the
DED current excitation threshold of an m/n = 2/1 tearing mode to high DED
currents (> 3.75 kA per coil) [12] and therefore no m/n = 2/1 tearing mode is
present in the plasma. The DED current excitation threshold of an m/n = 3/1
tearing mode is about 2.7 kA per coil. The application of the DED with IDED
< 2.7 kA per coil does not change the background plasma parameters, neither
at the edge nor in the core, with respect to the reference. A tearing mode is not
detected in the plasma.
Electron cyclotron resonance heating (ECRH) is applied in all of the discharges except for discharge 105351 and 105352. The ECRH has been used for
heat pulse propagation studies of the experimental working group which are not
subject of this thesis. The results of this thesis are not affected by ECRH as
will be shown below.
In order to perform the transient impurity transport studies approximately
5×1017 argon atoms are injected within 1 ms at t = 3.0 s. The injected number
of atoms is determined by the measurements of the pressure reduction in the
volume of the gas injection system. A cross check is performed with the help of
the measured maximum concentration of argon in the reference plasma. With
an average concentration of about cAr ≈ 2×10−3 the estimate yields about (7 ±
2.5)×1017 argon atoms in the plasma volume with an average electron density
of about 4 × 1019 .
The argon injection at t = 3.0 s does not change the measurements of the electron density and electron temperature (figure 5.2). Therefore, the disturbance
of the background plasma is negligible.
2
Fe XXIII, 13.3 nm, reference
Fe XV, 28.4 nm, reference
Fe XXIII, 13.3 nm, with RMP
Fe XV, 28.4 nm, with RMP
1.5
normalized signal
normalized signal
2
1
0.5
Fe XV, 28.4 nm, reference
Fe XV, 28.4 nm, with RMP
1.5
1
0.5
DED current, 2.4 kA
0
1
2
3
time (s)
(a) Hexos
4
DED current, 2.4 kA
5
0
1
2
3
time (s)
4
5
(b) Spred
Figure 5.3: Time averaged (100 ms) Fe XXIII, 13.3 nm and Fe XV, 28.4 nm
intensity time evolution from Hexos (a) and Spred (b) and the DED current
time evolution. Reference: 105354; with RMP: 105353
63
100
100
Reduction of C VI intensity (%)
Reduction of Fe XXIII intensity (%)
80
60
40
20
0
0
1
2
IDED (kA)
3
4
80
60
40
20
0
0
(a) Fe XXIII, 13.3 nm
40
80
20
0
0
2
IDED (kA)
3
4
3
4
100
105347
105348
105349, coil set 1 only
105351
105352
105353
Reduction of ω (%)
Reduction of Fe ratio (%)
60
1
(b) C VI, 3.4 nm
100
80
105347
105348
105351
105352
105353
60
40
105347
105348
105351
105352
105353
20
0
1
2
IDED (kA)
3
(c) Fe XXIII/FeXV
4
0
1
2
IDED (kA)
(d) Toroidal angular rotation ω
Figure 5.4: The reduction of the Fe XXIII, 13.3 nm, and C VI, 3.4 nm, intensity
and of the intensity ratio of Fe XXIII vs. Fe XV and the reduction of the toroidal
rotation ω with respect to the applied DED effective current IDED below the
excitation current threshold of an m/n = 3/1 tearing mode. All of the signals
are time averaged (100 ms). In the discussed experiments the angular rotation
is in counter direction of the plasma current (figure 3.1). The DED application
induces an acceleration in plasma current direction.
5.1.2 Observations
Intrinsic impurities like e.g. helium, boron, carbon and oxygen can usually be
observed in TEXTOR plasmas. Under special circumstances, e.g. when the
plasma heats up steel components in the plasma vessel, iron contaminates the
plasma and is available for spectroscopy. In the discussed plasma scenario iron
is detectable via the signals of at least three different ionization stages: Fe XV,
Fe XVI and Fe XXIII. Furthermore, before the DED is applied at t = 1.2 s the
signals of each of the ionization stages have the same normalized time evolution
in all of the discharges.
During the DED current ramp up phase the measured intensities of all of the
above mentioned impurity species reduce with respect to the reference in the
64
1
Reference
With RMP
0.5
Ar VIII, 70.0 nm
0
1
Ar XV, 22.1 nm
0.5
0
1
Ar XVI, 35.4 nm
0.5
signal (V)
signal (a.u.) signal (a.u.)
signal (a.u.)
0
2
Ar XVII, 0.4 nm, SXR r = 0
1
0
3
3.02
3.04
3.06
time (s)
3.08
3.1
Figure 5.5: Argon time traces in the VUV and SXR of the reference 105354 and
the discharge with RMP 105353.
plasma bulk (figure 5.3). The reduction of the intensities of Fe XXIII, 13.3 nm,
(figure 5.4(a)) which radiates in the plasma center and of C VI, 3.4 nm, (figure
5.4(b)) which radiates at about r/a ≈ 0.75 are plotted against IDED . Figure
5.4(c) shows the dependence of the intensity ratio of Fe XXIII (core) and Fe XV,
28.4 nm, (half of minor radius) on the DED current. The graphs show the change
with respect to the reference. A reduction of the intensity up to 50 % in the
case of Fe XXIII and up to 35 % in the case of carbon and the iron ratio can be
observed. The reduction of the Fe XVI and Fe XV intensities which radiate at
about half of the minor radius is the same as for the C VI intensity measured
by Hexos and by CXRS. The reduction of the impurities during the ramp up
phase of the DED current is very reproducible and the absence or presence of
ECRH does not change the observations.
In order to compare the correlation of the reductions on the DED current to
correlations which have been observed in the past, the reduction of the toroidal
angular velocity ω of the discharges derived by the Doppler-shift of the C VI
line from CXRS is plotted against the DED current (figure 5.4(d)). There are
no differences in the reduction factor of the angular velocity between the plasma
core and the plasma edge. The plot shows the same correlation between ω and
IDED as for the iron ratio and the C VI intensity measured by Hexos.
Since all of the discharges show the same correlations, starting from now we
focus on the discharges with the application of the full coil set and we discuss
the exemplary discharge no. 105353 and the reference.
The extrinsic impurity argon which is injected at t = 3.0 s is monitored in the
VUV and SXR. The time resolved observation of a selection of different argon
65
ionization stages is shown in figure 5.5. The upper three graphs show the normalized intensities of the VUV signals. The fourth graph shows the background
corrected signal of a SXR PIN diode channel with line of sight through the
plasma center. From top to bottom figure 5.5 shows Ar VIII (70.0 nm) which
is radiating at r/a ≈ 0.9, Ar XV (22.1 nm) at r/a ≈ 0.3, and Ar XVII (0.4 nm)
at r/a = 0. In the RMP discharge the amplitudes of the VUV signals from
the plasma edge to r/a ≈ 0.3 are smaller than in the reference discharge.
One of the several lines-of-sight of the SXR PIN diodes covers the magnetic
axis where the density distribution of Ar XVII is peaked. The background
corrected SXR signals in figure 5.5 show the radiation emitted by Ar XVII and
therefore, the signal represents the central argon ion density. Also this signal
shows a lower amplitude in the RMP discharge with respect to the reference.
In order to look for first indications of a modification of the impurity transport,
the time differences between the half maxima of the rising signals of different
ionization stages in figure 5.5 are measured. These time differences do not differ
between the two discharges which indicates that the transport properties remain
constant.
5.1.3 Discussion
In former experiments, it has been found that during the application of resonant magnetic perturbation coils intrinsic impurities have been reduced from
the plasma core [7], [106], [107], [108], [109], [110] attributed to the stochastization of the plasma. The mechanism of this so called impurity screening is not
known up to now. In this section we discuss new findings which result from
the monitoring of intrinsic iron during the application of high DED currents
without the excitation of tearing modes. As in the previous section we focus the
discussion on the discharge 105353 (RMP discharge) and the discharge 105354
(reference). The maximum DED current in the RMP discharge is 2.4 kA per
coil. We start with the presentation of the radial transport coefficients which
are derived from the STRAHL simulation of the transient impurity transport
experiments with injected argon (figure 5.6). The derived transport coefficients
do not change due to the application of the DED (figure 5.7). In the radial
distribution of the diffusion coefficient two regions can be distinguished. Near
the mid minor radius there is a transition from high to low diffusion.
We compare the determined diffusion coefficient with results from different
tokamaks. The transition of a high diffusion coefficient from the edge plasma to
a low diffusion coefficient in the plasma center which is found at Textor is also
reported from Aug [28] and Tore Supra [35]. Additionally, the location of
the transition from high to low diffusion coefficients in Jet L-mode discharges
and on Tore Supra is located at the position with a magnetic shear of about
0.5 [35], [47]. In the discussed Textor discharges with an edge safety factor of
about 4.5 a rough estimate of the shear confirms those results (figure 5.8). The
shear becomes 0.5 at about r/a = 0.25 where the low core diffusion coefficient
66
Ar VIII, 70.4 nm (r/a = 0.88)
Ar XV, 22.1 nm (r/a = 0.35)
Ar XVI, 35.4/38.9 nm (r/a = 0.3)
Ar XVII 0.4 nm (r/a = 0.24)
Ar XVII 0.4 nm (r/a = 0)
1.2
1
0.8
0.6
0.4
0.2
0
3
3.01
3.02
3.03
time (s)
3.04
3.05
(a) Reference discharge 105354
Ar VIII, 70.4 nm (r/a = 0.88)
Ar XV, 22.1 nm (r/a = 0.35)
Ar XVI, 35.4/38.9 nm (r/a = 0.3)
Ar XVII 0.4 nm (r/a = 0.24)
1.2
1
0.8
0.6
0.4
0.2
0
3
3.01
3.02
3.03
time (s)
3.04
3.05
(b) RMP discharge 105353
Figure 5.6: Experimental (continuous) and fitted (dashed) argon time traces for
the reference and the dc DED, 2.4 kA per coil discharge.
starts rise to the higher edge values (figure 5.7(a)).
We note that the determination of the absolute radial transport coefficients
requires large ion density gradients. Due to those large ion density gradients
the diffusive transport is much larger than the convective transport and absolute
radial diffusion coefficients can be determined. Large ion density gradients can
only be achieved if an impurity which is not present in the plasma is transiently
and locally injected. Therefore, the transport coefficients cannot be determined
for intrinsic impurities. The radial profile of v/D for intrinsic impurities is
accessible if the effective emission rates are known. For iron the effective emission
rates of the measured emission line intensities are only known for Fe XXIII (13.3
nm). Therefore, a radial profile of v/D for iron cannot be determined.
In order to compare the reduction of the iron signals between the discharges,
we calculate the respective central iron concentration cF e = nF e /ne . The com-
67
D (m2s−1)
10
1
0.1
0
0.2
0.4
r/a
0.6
0.8
(a) Diffusion coefficient
2
0
v/D (m−1)
−2
−4
−6
−8
−10
−12
−14
0
0.2
0.4
r/a
0.6
0.8
(b) v/D ratio
Figure 5.7: The transport coefficients for the reference 105354 and the dc DED,
2.4 kA per coil discharge 105353. The transport coefficients are identical.
5
safety factor
shear
4
a.u.
3
2
1
0
0
0.2
0.4
0.6
0.8
1
r/a
Figure 5.8: The estimated safety factor with the estimated magnetic shear. The
safety factor is estimated according to the description in figure 4.5.
68
parison is clearer when the electron density profiles of both of the discharges are
the same, e. g. at t = 4 s. Therefore, we use the time averaged (100 ms) profiles of the background plasmas at t = 4 s to perform the transport equilibrium
calculation with Strahl. The iron concentration at the magnetic axis is determined by changing the source at the wall until the calculated absolute intensity
of Fe XXIII, 13.3 nm, matches the absolute intensity measured by Hexos (see
section 3.3 and [68] for further information). We use the same transport coefficients for both discharges. This method to acquire the impurity concentration
at the magnetic axis is equivalent to a variation of the transport coefficients
−5 for the central iron
with the same source. The fit yields about cref
F e = 5 × 10
RM
P
concentration of the reference discharge and cF e = 3.5 × 10−5 for the RMP
−2
discharge. The concentrations of the impurities helium cref
He = 2.6 × 10 , boron
ref
ref
ref
cB = 6 × 10−3 , carbon cC = 4 × 10−2 and oxygen cO = 1.5 × 10−3 which
are the main impurities in Textor are derived with the same method. The
error of the concentration is about 34 %. The relative reduction of the concentration during the application of the RMP is about
P (35±3)
P%. This corresponds
to a reduction of the effective charge Zef f =
nI Z 2 / nI Z, with the sum
being performed for all species I (including the plasma ions) in the plasma, from
about 2.5 to 2.0. The impurity concentrations and background plasmas before
the DED application are the same. Therefore, we conclude that the impurity
sources in both discharges before the DED application are comparable. This
means that the application of the DED causes the reduction of the impurity
concentration in the plasma.
Basically, there are two possible mechanisms which lead to a reduction of
the impurity concentration in the plasma core. The first mechanism is a lower
yield of the sources at the wall which reduces the impurity inflow. This reduces
the total radial profile self similarly, i.e. the shape of the normalized profile is
conserved. Therefore, the intensity ratios between the different ionization stages
are unchanged. The second mechanism is a higher outflow due to a change of the
impurity confinement which is equivalent to a change of the impurity transport.
The consequences on the measured intensities and intensity ratios depend on the
radial position. When this change happens at a small radius which is larger than
the radius of the outermost observed line emissivity shell then the intensities
reduce self similarly. If the transport change happens between two emissivity
shells the ratio between the ion densities, i.e. the intensity ratio will change. As
soon as the respective transport mechanism changes the net-flow, the in- and
outflows will equilibrate again. Therefore, in transport equilibrium the impurity
intensities do not change due to constant DED application. A large change due
to a transport mechanism would shift the radial position of the emissivity shell
such that the derived concentration would not be comparable. In the case of
Fe XXIII, 13.3 nm, in both of the discharges the intensity time evolutions are
modulated by normal sawteeth. This shows that the maximum of the emissivity
shell is located inside the q = 1 magnetic flux surface. In addition the maximum
69
temperature is such that the maximum of the emissivity shell of this ionization
stage is always located on the magnetic axis.
The outermost measurable emission line of iron is Fe XV, 28.4 nm, at r/a ≈
0.6. The mechanism for its reduction during the DED application is not clear
since there is not sufficient information about the sources at the wall.
The carbon concentrations measured by Hexos with C VI, 3.4 nm, and with
CXRS also drop. In addition the C VI intensities measured by CXRS and the
Hexos show the same relative reduction. At all radial positions the drop of the
carbon intensity is the same. This means that the carbon transport is unchanged
in the plasma center. The reduction of the carbon concentration has also been
observed on Tore Supra during the activation of the Ergodic Divertor (ED)
[7], [32], [111]. At Tore Supra the stochastization of the plasma has been
found to be the cause of the impurity screening.
Two mechanisms which can reduce the impurity concentration are described
above. In addition, changes of the profiles of the electron density, electron
temperature and neutral hydrogen can pretend a reduction of the concentration.
We first dicuss possible changes of the electron density and electron temperature.
Due to the gradient of the electron density and temperature profiles a change of
these profiles can shift the radial position of the emissivity shells in the plasma
such that the intensities decrease. This mechanism can also change the intensity
ratios of different ionization stages. The change of the iron intensity ratio of
Fe XXIII to Fe XV (figure 5.4(c)) shows that at least for r/a < 0.6 a change
of the sources cannot be the only explanation for the intensity reduction of
Fe XXIII. In order to exclude that a change of the ne and Te profiles is the
reason for the reduction of the intensity ratio we calculate the expected change
of the intensity ratios. For both of the discharges this is performed on the basis
of the respective experimental temperature and density profiles at t = 4 s.
In order to perform this calculation the transport properties of the two discharges are assumed to be the same. The resulting relative changes of the emissivity are shown in figure 5.9(a). The emissivities of both of the iron ionization
stages of the RMP discharge are higher than in the reference. The integration
over the emissivity leads to the simulated intensities which are increased with
respect to the intensities of the reference. In order to compare the calculation
with the experiment, the intensity ratios are marked in figure 5.9(b) which shows
the time evolution of the experimental intensity ratios between Fe XXIII and
Fe XV. The calculated ratio of the RMP discharge is slightly larger than that
of the reference.
Contrary to the calculated intensities, the experimental iron intensities of the
RMP discharge are lower than in the reference. Based on this result differences
in the Te and ne profiles can neither explain the reduction of the intensities
nor the reduction of the intensity ratio. We consider two possible explanations.
One possibility to achieve the reduction of the intensity ratio is by changing
the transport of iron, i.e. the ratio v/D, between the radial positions of the
respective emission lines. A detailed discussion of this mechanism is given above.
70
Fe XVI, 33.5 nm, reference
Fe XVI, 33.5 nm, with RMP
1.5
normalized intensity ratio
Fe XXIII vs Fe XVI (a.u.)
normalized emissivity (a.u.)
2
t = 4.0 s
1
0.5
0
0
0.2
0.4
0.6
0.8
r/a
(a) Calculated iron emissivities
1
1
0.8
0.6
0.4
Reference
RMP
STRAHL, reference
STRAHL, RMP
0.2
0
1
2
3
time (s)
4
5
(b) Normalized iron ratios
Figure 5.9: (a) Calculated iron emissivities on the base of the respective ne and
Te profiles for the reference 105354 and the RMP discharge 105353. (b) Normalized iron ratios of Fe XXIII, 13.3 nm vs. Fe XV, 28.4 nm. The markers at
t = 4.0 s indicate the calculated ratios.
The change of the transport coefficients between the two radial positions is
not unambiguous because the spatial resolution is not sufficient. Therefore, we
abstain from showing any radial profiles of the transport coefficients for iron
which can explain the experimental findings.
Another possibility is an increase of the nN BI profile due to the reduction
of the Zef f during the application of the DED. An increase of the central
nH changes the ionization balance in the central plasma due to an increase
of charge exchange recombination processes. Therefore, the fractional abundances nI,Z /nI , with nI being the total impurity density, in the central plasma
are changed. In the discussed plasma the increased recombination process leads
to a reduction of the Fe XXIII density. This leads to the additional reduction
of the Fe XXIII emission line intensity and the change of the intensity ratio of
Fe XXIII to Fe XV. In the discussed experiments Zef f is changed from 2.5 to
2. The neutral hydrogen profiles due to NBI have been estimated with the code
described in section 4.3 to increase by about 13 % for these values of Zef f . Calculations with the Strahl code show a reduction of the intensity of Fe XXIII
(13.3 nm) by about 1 - 2 %. Under the assumption that also the thermal neutral hydrogen density is increased by about 13 % an additional decrease of the
Fe XXIII intensity of 0.5 % occurs. The transport coefficients do not change
significantly due to the different neutral hydrogen densities. Therefore, we conclude that a change of the neutral hydrogen profile due to NBI is not sufficient
to explain the complete reduction of the Fe XXIII intensity.
Since Ar XVII is also located in the central plasma the increased recombination processes also affect this ionization stage. However, the observed reduction
of the Ar XVII intensity is the same as for the lower ionization stages located
further outside in the plasma. This can be explained by the following consid-
71
100
100
corona approximation
Fe XVII
Ar XVII
60
40
20
0
corona approximation
80
nFe,Z/nFe (%)
nAr,Z/nAr (%)
80
60
Fe XXIII
40
20
500
1000
Te (eV)
1500
2000
(a) Fractional abundance of argon ions
0
500
1000
Te (eV)
1500
2000
(b) Fractional abundance of iron ions
Figure 5.10: The fractional abundance of argon and iron in the corona approximation with respect to the electron temperature.
eration. For ionization stages with an ionization potential being higher than
the electron temperature an increase of the recombination processes leads to a
reduction of their fractional abundance. For those ionization stages the same
reduction can be achieved by a reduction of the electron temperature. This is
also shown in section 4.3, figure 4.9 in which the change of the argon emissivity due the additional neutral hydrogen density is analyzed. Figure 5.10 shows
the fractional abundances of argon and iron in the corona approximation with
respect to the electron temperature. We note that the electron temperature in
the discussed plasma is about 1.2 keV. For Ar XVII the fractional abundance
stays approximately constant for a small change of the electron temperature
(figure 5.10(a)). Therefore, the Ar XVII intensity will also stay constant. For
Fe XXIII a small reduction of the electron temperature leads to a decrease of the
fractional abundance (figure 5.10(b)). This leads to a decrease of the Fe XXIII
intensity.
Since the application of the DED is the only difference between the discharges,
the reduction of the core impurity intensities and the reduction of the intensity
ratio of iron have to be caused by the magnetic perturbation field of the DED.
The RMP causes a stochastization of the plasma edge which causes a net
outward flow for the impurities. There are theoretical studies which discuss an
increased diffusion [48], [49] and an outward convection [50] as a consequence of
the stochastization of the plasma. The discussed findings cannot clarify which
of the proposed mechanisms can be excluded.
As discussed above the calculated iron intensities of the RMP discharge are
expected to be larger than in the reference. This also holds for all of the line
emissions from the plasma core, e.g. for argon and carbon. This shows that
concentrations of those impurities are also reduced. In the case of the C VI
intensity measured by the CXRS diagnostic, no change of the intensity ratios
is found for different radial positions. This indicates that in the case of carbon
72
there is no detectable influence on the transport. Furthermore, the application
of the RMP does not change the radial transport coefficients of argon (figure
5.7). In the case of the intrinsic impurities which have continuous sources at
the vessel wall like boron, carbon and oxygen an additional flow immediately
changes the equilibrium between the in- and outflows as it happens for iron.
In order to discuss the correlation of the transport mechanism due to the DED
current we analyze the correlations in figure 5.4. The developing of the reduction
of the central iron intensity and the iron intensity ratio remains constant for a
DED current > 1.5 kA per coil. This indicates that the mechanism which
changes the iron contamination does not increase. It is possible that this is
caused by a saturation of the stochastization of the plasma due to the RMP. In
the case of the C VI intensity and the toroidal angular velocity the reduction
increases above a DED current of 1.5 kA per coil. Below that current the
identical correlations of the changes of the C VI and Fe XV/XVI intensities, the
iron ratio, and the toroidal angular velocity with respect to the DED current
indicate a very similar dependence on the resonant magnetic perturbation.
Taking into account the different behaviour for different impurities indicates
that the change introduced by the RMP is Z-dependent. In impurity transport
experiments in plasmas without RMPs at Pbx [30] (with 8 ≤ Z < 30) and
Aug [28] (with 10 ≤ Z < 40) the transport coefficients in the plasma core,
i.e. the convective part v, have been found to be Z-dependent. The transport
coefficients for Z > 20 can be fitted best with an increase of the inward pinch
velocity. At Jet dynamic transport experiments with Ne and Ar do not show
differences of the impurity transport [29]. Therefore, a possible explanation for
the discrepancy between iron and the lower Z elements is either a Z-dependent
transport mechanism due to the RMP or a change of the neutral hydrogen
background due to the reduction of the Zef f .
5.1.4 Conclusion
We briefly summarize the results of the discussion of the impurity transport
experiments in the m/n = 3/1 dc DED base mode with a DED current below
the excitation threshold of an m/n = 3/1 tearing mode.
The RMP induced by the DED reduces the impurity content in the NBI
heated L-mode plasma with an edge safety factor of 4.5. This has also been
observed at several experiments in the past at Tore Supra and Textor [7],
[110], [111].
In the experiments performed in the course of this thesis the Fe XXIII intensity
in the plasma core reduces more than the Fe XV intensity at mid minor radius
in the plasma. The reduction of intrinsic iron at mid minor radius can be
explained by a reduction of the sources. The increased reduction in the plasma
center could have two possible explanations. One explanation is a change of
the iron transport in the plasma core. The transport in the plasma core of
the rest of the observable impurities remains unchanged. A different transport
73
between iron and the lower Z elements would indicate a Z-dependent transport
mechanism of the RMP.
A second explanation is an increase of the neutral hydrogen density introduced
by the neutral beam injection. Since it is observed that the contamination of
all of the impurities is reduced in the central plasma during DED application
by an unknown mechanism between r/a ≈ 0.8 and the wall, the contribution
to the neutral hydrogen density by the neutral beam injection increases. Due
to an increase of the charge exchange recombination processes the fractional
abundance of the iron ionization stages in the central plasma is changed. For
Fe XXIII the increase of the recombination processes leads to a reduction of the
ion density.
5.2 Impurity transport with tearing modes
The DED is a very useful and efficient tool to excite tearing modes in a tokamak
plasma [8]. This provides the opportunity to study the impurity transport in the
presence of magnetic island structures. Reports of former impurity transport
experiments with m/n = 2/1 tearing modes excited by the DED describe several
observations which have not been understood up to now. The most prominent
which is observed in transient impurity injection experiments is a slower time
evolution of the intensities of the argon ionization stages in the plasma with q >
1. In the core plasma with q < 1 intensity time evolutions indicate a very fast
transport. In order to understand this phenomenon, two plasma scenarios with
different tearing modes are analyzed. In the first scenario the m/n = 2/1 tearing
mode is stabilized which allows for an excitation of a locked m/n = 3/1 tearing
mode excited by the RMP. The advantage of this scenario is the negligible change
on the background plasmas due to the small size of the locked m/n = 3/1 tearing
mode in contrast to the severe changes of the background plasma which occur
in the case of the excitation of a locked m/n = 2/1 tearing mode. The second
scenario analyzes the impurity transport in the presence of a rotating m/n = 2/1
tearing mode without the application of the DED. The DED base mode in the
scenario with the m/n = 3/1 tearing mode excitation is m/n = 3/1.
5.2.1 Plasma scenarios
m/n = 3/1 tearing mode
The threshold DED current which is required to excite m/n = 2/1 tearing
modes can be controlled by manipulating the rotation of the central plasma
[12]. At Textor there is the possibility to control the plasma rotation with
the help of the neutral beam injectors [112], [113]. In the scenario investigated
here the rotation is chosen such that the excitation threshold DED current for
an m/n = 2/1 tearing mode is > 3.75 kA per coil. Nevertheless, the application of a DED current above 2.7 kA per coil has led to the excitation of an
74
ne (1019m−3)
6
4
2 r/a = 0
0
1 r/a = 0.97
Reference
3/1 discharge
IDED (kA)
0
4
2
0
1000
500
0
Te (eV)
Te (eV)
ne (1019m−3)
50
0
1
r/a = 0
r/a = 0.97
1.5
2
2.5
3
time (s)
3.5
4
4.5
5
3
1.5
−3
ne (10 m )
0
4
3
2
1
0
1500
1000
500
0
Reference
2/1 discharge
r/a = 0
Te (eV)
Te (eV)
19
ne (1019m−3)
(a) Locked m/n = 3/1 tearing mode
100
r/a = 0.97
r/a = 0
r/a = 0.97
50
0
1
1.5
2
2.5
3
time (s)
3.5
4
4.5
5
(b) Rotating m/n = 2/1 tearing mode
Figure 5.11: Plasma scenario of the dc DED experiment with a locked
m/n = 3/1 tearing mode (105347) and the reference (105354) (a) and the
discharge with a rotating m/n = 2/1 tearing mode without DED application
(106448) and its reference (106447) (b). In (a) the excitation of the m/n = 3/1
tearing mode is indicated at 2.5 s and in (b) the unlocking of the m/n = 2/1
tearing mode is indicated at t = 1.3 s.
75
2000
reference (102501)
3/1 tearing mode (102500)
Te (eV)
1500
1000
q=3
500
steepening of the profile
0
−0.5
0
z (m)
0.5
Figure 5.12: Temperature profile of a plasma with an m/n = 3/1 tearing mode
measured by a Thomson scattering diagnostic. In the vicinity of the O-points
of the m/n = 3/1 tearing mode the profile steepens [8]. The steepening of the
profile can be interpreted as a transport barrier since the temperature does not
decrease in the central plasma.
m/n = 3/1 tearing mode which is locked to the resonant magnetic perturbation.
The findings on the impurity transport are discussed in this section. For the discussion we compare the reference 105354 to the exemplary discharge no. 105347
(3/1 discharge) with a maximum DED current of 3.75 kA per coil and a locked
m/n = 3/1 tearing mode. The background plasma parameters are very similar
in both of the discharges (figure 5.11(a)). At t = 2.5 s, simultaneously with the
excitation of the m/n = 3/1 tearing mode the amplitude of the electron density
profile reduces permanently. The m/n = 3/1 tearing mode has an island width
of about 6 cm and the q = 3 surface is located at r/a ≈ 0.8 [114]. Additionally,
the electron temperature reduces around r/a ≈ 0.8 (figure 5.11(a)). The electron temperature profiles which are measured at the O-point of the island show
steep gradients in the vicinity of the island edges (figure 5.12). This has also
been observed in former experiments [8]. The argon puffing is performed in the
same way as in the previous plasma scenario (see section 5.1.1).
The reproducible excitation of a tearing mode without the application of the
DED is achieved by destabilizing a low density plasma during the density ramp
up phase with full neutral beam injection in co current direction (1.3 MW)
[115]. The m/n = 2/1 tearing mode is always excited during the application
of the neutral beam and unlocks after the neutral beam is switched off. The
background plasma parameters are shown in figure 5.11(b). The ohmic plasmas
are set up with an axial toroidal magnetic field BΦ,axis = 2.25 T, a plasma
76
100
80
100
105347
105348
105351
60
40
20
mode onset
0
0
1
2
IDED (kA)
3
4
80
60
40
20
0
1
3
4
100
105347
105348
105351
Reduction of ω (%)
80
60
40
20
105347
105348
105351
60
40
20
mode onset
mode onset
0
0
2
IDED (kA)
(b) C VI, 3.4 nm
100
mode onset
0
80
105347
105348
105351
0
1
2
IDED (kA)
3
(c) Fe XXIII/FeXV
4
0
1
2
IDED (kA)
3
4
(d) Toroidal angular rotation ω
Figure 5.13: The reduction of the Fe XXIII, 13.3 nm, and C VI, 3.4 nm, intensity,
of the intensity ratio of Fe XXIII vs. Fe XV and of the reduction of the toroidal
rotation ω with respect to the applied DED current IDED in discharges with a
locked m/n = 3/1 tearing mode.
current Ip = 310 kA, an edge safety factor qa ≈ 4.5, a central electron density
ne (0) = 2 · 1019 m−3 and a central electron temperature Te (0) = 1.2 keV. In a
series of discharges (106440 to 106450) the amount of the injected argon particles
is varied but remains in the order of about 1018 particles. We compare the
reference discharge without a tearing mode 106447 (reference) to the discharge
106448 (2/1 discharge) with a rotating m/n = 2/1 tearing mode. Neither in
106447 nor in 106448 the DED has been applied.
Except for the electron temperature the background plasma parameters are
very similar. The electron temperature in the 2/1 discharge in the center and
at the edge is reduced by 15 % and 30 %, respectively.
77
1
signal (a.u.)
Reference
With m/n =3/1 TM
0.5
Ar VIII, 70.0 nm
0
1
signal (a.u.)
Ar XV, 22.1 nm
0
1
signal (a.u.)
Ar XVI, 35.4 nm
0.5
0
2
0.5
Ar VIII, 70.0 nm
3.02
3.04
3.06
time (s)
3.08
3.1
Ar XV, 22.1 nm
1
0.5
0
Ar XVI, 35.4 nm
1
0.5
signal (V)
1
0
3
Reference
With m/n =2/1 TM
1
0
0.5
signal (V)
signal (a.u.)
signal (a.u.)
signal (a.u.)
0
1
0
2
2.02
2.04
2.06
time (s)
2.08
2.1
(a) Locked m/n = 3/1 island, 105347 with (b) Rotating m/n = 2/1 island, 106448 with
105354 as reference
106447 as reference
Figure 5.14: Argon time traces in the VUV and SXR during tearing mode excitation with the respective references.
5.2.2 Observations
The excitation of the m/n = 3/1 tearing mode at a DED current of 2.7 kA per
coil is observed with an ECE-Imaging camera [114] in the discharges 105347,
105348, and 105351. Before the onset of the m/n = 3/1 tearing mode the
intrinsic impurities which are usually observed in the plasma decrease in the
same way as described before (figure 5.4).
Figure 5.13 shows the reduction of the core iron intensity, the C VI intensity,
the iron intensity ratio between Fe XXIII and Fe XV and the angular velocity
each with respect to the DED current. The excitation of the locked m/n = 3/1
tearing mode results in a sudden reduction of the core iron intensity and the
iron ratio. This sudden reduction coincides with the reduction of the edge electron temperature and of the electron density profile (figure 5.11(a)). The C VI
intensity from Hexos (figure 5.13(b)) as well as the toroidal angular velocity
derived from CXRS (figure 5.13(d)) do not show this abrupt reduction due to
the m/n = 3/1 tearing mode. Their signals continue to reduce monotonously
during and after the mode onset. In contrast to the emission line intensities
and the angular velocity, the iron ratio does not reduce anymore after the onset
of the m/n = 3/1 tearing mode. The ratio remains constant up to the maximum applicable DED current of 3.75 kA per coil. We note that the iron ratio
before the mode onset also remains constant. The total reduction of the core
iron intensity is up to about 80 % and the reduction of the iron ratio, the C VI
intensity and the toroidal rotation is up to 55 to 60 %.
78
In the case of the dynamic time evolution of the argon intensities the Ar VIII
signal decreases in discharge 105347 with respect to the reference 105354. The
rise time as well as the decay time of the intensity are slower than before the
mode onset (figure 5.14(a)). The Ar VIII intensity of the 3/1 discharge is still
detectable 100 ms after the argon injection whereas in the reference it is not.
The time differences between the rising signals of the intensities of the high
ionization stages of argon and the lower ionization stages increase. In addition,
the amplitudes of the intensities of the central argon ionization stages as well as
their decay times increase with respect to the reference.
An increase of the time differences as well as of the rise and decay times of the
ionization stages up to Ar XVI is also observed during the excitation of an rotating m/n = 2/1 tearing mode (figure 5.14(b)). In contrast to the observations
for the 3/1 discharge the time delay between the time evolutions of the SXR
channels as well as the sawtooth activity vanishes. A small reduction of the Ar
XVII intensity is observed. Due to the low electron density in the 2/1 discharge
and the reference, the intensities of the intrinsic impurities are too low for a
proper analysis.
In the course of the experiments with the rotating m/n = 2/1 tearing mode
it has also been observed that the MHD frequency and the island width of
the m/n = 2/1 tearing mode reduce simultaneously with the argon injection
[116]. Therefore, the presence of argon in the plasma influences the background
plasma. Also Alfvén modes have been observed in this experiment. As soon as
the argon particles flow out of the plasma the MHD frequency and the island
width recover.
5.2.3 Discussion
The excitation of a locked m/n = 2/1 tearing mode with the help of a resonant
magnetic perturbation leads to several changes in the plasma which are not
completely understood up to now. The most distinctive changes are the reduction of the electron density and the electron temperature as well as changes of
the time development of the impurity intensities in transient impurity studies.
The cause for the change of the impurity intensities can either be the island
or the alteration of the density and temperature profile. In order to evaluate
the cause of the intensity changes we analyze a plasma scenario in which the
m/n = 2/1 tearing mode is stabilized [12]. In this way only a locked m/n = 3/1
tearing mode has been excited which has a smaller island width than the locked
m/n = 2/1 tearing mode. In comparison to the m/n = 2/1 tearing mode the
consequences on the background plasma are less distinct and the sawtooth activity does not disappear during the excitation of an m/n = 3/1 tearing mode.
During the application of the Ergodic Divertor (ED) on Tore Supra simi-
79
lar changes which are comparable to the observations reported above have also
been observed with the exception that a tearing mode has not been reported
in [7]. A reduction of ne , the sudden reduction of the C VI intensity and the
sudden rise of the edge carbon intensities have been observed. In a simulation
the change of the carbon ratios (C VI to C V) during the ED activation has only
been achieved by increasing the transport at the plasma edge. In contradiction
to this increase the modelling of the slower time evolutions of the ionization
stages of the injected impurity nickel have led to the conclusion of a convective
transport barrier at the plasma edge. It has not been possible to find transport
coefficients which satisfactorily model both of the observations at the same time.
At Textor a decrease of the edge transport corresponding to the slow down
of the time evolutions of injected argon during the excitation of a m/n = 2/1
tearing mode has been reported [8]. We note that the transport coefficients have
not been determined in this paper.
In order to examine the expected changes of the impurity transport around
an island, we consider the changes of the radial electric field which has been
observed during DED application with and without an m/n = 2/1 tearing mode
[117]. In similar reference plasmas without DED application a radial electric
field Er of ≈ -50 V/cm is measured at the q = 3 magnetic flux surface. In [117]
it is assumed that this Er causes an electron flow towards the wall. This flow
would pretend an inwards directed impurity transport in the case of a plasma
without DED application. As soon as the DED is applied and generates open
magnetic field lines at the plasma boundary without exciting an m/n = 2/1
tearing mode, Er at q = 3 becomes about -35 V/cm. After the onset of an
m/n = 2/1 tearing mode Er = 0 at q = 3.Now there are two possibilities to
explain the disappearance of the radial electric field. One possibility is that the
electron flows to the wall vanish due to a transport barrier in the vicinity of
the m/n = 2/1 tearing mode. A transport barrier can be assumed because of
the high Te gradients which are observed in plasmas at the O-point of locked
tearing modes. An example is presented in figure 5.12. The second possibility
is that an ion flow towards the wall occurs due to an increase of the particle
transport generated by the m/n = 2/1 tearing mode. An increase of the particle
transport in the vicinity of tearing modes is predicted by former theoretical work
[9]. We first determine the transport coefficients for the plasma with the locked
m/n = 3/1 tearing mode.
As reported above for the m/n = 2/1 tearing mode in the vicinity of the
m/n = 3/1 tearing mode the Te gradients steepen which can be an indication for
a transport barrier. The determination of the transport coefficients shows that
with respect to the reference the 3/1 discharge (figure 5.15) requires an increased
diffusion coefficient at the location of the m/n = 3/1 tearing mode (figure 5.16).
Except for Ar VIII, the increase at q = 3 improves the fit for all ionization
stages. Ar VIII remains nearly unchanged due to the increased diffusion. Within
the error, the determined profile of the radial diffusion coefficient is the only
possibility to improve the fit. The core transport for argon is not affected by
80
Ar VIII, 70.4 nm (r/a = 0.88)
Ar XV, 22.1 nm (r/a = 0.35)
Ar XVI, 35.4/38.9 nm (r/a = 0.3)
Ar XVII 0.4 nm (r/a = 0.24)
1
0.8
0.6
0.4
0.2
0
3
3.01
3.02
3.03
time (s)
3.04
3.05
(a) 3/1 discharge
Ar VIII, 70.4 nm (r/a = 0.88)
Ar XV, 22.1 nm (r/a = 0.35)
Ar XVI, 35.4/38.9 nm (r/a = 0.3)
Ar XVII 0.4 nm (r/a = 0.24)
1
0.8
0.6
0.4
0.2
0
3
3.01
3.02
3.03
time (s)
3.04
3.05
(b) 3/1 discharge without corrections
Figure 5.15: Experimental (continuous) and fitted (dashed) argon time traces
for the 3/1 discharge (105347).
D (m2s−1)
10
1
q=3
0.1
0
0.2
0.4
r/a
0.6
0.8
Figure 5.16: Diffusion coefficient for the reference (continuous) and the 3/1 discharge (dotted). The ratio of v/D is the same as in the reference (figure 5.7(b)).
81
the m/n = 3/1 tearing mode within the error margins. An additional effect due
to the RMP on the core transport is not observed for argon and also the ratio
of v/D does not change significantly. The increase of the diffusion coefficient
supports the assumption discussed above that the plasma ion flow towards the
wall is increased whereas an impurity transport barrier in the vicinity of the
island which is has been assumed due to the steepening of the Te gradients
around the O-point of the island can be excluded.
An increase of the flows towards the wall also enhances the source mechanisms of the impurities. Therefore, the observed slower temporal decay of the
Ar VIII intensity in the 3/1 discharge (figure 5.14(a)) is a result of a high level
of recycling flows which re-fuel the low ionization stages at the plasma edge. As
a consequence, all of the normalized time traces of the higher ionization stages
have a slower time evolution than in the reference plasma even though the impurity transport is increased. The slower time evolution of the normalized time
traces results from the convolution of the slower developing source function with
the transport function of the particles. Therefore, if the impurity source functions change between two discharges it is not possible to predict any changes
of transport without a determination of the transport coefficients. Before we
analyze the 2/1 discharge we give a brief report of former findings on the impurity transport in the plasma core. Former impurity transport experiments
with argon at Aug have shown that before a sawtooth crash takes place, only a
very small amount of argon reaches the plasma center [28]. This observation is
a result of the very low diffusion coefficients in the plasma center which assume
values which are in the order of 0.06 m2 s−1 . Therefore, the first sawtooth crash
after the argon injection is the cause for the transport of argon into the plasma
core. Without sawteeth the impurity flow near the transition region from high
to low transport will reduce and the impurities reach the plasma center only
very slowly. Due to this reduction of the central transport, the time evolution
of the central argon ionization stages is expected to slow down significantly in
the absence of sawteeth. We now discuss the case of the excited m/n = 2/1
tearing mode. In [8] and [117] the vanishing time difference between the rising
signals of different channels of the SXR PIN diode has been interpreted as an
indication of a very fast transport (see also figure 5.17) but the transport coefficients have not been determined for those experiments. The vanishing time
difference has been observed in plasmas with an excited m/n = 2/1 tearing
mode in which sawteeth disappeared.
The transport coefficients of the 2/1 discharge determined by a Strahl simulation show an increase at the position of the q = 2 surface and also an increase
at r/a ≈ 0.23 where the q = 1 surface is located in the reference discharge (figure 5.18). We note that the transport coefficients are averaged over the flux
surface. Local transport measurements around tearing modes can yield different profiles. We first discuss the increase at the q = 2 surface. The increased
diffusion at the location of the m/n = 2/1 tearing mode confirms the results
of the m/n = 3/1 tearing mode. Around the m/n = 3/1 tearing mode as well
82
Ar VIII, 70.4 nm (r/a = 0.86)
Ar XV, 22.1 nm (r/a = 0.4)
Ar XVI, 35.4/38.9 nm (r/a = 0.3)
Ar XVII 0.4 nm (r/a = 0.24 )
1
0.8
0.6
0.4
0.2
0
2
2.02
2.04
2.06
time (s)
2.08
2.1
(a) reference
Ar VIII, 70.4 nm (r/a = 0.83)
Ar XV, 22.1 nm (r/a = 0.35)
Ar XVI, 35.4/38.9 nm (r/a = 0.29)
Ar XVII 0.4 nm (r/a = 0.24)
1
0.8
0.6
0.4
0.2
0
2
2.02
2.04
2.06
time (s)
2.08
2.1
(b) 2/1 discharge
for the reference (106447) and the 2/1 discharge (106448).
as around the m/n = 2/1 tearing mode the impurity transport is increased as
theoretical work has predicted [9]. In addition, the transport around a tearing
mode does not depend on whether the island is phase locked to another magnetic structure or not. The increase in the vicinity of q = 1 shows that the
assumption of a very fast transport in [8] and [117] is correct. In combination
with the vanishing of the sawteeth the second increase of the diffusion coefficient
at r/a = 0.23 indicates an MHD phenomenon which coincides with an increase
of the diffusive transport and a convective outward flow. Since it occurs simultaneously with the m/n = 2/1 tearing mode there seems to exist a coupling
between this MHD phenomenon and the m/n = 2/1 tearing mode. In [18] a
coupling of a m/n = 1/1 internal kink mode with a locked m/n = 2/1 tearing
mode has been reported.
We conclude that the presence of the m/n = 1/1 internal kink mode increases
83
10
q=2
D (m2s−1)
q=1
1
0.1
0
0.2
0.4
r/a
0.6
0.8
20
15
10
q=2
q=1
v/D (m−1)
5
0
−5
−10
−15
Reference
2/1 discharge
−20
−25
0
0.2
0.4
r/a
0.6
0.8
(b) v/D ratio
Figure 5.18: Continuous: Transport coefficients for 106447 without a tearing
mode; dotted: 106448 with rotating m/n = 2/1 tearing mode. The indicated q
values are determined for 106447. The peak widths in the diffusion coefficient
are determined within ∆(r/a) = ± 0.03.
the diffusive transport of argon which is observed at the q = 1 magnetic flux
surface.
Having discussed the transient impurity transport experiments we now focus on the intrinsic impurities of the 3/1 discharge. Taking into account the
conserved reduction of the toroidal rotation although the excitation of the
m/n = 3/1 tearing mode changes the background plasma we expect that the
influence of the resonant magnetic perturbation on the impurities still persists.
The core iron concentration derived with the help of a transport equilibrium
calculation of Strahl at t = 4 s reduces to about 1.1 × 10−5 . We note that
it is assumed that the neutral hydrogen profile in the plasma center does not
differ from the reference discharge 105354. This is about 80 % less than in the
reference and is reflected by the reduction of the Fe XXIII intensity which is
84
presented in figure 5.13(a). Since the iron ratio above IDED ≈ 1.5 kA remains
constant except for the moment of the mode onset (figure 5.13(c)), the further
reduction of the central iron content is a consequence of the reduction of the
sources due to the DED. The sudden change at the moment of the mode onset
is a direct consequence of the changes of the ne and Te profile. This results in
a change of the transport equilibrium which alters the ionization balance in the
plasma.
In the case of the C VI intensity the conservation of the reduction behaviour
with respect to the DED current shows that the m/n = 3/1 tearing mode does
not influence this parameter. Only an effect of the DED on the source of C VI
is observable. The conservation of the reduction behaviour of C VI contradicts
to the observed changes of the iron reduction. But we have to take into account
that the C VI, 3.4 nm emissivity shell with its maximum at about r/a ≈ 0.75 is
located very close to the m/n = 3/1 island at r/a ≈ 0.8. There are at least two
possible reasons which can explain the conservation of the correlation. The first
reason is that due to the drop of the edge temperature the C VI emissivity shell
is shifted towards the plasma center in a plasma region with a higher electron
density. A higher electron density results in a higher emissivity, i.e the intensity
rises. Since the electron density profile is reduced during the mode excitation
it is possible that this reduction just compensates the radial shift of the C VI,
3.4 nm, emissivity shell.
A change of the ionization balance due to the changed transport around the
tearing mode is another possibility. The changed ionization balance can also
compensate the changes of the background plasma induced by the tearing mode.
We now briefly discuss the observed braking and growing of the m/n = 2/1
tearing mode during the argon injection (figure 5.19). The width of the island
can be controlled either by driving currents in the island or by heating the island
[118], [119]. Both of these reduce the resistance of the island such that due to
higher currents the island width decreases. We assume that if a large amount
of argon particles is injected into the plasma, the presence of argon increases
the resistance which increases the island size and at the same time brakes the
island rotation.
5.2.4 Conclusion
In this section the impurity transport around m/n = 3/1 and m/n = 2/1 tearing
modes has been studied by means of transient impurity transport experiments.
A clear increase of the diffusion coefficient at the location of the tearing modes
is found although the time delays between the rising signals of the several intensity time evolutions change. Due to the increase of the diffusive transport
the impurity contamination of the plasma core reduces. The increased outflow
is balanced by an increased inflow from the wall which can be measured by low
ionization stages.
The increased inflow leads to a re-fuelling of injected species. This re-fuelling
85
MHD frequency (Hz)
2500
2000
1500
1000
SXR signal (a.u.)
500
0
1.5
2
2.5
3
3.5
time (s)
4
4.5
5
Figure 5.19: The drop and the recovering of the MHD frequency (yellow) derived
by a frequency analysis of the central channel of SXR PIN diode in the presence
of about 5 × 1018 argon particles. The SXR signal (blue) shows the argon
injections in discharge 106450. In all of the discharges with a rotating m/n = 2/1
tearing mode a reduction of the MHD frequency is observed after injecting argon.
process leads to a slower temporal decay of all of the ion intensity time evolutions.
At the same time as the excitation of the m/n = 2/1 tearing mode the sawteeth disappear. An m/n = 1 internal kink mode which is coupled to the
rotating m/n = 2/1 tearing mode has been observed. It causes an increase of
the impurity transport at the position of the q = 1 surface.
5.3 Plasmas with density pump out
During the activation of the DED in the m/n = 6/2 base mode a reduction of the
electron density has been observed which appeared in plasmas which have been
shifted to the low field side [120]. In addition the particle confinement time for
the plasma ions drops. The reduction resembles the reduction of the impurities
described in the former sections. This so called pump out of the electron density
has also been observed at DIII-D [121], Jet [54] and Tore Supra [7] during
the activation of resonant magnetic perturbations.
In this section we discuss the question whether the impurity transport during
the electron density pump out is changed. In order to analyze the experiments
we apply the methods described above. In the series of the discharges 105781 to
105793 a reduction of the electron density with respect to reference discharges
in this series has been observed during the application of the DED. Due to
several short impurity contaminations from the plasma vessel which disturb the
monitored intensity time evolutions we have to discuss the intrinsic and extrinsic
86
ne (1019m−3)
6
4
2
0
0.8
r/a = 0
0.4
IDED (kA)
r/a = 1
0
6
4
2
0
1000
500 r/a = 0
0
100
50 r/a = 1
0
1
1.5
Reference
PO
Te (eV)
Te (eV)
ne (1019 m−3)
2
2.5
3
time (s)
3.5
4
4.5
5
6
4
2
0
0.8
r/a = 0
0.4
IDED (kA)
r/a = 1
0
6
4
2
0
1000
500 r/a = 0
0
100
50 r/a = 1
0
1
1.5
Reference
Ar PO
Te (eV)
Te (eV)
ne (1019 m−3)
ne (1019m−3)
(a) Scenario for the evaluation of the intrinsic iron
2
2.5
3
time (s)
3.5
4
4.5
5
(b) Scenario for the evaluation of extrinsic argon
Figure 5.20: Plasma scenario of in the m/n = 6/2 DED base mode with density
pump out. (a) Pump out discharge (105784) and its reference (105785), (b)
Pump out discharge (105793) and its reference (105791).
87
impurities in different pairs of discharges.
The discharges 105784 and 105793 with electron pump out are investigated.
In discharge 105784 (PO) the reduction of the iron intensities is analyzed. The
reference of 105784 is 105785. The determination of the impurity transport
coefficients is performed in discharge 105793 (Ar PO) with 105791 as reference.
Figure 5.20 presents the plasma parameters of the experiments with density
pump oout. The discharges are performed with a central electron density of
about 4 × 1019 m−3 , a central electron temperature of 1.1 keV, and an edge
safety factor of 3.1. The DED current is ramped up to 7.5 kA per coil. From
t = 1 to 3.8 s neutral beam injection in co current direction is applied with a
power of 630 kW.
Above a DED current of about 1 kA the electron density at the LCFS reduces.
The central electron density reduces with a temporal delay of about ∆t = 100 ms
with respect to the edge density. Within this time the electrons are transported
about ∆s = 46 cm from the plasma center to the edge. This corresponds to an
average radial diffusion coefficient D = ∆s2 /∆t of about 2 m2 s−1 which is also
the average radial diffusion coefficient for the impurity transport as discussed
below. The total reduction of the electron density is about 20 % in the core and
at the edge. In the flat top phase of the applied DED current no changes occur.
With ramping down the DED current the electron density recovers again. The
electron temperature at the LCFS measured by the He-Beam diagnostic also
decreases. The argon injection is performed at t = 2.0 s at the beginning of the
flat top phase of the DED current.
5.3.2 Observations
As reported in the previous sections the ramping of the DED current leads to
a reduction of the central iron intensity (figure 5.21(a)). This reduction occurs
above a DED current of about 0.8 kA per coil. At DED currents between 2.22.4 kA and 4.3-5.0 kA the reduction seems to remain constant. At 7.5 kA per
coil the Fe XXIII intensity reduces to about 45 % with respect to the reference.
The ratio between the Fe XXIII, 13.3 nm, and the Fe XV, 28.4 nm, intensity
does not change up to a DED current of about 3.5 kA per coil (figure 5.21(c)).
Above this current the ratio is reduced up to 20 %. Between 4.3-5.0 kA DED
current the ratio remains constant. The same evolution of the reduction is
observed for the intensity of C VI, 3.4 nm, and the electron density (figures
5.21(d), 5.21(e) and 5.21(f)).
The intensities of Ar VIII to Ar XVII decrease (figure 5.22). The normalized
time evolutions do not show significant changes in the rising signals but the
decaying signals seem to be faster in the plasma with density pump out. The
88
100
100
105784
105786
80
Reduction of Fe XV intensity (%)
60
40
20
0
0
2
4
IDED (kA)
6
8
105784
105786
80
60
40
20
0
0
6
8
100
105784
105786
80
4
IDED (kA)
(b) Fe XV, 28.4 nm
100
60
40
20
0
0
2
4
IDED (kA)
6
8
105784
105786
80
60
40
20
0
0
(c) Fe XXIII/Fe XV
60
40
20
0
0
4
IDED (kA)
6
8
6
8
100
105784
105786
Reduction of edge ne (%)
80
2
(d) C VI, 3.4 nm
100
Reduction of ne (%)
2
80
105784
105786
60
40
20
0
2
4
IDED (kA)
(e) Central ne
6
8
0
2
4
IDED (kA)
(f) ne at mid minor radius
Figure 5.21: The reduction of the Fe XXIII, 13.3 nm, Fe XV, 28.4 nm and C VI,
3.4 nm, intensity and of the iron intensity ratio and the electron density ne in
the center and at mid minor radius with respect to the applied DED current
IDED of two identical discharges are shown. The signals are time averaged over
20 ms.
89
signal (a.u.)
0.5
Reference
Ar PO
Ar VIII, 70.0 nm
0
1
Ar XV, 22.1 nm
0
1
Ar XVI, 35.4 nm
0.5
signal (V)
signal (a.u.)
0.5
signal (a.u.)
1
0
3
2
1
0
2.1
2.12
2.14
2.16
time (s)
2.18
2.2
Figure 5.22: Argon time traces in the VUV and SXR in a plasma with density
pump out 105784 and the reference 105785.
sawtooth oscillation recorded with the SXR PIN diodes is not stable. Since the
background subtraction of the SXR signals assumes very similar sawteeth, a
background correction of those SXR signals has not been possible.
5.3.3 Discussion
The mechanism of the electron density pump out is unknown up to now. In
the course of the following discussion we try to analyze whether the impurity
transport is changed during the reduction of the electron density.
The transient impurity transport experiments with the injected argon (figure
5.23) show that the transport coefficients of argon do not change during the
pump out of the central plasma (figure 5.24). The average radial diffusion
coefficient is about 2 m2 /s−1 . Therefore, the average time an impurity particle
needs to be transported from the plasma edge to the plasma core (≈ 46cm) is
about 100 ms. The drop of the central electron density starts about 100 ms
after the drop of the edge electron density. Therefore, the plasma particles in
the plasma center are transported to the plasma edge with the same average
radial diffusion coefficient as the impurities.
We will now discuss the observations made on the intrinsic impurities. The
iron intensities start to reduce when a DED current of 0.8 kA is applied. Due
to the fast ramping of the DED current this value is applied within about 100
ms. A change of the edge iron flows does not immediately change the central
90
Ar VIII, 70.4 nm (r/a = 0.91)
Ar XV, 22.1 nm (r/a = 0.43)
Ar XVI, 35.4/38.9 nm (r/a = 0.36)
Ar XVII 0.4 nm (r/a = 0.24)
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
2.1
2.11
2.12
2.13
time (s)
2.14
2.15
(a) Reference without pump out
Ar VIII, 70.4 nm (r/a = 0.91)
Ar XV, 22.1 nm (r/a = 0.43)
Ar XVI, 35.4/38.9 nm (r/a = 0.36)
Ar XVII 0.4 nm (r/a = 0.24)
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
2.1
2.11
2.12
2.13
time (s)
2.14
2.15
(b) Discharge with density pump out
for the PO reference and the PO discharge.
iron intensities. Simulations with the Strahl code show that changes of the
impurity flow balance induced by an alteration of the edge impurity transport
need about 100 to 200 ms to take effect on the central ionization stages. The
exact time delay cannot be determined without the knowledge of the transport
coefficients for iron. Therefore, we abstain from a correction of the correlation
between the iron intensity reduction and the DED current.
The observed reduction of the carbon emission line intensity in the VUV
coincides with the reduction of the electron density. Since the local emissivity
is proportional to the electron density, the reduction of the carbon intensity is a
consequence of the electron density reduction. There is no significant reduction
of the C VI source. In contrast to the findings for carbon the strong reduction
of iron without the change of neither the iron ratio nor the electron density up
to a DED current of about 3 kA shows a clear reduction of the sources for Fe
91
D (m2s−1)
10
1
0.1
0
0.2
0.4
r/a
0.6
0.8
0.4
0.6
r/a
(a) v/D ratio
0.8
30
20
v/D (m−1)
10
0
−10
−20
−30
0
0.2
Figure 5.24: Transport coefficients of the reference (continuous) and the Ar PO
(dashed).
XV. As discussed in section 5.1.3 this does either mean that the sources at the
wall are weaker or that there is a transport mechanism between the emissivity
shell of Fe XV and the wall.
With the onset of the reduction of the central electron density the iron intensity ratio reduces. Transport equilibrium calculations with Strahl which
use the electron density and electron temperature profiles of the respective discharges do not show significant changes between the iron intensity ratio of a
plasma with density pump out and a reference. In addition the simulated intensity of Fe XXIII (13.3 nm) can only explain half of the observed reduction
of about 45 %. Therefore, the reduction of the iron intensity ratio cannot be
explained by the changes of the ne and Te profiles. This means that the same
explanations as in section 5.1.3 can be applied. We note that in the discussed
plasmas with density pump out NBI has been used. Therefore, either a Z-
92
dependent transport mechanism or a change of the neutral hydrogen profile can
cause the reduction of the change of the iron intensity ratio. Whether a Zdependent transport mechanism could cause the electron density pump out has
to be determined in further studies.
5.3.4 Conclusion
In plasmas with density pump out the transport coefficients for impurity transport determined by transient impurity transport experiments remain unchanged
with respect to the reference. The intensity ratio between Fe XXIII and Fe XV
decreases whereas the transport of carbon does not seem to be affected by the
resonant magnetic perturbation. The intensity reduction of C VI (3.4 nm) follows the reduction of the electron density profile.
There is evidence for a Z-dependent transport mechanism due to the resonant
magnetic perturbation. Whether such a mechanism also causes the electron
density pump out needs further investigation.
5.4 Influence of dynamic RMP fields on impurity
transport
The DED on Textor offers the unique possibility to analyze plasmas with
rotating resonant magnetic perturbations. In particular, the consequences of
the relative rotation between the resonant magnetic perturbation and the electron fluid can be analyzed in ohmic plasmas. In this section the first impurity
transport experiments in such plasmas are presented and analyzed. Furthermore, a correlation between the effectiveness of the iron reduction and the DED
frequency is presented.
The impurity transport experiments for the study of the consequences of dynamic DED operation in the m/n = 3/1 DED base mode are performed in
an ohmic deuterium plasma with a toroidal magnetic field of Bt = 2.25 T, a
plasma current of Ip = 310 kA, and an edge safety factor of about 4.5. The
central electron density ne (0) and temperature Te (0) are 3.1 × 1019 m−3 and
1 keV, respectively (figure 5.25). The application of the DED does not influence
the background plasma parameters except for the electron temperature around
the LCFS. The edge electron temperature measured by the He-Beam diagnostic
reduces during the dynamic DED application [122]. All of the analyzed discharges have the same background plasma parameters. The series of discharges
104716 to 104728 with DED frequencies of +1, -1 and -5 kHz is used for the
analysis. The discharges with the application of +5 kHz DED current are not
useful for any impurity transport analysis because many short impurity bursts
disturbed all of the impurity intensities during the whole DED application. We
93
ne (1019 m−3)
4
2
0
0.50
r/a = 0
r/a = 0.97
IDED (kA)
0.25
Te (eV)
Te (eV)
ne (1019 m−3)
0
1.5
0
−1.5
1200
600 r/a = 0
0
60
30 r/a = 0.97
0
1
1.5
2
2.5
3
time (s)
3.5
4
4.5
5
Figure 5.25: Plasma scenario of the ac DED experiments. From top to bottom: core electron density, edge electron density, ac DED current, core electron
temperature and edge electron temperature.
assume that those impurity bursts are caused by overheated wall elements. The
applied peak amplitude of the DED current is 1 kA per coil which results in an
effective DED current of about 0.7 kA. Tearing modes are not excited in this
plasma scenario. The argon injection is performed as described in the previous
sections.
5.4.2 Observations
During the application of the dynamic DED varying impurity screening is observed for different DED frequencies (figure 5.26). With respect to the reference
the application of a DED frequency of -5 kHz does neither influence the iron
concentration in the central plasma nor the C VI intensity. In the discharge with
-1 kHz DED frequency the central iron concentration reduces. The intensity of
C VI is not changed with respect to the reference but with respect to the -5
kHz discharge the intensity is reduced. The application of +1 kHz increases the
reduction of iron and of C VI.
Figure 5.27 presents the relative changes of intensity time evolutions of the
argon ionization stage intensities. Significant changes are only observed for the
Ar VIII, 70.0 nm, intensity time trace which rises during the application of +1
kHz. The normalized time traces of argon are not significantly modified.
As reference discharge we refer to discharge 104726. The discharges with -5,
-1, and +1 kHz DED frequency are 104728 (-5 kHz discharge), 104724 (-1 kHz
94
norm. signal norm. signal
IDED (kA)
2
1
−0
1
2
DED
1
0.5
Fe XXIII
0
1
0.5
0
1
C VI
2
3
time (s)
4
5
Figure 5.26: Continuous: no DED (104726), dashed: -5 kHz (104728), dotted:
-1 kHz (104724), dash dotted: +1 kHz (104716). The normalized intensity
time evolution of Fe XXIII and C VI during the application of different DED
frequencies. Brief impurity events of about 100 ms in the -1 and -5 kHz Fe
XXIII signal have been removed manually. The intensities are time averaged
(100 ms).
discharge), and 104716 (+1 kHz discharge), respectively.
5.4.3 Discussion
The argon transport and the observed differences in the reduction of the impurity intensities which occur with the application of different DED frequencies are
discussed in this section. The reference parameter for the change of the intrinsic
impurities is the relative slip frequency fslip = fϕ − (fDED − fe∗ ) with the
toroidal plasma frequency fϕ , the DED frequency fDED and the diamagnetic
drift frequency of the electrons fe∗ equation (2.3).
We start with the discussion of the transient impurity experiments with argon.
The observed increase of the intensity of the low argon ionization stage Ar
VIII can be explained by the reduction of the edge electron temperature. This
reduction shifts the emissivity shell towards the plasma center where the electron
density is higher. This results in an increase of the intensity.
Figure 5.28 presents the normalized experimental and simulated time evolutions of the transient argon injection experiments. The transport coefficients
for argon do not show any changes in the central plasma for the different DED
frequencies (figure 5.29). The transition region from high to low diffusion is
located at approximately the same radial position as in the experiments with
dc DED which are discussed in section 5.1.3.
The intensity time evolution of the C VI line emission intensity, which in this
95
1
Ar VIII, 70.0 nm
0.5
no DED
−5 kHz
−1 kHz
+1 kHz
signal (a.u.)
0
1
0.5
signal (a.u.)
signal (a.u.)
1.5
0.5
Ar XV, 22.1 nm
signal (V)
0
1
Ar XVI, 35.4 nm
0
2
1
0
2.5
2.52
2.54
2.56
time (s)
2.58
2.6
Figure 5.27: Argon time traces in the VUV and SXR during DED application
with different DED frequencies. Continuous: no DED (104726), dashed: -5 kHz
(104728), dotted: -1 kHz (104724), dash dotted: +1 kHz (104716).
plasma scenario is located at about r/a = 0.5, is only reduced in the +1 kHz
discharge. In the -1 kHz discharge the C VI line emission intensity is unchanged
with respect to the reference but is increased with respect to the +1 kHz discharge. The reduction of the C VI intensity is a consequence of the resonant
magnetic perturbation [106]. It is possible that differences between the DED
frequencies applied are a consequence of different penetration depths of the rotating resonant magnetic perturbations.
With respect to the discharge with the application of -5 kHz DED the carbon
and the iron intensity decrease when applying -1 and +1 kHz DED. In this
behaviour, the observations for the central iron concentration do not contradict
the observations for carbon. Differences between carbon and iron are found in
the observed decrease during the application of the different DED frequencies.
The reduction for iron is more pronounced than for carbon. The carbon intensity
in the reference plasma is lower than in the plasma with -5 kHz DED application
whereas for iron the intensities are unchanged. The reason for the increase of
the carbon intensity seems to be an effect on the sources at the wall but cannot
be clarified in this study.
Figure 5.30 presents the dependence of the reduction of the central iron intensity with respect to the relative slip frequency fslip between the electron fluid
in the plasma and the resonant magnetic perturbation. The diamagnetic drift
96
1.5
Ar VIII, 70.4 nm (r/a = 0.85)
Ar XV, 22.1 nm (r/a = 0.36)
Ar XVI, 35.4/38.9 nm (r/a = 0.3)
Ar XVII 0.4 nm (r/a = 0.24)
1
0.5
0
2.5
2.51
2.52
2.53
time (s)
2.54
2.55
(a) Reference 104726
1.5
Ar VIII, 70.4 nm (r/a = 0.85)
Ar XV, 22.1 nm (r/a = 0.36)
Ar XVI, 35.4/38.9 nm (r/a = 0.3)
Ar XVII 0.4 nm (r/a = 0.24)
1
0.5
0
2.5
2.51
2.52
2.53
time (s)
2.54
2.55
(b) -5 kHz discharge 104728
1.5
Ar VIII, 70.4 nm (r/a = 0.85)
Ar XV, 22.1 nm (r/a = 0.36)
Ar XVI, 35.4/38.9 nm (r/a = 0.3)
Ar XVII 0.4 nm (r/a = 0.24)
1
0.5
0
2.5
2.51
2.52
2.53
time (s)
2.54
2.55
(c) -1 kHz discharge 104724
1.5
Ar VIII, 70.4 nm (r/a = 0.85)
Ar XV, 22.1 nm (r/a = 0.36)
Ar XVI, 35.4/38.9 nm (r/a = 0.3)
Ar XVII 0.4 nm (r/a = 0.24)
1
0.5
0
2.5
2.51
2.52
2.53
time (s)
2.54
2.55
(d) +1 kHz discharge 104716
for the ac DED discharges.
97
D (m2s−1)
10
1
0.1
0
0.2
0.4
r/a
0.6
0.8
15
10
v/D (m−1)
5
0
−5
−10
−15
−20
−25
0
0.2
0.4
r/a
0.6
0.8
(b) v/D ratio
Figure 5.29: Transport coefficients determined with the transient impurity
transport experiments with argon for the ac discharges and the reference. The
transport coefficients do not change between the discharges.
of the electrons which is calculated according to equation (2.3) is about 600 Hz
at the edge plasma. The toroidal plasma rotation frequency of about 760 Hz
is measured by the edge CXRS diagnostic [91]. The frequency does not change
significantly between the application of -5, -1 and +1 kHz DED.
The figure shows a correlation between the reduction of the central iron concentration and the slip frequency. Under the assumtion that the stochastization
of the plasma causes the impurity screening, a low screening of the resonant
magnetic perturbation field leads to a high reduction of the impurity contamination an a high screening of the resonant magnetic perturbation leads to a low
reduction of the imputiy contamination.
The observed reductions indicate a screening of the magnetic field which depends on the slip frequency. Therefore, we compare the strength of the reduction
98
Reduction of Fe XXIII signal (%)
30
+1 kHz (104716)
25
20
−1 kHz (104724)
15
10
5
−5 kHz (104728)
0
−5
0
1
2
3
4
5
fslip = ftor−(fDED−f*e) (kHz)
6
7
Figure 5.30: The reduction of the Fe XXIII, 13.2 nm intensity with respect to
the relative rotation fslip between the plasma and the resonant magnetic perturbation. The line between the data points should guide the eye.
with a simulated screening of the resonant magnetic perturbation. This comparison is performed by calculating a screening factor Sf which is derived from
an ansatz of a visco-resistive plasma [123] - [126]:
Sf = r
1+
1
fslip τvr
2m
2
(5.1)
with the visco-resistive time τvr (see [124] and [125] for further information).
The screening factor Sf is defined according to Bs = Sf Bv with Bs being the
screened magnetic field and Bv the magnetic field in the vacuum. Therefore, a
screening factor of 1 means no screening and a screening factor of 0 means total
screening of the perturbing field. If we apply different DED frequencies with
the same plasma conditions τvr and m will not change. A simple calculation
can show that the screening factor Sf can qualitatively describe the correlation
between the impurity screening and the slip frequency: With fslip → 0, Sf
becomes 1 which means that the perturbing magnetic field is not screened.
With fslip → ∞, Sf becomes 0 which means that the perturbing magnetic field
is totally screened. Assuming m = 3 and τvr ≈ 1µs, the screening factor at r/a
= 0.9 becomes approximately 0.4, 0.75, and 1.0 for the DED frequencies -5 kHz,
-1 kHz, and +1 kHz, respectively.
The total screening of the perturbing magnetic field is equivalent to its absence
in the plasma. Since in the reference discharge there is no resonant magnetic
perturbation we conclude that with Sf = 0 there will not be any reduction
of the impurity content. The consequences of Sf > 0 are comparable to the
findings for dc DED application in which a reduction of the impurity content in
the central plasma appears.
99
5.4.4 Conclusion
In this section we have presented impurity transport experiments with rotating
resonant magnetic perturbations. The transport coefficients derived with transient argon injection experiments do not show significant differences. We have
shown a correlation between the amount of the central iron reduction and the
relative rotation between the resonant magnetic perturbation and the electron
fluid. The lower the relative rotation, the more reduces the central iron content.
A reduction of the intensity is also observed for C VI but less distinct.
The reduction of the iron intensity is consistent with a magnetic field screening
2 )−1/2 .
factor which is proportional to 1/(1 + fslip
100
Magnetically confined fusion plasmas have to be sufficiently hot and dense.
The interaction of the plasma with the vessel contaminates the plasma with
impurities. The low-Z impurities dilute the plasma such that the reaction rate
of the fusion process is reduced. The high-Z impurities cool down the plasma
due to radiation. The reduction of the temperature reduces the reaction rate.
Up to now there is no adequate theory which is able to describe the impurity
transport. The scope of this thesis is the analysis of the impurity transport
in tokamak plasmas with an applied resonant magnetic perturbation. In many
plasma scenarios, resonant magnetic perturbations reduce the impurity contamination. In order to study the impurity transport in plasmas with an applied
resonant magnetic perturbation, experiments at the tokamak Textor have been
performed. Transient argon injections and the monitoring of the intrinsic impurities are analyzed. The line emission of the ionization stages in the plasma
have been monitored in radial direction with the help of the absolutely calibrated
VUV-spectrometer Hexos and SXR PIN diodes. The absolute calibration of
the Hexos enables the determination of impurity concentrations in the plasma.
Therefore, the reduction of the impurity contamination can be quantified and
effective charge Zef f can be determined. The knowledge of Zef f is necessary
for the determination of the neutral hydrogen density profile which is used in
the analysis of the transport coefficients. The process of the calibration and its
application are presented in this thesis.
In order to determine the transport properties of the experiments are analyzed with the one dimensional transport code Strahl up to r/a ≈ 0.8. The
code assumes a radial impurity transport being poloidally and toroidally symmetric. The edge transport is not dicussed. The code describes the flows of the
impurity ions with a simple combination of a diffusive and a convective contribution. The coupled set of continuity equations of all the ionization stages of
a specific impurity are subsequently solved. With the help of the experimental
radial profiles of the background plasma the emission of the ionzation stages
is computed. In transient impurity injection experiments the time evolution of
the radiation is modelled and can be compared to the experimental intensity
time evolutions. By changing the modelled diffusive and convective impurity
fluxes the simulated intensity time evolutions are adapted to the experimental
ones. This process yields the transport properties in the form of local values
of a diffusion coefficient and a drift velocity. The neoclassical transport is not
discussed in this thesis.
The impurity transport experiments have been performed in four different
101
plasma scenarios with different configurations of the DED base mode. The
plasma scenarios are sorted by the consequences of the DED application on the
impurities and tearing mode excitation.
The first is with static m/n = 3/1 DED base mode in an NBI-heated L-mode
plasma without detectable tearing mode activity. The transport coefficients
determined by the analysis of the transient impurity experiments remain unchanged during the application of the RMP. The monitoring of the intrinsic
impurities confirms a reduction of the impurity contamination which also has
been observed earlier, e.g. on Tore Supra. The reduction of the C VI intensities measured by CXRS confirms the reduction of the carbon concentration
measured by Hexos. Only for iron it is observed that the intensity ratio between
Fe XXIII and Fe XV is changed.
There are two possible explanations of the change of the intensity ratio. One
explanation is a Z-dependent transport mechanism induced by the RMP. For
argon and lower Z elements this mechanism does not significantly influence the
transport. For iron the radial profile of the impurity density would be changed
due to a change of the ratio of the convective and diffusive transport coefficients
v/D.
Another possible explanation is a change of the neutral hydrogen density profile. The Zef f , derived with the help of the absolute calibration of Hexos,
reduces from 2.5 to 2 during the RMP. This leads to an increase of the neutral hydrogen density profile. This increase changes the ionization balance in
the plasma. The change of the ionization balance leads to the decrease of the
Fe XXIII intensity.
The neutral hydrogen density profiles determined by Zef f have been estimated. The reduction of the Fe XXIII due to the increase of the neutral hydrogen density has been computed with the Strahl code. The increased neutral
hydrogen density in the plasma center can explain a reduction of about 1 - 2 %
of the Fe XXIII intensity. On the basis of this estimate, we conclude that a
Z-dependent transport mechansim induced by the RMP cannot be excluded.
An estimate of the experimental central neutral hydrogen density can be performed with the help of argon injections monitored with x-ray spectrometers. A
comparison of the theoretical x-ray intensities of Ar XVII with the experimental
ones can confirm and quantify the reduction of the neutral hydogen density.
In a second investigated plasma scenario a tearing mode is present. The
transport effects of an unlocked m/n = 2/1 tearing mode in an ohmic heated
plasma and a locked m/n = 3/1 tearing mode in an NBI-heated plasma have
been analyzed. The result of the transient argon injection experiments shows an
increase of the diffusive transport at the radial position of the tearing mode. In
addition, in the plasma scenario with the unlocked m/n = 2/1 tearing mode, an
increase of the diffusive transport has also been found near the q = 1 magnetic
flux surface. During the injection of argon the island width of the m/n = 2/1
tearing mode is increased and its rotation frequency is decreased. A possible
explanation can be that the argon increases the resistivity in the island which
102
leads to an increase of the island width and a braking of the island.
The application of the DED can also lead to a reduction of the electron density
which is called density pump out. In the m/n = 6/2 DED base mode in an NBIheated L-mode plasma the transport coefficient which are derived with the help
of the analysis of the transient argon injections are not changed in the plasma
core but there seems to be an additional outward drift at the plasma edge with
respect to the reference scenario. The radial concentration profile of iron is also
changed like in the plasma scenario without tearing mode with the application
of the m/n = 3/1 DED base mode.
The fourth plasma scenario is an ohmic heated plasma with the application
of dynamic DED in the m/n = 3/1 base mode. A scan of the rotation frequency
of the DED induced resonant magnetic perturbation has been performed. The
transport coefficients of argon are found to be independent of the applied rotation frequency of the RMP. The reduction of the intrinsic impurity concentration
shows a dependence on the applied rotation frequency. It is assumed that the
impurity sceening increases with a decreasing magnetic field screening. A comparison with a magnetic field screening factor derived with a model of a visco
resistive plasma is performed. The comparison shows that the impurity reduction depends on the inverse relative frequency between the electron fluid in the
plasma and the rotation of the RMP.
In summary the analysis of the impurity transport in Textor-plasmas with a
resonant magnetic perturbation shows no changes of the transport coefficients of
argon and lower Z elements. For iron a change of the intensity ratio of Fe XXIII
to Fe XV has been observed in NBI-heated L-mode plasmas. In addition it
has been found that the screening of intrinsic impurities depends on the slip
frequency between the electron fluid and the RMP.
A different transport of iron in comparison with the lower Z elements would
implicate a Z-dependent transport mechanism which is induced by the RMP.
The possible Z-dependence of the outward transport mechanism due to the
resonant magnetic perturbation which seems to increase with Z would be a very
interesting feature in view of future fusion reactors. If the impurity shielding
of high Z impurities is at least as effective as for iron the use of e.g. tungsten
as first wall might have less disturbing effects on the plasma. In how far the
sputtering of tungsten is influenced due to the change of the fluxes onto the wall
has to be analyzed. The tokamak Asdex Upgrade is successfully operated with
a full tungsten wall [127]. In addition the device will soon be upgraded with a
coil system in order to study resonant magnetic perturbations. Therfore, there
is a unique possibility to study the discussed effect with intrinsic tungsten.
103
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x
Acknowledgements
This thesis would not have been possible without the support of many people
and I wish to express my gratefulness to all of them.
First of all, I would like to thank Prof. Dr. Robert C. Wolf for giving me the
opportunity and the support for this interesting and fruitful thesis.
I thank Dr. Wolfgang Biel for the supervision of the thesis and for the possibility to work with the formidable Hexos spectrometer.
For the support from the institute of energy research - plasmaphysics I would
like to thank Prof. Dr. Detlev Reiter and Prof. Dr. Ulrich Samm.
One of the first and most exhausting topics of this thesis has been the mounting of the Hexos spectrometer on the tokamak Textor. I thank all of the
people who have been involded in this task, especially Mr. Jochen Aßmann who
has also helped me in the adjustment of the spectrometers.
The experiments on Textor always need a lot of manpower and preparations.
For this I would like to thank the Textor team of operators and engineers, who
delivered the necessary plasma conditions. For communicating the experimental
needs to the Textor team and uniting the experimental proposals from many
collegues I thank Dr. Oliver Schmitz. He has also contributed valuable parts to
the discussions which have led to the results of this thesis.
In the course of the last three years there have been active discussions in the
core diagnostics group about a variety of topics. The fruitful discussions about
the experiments with Dr. Yunfeng Liang, Dr. Günter Bertschinger and Dr.
Oleksandr Marchuk guided me to the main results of this thesis. Especially the
inspiration and broad overview over the field of plasma physics which Dr. Liang
provides, has been very helpful. The saying ”Discrepancy is progress!” and his
anecdotes which Dr. Manfred von Hellermann has always recited in the daily
group meetings, have also been a great source of inspiration for me.
I would like to express special thanks for the warm welcome into the core
diagnostics group to Dr. Oliver Zimmermann who welcomed me in my first
office on the third floor of the plasmaphysics building.
After my relocation to my third office, Dipl. Phys. Krischan Löwenbrück
has been my office neighbour and friend who has been a great help for me in
the experiments and who has helped me to survive in the daily life of a Ph.D.
student.
The fruitful discussions during lunch and the for the friendship I would like
to thank Dipl. Phys. Christopher Wiegmann.
Dr. Hans Rudolf Koslowski deserves some special thanks because he has
provided me with his private third edition of the Wesson and has significantly
improved the english of this work. In addition he has given me valuable informations about tearing mode physics.
I would like to thank Dr. Jürgen Rapp, Dr. Bernhard Unterberg, and Dipl.
Ing. Hubert Jaegers for the collegiality and help.
For the help in using the transport code Strahl and the ideas which have led
to a significant improvement of the experimental analysis I would like to thank
Dr. Ralph Dux from IPP Garching.
During my visit of IPP Greifswald Dr. Rainer Burhenn has given me a very
warm and cordial welcome for which I am very grateful.
In the institute of energy research - plasmaphysics there are many Ph.D. students and all of them support each other which creates a very nice atmosphere.
For the great time we had together at several occasions, especially at the kart
races in Maasmechelen, I thank Dipl. Phys. Meike Clever, Dipl. Phys. Heinke
Frerichs, Dipl. Phys. Dominik Schega, Dipl. Phys. Jan Willem Coenen, Dipl.
Phys. Henning Stoschus, Dipl. Phys. Christian Schulz, Dipl. Phys. Evren
Uzgel, M. Eng. Mikhael Mitri, Dr. Abhinav Gupta, M.Sc. Rui Ding, Dipl.
Phys. Miroslav Zlobinski, Dr. Florian Irrek and Dr. Uron Kruezi.
I also express my thanks to Dr. Youwen Sun and M.Sc. Tao Zhang the new
chinese colleagues who have accompanied me during the last parts of this thesis.
The team of visitor guides from the research center Jülich with their head
Mrs. Gerda Müsgen and her colleague Mrs. Annemarie Winkens have helped
me in my personal development and have provided a professional and efficient
working atmosphere.
Due to my dedication in the initiative of the Ph.D. students of Jülich, the
”Studium Universale”, I have found many friends and I have learned a lot. In
particular I would like to thank Myriam Unold, Sarah Garré, Natascha and
Christian Spindler, Frank Sommerhage, and Dr. Morten Schonert who have
become very good friends of mine in the last three years.
Last but not least the support of my mother Mei Liang Tio Greiche, my uncle
Dr. Heng Tie Tio, and from my siblings Robert J. Greiche and Nadine Greiche
has helped a lot in the course of the last three years.
Thank you all!
Curriculum Vitae
Personal Data
Name
Surnames
Place of Birth
Date of Birth
Nationality
Marital status
Occupational career
2006 to 2009
Study
2000 to 2005
Schooling
1990 to 1999
Greiche
Albert Josef
Darmstadt, Germany
12th May 1980
German
Single
Research associate (Ph.D. student)
Forschungszentrum Jülich GmbH
Study of physics
Technische Universität Darmstadt/Gesellschaft
für Schwerionenforschung mbH, Darmstadt
Diploma thesis:
Einfluss statischer und quasistatischer Magnetfelder auf lasererzeugte Plasmen
Secondary School
Edith Stein Schule Darmstadt
.........................................................
Name, Vorname
Versicherung gemäß § 7 Abs. 2 Nr. 5 PromO 1987
Hiermit versichere ich, dass ich meine Dissertation selbstständig angefertigt und
verfasst und keine anderen als die angegebenen Hilfsmittel und Hilfen benutzt habe.
Meine Dissertation habe ich in dieser oder ähnlicher Form noch bei keiner anderen
Fakultät der Ruhr-Universität Bochum oder bei einer anderen Hochschule
eingereicht.
Bochum, den ............................................
..........................................................
Unterschrift

The effect of resonant magnetic perturbations on the impurity

Transcription

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