IPPJ-AM-61(PDF 5421KB)

Transcription

A;∃
≦E
.i
喜
匡
∃
匡
喜
雪
≡≡
_?I
≡
毒
害
匡
･l
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萱
-≡
二書
≡-
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二≡ョ
書
医
書
巨
=貞
ヨ
喜
肝PJ-AM-6
THE
APPLICATION
m
ATOMIC
OF
FUSION
AND
PLASMA
H. W.
Institute of Plasma
Cbikusa-ku,
leave from
Centre
DIAGNOSTICS
DRAWIN*
Physics,
Nagoya
July
*On
Nagoya
F-1 3 I 08 St.
University
1 , Japan
464-0
1988
the Association
d 'Etudes
MOLECULAR
Nucliaires
EURATOM･CEA
de Cadarache,
Paul-le∑-Duranc￠/France
PHYSICS
1
This
research
document
is prepared
sponsored
fully
future publication
rearrangements
ment
in
JOumal
of its contents.
of the authors.
Research
a
or
lnformation
EnqulrleS
as
a
preprint
partly by
or
of compilation
This
about
University.
the IPPmagoya
will be included
document
in
Center, IPPmagoya
a
should
copyrightand
University,
of at.omic data
data book
not
This
after
be referred
reproduction
Nagoya,
is intended
some
evaluations
withoutthe
should
Japan.
for fusion
be
for
or
agree-
addressed
to
Abstract
This
report
Chapter
pure
I
gives
hydrogen
The
are
are
general
a
Chapter
a
of lecture
summary
presentation
ll contains
a
presented
and
Ⅳfor
emphasi2:ed.
terms
discussed
edge
and
detailed
divertor
of the rate
atomic
Diagnostic
The
heat
and
on
are
properties
for the density
of the rate
hot
in
species
processes.
molecular
confined
removal
atomic
equations
applications
班 for magnetically
plasmas.
by impurity
possibilities based
including
discussed.
in Chapter
effects caused
derivation
energy
are
notes.
of plasma
Diagnostic
plasmas.
(mass), momentumand
collisional-radiative
in Chapter
of
(deuterium)
enumerated.
of particles
consists
core
capabilities
equations
plasmas
and
of molelcules
Preface
and
Acknowledge些eHnis
The
text
presented
given
I
while
University
(A &
from
was
guest
in particular
●
I
Chapter
II , the
basic
aredeveloped
Ⅳ treat
particular
of Plasma
been
Physics
has
rather
of Nagoya
(IPP)
Atomic
to treat
avoided
it been
were
which
andMolecular
tried te
A
see
&
M
how
to show
A
&M
of plasma
help
can
physics
to get
better
a
devices.
due
physicaleffects
to atomic
and molecular
plasmas.
rate
and
series oflectures,
physicalapplichtions..
descriptions
glVeS
1t has
a
of
in magneticandinertialfusion
high-temperature
species in
energy
plasma
of plasmas
Chapter
the Institute
subject matter,
intention
my
summary
short
1988.
independent
with
a
at
to April
an
as
is
professor
January
in connection
undetsねnding
In
a
M) Physics
Physics
It
was
in this report
for the density
equations
form
puもinto
a
in hot
applications
which
core
momentum
direct application.
permits
plasmas
(mass),
of particles
andinthe
colder
and
Ⅱ
Chapter
edge and
and
divertor
plasmas.
To
コ
the text
give
effects in atoms
I would
have
like
my
stay
not
been
to thank
Information
Professor
contributed
at
Center,
H.
the IPP.
Professor
much
and
inaiding
included
Director
the
has
who
TAWARA
so
homogeneity,
certain
A. MIYAHARA
Professor
during
a
i
pellet 3ru'ection phenomena
althoughthey
of the lPP,
am
initiated
H.
very
much
to Dr.
me
T.
KATO.
to surmount
Professor
T. UCHIDA,andinparticular
their continuous
the Directorof
obligedto
his collaborators,
I
am
indebtedto
the language
high-density
in the lectures.
treated
were
the invitation,for
OBAYASHIand
and
support
the Research
in particular
Mrs.
ITONAGA
problems
associated
to
who
has
with
daily
life.
Thanks
to every
one
for making
my
visit to Japan
a
pleasant
H.W.
delightfulexperience.
and
Drawin
CtlntentS
PREFAC五AND
ACKNOWLEDG五MENTS
I
CHAPTER
IntroducLion
I.1
Atoms
in Magnetically
andMolecules
Plasmas
Confined
‥‥
‥‥
‥....
1
‥‥
I.1.1.Radiationlossesinhotcoreplasmas..................................
1
Ⅰ.1.2.FurtnerefFectsdue
3
toimpurityspecies‥‥‥‥‥
‥.‥‥‥‥‥‥‥..‥.
(a)electricalconductivity...........................................
3
(b)particlediirusion..‥‥‥‥‥...‥‥‥‥‥..‥‥...‖‥‥..‥‥.
4
(c) thermalconductivity........................................,...
5
(d)viscosity---･------------‥‥.---‥.‥‥‥‥
6
I.1.3.
Pelletsandimpurityatomsinjectedbypellets..........................
7
I.1.4.
Impurityatomsinedgeplasmasa,nddivertors..........................
9
I.1.5.
Atomic
I.1.6.
Veri{1Cation
I.2.
Atomsin
(molecular) impurity
of atomic
species
structure
for diagnostic
for plasma
I
10
･........
diagnostics
･
10
ll
II
for Magnetically
Equations
base
･...
............................
CHAPTER
Basic
data
calculations;
Plasmas
Laser/IonBeamsIDriven
purposes.
Plasmas
II.1.
The
ⅠⅠ.2.
RateEquationsforParticle
II･3･
Rate.EquationsforMassDensity･････････････････････････････････････
19
ⅠⅠ.4.
CouplingofRateandFieldEquations-･-･･･--･---------･･
19
II･5.
RateEquationsforMomentumDensity････････････････････････････････
20
II.6.
RateEquationsforthe･EnergyDensity
22
Basic
II.6.1.lnternalenergy
Electro-Magnetic
and.Particle
Kinetic
Confined
Equations................
Densities..‥..‥.‥.‥‥.‥‥‥.....‥...
･･･････････････････････････････
15
17
22
･･････････････････････････････････････････････････
II.6.2.Translationalenergy･････････････････････.･････････････････････････
26
II.6.3.Thermalenergy.....････････.･･････..･･.･.･･..･･････.............
29
II.6.4.Totalenergy.....................................................
31
II.6.5.
33
The
terms
......................................
Ⅱ
CHAPTER
to Hot
Applications
Core
Plasmas
in Magnetic
Con丘nemenもDevices
Ⅱ.1.
Introduction‥‥‥.‥‥‥‥‥‥‥‥‥‥.‥‥‥‥...‥‥‥‥‥‥..
Ⅱ･2
Determination
Ⅱ･3･
ConfinemenもTimes
Ⅱ.4.
Determination
HI･5･
TheParticleDensityDecayTimeFp*---･---･･･----･----
班.6.
Determination
Ⅱ.7.
Det･erminationof
Ⅱ.β.
Radiation
Ⅱ.9.
Further
of Particle
ConfinementTimes
of Energy
ofParticle
-
ConfinemenもTimes
Flu又es and
rE
･
--
CoefTICientDa
Diffusion
Tpand
Tp･
44
･
-
･
-
･
-
-
-
-
-
･
-
-
-
-
-
-
-
･
･
-･
-
-
･
-
-
-..
-
-
-
-
-
-
Velocities‥
‥
‥
‥
‥
‥
‥..
‥
‥.
‥
‥
Species‥.
to Edge
‥
‥‥
51
‥.
59
62
‥
‥
‥
‥
‥
‥..
‥.
Ⅳ
CHAPTER
Applications
47
57
Losses‥‥.‥‥‥‥‥‥.‥‥.‥‥‥‥‥‥‥‥‥‥‥‥‥
usingAtomic
47
49
ConvectionVelocity----..----..-.-..--..
Applications
44
and
Divertor
Plasmas
N.1.
Introduction.....................................
Ⅳ.2.
Definition
Ⅳ.3.
FormaもionoftheScrape-offlJayer..‥..‥.‥..‥‥..‥‥‥.‥‥‥....
67
Ⅳ.4.
RecyclingCoefficienも･--･･--･‥‥...‥‥‥‥‥‥‥‥‥‥‥..‥.
70
N.5.
PropertiesofDivertedPlasmas......................................
71
Ⅳ.6.
AF10lecules in Recy二1L:gDivertorPlasTnaS....‥..‥‥‥‥..‥‥‥‥‥‥
72
N.7.
Co11isional-Radiative
79
N.8.
AtomicandMolecularDataforEdgePlasmas････.･･･..................
of Boundaryand
Models
Scrape-off
Layer
64
...............
and
Divertor
Plasmas...
forMolecules.............................
REFERENCBS‥‥‥‥‥‥.‥.‥‥‥‥.
APPENDIX...........................
‥
‥
‥
64
81
82
86
1
CHAPTER
Intro ducti
I.1
Atoms
I.1.1
Radiation
Atoms
the type
wall
tosses
and
stellarator,
spatio-temporal
influence
parameters
the hot
core
properties.
desired
quantities
serve
of impurity
wall
they
thus,
ioni2:ed atoms
reali2:ing the fusion
is necdedfor
●
burning
might
deleterious,
plasma
cold edge
the
on
ln
oLr energy
radiating
Ionized
impurity
The
presence
device.
state.
jusもbecause
or the radiation
increases
wall erosion
its
the impurity
tosses.
in the hot
species
●
core
plasma
a
at
demonstrate
suLTICient
this effect.
The
at
of machinesaimlng
(T) ions, because
tritium
the temperature
1 may
Figure
direct effect
a
the plasma
about
Increased
(D) and
maintaining
have
confinements
be very
induce.
unwanted
of deuterium
Of thefuel.
band
the radiation
are
magnetic
information
whichgive
the other
on
erosion
and,
concentration
which
Can
a
of
of
effects and
the
in
for instance
development
in both
molecules
and
be benerlCial,
can
parts
particular
atoms
molecular
of the plasmaand
different
concentrations
of the
composition
temporal
state
of very
number
molecular
inversely,
eLrect
``probes"
as
species
tosses and
The
This
in
and
And
plasma.
plasma
can
the atomic
a
the
and
and
changewith
atomiぐand
instantaneous
of the
terms:
other
abundances
structure
The
conditions
functions
are
In
evolution.
into contact.
comes
the ou七gasing
on
They
contact.
the particular
(tokamak,
plasmas
confined
eもc.).Their
plasmas
conditions,
the plasma
strongly
of all magnetically
rleld pinch
vacuum
which
depend
the plasma-wall
atoms
the
Plasmas
Confined
plasmas
constiもuents
reversed
of machine,
abundances
core
are
molecules
with
in Magnetically
in hot
spheromak,
material
and
Molecules
and
o n
they
oLr energy
radiate
level which
broken
ensures
curve
shows
the
●
total
density
power
(nD-nT=ne/2;5×
PD_T
Of
1Q19m
a
pure
3). The
D-T
of total density
n=2×
below
broken
plasma
curve
continuous
the
1020tn-3
one
represents
the
●
density
power
血ring
bulk
a
Pagiven
su瓜cient
plasma
time
according
to the
so
a-particles
that they
to the
which
are
assumed
to be conrlned
traLnSfer their kinetic
can
in the plasma
of 3.5MeV
energy
to the
reaction
(I.1)
2D+tlTー4He(3.5
The
I:や田並d也㈱
Melr)+
heat嘘蛤13}dk.plasma
andthe
,
-1-
1n
(14.1 Mew)
neu'tr8nS
escape
tO
the walls･
(w/m3)
10:1
{k三%3,
1んT287kOev
4p
Figure
1
Comparison
densities
of power
●
due
to D-T
thermonuclear
reactions
(PD_T and
■
Pa) and
radiation
(Rq=free-free
or
Bremsstrahlung)
of
a
pure
D-T
pla$1na,
■
los芦With
R=radiation
nD=
nT=
ne/2=
0.1%
Fe
5･1019れ･3･
-2-
or
0.1%
W
add@d.
AssLTmption
is made
that
The
When
bulk
we
rplasma
that
assume
case
at the
pure
D-T
beginning
plasma
in form
off energy
radiates
the a-particle
to the
is
concentration
ofもhe thermonuclear
according
of free-free radiation
burning
losses, it yields
energy
ion temperature.
The
tosses
a
minimum
Figure
are
density
present
lost by
of impurities
"21''having
state
of charge
the
radiation
power
in the plasma.
The
radiation
mentioned
nO
for Te=Ti,
of 4.28heV
･2)
Other
Ti being
the
whereか=?a).
the thermonuclear
1 shows
a
■
Te in hey.Assuming
temperature
Ignition
(Ⅰ
[w/tn3】
temperature
electron
●
decreases
and
tungsten
power
m-3,
of ioni21ed species
of the fuel.
0.1 %
ln
(Intersection
presence
radiation
ne
loss is thaもof
the radiation
relation
●
density
the electron
be the
will surely
negligible -which
process-
長ff=418x10-31ne2
Teln
with
(bremsstrahlung).
above,
at T=9
hey
R
thermonuclear
T=20
dilution
of dilution
0.1%
iron
equals
the
density
power
hey,
because
is lost when
which
for the two
respectively,
of the D-T
the
Ttlincreases
rate
production
density
and
no
aSSuming
power
the density
or
cases
affects PD_T
fuel (which
and
4
Pa) and
Impurities
in
●
regions
Where
thermonuclear
the
more
can
also compensate
One
can
all the
probably
not
drastically
the
that
the radiation
●
impurity
plasma
those
Particular
with
ralSlng
itill
approximately
containing
to the
way
only
losses.
energy
of significantly
losses, that is to reduce
highatomic
is still of major
reducing
1t is because
in thermonuclear
COnCern
Since
the
Z-values.
●
problem
that the
means
hence
plasma
tosses.
radiation
be reduced,the
tosses is to reduce
1n
D-T
a
negligible.
This
tosses,
energy
contributJe SignirlCantly
convection
and
that
is
tosses in the colder
the energy
these
show
loss
radiation
is insignificant.
production
compensatealone
of inlPurities,
situation
must
temperature.
energy
concentration
this
core
plasma
to the
particular
power
conduction
very
the overall
plasma
in
increase
the thermonuclear
iron cannot
Thermal
they
D-T
a
ignition
1%
0.6%+
of He2+
that the contribution
assuming
of
fusion
resear(血.
I.1.2
Further
The
presence
effects due
of
to impurity
(highly)ionized
species
species
further
causes
efrects･
(a) ElecIT.lcal Con血ctlvity
Species
with
zl>1
increase
the electricalresistivity
by
8
factor
Zen
●
given
by
∑niZ…
∑niギ
‡
(i.2)
一
_
.. ..
eu一貫niZi拝e
暮
whe'r'er払e suThmAtion
bulk
i岳made
●
olverall
ioh specleS
ー
eleetrons.
-3-
``i''having
ionic charge
eozL
Seen
by
the
The
Law
Ohm's
generali2:ed
for a申agne軸ed
一事
E
is the
to the
1/tec
･ee=
goo-Coulomb
(I.3)
of the elctric Tleld,
(vec=2･8×
gyrofrequency
denection
the
B?,3o the
induction
magnetic
the electron
the expression
7u(i,
8･u･i･言oxB?+筈【Jix言+v?pe･
intensity
(perpendicular)
by
⇒･
T?
-w･
-チ
E
where
is glVerl
plasm?
density
current
mass
the electron
velocity, pe
m
1010B
parallel
the electron-ion
Tei
and
see-1)
pressure,
time:
A T3J2
e一
Te is the electron
where
logarithm.
All terms
The
charge･
(Te
e2FfneeTLA
in Kelvin, ne
temperature
of the
even
and
right-hand
B
Tn-3
eTL^ the Coulomb
and
depend
the plasma
on
innuenced
are
on
(n打,花⊥)(conductivity刊,
of electricalresistivity
in Tesla
●
ln
side (r.h.s.) of eq. ( I.3)
the fields acting
since
vo,
coemcients
in Kelvin,
(I.4)
[s]
z
:≡コ
impurityions,
e
2.51×108
石.=
by the
mass
and
by
O1) aregiven
)
1
TLA
1Z ewe
花甘= --6･87×10
qD
【β･m】
(I.5)
[L2･,n]
(I.6)
T3R
e
1
1･37×10
Ze[feTLJl
2
B2
n⊥=キ=
A
measurement
It isrnot
U
Howeverl
r･
radius
an
yields
to
a
average
information
about
Zed
when
ne
and
as
a
Te areknown･
ne
for enA.
expression
possible
e
an
of判yields
in the
intervenes
Ty2
in
measure
a
of Zen,
See
and jn directly
total plasma
meaSuremenもo-(払e
value
EI
tokamak
Eq･
function
Jp and
current
of the
of the loop voltage
(H･56)･
(b) ParticleDi(fusion
3o
Let
diffusion
The
be the
velocity
density
local
mean
-÷
mass
"s"
of the species
nux
of the particle
=き
of the plasma
velocity
to
relative
a
whole
and
the
<V8>
by
the relation
(seealso Eq.(II.10.c))
IT>
T8-nBUo+n8<7s>
where
bulk
ns<Vs>
plasma
velocity
essentially
ambipolar.
(neglectingthe
density
representsthe
Hall
(I
of the so-called
(or m?ss velocity)?o
In
and
a
strong
uniform
thermoelectric
mean
･
isgiven
"s"
of species
3o
as
For
･
charged
magnetic
contributions)
-4-
"difRISion
species･
nu又,I with
the diffusion
Tleld蛾eミde耶ity
is expressed
regard
by
nux
･7)
to the
is
'of吐血e･dif6t19ion･hx
the followipg
relations:
⇒
to B
●parallel
:
the parallel
with
Vanlb>･且=-tDEV
<
( I.J8)
べI
Tケ
he
diLrusion
ne
by
DEgiven
coefTICient
T5J2
e
D控-2×D蒜ons=5･62×1011
ze3uAIBn
eTL^
(I.9)
【''12s-1
]
e
=:王コ
to ら
●perpendicular
:
ぅ
ー}
<Vamb>.L=-DVJ_ne
n
(I.10)
e
diffusion
the perpendicular
with
coeLrlCient Dl
given
by
Tlend
e
D⊥=2×DellecLrons=7･42×10-21
[-2s-1】
(I.ll)
BT*
e
(ne
●
ln
m-3
,
Te
(c) TherTnal
The
in Kelvin,
B
in Tesla,
A
is the relative
atomic
weight)･
conducllvity
of the
density
+
to BXVT
proportional
thermal
.+
where
heat
T
nux
due
is either
Te
E:
to
or
thermal
Ti) isgiven by
=ヨ
(neglecting
conduction
the
a
term
expression
E
(Ⅰ.12)
q --1C耳∇lT-tc⊥V⊥T
一
The
coefrlCients of thermalconduction
in
a
strong
uniform
field of induction
magnetic
B
fare
≡コ
●para11el
-for
the
to β
:
elctrons:
･Ll∽
｣｣
eTLJl
･c;-2･48×10
_
10
[wxK11xm-1]
(I.13)
[wxK-1xTn-1]
(I.I4)
for the ions:
T
5F2
e
〟;-5･82×10
ZIA
一
12
㌍en^
l
-チ
to B
●pe叩endicular
_
for the
electrons
:
=
2enJl
⊥n
(WXK-1×T'1-1
IJ2
lCl=7･68×10-44
B2T
)
(I.15)
e
_血r
,tbeions
:
A
T3z苧nぞe
nJl
1
一
･cl=3･19×10-42B2T
I
!J2
l
.
-5-
:[･wxK-1
×･,a-
1
]
(I.16)
(d) Viscosity
The
coefficient
●
丘e一d are
(ne Tl`)for electrons
ofviscosity
ions, in the absence
and
,
a
of
magnetic
by
glVen
(I.17)
ne.-1･09×10-17芸[JS]
1J2TF2
A.
1
L)mx,s
i
■
巧乙=4･66×10
16
zlenJl
(I.18)
一
･..+
In
a
strong
uniform
frequency)
the components
B
field of induction
magnetic
to富are not
of ne･i parallel
larger
(gyrofrequency
the components
perpendicular
corresponding
●
glVen
respectively.
to B
of nell perpendicular
coeLTICients
experience
of viscosity
for the
collision
nut-巧.I)
(i･e･,析ne.
modiTled
,
-◆
whereas
than
strong
The
modification.
electrons
and
ions
are,
by
茅[JS]
e
花el=3･38×10-61
(I.19)
zヲAy2n.en^
l
一
巧(1=2･64×10-46
B2T
一
(Ⅰ.120)
y2
一
(a in
T
m-3,
B
in Tesla,
conTlnement
devices
in Kelvin,
A
isthe
relative
atomic
weight).
Remark
ln
magnetic
distributionsl
than
the
into account.
so-called
which
describe
are
when
not
of numerical
given
by
a
They
-･6-
,
1C⊥ n⊥巧t⊥
by plasma
represent
transport
theory.
nonuniform
the particular
rlndings
coefficients.
to fit the results
coeLrlCienもs
even
the experimental
transport
anomalous
permit
transport
To
ones,
predicted
strong
coef{lCienもs D⊥
the measuredもransport
theoretically
have
which
magnetic
are
and花e⊥
actually
one
has
larger
is taken
stluCturC
magnetic
models
field
introduced
phenomenologicalcoeLTICienもs
codesもo
experimetltal
data.
These
I
Pellets
･1･3
The
inform
species
or
pellet
a
plasma
has
temperature
in the
that
be applied,
has
evolution
which
some
some
in nature
similar
but
flux of electrons,
the density
during
ablation
to the
compared
times
or the
AIso
order
during
features
in
so
also marked
a
faras
target
temperature,
thus
一eading to
now
until
some
One
and
cansay
represent
Figure
and
diagnostic
experiments,
interesting
The
plasmas
decrease
a
types
purposes.
The
of the
are
to
are
effects
diferences
have
The
submitted.
a
laws
(L.T.a.)
the hydrodynamic
These
relatively
solid
weak
energy
of (1-10) 109 w/m2
order
microseconds,
types
is
which
targets
are
negligible
during
exposed
have
of plasmas
a
a
is that
one
hotbasic
and
now
by
increase
into
finally becomes
a
of theもhermal
at low
gas
common
there
ablated
it is
which
velocity
velocity
expand
the pellet matter
plasma
the now
some
However,
regime.
in
density
are
complementary
and
a
and
a
until
The
supersonic.
density
are
continuously
continuously
energy
high･density plasmas
of
their state
studying
presentations
ideal
targets
and the
(evaporation).
density
values.
the
laser
low
decrease
orthe
limit is reached.
objects for
schematic
the H2
density
collisionless
that both
2gives
into
plasma.
Also
●
important
its energy
permits
formin
equilibrium
(orion) -beam
the two
towards
flows
thus
a
less.
phase
the most
(or ion) beams-irradiated
laser
orAr
is high
ablation
subjected
being
hundred
which
or
evolve
device
Therefore
velocity
to
nanosecond
both
nux
energy
or several
w/m2
that of the basic
reaching
the pellets and
the later expansion
confinement
up.
to which
of the
-1020
or
in their absolute
process
diffbrences;
magnetic
heated
1018
different
plasmas
density
characteristic
are
Ne
is to create
which
simulation.
Further,
confined
and
of the
stage
local thermodynamic
cases.
frozen
this way
The
plasmas.
initial
the
impurity
finds in similar
one
which
target
diagnostic
inJ'ecting
a
of
to realize
otherwise.
facilitates numerical
very
in
the whole
during
in both
nuxes
theenergy
origin
pellets injectedinto magnetically
their
properties
high-density phase
similarities
in
localised
impossible
or
irradiated
considerably
by
or
density
for plasma
injectionof
is rather
which
diLTICult
relatively low, at least
means
(D2) pellets
of injectingimpurities
sink
more
proper
to H2
the plasma
be applied
pellet (for instance
advantage
much
to increasing
means
injectioncanalso
impurity
or lase〟ion-beams
expandingpbase
quite
are
a
species
temperature
a
which
pellet
Pallet
impurity
entire
and
measurements
The
an
is
pellets
pellet). The
metal
source
particle
ice
plasmas･
adding
of
inJ'ected by pellets
atoms
(D2)
confined
either by
purposes･
can
H2
injection of
magnetically
This
impurity
and
case
(D2) ice pellets have
of asphere
always
-7-
is only
the form
their spatio-temporal
and
of pellets which
to each
have
been
a
evolution.
appliedforfueling
reali2:ed in the Nagoya
of
other
cylinder･
1
仁⊃
ASDEX
1mm
vp-720ヱL
_{=
S
D2
1.2mm
ー享ilニ
由圭
TFR
⊥
Q⊃
PLT
≠-I.2mm
m
)
)
Vp=600
L- =2mm
≠2-0.85mm
m
Vp=700
L2-
1mm
H2,
D2+neon
vp-450エ
S
S
doped
S
D2
I
L｣
≠l-0.6mm
I.5mm
≠l=L--1mm
≠2=L2-I.65mm
A
｣ FT-2M
iy
Vp
upto9了0-
S
Al
メ-0.5mm.
1
JIPP一丁II
H2+D2
mixture
≠-0.226
0
†
C
0.46mm
and
(Plastics)
≠-0.5mm,
SUS
steel
Vpごゴ400
1
Figure
2.
Some
various
types
i2-L2-4mm･
of pellets (listing not
tokamak
Vp-1350
≠l-Ll-2･6了mm･
児享
TFTR
plasmas.
-8-
exhaustive) which
Vp-1300
have
been
injected into
in
Byincluding
larger
a
as
sphericalhydrocarbonpellet
the
Impurityatoms
they
Can
produce
huge
amounts
walls
An
impurity
possible
and
thermal
energy
in
sheath
nor
in front
the fusion
technical
some
is met
divertor
density
high(宅1020m-8)I
of that
energetic
one
those
side and
on
the other
to be
as
plasma
An
point
has
as
other
the
impurity
task!
enormous
have
been
yet
(see Fig･
of view
as
much
the deleterious
problem
any
of
optimizing
radiatively
place･
of this
compromise
the edge
onthe
take
in
or
system
to cool
control
found･,
1
and
found･
of the parameters
afunction
of the
the
materialwalls急nd
side is therefore
an
important
diagnostics.
plasma
close tothe
the
in front of the
will be the entire
to minimize
solution
in the diverbr
and
musもconsisもof
reactions
exciting
erosion.
in order
and
from
of the materialwal1s
plasma
properties
walls
energy
by
temperature
reactor
control
regions
behaviourin
of the coreplasma
wall
since
an
represents
the energy
reglOn
plasma
and
This
properties,
コ
the plasma
●
plasma
furnish
inane･ventualdivertor
contradictory
impurity
particularsituation
transport
ln
region
plasma
radiation
production
Which
fusion
a
system･
there) and
comment
in fusion-oriented
A
are
radiation
lower
of
the plasma
where
favourable
sputtering
operation
satisfactory
requirements
of the
This
front of the material
a
have
to
wall
exhaust
plasma
core
physical
properties
task
the outer
●
deep
divertors
in the edge
property
in the edge
the plasma
study
plasma
including
region
the corresponding
The
in the
problem
edge
the two
also
of impurities
to decrease
thus
concentrations
a
a
to introduce
be possible
contaminating
the electronsI
Particle
the beneficial
and,
eLrects in the hot
Neither
1n
presence
●
particleand
and
of radiation･
particles,
important
the plasma
plasmas
●
have
therefore
material
sourcewithout
ioni2;ation stages
medium
The
the partieles･
could
impurity
and
for the plasma
sink
2, itwould
for instance
pellet,
smal1erimpurity
in Figure
shown
in edge
in low
Atoms
a
of impurity.
type
withthis
I.1.4
well defined
a
plasma
(D2) ice pellet
H2
in the divertor
target
plates
Molecules
region,
(H2
see
where
,
scrape10Lr
the temperature
02) have
Chapter
-9-
layer
N
an
･
innuence
and
in particular
is low
on
the
(a few
in the
eV) and
radiation
and
the
Ⅰ
Atomic
･I･5
lmpurity
atoms
appropriately
quantities
of
to be
Thefo1lowing
methods
Te
2-Electron
density
plasma
be mentioned
may
permiもwben
parameters
and
(not exhaustive).･
Method
measurement
ratios
Measurement
ne
rate
and
intensities
line
of absolute
intensity
-
They
tool.
numerous
of
determined
temperature
purposes
diagnostic
the determination
applied,
･.
llElectron
and
interest.
for diagnostic
ions represenもpowe血I
and
chosen
Quantitv
-
(molecular) irrlPuriもy species
interpreted
by rate
of line intensity
equations,
measurement
ratios
Of line
Ib･ Or
equations.
interpreted
and
by
line intensities
of absolute
of
injected impurities.
Ti
temperature
-3-Ion
ratios,
-
-
-
4-Rotation
velocit.y
5-Magnetic
fields
6-Magnatic
field
of Doppler
measurement
ur
tBI
broadening
line intensity
or
of "charge-exchange
measurement
measurement
of Doppler
shift of
Measurement
of Zeeman
splitting.
measurement
of the polarization
a
neutrals."
line.
spectral
of the Zeeman
angle
=コ
direcもion β
Components
of
injectedpellets.
measurement
of absolute
by
decay
I)1asma
of line intensities
clouds
-
times
7-Con丘nement
8-Diffusion
nuxes
convection
rate
line
equations･,
striated
ablation
and
interpreted
measurement.
interpreted
of nuorescence
measurement
of the pitch
intensities
equations;
measurement
and
determination
丘eld lines from
of the magnetic
angle
_
line,
of a叩eCtra1
by
rate
profiles (for edge
plasmas).
-
9-BLrective
ion charge
Zed
number
measuremenもor
absolute
connection
the solutions
with
of intensity
measurement
Ⅰ.1.6
Verification
the
Severalof
atomic
models
The
measurement
diagnostic
in which
transition
radiative
of atomic
regions
theoretical
data
calculations;
●
methods
SPeCtral
using
the level structures
probabilities)
intervene.
of the wavelengths
●
plasma
both
structure
of impurities
Permits
identification
obtained
from
(molecular)
-10-
data
base
line
emission
for plasma
the atomic
emitted
species.
structure
in
to
local
hydrogen
exchange.
It is essential
of impurity
atomic
and
of 'rate equations;
ratios of impurity
by charge
lines popu一ated
line intensities
spectral
diagnostics
impurities
from
data
(cross
to possess
a
from
the
Their
both
calculations
sections,
data
reliable
comparison
hot and
with
can
on
rely
base.
cold
the
be useful
to
the identi丘cation.
re丘ning
intensities
important
An
function
rate
with
lead
Atoms
Atoms
of low-and
is sometimes
The
in
fusion
difference:
have
introduces
transfer
mass),
afurther
equations
and
momentum
of nanoseconds
measurements
-tllation studies
or
Figures
3 and
a
in
plasma
the particularconstruction
An
impurity
4 show
typical
(e.g., argon)
gas
structures
is determined
of
in
shorter
plasma
the evaluation
ICF
simultaneously
studies,
studies,the
by
resolutions
一Flu=
types
of
There
can
of the
with
often
measured
the rate
the characteristic
period"
(ten
scalefor
in inertial
applied
I.1.3.
We
of plasmas.
is, however,
not
be
data,
important
high-speed
This
neglected.
since
equations
time
an
thus,
short,
are
plasmas
the
radiative
for particles
scales
are
of the
(or
order
spectral1ine
(severalmilli-seconds)･
to hundred
of the
plasmas
bt!ams-driven
is extremely
shorte.st time
the ''saw-tooth
time
of laser/ion
Opticalabsorption
be solved
In
a
those
in Section
two
devices.
expanding
and
discussed
of these
confinement
applied.
energy.
been
(MCF)
for the diagnosis
the duration
to
betweenthe
fusion
parameters
in magnetic
to be
diLrerences
havealready
essential
less. In MCF
require
as
species
(molecular) data
atomic
of other
and
is enclosed.
mixture
confinement
complication
have
fuel
applied
studies,
detectionsystems
Unreliable
originate from
generally
the main
in magnetic
methods
in ICF
impurity
Plasma
purposes.
of and
for plasmas
as
D-T
(ICF) studies
diagnostic
same
elements
the
in Figs. 5a, bthe
summari2:e
plasma
for specific purposes.
pellets
clouds
the
or
line intensities
spectral
concentrations
Beams-Driven
which
features
common
line
spectral
methods.
fordiagnostic
irradiated
confinement
the
similar
from
processes.
atomic
impurity
of the
medium-Z
added
pellet ablation
Thc
by
absolute
of the various
concentration
determined
are
for the
in Lase〟Ion
of the solid targets
directly
These
values
determined
parameters
and
(molecular] data
refining the atomic
is the absolute
equations
to unreliable
in
relative
applied.
are
time.
and
of both
measurement
help
valuable
quantity
of space
connection
I.2.
a
the data
to which
models
will
be
can
The
nanoseconds)･
Only
pellet
Figure
3.
Target
for laser
implosion
Ref.
AIL
studies,
radiation
a氏er
[1].
measure:S
in micrometers
(1)
(2)
Exploding
∠身G"a
200-300
pmO
pusher
(Neutron)
芸卦cH
Ablative
ユoo一-500
(high
compression
density
compression)
Crl
GM8
I
(3)
(4)
( &
∠cD1
300-400
(5)
Multト:ayered
DT_罷芸
200-500
measurement)
Shet卜target
pm￠
三≡針G"a
300-400
Cryo-target
pmO
GMB
(6)
aspect
∠j''cH'L｡,｡e(stab=ty)
400-1500
pmO
(shock
Corrugated-target
(7)
∠芸cH
300-700
Figure
4.
Typical
balloon),
mu(tipfication)
structures
artcr
Pm￠
of irradiation
targets
Rcr. 【2】.
-12-
(stab=ty)
for specirlC
Pul･POSeS
(GMB=glass-micro-
Te keV
O
AblQtion
①
preheQt
伝)
Light
Figure
5a.
The
→
r
high-density plasma
of
pressure
100ドm
Pressure
pressure
essentialparameters
studies. Irradiation
diameter
rlgure.
conditions:
1015 wJcln2
target
of medium
sphericalsolid
irmdia岱on
the plasma
After
of the
flow
would
Ref. [3].
-13-
be
at
an
wavelength
atomic
steadywith
number.
pellet in MCF
ablating
l=
1pm
loops
the parameters
on
a
lOOLLm
after
shown
in this
rp=0･28cm
Figure
5b･ Temperature
ablating
H2
T
,
pellet
Mach
of initialradius
with
without
After
r
p
surface
Ref. [4].
-14-
of ionization
injected
=0･28cm
dissociation
surface
degree
and
Te(-)=11･5
of ne(∞)=1･01×1020m-Band
.
M=u/ulh
number
into
a
keV･
and
dissociation
ioni2;ation.
and
ionization.
f1 0f
background
an
plasma
CHAPTER
Basic丑quations
ⅠⅠ･1･ The
For
M二agnetical1y
Electro-Magneticand
Particle
Basic
in
Plasmas
m8gnetical!y
andもo
induction盲=LLHi,
of
a
Owing
highplasma
to the
relative
stationary
or
Eqs.(I.3)
and
weak
densities,
see
ConTlned
Plasmas
Kinetic
are
Equations
to strong
submitted
electric fields of strength
medium
fluctuating
a
and
or
devices
plasma
confined
low
of
stationary
II
fields
magnetic
E-''which
are
c.mposed
part.
temperature
the plasma
quasi-stationary
electric
is extremely
conductivity
field strengths
can
high,
thus
1-;ghcurrent
produce
(I.5).
=≡コ
The
by the toroidal
rleld coils,
frequency
or
a
electric field E￠
Maxwellian
velocity
high-frequency
distribution
deviations
a
either
electric induction
pure
The
inductive
distribution
in
from
the
a
velocities
Maxwellian
still be considered
distribution
velocity
by
can
a
current
whose
cause
a
produred
electrons
which
velocity
Maxwellian.
as
it is
or
displaced
non-inductive
plasma
high-
modes,
of decoupled
group
in the bulk
movlng
first approximation
The
low-density
a
wave
transported
electrons.
●
to relativistic
can
of the plasma
inJ'ection and/or
accelerating
is generally
Created
Jind
in
the poloidal
magneticnux
by particle
to particle
Current
originates from
waves
the changlng
7m･nd
Sustained
converted
current
●
originating from
waves
electromagnetic
accelerated
IS
current
non-inductive
or bo仙.
are
●
jp
=∃
Combination
by
of density
current
plasma
However,
atomic
significant
the
physics
effects.
The
to
plasma
and
a
all ions
a
as
highly
first approximation･the
of densities
nk&,i
COmPenSate
of the negatively
(s=e) orpositively
n8
,
internal
each
"h''in
density
isglobally
electric charges
chemicalele.ment
particle
nuid
conducting
other
quantum
state
(s=(2[,h, i))
the quasineutrality
condition
neutral･, i.e., on
●
a
macroscoplC
of density
of the electrons
ne
(z=ionic charge
state
Ii>).
by the subscript
charged
Denoting
species with
isgiven
by
(eo
SCale
those
and
of particles
of
"s''either
q8 and
electric charge
means
of
the elementary
charge)
∑qsns-e.(-ne+
∑ zh,inZk,i)-0
for
an
ionized
c-co
gas,
and
う
electric displacement
and
･1)
i.A,a
s
Further,
(II
D
.
given
are
by
the vectors
for magnetic
induction首
.
the followlng
COnStitutive
relations
斗
一
B?=poH
hold; thus,
p巴Po
(a)
･･方-8oE
(b)
(ⅠⅠ･2)
⇒
where
The
H
is the magnetic
Amp8re-Maxwell
electromagnetic
{1eld intensity
and
∫;el°quantities
Faraday
vector.
relations
:
-15-
couple
the
material
to the
currentdensiもy7p
雲-音×言-,,
'a';雷ニー音×E-恥)
(lI.3)
一事
ーナ
B
D
and
(because of Eq. (II.1))
-
are
free:
source
1>
+
V･B=0
(a)
+
∑qsns望Oa,)
V･D=
,
(lI.4)
S
->
The
density
of the plasma
densities
current
is the
jp
current･
+
->
･3･a)
-+
the toroidal
( ⅠⅠ
･5)
⊆コ
is thetoもalplasma
ofj
componen三j￠
E is the inductively
E￠
component
drives
current
inductive
of
In
curren七density7p
･
-･}
(ⅠⅠ
the toroidal
･3･b)
the
Unind)
non-inductive
+jnI･nd
E
(Il
Ulna) land
:
Jp=J.･nd
In Eqs･
ー
｢ト
of inductive
sum
field strength
created
Eq･
which
-i)
of density
jind
･
一
The
so-called
The
particle
density
integral
velocity
the
represents
MHD-approximation
n8(r, i) at space
yelocity
to
relative
7
point
distribution
the velocity
over
0.
aD/8l=
assumes
inthe
laboratory
function
the laboratory
system･
Fs(r,t･ i3s)of
at
t･ is the
time
species以s"I
Then
system.
#w8f8(r･t･蒜｡,
Iw_
ns(r･ i,-
7Bs
where
(II.6)
S
with
by
F8given
the kinetic
Bolもzmann
non-relativistic
equation
r}
警十蒜s･蓋Fs･吾･豊-[%]-[警】c
(II.7)
S
is is
force acting
the self-consistent
■-
rI
on
>
-
8
a
particle
of
mass
ms:
う
F8-qs(E+OSXB)
(ⅠⅠ.8)
→
h
this expression
of externally
and
fields, plasma
of the velocity
expressions
forces have
non-magnetic
electric fields and
applied
(i.e.Debye
themselves
The
non-electric
in
of fields created
been
E is the
neglected.
the plasma
by
sum
the particles
fields,･･･).
wave
integrals
in the
of the ter･m.S in Eq･ (ⅠⅠ.7)
aregiven
Appendix.
一
In
magnetic
｣･
->
ヰ
B=B￠+Bo+Br･
conTlnemen七devices･
ーゝ
where
B￠
--i
is the toroidal
Be払e
and
⇒
poloidal
magnetic
distance
between
r.h.s. of Eq.
radiation
B,
induction･
is the
rleld coils and
the toroidal
is the
(ⅠⅠ.7)
processes
In the following
to
leading
we
will
∂
⇒
use
a
(magnetic
radial componel･t
change
of
∂
the vertical field induction.
term
which
contains
F8･
the gradient
-I
諺≡V and訂=Vw
S
-16-
ripple) caused
(Nabla)
operator,s
The
the various
term
by也e
on
the
collision and
ⅠⅠ.2 Rate
Equations
integrating
for Particle
(ⅠⅠ.
7)
Bq.
ns(T',i) seee.ど.ref. [6]
,
Densities
over菰yieldsthe
pp. 155-159
or
balance
or
rate
for the particle density
equation
ref.[6] :
登.7･(n8<品8,,-倍】cR
'ⅠⅠ
･9'
<あ>
where
is the
I(,,i) of the plasma
(r, i) has
two
as
mean
species
a
whole
3o
to
part
one
,the other
the particle
represents
thus
h8Ve
relative
the peculiar
and
introducethe
is
a
random
and
<78>
of
-0,
<.Vs (r, i)>
is
hydrostatic
zero.
pressure
This
p.
E:
latter
We
(II.10.a)
-i..予e(u)-uo(r･ i). <v8(r･ i)>.y8(r･ i)
(II.10.a)
>
<w-'>=S.+<S
8
because
to品.The vector苛8
velocity
average
yieldsthe
E=
E
3s
diffusion
mean
7s(r,i) whose
velocity
to heat
due
motion
the
local空室近Velocity'7T.
mean
V)8(r, i) relative
velocity
originating from
one
contr･ibdions,
We
velocity.
e
and
∑nsmB<wi8> ∑p8<註s>
i. (r･i)=
S
∑
∑p8
ns,ns
8
Note
(II.10.c)
8
8
that
う
∑n8m8<V8,-0
∑n8m8<Ve,<ivs,≠o
and
S
the Eq.
Then
う･
【
(lI.10.a)
S
(II.9) becomes
登･7･(ns?.,･苛･(ns<.v8,
[登cR-Iw
㌔ws[警】cR
(II.ll)
,-
β
t7oand
forces
<7s>
acting
For
depend
on
in acomplicated
manner
on
the particular
collision processes
and
the
the particles.
the electron
density
hare
we
in particular
the rate
equation
登･音･(ne3J･亭･(ne<ie,
[登]cR
'ⅠⅠ･'2'
,-
辛
one
,can丑iso由蜘duce
p-eculi･au !a-nd mean
a
mean
velocities respectively
by w'+s=iz,.+
ans/at+守･
(ns品)+v?
(ne<邑>)=_[an8/･at]cR
(niu.)-馳/胡電R
ぬJ7i8汁守･
･because 8Ens <5s> =(o a･･nd.sEn8 mS <Vs>均h,tThen
These
･
differences
by亀=sEns <38>/sEn8
local幽velocity
but
in analysing
m呼b'e'冊.:important
-17-
5s
,
<
w8>
=
Us>.
<
ZLo+
(compare with
and
≡巴
≡コ
Eq.
(J･l.14))
う
<菰>
≠
<v･8>.
par't'iclevelocities
and
nuxes.
the
The
h･
12) describes the instantaneous
of Eqs･ (ⅠⅠ
･1L,
(respectively ne) changes due to collision and radiation
r･
The
local rate
S･
the density
which
sum
processes.
Summation
ofal1
density
sum
of all volume
ionization
rates
rates
reのmbhation
(Il.ll) yields the following
equations
]
of all volume
rate
'II
one
:
n=8En8
the
on
writes
r.
飢Im
h.
all the individual
s.
dissocation
sum
This
rates
volume
sum
rates
(II.14)
of all atomic
sum
rates
rates
recombination
recombination
rates
of all volume
particle capture
nuclear
●
also be written
can
obtains
of all volume
of all volume
particle creation
la8もequation
one
sum
of all volume
ionisation
sum
terms
Of all molecular
volume
nuclear
･L3'
for the total
equation
冨.苛･(n3o,･字音･(n8
<Vi8,,-臥
When
tis
of Eq. (II. 12)writes
r.h.s
particle
with
in the followlng
rates
form
COmPaCt
:
an
【冨】cR-t架】cR･t箸】cR･
(lI.16)
nucl
∂t
the terms
where
the
on
h.
r.
account
respectively
and
disappearance
of heavy
and
disappearance
of electrons
(iii)creation and
disappearance
of particles
Plasma
and
(i)
creation
(ii)creation
exhaust
the boundary
In the
equations.
which
corresponds
At
this point
●
the rate
a
from
is conserved
because
inany
and
drive
be accountcdfor
must
sinks
r.
onthe
to add
case
for the particle
that
nuxe5.
or
For
disappearance
energy
transfer.
during
and
a
be
can
is created
photon
sinks
terms
the radiative
of the particle
These
term
localsource
a
density.
instance,
The
either in
h. s. of the rate
the collisional-radiative
(the electron) disappears
the plasma).
for three-body
rate
to mention
to particle
particle
in pressure) which
ln the rate
energy
leading
for particle
equations
difference
be useful
has
one
:
reactions.
heating
terms
source
additional
●
process
to I!SCaPe
assume
it may
to nuclear
additional
local deposition
to the
OffoTCeS
recombination
as
of pellet fueling
case
●
the orlgln
or
due
Processes
(atoms, molecules)
particles
injectionfor
particle
conditions
for the followlng
●
s.
(which
a
represents
lead to forces
in
sink
(e.g.
to
we
a
the fluxes.
also
recombination,
the third body
an
electron
(an electron) takes
-18-
disappears;
over
the
however.
thermal
the total
energy
of
the recombining
taken
electron
by the
over
third body
●
energy
lS
nuxes
too.
lI.3
not
From
but
COnSerVed
Rate
Equations
Eq.
the internal
and
in form
recombination
of translationalenergy,
for Mass
for the
follows
(ⅠⅠ.9)
a
causlng
all the energy
increase
pressure
is
that the thermal
means
which
●
increases,thus
Thus,
energy･
drive
can
which
Density
density
mass
ps=msTLs
the
Of species``s"
rate
equation
倍]･亨･bs<w+s,,-倍]cR
(II.17)
In the
absense
Summing
of nuclear
all, Eqs.
up
holds.
【aps/at]cR=Tns 【∂T8s/all
cR
reactions,
(II.17) yields the
rate
for the total
equation
density
mass
p=sEps.'
(II.I8)
冨･苛･b3.,-[引cR-【警】cR
In the
In
absence
D-T
a
The
of nuclear
[annucl/al]cR
plasma,
The
(lI.17, 18).
by adding
or
Conditions
forthe
accounts
injectionand
effect of particle
boundary
lan,1uCE/∂t]cR=0.
reactions
change
is taken
into
source
terms
Corresponding
due
mass
of
exhaust
to
pellet
from
of the neutron
escape
injectionis
the plasma.
by chosing
account
(sinks)
on
the
into account
taken
r.
appropriate
h. ら. or Eqs.
by
additional
terms.
source
II.4
Coupling
Assuming
of Rate
Field
and
Fs(r, i, w-Bs)iobeknown
Equations
one
Lie(r･i,-n8<as,
-
can
the density
calculate
I
wi8
of the diffusion
Fs(r･l･ as)･
nux
:
(ⅠⅠ･19)
_"d3ws
S
W
Multiplying
density
●
by the charge
qs and
summlngall
equations
⇒
∑ psns<蒜s,--e.ne<亨e,.
S
Eqs.
The
is the
the total electric current
:
J'(r,i)where
"s''yields
1
(lI.10.b) have
(Ir.1) and
toroidalcomponent
link between
the rate
been
applied.
(ⅠⅠ.20)
represents
of Eq.
equations
∑ e.zk,inlk,i<Ⅴ乙`,(II.20)
the plasma
density.
current
for the particle densities
and
the
Eq･
(lI
･20)
electromagnetic
●
Tleld equation?.
wh｡n
momentum
i) multiplied by
j:(r,
neutral
transfer
particles
are
electric voltage yields
=the
十>
are
absent,
and<Vk,;･Z>
<Ve>
throughColomb
collisions and
_19-
L2,
Eqs.
see
exclusively
the fields acting
on
(ⅠⅠ.51,
54)･
determined
the particles･
by
ⅠⅠ.5 Rate
The
rate
density
･う･
in Eq. (ⅠⅠ.7)
Fs byれs
of the species'.s"
ps
Density
for the momentum
equation
by multiplying
density
fTor Momentum
Equations
Ws
the
and
density
mass
rate
general
becomes
of the
over
Gs.
p of the
plasma
we
densi.ty ps
as
The
mean
The
r.h.
describes
s.
is de{1ned
<範>
value
Every
of the
of change
be split intoもwo
It may
density
terms
momentum
system
non
Forinstance.
(II.21, 22).
iq.ected
and
particles
Multiplying
equilibrated
Eq.
particles
by
(ⅠⅠ.L7)
<i3s>
?s=ps<亨s
The
component
The
first term
term
For
psxx
is
is, for
related
is related
a
Species'temperaもure
to the
Ts
kinetic
kinetic
velocity
and
Psyy
Psyz
Pszx
Pszy
Pszz
by ps,x=ps
diffusion
energy
due
of
(ⅠⅠ.21)
yields the
[
(Il.23)
at
introduce
the
(ⅠⅠ.249
<V8>
energy
to the
x
<Vs>x+ゐ<JVsx･VsE>.
in x-direction
random
･(位L鈎.ps<Vs>2x),
veloc主b3 Land
represents
rthe followirlg rel如ions
(hy血os'tatic)iP故地圭d'IPZi戯ure
-20-
s.
system.
dist癌buもi'on function
the scalar
h.
Psxz
Psyx
instance,given
to the
maxwellian
Vs,-(
r.
neutralbeam
Eq.
result from
) and
tらe hydrodynamic
terms菰=?o+7s (see Eq. (ⅠⅠ.IO.a)
<p?sfor
flux tenser
the species ･･s"with the components:
P8ぷPsxy
to the
between
<3s,亨･ (ps<3s,'-ns<?s,-ps
ps写･守･
momentum
the
laboratory
the
in principle
'II
･22'
by the CR-term.
subtracting
in
to collisional-
due
]cR
β
transfer
is described
and
"s"
species
'p8<誘sa8,'-
r,ut i｡
contributes
the collisionalmomentum
plasma
for the
of motion
process
volume
(II.21)
:
孟b8<3s,
,】cR-<h,s,
spatially
energy.
by
whole
also Eq.(ⅠⅠ.31.a).
a<w>>
second
mass
孟bs<;s,
,jcR
S
by Eq. (ⅠⅠ.10.a),
see
the rate
again
processes.
radiative
we
a
obtained
the
in the laboratory
<w.s>
｢>
..ー
言bs<as>)+V･b8<蒜s諒s>)-ns<声>=
equation
introduce
:
∂
Eqs.
is
"s"
species
p=sEps.
,
for the momentum
equation
<w.8>
ms
integrating
and
ps=nsms
The
ns
Ps
holds
:
between
the
heat
l
旦hT=_帆
2
2
$
1
1
TL
2
(II.25.a)
<γ2>=__,a
S
S
sにγ$2fs(3s,#vs
S
■
Tlle equation
is glVen
or state
by
the scalar
and
of the plasma
pressure
(II.25.a)
kTs
ps-ns
as
a
by
whole
(II.25.c)
p-Zps
S
Thus,
●
the scalarpressure
ps
hence
p8=Ps<vi83s>;
Making
･p8<･Ns,･γs,,
p8-吉bs<vsx
-+
of the relation
use
of the hydrostatic
components
:
γsx,
･
of the diagonal
to each
equal
く-i
Censor
pressure
IS
p8 <YsVs>=p8
･ps<γsz
->
-)
(II
,
･γsl,
->
<V8>
<y+sy''s>
<Vs>+ps
,
･25･d
the Eq. (II.23)
becomes
(II.26)
The
rate
for the momentum
equation
transfer
the Eq. (II.21) overall
summing
"s".
species
of the plasma
If follows
as
8
the rate
is obtained
Whole
by
equation
∑
孟bu･o,･亨･鴫uiJ･V?･FF+._,-ほpu･.]cR
(Il.27)
n8<
⊂:Eコ
with
the
density
mass
the
p and
Censor
nux
momentum
P
●
for the plasma
as
a
given
whole
by
P=sEP8
(a)
p=sEps
■⇒
or P
the components
where
.
by
glY8n
are
(b)
P∬
Ply
p=(
Pp
Pxz
(II.28.a-c)
PガPyz
PzxPlyPzz
Eqs.
Because.f
scalar
pressure
the diagonal
(ⅠⅠ.10.a)and (ⅠⅠ.25.d)
The
p
plus the totalkinetic
the local vector
results
The
h.
r.
s.
i芦Submitted
diLrerent from
force equation
Eq.
appliesthe
an
external
zero.
irljectionis
The
due
zero,
isotropically)alone
distributed
to
one
total
(1/2)sEps<V>2･
energy
for the plasma
is generally
of七his equation
to be
(assumed
when
;'representthe
of
as
a
by
(ⅠⅠ.L8)
multiplied
particle
increased
to
a
non
and/or
toroidal
vanishing
Since collisions and
cannot
nu又, the
photon
rotation
value
-2l-
of
a
radiation
3o. However,
modify
r.
h.
s.
tokamak
of this term.
ilo;
iも
:
whole
e･pv･o･7-v,.･"一字ns
<Fs,-婚cR
p
particle
be simpliTled
can
Eq. (ⅠⅠ.27)
diffusion
components
In
processep･
when
a
can
of Eq. (ⅠⅠ.2g)
during
plasma
such
a
case
(II.29)
plasma
become
tangential
the
non
イL与
diagonal
of P
components
We
will
laboratory
have
can
a
l∃q.(ⅠⅠ.29)
to modify
use
frame.
The
TlrSt term
influence
great
the velocity
on
the Eq. (ⅠⅠ.26).This
(friction).
last equation
is, for instance
Of Eq. (ⅠⅠ.26)
refers to the
of two
composed
terms,
=E
/al=psav.o/al+psa<Vs>
psa<w.s>
as
plasma
a
and
the second
whole.
that part
eliminate
one
for
accounts
Bq. (ⅠⅠ.26)
; one
resulもfrom
is due
one
a
to
velocity
to changes
is connected
which
the
subtracting
/aL, the first
3o
of
a
velocity
by
to v+o.
relative
change
of the
change
Eq.
multiplying
we
can
by ps/p
(ⅠⅠ.29)
obtains
(II.30)
the
represents
which
with
the
mass
3o.
velocity
of the velocity
The
equation
The
term
on
the
a
system
coordinate
l.h.
s.
movlng
for interactions
account
<Vs>.
from
is calculated
<wis>
velocity
fourth
third and
●
in
-･与
flelds司)and
mean
"s"
of the species
of motion
(ⅠⅠ.βJ.α)
vsFs(r･E･ Vs,dVs-uo+くⅤs,
･w.s,-3o･去Iv
S
the
and
is given
term
by
>
a<w.
S
】cR-去I3
-sW-s[警】cR
(II.31.b)
㌔we
∂f
S
The
values
of
ⅠⅠ.6 Rate
A
[aFs/at]cRdepend
Eint stocked
ll.6.1
The
heavy
in the
excitation
quantum
The
cross
sections.
Density
of density
energy
ionization
to establishもhe
simplesもway
(molecules,
Etr and
internalenergy
(dissociation) levels.
We
of density
will first consider
the
atoms,
rate
equations
isもo glVe
ions, atomic
molecular
all internal
ions). Thus
energy
the
electrons
to the
possess
energy.
EkZ,i be
the
state
ii>.
definition
Colomb
Energy
Internal
translational
Let
and
(molecular) and/or
Dint.
governlng
particles
only
Energy
possessesもranslational
●
equations
the atomic
for the
Equations
plasma
on
of
internalenergy
Ei,iis
●
given
of
a
ionized
I-times
in Fig. 6 where
-22-
we
have
particle
assumed
of chemical
thatもhe
species
"h!･ in
energetically
lo＼∫_･ststate (the "reference
When
can
atoms
originate
role in the energy
the molecular
the walls
stages
The
the
El,i COntains
energy
the
when
of species
"k" ) is the atomic
molecular
internalenergies
●
is given
state
the
by the ground
for D2
case
The
be taken
must
molecules
state
aムdfor hydrocarbons
can
off energy,
radiate
●
state.
energy
found
a
play
of
near
therefore
into account.
sum
of the ionization
energies
of all lower
lying
of ioniz8tion.
totalinもernal
density
energy
h
&
``s"
stands
for
of all heavy
particles
■
is then
given
by
∑∑∑ nzh濁…∑nsE!nt-∑豆s如
a-int-
where
the reference
in tokamaks.
state
species,
and
is for instance
limiters
of carbon
for the internal
molecules,
then
This
system.
imized
from
balance,
their internalenergy
For
state"
s=(I,
h,
i
i). E8lnL
s
is the energy
i).
-23-
(II.32)
s
density
of
a
particular
species
s=(a,
k,
pQrlic(e
Levels
pQrl
with
I
oI
l'cks
z=0
Reference
stQte
≡.rod,wjERQQ.teem
:
Fig･
6
of the
Definition
element
internal
h in quantum
Ei. or
energy
state
Ii>.
When
a
I-times
nuclear
ionized
reactions
particle
of chemical
become
important,
Z
r･･)1ativistic
energy
mh･
C2
must
be included
-24-
in
A氏即ref･
E;.,･.
【7】･
the
Since
the excited
ionized
and
internal
energy
is thus
internal
energy
(sometimesalso
density
of internal
internal
density
S
S
at
is identicalwith
which
species
follows
the
Eq.
from
i).
The
rate
the flux
of the
equation
(lI.9) by replacing
the particle
:
nsEsl'nt
an
･亨･(nsEsint<w-s,
i
,-
int
E
S
i
S
'II.33.a'
cR
at
expression
inf
E
an
;･S･(n8<w･8,
,ii I
E8int[
S
8
-
in the parenthesis
the expression
of the 1. h.
an
terms
equation
for
the particle
density
energy
density
ns
$
by
the l.h.
``s"
all species
of
lh. (ⅠⅠ.9)
yields
int
to the
"s''is equal
energy
the rate
yields
'II.33.c'
of species
energy
by the internal
multiplied
s.
8
the internal
equaもionfor
over
Eqs. (ⅠⅠ.33.a)
Summing
ら.
lcR
Esint[箸】cR-
the rate
･.
In other
E
'II.33.b'
cR
at
substituting
the
of
be
<w+s>
n8Esint
h,
With
the transport
describing
s=(I,
int
E
an
then
density
energy
flux vector
the
in space.
candifruse
``reacもion energy").Let
with
"s"
of species
by the internal
ns
termed
they
mobile
particular
associated
density
energy
a
associated
energy
are
particles
E8inL of
equation
Dne
rate
Parもicle･
for the totalinternal
:
誓･亨･
[?E-sint<as,i-[誓】cR
(II.84,
The
in the parenthesis
expression
【
the species'density
】contains
diLrusion
mean
:
velocity
∑言sinE<wl+s>∑ E8LnLn8G.+
S
where
and
3o
nsE8lnt
is
nsEsinL<Vs>
is
a
a
nux
一事
)
<v's>
(ⅠⅠ.35)
S
nu∑ vector
vector
the plasma
associatedwith
tr8nSpOrting
internalenergy
as
in
a
a
whole,
coordinate
whereas
frame
moving
ilo.
with
we
n.w
define
a
nu又 vector
Q.sint=n
The
nux
vector
representirtg
the
the
a?6intfor
S
transport
of internal
energy
relative
Eint<亨,…豆int<亨,
S
transport
S
S
of the whole
辞nt=∑ 5s山
Jo by
(ⅠⅠ.ββ.α)
S
internalenergy
to
density
is
(lI.36.a)
S
Thus,
the Eqs.
(II.33.a) and
(II.34) become,
respeLCtively
誓+亨･
(ETsint;J･呼斗誓]cR
(II.37.a)
-25
-
誓+ぎ･(E-int3.･iint,f誓】oR
(II.37.a)
The
h･
r･
of these
S･
rleld, since
the radiation
density
a
The
<乾>
And
The
energy,
and
associated
diLrusion
also五neanS
as
a
with
●
energies"
wholewill
directionaland
these two
random
types
kinetic
is generally
small
have
generally
velocity菟whosea,verage
is
(1/2) p8<V6>2.
energy"
but
not
directional
some
Particle
of movement.
of "diLrusion
zero;
kinetic
is relatedto
zero
the
velocities and
energy
heat
and
Eqs. (ⅠⅠ.25).
F8 in
Eq. (ⅠⅠ.7)
by
for the Censor
of twice七he
equation
"s''in
are
finally, the random
multiplication
the rate
of radiation
energy
II.6.5.
betweenthe
``diffusion kinetic
the plasma
See
pressure,
distinction
a
Which
of all these
(1/2)LWo2.
species
to make
energies
furthermore,
andwith
the totalinternal
chang色of
(thermal)and/or
in Chapter
energy
Energy
of velocity
sum
of tran$1ational
change
the translational
with
radiative
二-
translational
difrusion
collisional-
will be given
ⅠⅠ.6.2 Translational
lt is useful
any
●
Details
versa.
vice
to
EL-nE leads
the coupling
ensure
equations
of
the laboratory
Tn8i3s3sand
translational
thaもis
system,
integration
the velocity
over
(or kinetic)
yields
density
energy
of
:
(II.38)
owing
Eq8. (ⅠⅠ.10)
and
⇒
tothe
5?sand
aflux
this
(ⅠⅠ.24),
q8かforthe
species
tenser
equation
canbe
deTlned
"s"
as
expressed
a
function
(II.39)
岩E:E:
<v8VsVs>
geLr-pe
the development
of the various
Eq. (ⅠⅠ.38)
becomes
terms,the
and
by
E
A氏er
3o
of
:
58 3o.?s)
孟bs3.3.･p$3.<7s
,
･ps
<
,
3o3o< 58>
･亨･tp8 【i杭3o･
･3.<Vs>3.･ <7s>3.5.･ <v.Sit.Ss>])
(II.40)
■>
2ns<F.e,3.-2n8
･亨･や硫･Ps3.+繁り-
The
terms
<F.s78,
]cR･ほFs]cR
-ほpsv･.u･.]cR･ほps_<7s,屯】cR･ほps3o
have
(a/8t)p晶3oand
the following
-+
V
･
b$ 3o
v.o
●
meaning
3o) are
connec七edwith
-26-
the temporal
and
spatial
variations
of the
kinetic
a
"s"
due
the species
"s"
are
counter
part.
of the species
energy
in which
whole
to changes
ofもhe translaもional
imbedded.
The
ヰ⇒
(a/ al)<p?sand V Qlrare connectedwith
theもemporaland
･
energy
the
ofもhe
h.
r.
is the
s.
･ナ
to
relative
a
t･he tensor
twice
represents
moving
Vs relative
with
7To;
to
With
3o.
The
of the kinetic
lasもterm
on
一事
done
of the work
force Fs by the
againsもthe
for
tensor
the corresponding
movlngwith?o.
=岩
The
movlng
-2ns<Fs>ちis
●
particles
variations
counterpart.
collisionai-radiative
･･･}
particles
spatial
as
plasma
is the
the r.h.s.
on
●
frame
coordinate
of也e
ナ>
Vs>
-2ns<Fs
``s"
species
first term
energy
term
E
ns<F8
All other
"s,,
the nuid
When
V8>
･
terms
one
translaもional
of kinetic
represenもchanges
moveswiththe
density
the power
represents
and
for all species
the Eqs. (ⅠⅠ.40)
sums
density
enばgy
∂⇔
of the plasma
thermal
as
a
"s"
whole
heating
to ohmic
in the nuid
<7s>
velocity
due
ofall
one
due
energy
other
of the species
to the
facもthaも
species.
the Censor
obtains
"s''.
of twice
the
:
(∑ps<芋s3.?8,
豊嶋3J･蒜P･V
(p3.3.3.,･亨奇r･守･
I+
,
･
S
S
where
hasbeen
use
The
rate
obtained
by
expression
made
8
-ほ鴫v･.,]cR･ぽ】cR
(ⅠⅠ.10d).
for the translational
equation
taking
o柑q.
the
trace
(Il.41)
∑花s<F.s,3.-2
∑ns<Fis苛s>
･亨･Q.F･Fg.)-2
ofEq.
energy
(ⅠⅠ.41)
and
density
dividing
by
of the plasma
two;
this
as
a
is
whole
leads to the following
:
￡(吉pu.2)･
￡(Trace三P)･守･(三pu.23.)･Trace
i;7･寄Lri
(P3o,i
,･主音poP,･主音･
･Tra梯(亨ps<Vs;oVs,
-
No
(Il.42)
! ns<#s, ･3oや<F?a
･7s,-ほ(吉pvo2)lcR･ほTrac胡c
have
approximations
cqntipuity equatiqn
been
for the density
Th.e individu?i_ Trace
so
made
of the
terrr!S of Eq.
far.
Thus
Eq. (王Ⅰ
represents
･42)
translationalenergy
(.II.42)writewithout
-27-
of
making
a
plasma
the full
as
a
approximations
whole･
:
(;pl-芸p･韓8<Vs,2
･-ce
-亨･Qh･S･
(;v'･を‡
(韓s<v8,2<vis,,
(II.43.b)
･-ce
the
with
heat
thermal
(II.43.a)
athgivenby
flux vector
∑5nhT<V>
2
盲Lh-
≡∃
∑芝ps<v.s,8
S
β
(II.43.c)
S
β
(吉子･(ail)
-音･(芝p3o)･才･
(吉ps<vs,23.,
(II.43.a)
･-a
(?v･.,
-亨･(掬)-吉i･･
‡芸才･
(P3.,)
(P3o,
(吉?･3o)-吉v?:
‡吉:v?
i
･亨ps<v.8;ov.8,
(ⅠⅠ･43･e)
･--
･-ce
In
the trace
calculating
associated
--v>
have
we
the "di触sion
with
kinetic
(Il.43.I)
･
of the Eqs.
use
made
(ⅠⅠ.10.a).We
The
energies".
頑
now
Eq. (ⅠⅠ.42)
thus
terms
neglectal1
reduces
to the
●
following
expression
(喜pv.23.･盲Lhi･v?･(芸pv･.)
孟(吉pu.2･言pi･亨･
(II.44)
n8<F?8･Vi8,-[豊吉pvo2]cR･ほ芸
-!ns<F.s,･3o-i
項
The
is submitted
plasma
term
of the plasma
to
an
[ (∂/∂t)pvo2/2】cRis only different from
external
flux which
energy
via collision and/or
increases
the
the kinetic
when
(1/2)puo2
energy
thus
processes,
radiation
zero
￡吉pu.2】cR-0
except
casesinwhich
of the
kinetic
The
One
synchrotron
escape
transitions
thermal
fn)m
(spontaneous
plus
ionization
【(a/∂t)3p/2】cR
,
processes
[ (∂/∂t)
3p/2]cR is for
term
to this term
radiation.
can
volume
･45,
responsablefor
an
increase
(1/2)pvo2.
energy
contribution
which
are
(ⅠⅠ
originates from
Free-free
transitions
Another
the plasma.
tedombination).
energy.
the disappearance
The
free-free
transforTnS
contribution
The
photon
thermalcontribution
of ionization
-28-
a
energy
plasma
always
transitions
thermal
different from
(bremsstrahlung)
energy
into photon
originates from
hγ created
to
in the
2;ere.
and
energy
fl･ee-bound
in this event
hv is taken
radiates
recombination
into acco･Jnt
process
off
in
is taken
into
in
account
r･h･s･ of Eq･ (ⅠⅠ
･44)
thI･ee-body
and
a
newly
created
three-body
as
appears
which
apositive
term
beam
to the plasma
the r.h.
of Eq. (ⅠⅠ.44).That
ら.
of the
h.
r.
s.
It is evident
as
that
a
kinetic
ther血alenergy
as
a
in
one
negative
which
is taken
isthen
is tr&nsfered
energy
to the
contributes
energy
(pvo2/2)
this contribution
beam
rate
beam
whole
h
leads
to
into account
terms
on
increase
an
in the first
lost for the
heating
the omission
of the
the energy
balance
process
(3p/2).
proper
In the present
diagonal
context
T
contribute
●
are
it may
of POcan
components
viscous-stresses
Censor
The
plasmas.
of theneutral
part
heating.
tothis
of Eq. (ⅠⅠ.44)
and
s.
in
consumed
for the internalenergy.
equation
to heat
of the plasma
energy
h.
r.
due
into
isもransformed
via collisions, i.e., a corresponding
particles
of directional
term
of the rate
in)'ection is used
the
on
contribution
decreases
temperature
the
on
thermalenergy
is not
energy
term
ionization,
consume
processes
Thermal
internalenergy
process,
Neutral
howeverthe
last
The
to collisionalexcitation,
ioni2;ation
and
whiTCll is increased.
electrons,
recombination
due
rates
Excitation･
recombination･
to the proTIt Of intern-al energy
heating
energy
containsalsoall
internalenergy.
for the
term
be useful
have
to the
to remember
that
consequencesinevaluating
The
transfer.
energy
components
of･the
non
When
viscous-stress
●
glVen
by the following
relation
∑ rs,qp--
Tqp--qp-
∑ bs,qp-ps64,)
8
S
∂4
where
-字【ps<vs,ays,p,一言ps<vs,￠v8,a,
is overall
the summation
components
x,3,I
a,
and
"s".
species
Sap is the
F'urther,
Kroneckerdelta
a
and
P
the three
represent
symbol
64-(:≡:≡p?
II.6.3
Thermal
Changes
Energy
of the thermalenergy
described
are
Censor
by
the
change
of the
subtracts
from
momentum
flux
【≡】
EE
Palone.
To
rate
obtainthe
(ⅠⅠ.41)
the
two
Censor
right hy 3D
and
Eq.
equations
are
which
fromもhe
(ⅠⅠ.28)
for P
equation
one
obtained
lefb by 3o.
when
The
Eq.
resulting
the Censor
equation
(ⅠⅠ.27)is rr▲ultipliedfrom
equation
the
writes
Eコ
aji'
亨･Qr･才･
-+
∂f
Js, )･P･igo-3.7･軍
∑ps<亭s3.
‡v'#･
S
一字n8(<F?s, !
3o-3o<F?s,
,-2
-29-
(II.46)
ns<-F's
vs,-鮎
The
by taking
for the thermalenergy
equation
rate
from
trace
Eq. (II.46) the
density
dividing
and
of the plasma
two.
by
The
as
is
awhole
result is
obtained
:
1.+
孟(芸p･手芸p8<V8,2)･亨･(芝p3o･qth)･守･(∑吉
,2<7s, ).
-∇
2
8
;(p
･4乃
･吉P:73o一言甲:?T享n8<F)e･7s,=ほ言p]cR
Since
rate
we
no
for
equation
have
introduced
th占totalthermal
plus
of Eqs. (Il.43) and
use
made
been
have
approximations
Eq.
neglect
kinetic
equation
represents
"
energy
densities.
the
In
all contributions
exact
Eq.(ⅠⅠ.47)
of
(ⅠⅠ･48･a,
‡三3.?
･?i-去u.･守‥軍
･-now
"diffqsion
this
:マ3o
(三軍･v78.i=吉p7
･raα
We
far,
so
associated
the ``difrusion kinetic
with
energy''.
(ⅠⅠ･48･b,
Then
the
(lI.47) becomes
(II.49)
￡(言p)･苛･(言p;o･4Lh)-io･?p! ns<is･Vs,-は芝p]cR
This
be
can
equation
in
written
useful
other
8
and
put
ゐBy
using
the relations
aT
-
+
∂1
now
make
use
or state
(II.50)
(II.51)
=≡二
=≡コ
∑n8<F8･V8>
,the
Eq.
(II.49) becomes
3
?.
2
2
-kT聖+旦nkao･苛r+旦kTV7･(nco)+守･苛th
∂t
･kTn-v
We
equation
･苛n=-sk舟(nco)+nkTWoand
-hT3o
3
the
8
【∂/∂t
3p/2】cR=(3/2)nh 【∂T/at]cR+(3/2)hT[肋/∂t】cR
-nh
2
apply
density
power
ohmic
We
∑ pe= ∑托ehT8=nkT
p-
for the
forms.
･
(II.52)
;]cR･;kT[=]cR･i
8.-言nk
of l弓q.(ⅠⅠ.L4)
and
obtain
旦nh竺+旦hnao･JvT'nkTV?･3o.苛･首Lh一旦k絹･(∑
'
ns<∇8,
2
∂t
2
2
β
(II.53)
=anh
2
The
fourthand丘托h
following
"rate
terms
equation"
can
be contracted
for the
(see the Eq. (ⅠⅠ.43.c)).We
T
temperature
-30-
:
thus
obtainもhe
3
aT
-nh-+
2
,･守r･∑ nsk<予s,･む･nk掃･i.
∑芸n8k(8o･<Vs,
at
8
S
(Il.54)
-芸nk[;]cR･ゐ
Bo+
where
<-ds>,
=
<Vs>
in the laboratory
Eq.
see
(ⅠⅠ.10.b).We
the
introduce
density
of the diffusi.n
nu又
by
system
?s-n8@..
-チ
(II.55)
)-ns<1ws,
<V8,
Then
芝nk冨･;k!(Ps
･言ns<予8,
･-hnkTS･3o-芝nh[;]cR･占
(1I.56)
The
Eq. (II.49)
into
be put
can
another
form:
useful
ち.'vp-孟(芸p)･守･(
∑言hTsf8)-∑言kns倍】cR･∑;k
(II.57)
S
We
innuence
be omitted
cannot
terms
corresponding
Ill.7 where
more
Total
The
rate
as
a
a
We
density
and
a
the
neglected.
details
see
their
in
diagonalcomponents
non
Eqs.
When
complications
the
and
(ⅠⅠ.85)and
(ⅠⅠ.84.b)
Chapter
-I
to determine
vo.
internal
and
whole
andthe
energy
sum
The
plasma
as
to the
is equal
densities.
Only
of the thermal
Of physicalrelevancy.
will hardly
density
the
energy
equation
obtain
the rate
of the rate
equations
equations
for the
corresponding
internal
and
sum
densities
energy
for individual
for the plasma
species
"s''is too
be applied.
the Eq. (37.b) to Eq.(II.42) and
add
of
applied
for the total energy
equation
whole争re
complex
is
account
been
is not dif{1Cult but introduces
further
For
have
into
take
must
stresses
Energy
for translational
plasma
one
complex.
Eq. (II.57)
ⅠⅠ.6.4
to viscous-Sheer
of Eq. (ⅠⅠ.47).This
applications
makes
as
effects due
that
remember
a
whole;
this equation
-31-
writes
without
equation
any
for the totalenergy
approximations
:
孟ほpu.2･ ;Pi
1
･v?･ほpu.2b'.･
E-int3.･L6"i
+T-ceほ亨･5>1
a-L'nL･T-ce
(II.58)
n8<?s, ･3.一品
･Traceほ亨･(享ps<vi83.7s,,･芸才･(a#,･吉亨
When
を_a:_:nl.隻_
-は吉pv.2]cR･ほT-ce喜P]cR･
the diagonalcomponents
only
from
contributions
following
the "diffusion
iS
OfP
kinetic
derivatives
1their
and
are
retained,
and
neglected, Eq. (ⅠⅠ.58)leads
energy''are
to the
:
expression
･号･‡喜puo23o･
･3o-a
E-inti
E-int7o･芸p3o･-81h･8inlト
i(;
(I.I.59)
-は吉pv.2]cR･ほ言p]cR･ほiint]cR
●■
Apart
on
from
the r.h.
When
s.
one
is
is only
rate
corresponding
i.e. the
zero,
Eq.
interested
equation
beam
(e.g. neutral
particularsituations
the first term
irb'ectionor curren七drive)
holds.
(ⅠⅠ.45)
in
the thermal
plus
the internal
density
energy
the
approximations
writeswithout
-t
｢‥-I-'''-nT叫一
.
【.
･亨･
孟‡
aP,i
(ETL'nL?.･4inL,･T--ほ亨･Str･喜
E-･'nL･T-ce喜Fi
_.1
(II.60)
･T-ce
In
the expressions
their derivatives
then
leads
l日L.
to
and
i;亨･(!
ps<ivs3oi8,,･吉夢･現一掃宮卜占
;.pIcR.ほET..Ij_∼ce
-はpTT?7
of声and
for'the
Traces
we
from
all contributions
(see also Eq.(II.83))
will omit
all
non
the "di飢1Sion
diagonalcomponents
kinetic
The
energy''.
Eq. (II.60)
:
･-
-A----一
言
5p
(芸p3.･
孟(芸p･
E-･'nt).守･
a-inL3.･#h･寄inL)-3.･
(II.61)
Thermal
energy
-ほ言p]cR･【孟E-LnL]cR･点
considerations
or
a
plasma
-32-
have
to be
based
on
this rate
equation,
because
changes
energy.
A
the
rate
simpler
Wewi1l
the processes
Collisional-
The
The
two
numerous
collisionand
to the
heavy
(h)
particle
h.
r.
onthe
Both
processes.
radiation
terms
collisional- radiative
Separating
parts.
terms
radiative
-
terms
Chapters
the
exist.
forms
of
of the rate
Ⅳ.
Ⅱand
Terms
Radiative
collisional
contribute
in
not
Particular
of Eq.(II.61).
(ⅠⅠ.14)
will be discussed
tit.9) and
does
to the
contribute
of the internal
of changes
considerations
which
of Eqs.(II.12, 14), (II.57) and
equations
independent
not
for energy
equation
discuss
now
r.h.s.
II.6.5
are
ofthethermalenergy
h.s. of Eq.
On
terms,
the two
r.
(II.61) into
terms
an
processes
superelastic
(e) and
electromic
be decomposed
can
by
be decomposedintwo
shall therefore
which
linked
intimately
are
elastic, inelastic and
the {1rSt term
the
of Eq. (II.61)
s.
a
follows
as
:
ほ芝p]cR･はE-inL]cR
∂ 3
; EPe
￠eta
where
instance
fromthe
density
energy
d8EnsTn8C2
which
causes
neglected.
nuclear
We
which
We
So
that
further
level of the
bealn
This
they
that
that
of kinetic
heatingthe
is
beam
no
decreases;
a
new
[apuo2/2at]cR
heating
(3/2)nTkTr,
beam
neutral
canbe
causing
additional
translationalenergy.
be taken
must
direct relevancy
no
もritons
and
and
rates
reaction
into plasma
in
for inヮ.
be accounted
nuclear
The
in the plasma
of deuterons
intense
mass
diLrerence
the
species
When
Fig. 6)
the
of the nelltrOnS.
neutralbeam
energy
term
has
complicationsand
must
reactions
co血in
energies, (3/2)nDhTD
the plasma
there
reactions,for
must
disappearance
neutrons.
all
internalenergies (see
8En8Tn8C2
appearas
and
nuclear
case,かt
reaction,
and
reactions
assume
nuclear
of the a-parもiclesand
a's
collisions
When
collisions.
of their thermal
assume
transfer
and
of neutral
causes
processes
shall
shall also
reactions
the presence
we
nuclear
the
D-T
additional
In the following
in D-T
disappeared.
amongst
superelastic
originate from
still
energy
disappt!arance
a
and
the a-particles
trito1一S have
and
injectionproduces
D･T
whereas
be distributed
must
the
translational
as
can
￡E-int]cR-￠eEa･p
In this particular
'nsc2.
In
immediiitely
deuterons
additionally
which
the amount
appears
to p
sink, the reference
or
8EnsTn8C2.
latter escape
v) for inelastic
of a-particles
source
by
be changed
α+
a7言Ph
contribution
production
energy
an
represent
must
A
processes.
radiation
α+
for elastic and
accounts
(II.62)
∂ 3
to the
atomic
In
into account,
and
molecular
prOper･
will
we
respectively.
assume
a
talk of
can
We
suLrlCient
a
temperature
{1rSt Showthat
of the random
maxwellisation
Te
￠eh=O
and
Th
holds.
-33-
velocity
Of the electrons
and
distribution
heavy
particles,
functions
The
elastic processes
due
particles
to elas.tic
is the average
veh
the heavy
corresponding
the
(ⅠⅠ.63.a)describes
to energy
leading
particles
for the
Withもon_eobtains
masse
for elastic collisions
temperature
and
me
･63･a'
one
is the electron
ne
between
electrons
same
to
amount
￠ela,h With
2m
lS
a
positive
Eq.
heavy
●
glVen
and
Ti.I..The
and
density.
and
of energy
electron
mh
●
The
the contribution
between
respectively,
are,
Te.
and
of thermalenergy
of the electrons.
￠e,aj
'ⅠⅠ
-ne言語yeh
whose
in
appears
and
movlng
(Te-Th,
exchange
loss
heavy
and
;k
for the electronsare
values
electrons
●
frame
coordinate
collision frequency
species
particle
a
tra_nsfer between
relation
･elqewhere
In
collisions.
of ￠eEa the
part
electronic
for energy
account
simply
particles,
tOthe
heavy
:
sign
3
(II.63.b)
'ne∑言三γe?言h(Te-Th)--￠eEa,e
iT
-
o25
lnh
Thus
￠ela=￠ela,
can
only
We
and
that elastic collisionsalone
means
which
now
will
radiative
account.
above
Thefollowlng
the subscript
electronic
thefo1lowlng
processes,
to p.
contributing
the
energy
density,they
species.
For
the inelastic, superelastic
shall be taken
processes
rate
to "ordinary",
apply
reactions
denote
arrows
●
k dropped)
the different
COllisional-radiative
below
and
the thermal
change
amongst
the processes
consider
(Symbols
processes.
a.
energy
redistributethermal
cannot
(II.64)
0
h=
e+￠eLa,
for the relevant
coefficients
doubly,
triply
･･.
excited
ioni2:ationand
3-body
excitation
with
:
collisional recombination
(II.65)
AZ'i''e
electronic
states,
:
S.a
b.
into
辞Al'1'1''e
de-excitation
and
C?..
+e
(II.66)
AZ(i)+e一手些A&∽+e
F..a
IJ
c.
spontaneous
emission,
induced
emission
and
due
photo-excitation
to radiative
absorption
A号.
AZ
u)
(I)+hv子.JまAZ
I)
AZ(tl+2hゼ_.く･
LJ
--
AZ
(II.67)
∽+hv子∫
()
( 1-^Zb･)AIZ]･
Al(I)+h㍉.-∼-
--7
t)
The
coefrlCient
effective
radiative
for spontaneous
AZ∽
de-excitation
rate
is ^ZljAZEj nZj
de-excitation
J-i
and
-34-
^Zij
･
Where
the optical
AZ.j･ is the
Fjnstein
:
factor for thisl particular
escape
d.
For
transfer･
radiative
when
by Holstein
given
procedure
is
all radiation
radiative
These
[8], seealso
completely
are
processes
Refs･
described
of
1 holds･
^Z&･
=
0.
A;u･=
has
one
a
the equation
:
photoionization
recombinationand
symbolically
intervenes
equilibrium)
to
according
(no reabsorption)
transitions
(complete radiative
stimulated
calculated
in 'which
[9] and
thin
optically
absorbed
recombination,
^Z&･ canbe
The
transition･
by
R.a+1
AZ(8+hy.Z一｣
一
A2+1(1)+e(II.68)
AZ (I)+2hγ.ZーAz+1
一
(1
(1)+e-
-JL;'1)R;'l
Al (i)+ hv.a
I
The
^iZ'1
effective two-body
is the optical
be estimated
procedure
of the
radiation
where
,
It
i-th continuum.
in Ref. [9]. RIZ'1 is the rate
given
ne
niZ'l
can
for
coefficient
(spontaneous) recombination.
radiative
e.
a
(1)+e-
into level i is AiZ'1RiZ'1
rate
factor for free-bound
to
according
AZ+1
recombination
escape
+hv.I1
dielecもronic recombination
effect is de-composed
This
simultaneously
with
particle,
excited
eleetrons;
two
individual
into
capture
electron
followed
excited
into
either by
an
reactions,
autoionlZlng
namely
or
autoionizaもion
excitation
Of the formed
State
decay
radiative
doubly
of the
one
of
ion
an
of
two
:
symbolically
'ⅠⅠ
･69'
AZ(w堂AZ-1炉*,A&AZ-1(i,.hv;u;.1
For
●
the internal
energy
of thermal
only
loose enel･gy
hower
(i)
are
ionization･
prlnCipal
point
The
off depends
on
leading
of view
to
u柳)
a
itself does
process
AZ-1
the population
the collision and
AZ-1
For
zero.
a,f･=iEi2;the
system
on
are
same
radiation
can
reduction
it i畠therefore
not
not
-35-
and
any
in
to the
(i)+hvび州･
which
The
The
to intense
to
radiation
reasonable
a
reduced
to separate
soICalled
in
plasma
can
quantity
AZ-1
be submitted
1o'紳)
electrons
This
u*卓)･
both
Al
to
internal
as
energy.
of A=-1
nJ!=･1
processes
AZ(i)
is lost
returned
loose
density
of n&]+.and
from
amount
u糊)→AZ-1
in particular
limit of the
the passage
Az-lu榊)→AZ(i)+e
in the radiative
involved.
thus
by
process
energy.
radiated
depends
coefficients
Increased
in the autoionizing
(or simple) ionization
the ordinary
●
lS
energy
form
energy
below
ion, the rate
corresponding
Al-1
D蒜ニ1
all levels (i,J) lying
of
density'
(/紳)and
collisional
rate･
From
a
"dielectronic
radi8tion〃 from
recombination
taken
are
excited states
transitions
radiative
throughthe
limit to
an
triply to doubly
the doubly
decay
recombination
radiationn
be calculated
calculations
for the doubly
suffering
limit.
recombination
ionization
abovethe
Similar
･･･
hold
arguments
states.
states
other
detailed
with
"dielectronic
model
this part呈〇ular
the
of AZ(i･)and
nil
excitation
In
states.
the densities
by electronic
created
collisions, canthe
without
(multiply) excited
exists between
relation
state
triply,
bound-bound
model,the
excited
the ionization
(multiply) excited
radiatively
following
doubly
a
excited
before
capture
from
doubly,
the effect of dielectronic
contain
below
state
When
radiatiton.
automatically
excited
from
when
a
de-excitation
spontaneous
for transistions
Only
i去toaccounもin
should
ordinary
bound-bound
usual
case
a)!"of AZ-1
u-)
:
●70'確
a
Cj付i
be_ expressed
_ー________ bythe
____._
Can
detailed
Saha
,_____._,__
by
invoking
the principle
D4J･l(by
,.A_ー1.A?eST･_i?蔓_-:_[L?_;Jl;･1_Iチ7[u･f
⊥L_ーー三__三
balancing)
equation
and
of
1
ど;ニ1
q･..iD;u･=.1
(II.71)
-
X,F･･(Te)
2g;
where
Itfo1lows
Ef
E;･.-.I
h3
1
-
(2n,nekTe)3a
x;･..(Te)
that
(ⅠⅠ.72)
I
kT
g,z･ニ1
D;,･..
1
(ⅠⅠ.73)
a;･ニ1-nぞn
(
e
2g; X;..(Te)
D;...A;u･-.-.I
The
level j- or A>1u-) is
A;uI･lnJf･-･hγTj･1･
■
The
density
power
total
density
power
by
obtained
In
radiated
overall
the followlng
transitions
electron
temperature)
Charge
ln
states
-
under
bound
a
radiative
+lw(fJ=･11
radiati払"
particular
type
(low electron
conditions
is
radiation"
AZ-1u串*)→AZ-1(i)
recombination
represents
particular
-
recombination
transitions
"dielectronic
to bound
be additive
are
AJ
dielectronic
It simply
can
which
LJ
radiative
consider
phenomenon.
radiation
excited
Will not
We
radiative
￡
possible
●
independent
simply
o打by
to this ''unperturbed
due
summing
C
J
this particular
transitions
asan
of bound-bound
density,
in which
high
only
involved.
exchange
the most
general.case
we
have
to write
(ⅠⅠ.74.a)
AZ(i)+BZ+a(h)年AZ+n∽+BZ(h)
submitted
to the
energy
condition
E(intemal
energies)+a(tran$1.
-36-
energies)
=
0
(ⅠⅠ.74.a)
In
a
charge
intoもhermal
for
energy,
resonance
or
thethermal
"1"
the
a
and
transfer
charge
is the
between
one
is changing
ioni2:ed impurity
are
rates
reaction
reacもionsinwhi6h
HO(i) in its ground
atom
neutralhydrogen
par-uly transformed
prlnCipalbe
the largest
of the internalenergy
sum
reaction
canin
However,
versa.
vice
quasi-resonance
nor
important
and
●
internalenergy
reaction,
exchange
the
neither
The
noticeably.
sum
of
most
AZ(1) in the ground
species
(l=1)
state
obtained
in
or
an
excited
state
state
(i>1):
(II.75)
AZ(1)+HO(i)
This
of the reaction
The
the
state
electronic
low
highthat
so
densities
eLrect of charge
to the
``charge
symbolically
have
neglect
Collisions
between
population
replaced
source
densities,the
Only
other
in
AZ-1∽
it mayalso
undergo
situation
similar
of
for
as
spontaneous
The
"charge
radiative
collision rate
exchange
decay
of
of reaction
recombination
rates.
radiation
exchange
recombination
radiation"
as
independent
an
high
at
heavy
in
(free-free radiation)
electron
(II.76)
+hv
brem8Strahlung
in laser
important
are
which
beam-
densities.
particles
ionization
The
of impurity
reactions
are
be expressed
as
corresponding
by
species
hydrogen
described
ions
by
can
modify
(II.65, 66) with
by H+.
term
rate
p of Eq.
can
(ⅠⅠ.62)
coefficients
thaもal1 collision
radiation
loss will be included
power
to bremsstrahlung
ぅAZ+e-
and
densities.
in the radiative
(tehnee:;1
i
inverse
and
Co11isionalexcitation
see-s
the so-called
leading
collisions
absorption
interactions
p18Sma
one
the amount
rate.
radiative
We
The
a
quite
be neglected.
can
reactions
exchange
electron-ion
e-
have
energy
process.
Inelastic
the
however,
is the probabilityfor
yields
AZ+a-+
h.
We
by
the species
A2(1) yielding
oLr energy,
radiate
collisions
electronic
consider
the bound-bound
We
may
internal
only
is increased
of hydrogen
from
to reionization.
is additive
will not
radiation
g.
away
by hyzii then
radiation''which
The
is taken
state
leading
electron
(ⅠⅠ multiplied
･75)
We
energy
redistributes
recombination.
at
A之-1∽
internal
amount
"j". This
it prlmarily
radiation,
the
:
same
collisions
dieleetronic
Only
noもproduce
partners
13.6/i2ev.
excited
●
does
reaction
AZ-1∽+H'
ち
processes
terms
and
the
cancel
contribute
now
energies
each
to甲Which
-37-
involved.
other.
may
a
When
function
one
(This has been
be put
into
of the particle
down
writes
demonstrated
●
the followlng
all terms
in Ref. [7】).
′ヽ
lorn
including
(sy) radiation
electron-synchroもron
●
■
unit
volume
One
the
on
h･
r･
S･
represent,
the
respectively,
(ff) free-bound
(fb)and
,
power
radiation
bound-bound
per
(bb)
●
has
synebrotron
-RSy-iff-ifb_丘払
is 一ost due to free-free
which
transitions.
For
last terms
the three
(ⅠⅠ.77)
=
甲ニーR
where
:
thefo1lowlng
expressions.I
radiation
5hT
isy-霊(芸)ne(1+言4････)
(ⅠⅠ･78,
e
The
of this radiation
spectrum
in harmonies
emitted
Much
consists
than
higher
of the energy
the first
be redirected
can
harmonlCS
of many
The
one.
back
into
alec,
Of
distribution
angular
the plasma
by
is complicated.
the first wall
using
being
Of the energy
most
as
a
reflector.
For
free-free radiation
has
one
(with the subscript
32ne:
&ff:
3(4n8.)3c3,neh1
An
thin plasma
optically
Free-bound
has been
loss
radiation
&fb-
charge
A
When
electron
attachment.
included
in Eq･ (ⅠⅠ
The
For
･80)･
the
sections and
with
Bound-bound
(neutrals)
I-0
The
I-b
molecules
or
optically
thin
of order
A;,7)is
coefrleicnt
exact
isgiven
radiation
A
●
the lnglis-Teller
u$1ng
transition,
"charge
We
Eq.
and
by
or
It should
level
some
applying
be born
in
recombination"
that
the subscript
"h" denotes
ions
moleeular
case
a
Can
A-value
eontribtlte
to
or coronal
these
cross
other
singly
instance
criterion.
the chemical
tO the radiation
excitation,
for
(II.81)
For
and
multiply
be introduced
an
contains
thin
optically
the
by
so-called
radiation.
molecules
-38-
can
the
and
mindもhat紳also
"dielectronic
the partieular
to
to be
have
the recombination
on
(i,j=1)
for the summation
and
(II.8L) by assigning
In
due
radiation
(E:,j-Elk,i)
n乙J
the ground
cut-off value
relation,
holds･
remember
molecules
A
Jl;,ぴ-1
exchange"
depends
value
i,j
includes
andj
(i,j>1).
states
excited
i
they
present
the
by
z
over
are
represents
being
JIZh,l= 1 holds･
transitions
of unity, the
for z=O
ions
molecular
Z
withz=Z,
ends
distribution.
velocity
summation
and
radiation
滋抽- ∑∑∑ ^zk,ijAZh,ij
The
(1Ⅰ.β())
i
of the bare nucleus･
number
for this radiation.
by
begins
overz
summation
(II.79)
3'neノ
kTe)
∑∑∑ ^乞iRZk}ne
n乞1晒zk.ll･pzk,71
z
The
(警)wne∑享享z2nz"
ーーe号音L;
assumed
is given
"h" reintroduL:ed)
and
type
of the species.
tosses, they
molecular
the densitiesor払e
must
be
When
included
ions.
excited
statesノ>1
are
in
to those
proportional
excit.ed levels
below
for the ground
i=1
state
the ioni2;aもion limit
; for singly
levels
excited
and
multiply
:
nzh,j
Cijl
∑ AZhij
electron
excitation
nZh,
=
ne
1
(ⅠⅠ.β2)
i<j
Doubly
given
Eq. (II.73).
by
In
reactions
heating
by
Quite
the two
conclusion,
of nuclear
The
levels formed
excited
and
a
similar
heating,
to nuclear
reactions
and
into account
two
by
terms.
additional
density
levels.
excited
in the absense
tosses.
of the radiation
injection
neutralbeam
formally
can
be
J■
′
taken
forinner-Shell
the power
densities
population
represent,
of Eq. (ⅠⅠ.61)
terms
collisional-radiaもive
of neutral-beam
effects due
is obtained
expression
have
capture
with
〟 and
∫, respectively.
Weもben
have
:
ほ芸p]cR.t誓IcR--&･ふ.I'
(ⅠⅠ･83,
●
R,
■
●
N
I
and
are
term
The
positive
quantities.
be decomposed
Can
[∂豆int/at]cR
in
a
collisional
a
and
radiative
contribution
誓】cR-[誓】c･[誓
first term
The
the
alone,
of the
second
the
increase
-Eint due
to radiative
spontaneous
the
describes
is the
term
instance,
due
r.h.s.
of Hint
due
is taken
for instance,
we
neglect
due
to radiation
into account
and
processes
to collisions
ioni2;ation
alone.
or
in taEint/at]c.The
last
to the
contributes
(II.84)
of Eint due
rate
production
dissociation
to collosional
recombination
de-excitation,
the following
rate
Corresponding
●
In
volume
term
:
For
the decrease
decrease
of
of Eint
of Eq. (II.84).
●
I and
N.
From
the development
of Eq.
(II.83)
は芸p]?R･[砦】cR-甜hTs[;]cR･nsk[;]c
it follows
that
'ⅠⅠ･86'
芋蔓nsk[;]cR--i-t誓】cR一字;hTst登】
When
atom
in addition
is
by dissociation
production
do not
processes
have
negligiblewe
modify
=[an8/at]cR=[ane/at]cR･
the heavy
particle
When
temperature,
the relation
holds
and
?;kT8[;]cR-;kTe[%]cR
the Eq. (II.86)
can
be
written
in
the following
-39-
form:
(Il.87)
(ⅠⅠ.ββ)
手芸nshta;]cR--i-[誓】cR一芸hTe[;]c
The
by
terms
radiation,
volume-Created
of the
power
r.
h.
density
electrons
s.
have,
●
the following
respectively,
●
consumed
to the
in changing
temperature
T.
e
-40-
Eint, power
●
meanlngS:
density
POWer
consumed
density
lost
in heating
CHAPTER
Ill
A一叩l圭邸
班.1
In七roduction
Wewi1l
with
now
the
surface
is made
which
the configuration
up
hot
for
conditions,
however,
we
radius) ㌔
given
a
have
less
a
il
with
a
such
The
hit
a
magnetic
material
instance,
it.
{1nite gyro-radius
leave
or
wall
low
of extremely
leaving
before
lies
which
the outermost
do not
surface
ideal situation.
⇒
=
Under
actual
(or cyclotron
3
t.
Perpendicula,
(?.'nk I)1J2
>=
2edB
for the electrons
rc>
<r
C
that the partic13S
the consequence
strength
on
of the plasma
as
electron,for
wi
=c
of a: <
is defined
devices
conlhement
by
'n
width
is that part
field lines which
time
in magnetic
plasmas
plasma
tO Tit. An
long
very
core
separatrix
of magnetic
r
has
core
The
returnlng
without
will travel
velocity
The
separatrix.
so-called
to hot
physics
toknmaks.
on
emphasis
inside
atomic
apply
are
zed8
bound
Only
(because of charge
to the
magnetic
Further,
neutrality).
a
8urfacewithin
electric rle!ds of
i. drift pe,pendicularly
the particles
cause
(Ⅱ.I)
Ei
t.
B?
and
the velocity
(-2,
wDE=皇ゼ
β2
Furthermore,
a
to particle
of the magnetic
curvature
iwDR
drift
field lines
to岩and to
Pe,Pendicularly
causes
the
a
radius
centifugalforce
leads
which
curvature孟givenby
of
1
2
From
has
be used
a
has
qualitatively
Theknowledge
parameters
the plasma
closed
change
the plasma
on
properties.
and
magnetic
edge
where
This
-
reglOn.
``reglOn''ratber
a
strongly and
●
boundary
●
de丘nes
That
a
plasma-wall
will in Chapter
property
of the plasma
part
(the separatrix) defines
surface
than
(Ⅱ.3'
which
in the following
plasma.
2
ⅠⅠⅠ.
Determination
One
the separatrix
of view
direct influence
the outermost
core
point
the plasma
to derlne
lies inside
the hot
pbysieai
in which
interaction
Ⅳ
iwDR-2謎')RXあ<.WDR,
-蒜紬
the plasma
"surface"
mw8
of Particle
introduced
and
of
rather
∫
does
the concept
Confinement
Times
of the confinement
times
phenomenologically
not
mean
that
one
r
in order
transporもproperties
which
has
-41-
rp
understoodもhe
to discribe
●
are
stillan
physica一 phenomena
enigma.
which
are
that
responsible
particle
the
The
7.
pa,ticle
and
state,
of
shows
lower
part
to the
the
Vp
(high)
of the
values
high(low)
velocity
to diLruse
constancy
together
of the plasma
are
atoms
ofL･yp
time
and
the
excited
After
and
emit
level of atomic
e･g･ Ha･
hydrogen
Ref･ [10]･
hydrogen
pure
plasma
F=子In+foul.Charge
equal
flux densities,
●
pressure
requires
-42-
We
(see Fig･ 7)I
i･e･,Te=
the followlng
･う
T+
･
relation
have
forces elecもrons
neutralization
一事
with
radiationl
the
rp
a
with
a enclosing
surface
of the n=3
Hal
intensities･
of spectral1ine
foulacr.ss
coronalexcitation
containing
a｡d昂ul,
measurement
and
Hydrogen
emission
conTlnement
volume
T'.in
･
the
on
finin
fluxes
The
a
Low
one.
another
transportedwith
are
particles
is based
V'p
flux｡s
protons
rp
･)iとISma VOlume
local T}article
Consider
not
exists and
meanthat
difrusi.n
Particle
leading
The
r-v?1ue
volume.
plasma
determination
Figu,e
certain
Tp only
confinement
across
a･
a
In
the
to be
sぬtionary
ful{111ed for
the neutral
The
rate
Eqs.
(see
and
ll,
_(1/2) (己+T-).)=
densities,為-
for the neutralhydrogen
equations
(II.
}e.
flux
charged
12)and
where
a+
diLrusion
nux
(Ⅲ.4.a)
ら+亭･声=+a.neso-a.nea.≡
(Ⅲ.4.b)
e
ionization
the
ano/at=O
by
and
hold･
One/at=O
and
the divergency
replaces
of the
a
rp,
PIe
Because
time
con{lnement
of the charge
(ambipolardiffusion).
Therefore,
for the
Eqs.
The
electrons.
(皿.5)
_ユ=冒.I.i
o
the迦由particle
rp,e･
electrons,
now
the
the relations
,
define
One
In
coefficients, respectively･
recombination
塑-言･ri.
which
are
警･苛･Fi.ニーn.nes.･n.
nea.-[筈】cR
are
state･
stationary
the electrons
and
(II.55))
at
So and
atoms
of the neutral
neutrality,
the conTlnement
(Ⅲ. 4a,
b)
time
yield in the
thus
is the
of the protons
the
and
,
diffuse
protons
and
electrons
Tp,o
atoms,
together
same
state
stationary
no
(Ⅱ.6.a)
nea+
-=-noneSo+a+
rp,
o
TZ,
ヰ
う
To
to
owing
(Ⅲ.6.b)
nea+
-ヱ･=-noneso+a+
hence,
that
as
-Te-
it follows
-TTA+0
,
that
(皿.7)
It is thu貞possible
known.
In
model.
However,
level. and
the
a十is
electron
a+
densities
i.e., So is equal
sum
be
must
of all rate
a
hightemperatures,
and
to the
from
calculated
rate
So and
no･n+=ne,
of
ionization
the coronal
coefTICient for ionization
coefrlCienもs for recombination
a+are
into
the
from
the ground
ground
and
:
states
excited
aもlow
the local values
rpwhen
So and
the generalcase,
be applied,
can
model
to determine
0)
s.-鴇,I(Te)
The
no
which
The
then
crucial
point
practically
i=1
is the determination
equals
●
measurlng
●
of determlnlng
exacもway
the
of the neutral
fluorescence
by
laser
nOi7.1is
for instance
light,
-43-
hydrogen
in the ground
that of the particles
●
most
∑ RL,i(Te)
a.-
,
excitation
of Ha
or
state
from
particle
(i-1)I
the
L,ya.p. This
density
nIOl.l･
ground
method
level
and
is only
sufTICient but
possible
at
of too
large
a
F'requency
line prorlle)and
absoTpもion
too
not
beam
sufficienもIaser
a
(because
hightemperature
in the desired
energy
range.
is determined
In
densities,
highparticle
too
not
general硯1
line.
For instance
by measurlng
for the HQ
Spectral
line
●
the
emission
in
have
we
coe鮎ent
the optically
thin
hydrogen
a
-∫
case:
1
吃,3-4TT A笈,23瑞3h収23
where
A&,23is
the Einstein
corona
excitation
conditions
coef{1Cient for spontaneous
quantum
by the Condition
When
we
assume
level with
0f the
density硯3
,
is glVen
numberノ=3
de-excitation.
(see Fig･ 7) the particle
●
(Ⅲ･8)
principal
that
(Ⅲ.9)
c?i,31瑞1
-[Al,13.A]01,23略3
ne
which
yields
鴇,13･A監,23弦23
4n
(ln.10)
A.-瑞1ー0ーー"'1
(Te) is the
where
C&,31
ground
state
determination
In
This
:
no
of
a
conclusion,
hydrogen
In
i=1.
also
relation
frequencies,
state,
many
the rate
date
atomic
probabilities
of Te(T･), ne(T･) and
determination
a
how
shows
transition
measurement
line permits
the transient
hyL,23
nee?a,SI銘.,3excitation
of level
coefTICient for electronic
rate
and
excitation
the emission
of the local particle
Eq･ (Ⅲ･ 4･b) yields
for
are
from
j-3
fわr the
necessary
coefficients.
coefTICienもc
conrlnement
the
time
a
of
rp,e=Tp･
the expression
rp,e
(Ⅱ.Il.a)
impurity
When
species
are
rp.e
present
musもbe
fromもhe
valuated
expression
n
(Ⅲ.II.a)
e
=
石
p･e
b･
The
mean
or
The
mean
(or global) particle
to the
Let
the
global
total particle
/nedVp=Ne
separatrix･
The
particle
content
be the
in
lane/∂E)cLr
time
confinement
e
/at
rp
to
refers
some
mean
value
of
Tp
related
discharge.
total number
integration
time
confinement
a
an
over
of electrons
in the plasma
volume
Vp enclosed
by
Vp of EqA (Ⅲ･ 4･b) yields
登･I.v･,JewpI[箸]cRWp･Ce-t登]cR･Ce
'Ⅲ･j2'
where
crosslng
Ce is the integration
the
plasma
surface
constant.
The
second
term
on
the I.h.s. is the electron
LJliuX
a, thaもis
fe･dg
チ
I苛･riedVp-44-
(Ⅱ.13)
The
mean
particle
time
confinement
〟
P,e
Ce=01
no
Since
be defined
may
by
I7･Fewp- iTie･dSi
ir
Further･
of the electrons
rp.e
in
is deposited
source
additionalparticle
(Ⅱ.14)
Vp.
the volume
One
thus
obtains
(Ⅱ.15)
[∂Ne/at]cR
where
gas
lS
puf{1ng
taken
gas-puffed
neutrals
entering
coefrlCient
R
to
Bu七∂Ne/at=O
external
For
c･
can
gas
Particle
be obtained
see
R<1,
to
a
themisslng
●
when
atoms
neutral
plasma
a
with
recycling
nu又 is compensated
of impurity
ion-pZ
confinement
of the ionic
impurity
density
Z
I
TI
rTII
is nk,1=iEnZk,1･
The
to consider
.
be
can
species
It is
suLTICient
that of the electrons.
Their
determined
the particles
P
in the
a
localparticle
rateequation
in the ground
_∼
(Ⅱ.16)
㌔.A by
time
confinement
same
for nk,lWrites
.'
∂f
define
by
N.
也.v,･puWe
and
is constant.
density
the electron
since
and
the collisional-
since
recycled
for instance
∂NJ∂t=0,
with
Chapter
times
confinement
as
state･
also
Then
expressions
due
production
Consider
the plasma.
R=1.
one,
details,
particle
manner
in these
effect of recycling
puLTlng.
further
The
into account
The
of lane/at]cR.
value
also for the electron
accounts
equal
integrated
volume
automatically
term
radiative
is the
包-亨･iph,I
(Ⅱ.17)
Z
r
p.A
and
obtain
for particles
of the chemical
element仙k"
in the ion charge
state
"∼"
(Ⅲ.Jβ)
lone can曲o
individual
limited
･血arge
ileTlne
states
radial width･
a
mean
Or
global
"Z''of the heavier
particle
elements
not much
Thererore号;,hWill
-45-
confinement
are
deviate
However･
time言言,A
the
in
of
concentrated
from
an
annulus
1t is physically
rz,:･h.
more
interesting
of
to consider
impurity
agiven
the
the particle
"k"･
species
Their
of all ion
Of the enserrlble
conrlnement
mean
time
confinement
"a"
states
be obtained
Can
Fp,A
charge
from
●
followlng
System
of rate
:
equations
堤.v?･Fk.-ll-ぼ]cR
∂f
●
●
●
(Ⅱ.19)
!%z･亨解ぽ
at
A氏er
summation
integration
and
the plasma
over
Vp
volume
has
one
a
(警･Iv･.fh,lWpi-zil[警]cR
確
:e7ad::lan,eti:lemce.ann,1P:eriieciei
;p7,;lf:re?:ere:is:ニbf;I;
∑
(Ⅱ.20)
z三1
the
by
㌔
γol lme
plasma
"i-
I亨･Fi,Imp
言言.
(Ⅱ.21.a)
A
∑NZk.1
(Ⅲ.21.a)
Z
Tp.
EqB.
The
(Ⅱ.20) and
(Ⅱ.2I.a, a)
-譜
A
then
lead to
(BI
The
of Tp,A requires
determination
beknown
This
experimentally.
the
onlyknow
r-distributions
lines for which
spectral
be complemented
an
must
the radius
over
which
For
are
needed
are
Abel
is practically
a
for measured
radial
for the calculation
needed
nh2, 1
few
of
impossible･
ion charge
inversion
by solutions
the measuremen七of
probabilities
for
a
numerical
electron
nhZ.
"2"
sもaもes
code
-46-
actual
from
limited
a
whichgives
temperature
situations
Therefore
and
of the collisional-radiative
resonance
impurity
i(r) of all
Under
be performed.
can
the excitation
(unless the
distibution
the radial
number
ions to
one
will
of
the measurement
the so!utions
electron density
rates,
･22)
see
and
the Einstein
line is used
and
cascading
is
nh2,1
distributions
e.g.
coefTICients
for
Eq.
(Ⅱ. 19)
transition
neglected).
For
l
the
of [8nhZ,
evaluation
capture
electron
llI･3
the ens-emble
ll/al]cR
recombinationand
Fick's
apply
law
to
diffusion, D
is the ambipolar
a
termed
coeiTICienもD
all
toroidal
geometry,
dV=_
edVp-
For
coefETICient.
and
pair
electron-ion
have
thus
(Ⅲ.23)
e
dV
e
the meanelectron
Vn
dV=_
a
and
(Ⅱ.24)
･
plasma
radius
a,
we
have
(皿.25)
LTta2
=ne
P
of the
density
Da(VTn,
L-2TrRo
length
torus
a
with
V･D
a
discharge
whole
in
Wewill
volume.
particular
that
assume
;)a
ne(r,-ne(o,(1-
Tlnd thefollowlng
then
relation
p･e
Da
some
represents
be considered
as
much
with
change
Te-limits)
then
law"
the
Measure.ments
on
=
electron-iori diffusion
and
and
the plasma
have
assume
toknmak
of smaller
III･4
Determination
The
energy
rate
to be
this relation
si2;e With
plasmas
of Energy
time
conlhemcnt
tE:
does
(皿･ 27)
not
(within certain
parameters
can
vary
ne,
to a2.
ne,
thatち,e∝
hence
(Ⅲ.2β)
e
the
valid, then
of
higher
same
electron
Confinement
for the total energy
equation
that Da
assume
proportional
shown
Eq･
coefficient･
∝α2TL
PIe
we
is
confinement
TFR
we
; when
with
r
When
(Ⅱ.27)
=
8Da
for toknmaks
particle
AIcator-C
■=
4ne(0)Da
dimensions
theglobal
lag
a2
+
space-averaged
"scaling
a
-ne
l
=-
r
where
(班.26)
a-1
with
We
･･づト
to Vn
is proportional
We
with
beknown.
†亨･Da?nedVp
チ dg
-
∫
where屯is
Da
exciもaもion
(Ⅱ.14) yields
a
For
CoefTICient
coefrlCient Da.
diffusion
a
this into Eq.
must
diffusion
particle
T'e=-D?a
lnserting
processes
that the difrusionnux
states
which
proportional
Diffusion
and
rp
ionization･
coefrlCientsfor
exchange
charge
ConfinementTime
We
of rate
density
rp,e-value
can
be
obtained
in
a
a
local
density.
Times
isgiven
㌔
by
Eq･ (ⅠⅠ･59)･We
define
by
1
言PU.2･
E-L'nL
･:-p･
'Ⅱ･29'
-亨･ほpu:,e.･E-lntJ.･芸p3.･Qh･叫
-47-
When
introduce
we
(ⅠⅠ.
59)and
this expressioninto耳q.
(lI. 83)
applytheノEq.
we
obtain
l
言PU.2+芸p･盲inE
rE=
'Ⅱ●30'
【豊吉-o2t]cR･占.I'･*･享n8<F+s,･3o一
We
remember
low
impurity
to shear
that the efrecもdue
concentrations
and
is noもcontained
stresses
temperatures
highplasma
simultaneously
inthis
For
relation.
we
can
put
1
we
Eq.
assume
-芝p
言PV.2･芝p･E-inL
<F?s> ･to=0,
to be
(ⅠⅠ.
45)
(Ⅱ.31)
valid
put
and
hence
8∑n8
言∑
n8kT8
S
●
.
∂
.
S2+I+N_
-
8t
It
be
can
from
seen
in particular
at
highplasma
that bound-bound
The
the values
temperatures
local energy
be
can
radiation
1 that
the omission
of the internalenergy
(which does
p･i･aCticallyalwaysallowed
not
lS
mean
neglected).
time
confinement
i;!nskTs)
Table
glVenin
(Ⅱ.32)
due
to thermaland
convective
transport
alone
is
●
obtained
in
time
due
rEtr
omitting
R
in
to convection
Eq.
and
(Ⅱ.29), hence
diffusion
the definition
alone
for
the
local
energy
conTlnement
is
1
言Puo2･芸p･云inL
‡吉pv:v.･
-v
･
TABLE
The
Eq.
(ⅠⅠ.
59) then )Cads
to
(with the
same
-48-
(Ⅱ･33'
E-inEu.･言pv.･qLh･QinL‡
1
approximation
as
for Eq.
(Ⅱ. 32)
(Ⅱ.34)
One
has
rELr>rE･
0wing
to
●
diLrlCulties in
In
times.
confinement
S2
measuring
the
applying
same
one
o氏en
for the particle
as
method
the
only
considers
mean
energy
times
confinement
one
(Ⅱ.35)
(皿.∂β)
where
JpUthe total ohmic
represents
of the
L=2TtRo=1ength
The
atomic
torus,
physics
input
power
problem
I.7良知ndr
L
(Jp=total
a=plasma
can
radius) and
in the determination
U=loop
current,
plasma
be
easily
TEtr
of
(Ⅱ.37)
voltage,
measured.
COnSists
mainly
in the
●
loss term
of the radiative
evaluation
In the presence
-R.
of impurity
one
atoms
must
●
know
their radial
However,
atomic
Ts
temperatures
lII･5
The
now
will
nuxes
physics
is also involvedinthe
by charge
either
Density
the particle
both
the decay
the ionization
Integration
density
in order
to calculate
determination
I)ecayTimes
a
able
or
measurements
exchange
in
to be
discharge
of the Eqs.
reliable
of the heavy
for R.
values
particle
by spectroscopic
means.
fp*
can
be maintained
on
the divergency
on
consider
and
distribution
Particle
Whether
depen'ds
,
density
nuxes and on the source
of ･the diuusion
density due to an imbalance
of the plasma
a
constant
level
of ioni2;ation.
betweenthe
We
particle
sources.
(Ⅱ.4.a,
a) overthe
-49-
plasma
volume
yields
owing
to Eq.
(Ⅱ. 14)
≡ヨ
E
Tot dS=
∂Ⅳe
(班.ββ.α)
P]cR
i;
.〟e
-+=-≡
∂t
r
PIe
The
integration
plasma
are
constants
Apart
volume.
zero,
from
no
since
their slgnS,
(Ⅲ.38.a)
have
parf･icまesources
the
h.
r.
s.
are
been
inside
placed
hence
equal,
警】
CR
Eq.
and
(Ⅱ.38.b)
(Ⅱ.38.c)
the form
begiven
can
the
aN
aN
e
+
e
=
∵
_
-r
∂t
-
aNo
+
To･dS--
_
(Ⅲ.39)
al
Ple
The
total neutral
fit).x
particle
i
the plasma
crosses
which
1.現ec
parts
->
一手
(ro.R+Ilo,
flows
-T>
･
a)
dS
into the plasma
(Ⅲ.40)
be
can
thought
to be
neutral
atoms
I.
of two
composed
a and
surface
‡
｢>
･-}
To･dS=
-￠｡=
clin
The
part
R
plasma.
The
total flux of this part
of the
palrS
electron-ion
leaving
the
as
returns
plasma
toもhe
is
手7o,R･d叫,+elm+--R豊
`m･41'
R
is the
2.
Gas
By
recycling
Puffing
artificially increasing
to increase
possible
-Q..a
coeLrlCient.
the pressure
total nux
The
into
nux
the neutralparticle
-坑G･di.
Outside
the plasma
by
the plasma.
is
of neutralparticles
additional
This
thusgiven
gas
gas
puLrlng
pu岱ng
it is
nu又 is
by
(皿･42,
-￠.ニーRエー￠..G
T
PIe
The
minus
the
r.h.s.
dividir唱by
sign indicates
of Eq.
inward
(皿. 42), introduce
direction
of the nux･
thaもexpression
We
replace-Qo in
into Eq.
(Ⅱ. 39) and
Eq･
(Ⅲ･ 40) by
obtain,
after
Ⅳe,
1
aN
1
1-R
aNo
1
-
Ne∂t-｣=一ニー+N-￠0,a-N一首
ちp,e
e
-50-
e
(班.43)
This
determines
eqllation
For
tokamak
a
discharge,
be
case
particular
puffing, Qo,a-0,
the temporal
No<Ne
and
decays
Ne
holds
We
neglected.
beh8Viour
define
in the
The
last term
plaslna.
After
R<1.
-i(1-R)/言
P･
e
elecもrons.
in
can
that
of the gas
switch-off
time
(班.44)
e
fp串by
r
+
(臥45)
PIe
=
r
■■■■■
1_R
P
and
or plasma
to
according
eircctive elect･ron deti=ity decay
an
core
will assumethat
Ne(i) =Ne(0)
We
total number
or払e
obtain
+
_t/7
Ne(i)=Ne(0)e
By
●
measurlng
for R=O
Only
is the meanparもicle
This
offers
the
particles
another
the
on
this particular
ul. 6
possibility
walls
to obtain
of Particle
"z''.
nux
of the particle
the Eq.(II.
state
charge
time
a
Fp,e
rp,e
the recycling
by wall
gettering
R
close to
:
recycling
very
decay
to the
equal
coefTICient R
i/･
time
it is possible
9).
Withもhe
Fluxes
"s''=(I,A,i)
of species
We
the ground
consider
subscript
Velocities
and
``h''dropped
state
the rate
be determined
can
particle
equation
one
when
(l=1) of ions
in
density
of the
diffusion
●
flux given
is
the
writes
(皿.47)
at
the
to {1Ⅹ
henceら*苛7p,e ln
zero,
当･亨･,-12=
with
･
case.
density
to solve
able
and
detemine
to
confinement
of determining
Determination
The
it is
possible
fp,e and言●
P
Separately
(Ⅲ.46)
P
by
-I
(v'.･ <Vi11,
I7-nzl
The
term
cR-
)
(Ⅱ.48)
writ.es
a;'1
1+nea;+1
a;･neS; a;1
-nets;+a言】
(Ⅱ.49)
c;+1ーZ瑞i
-nzl∑c;.a-1桟,i･n;'l∑
一
The
SZl
,
a13･･･ are･
respectively･
eLrecもof dielectronic
exchange
between
the
ground
the
recombined
state
recombination)
ion.
It is assumed
When
the
cross
that
and
Ci
the
and
atoms
neutralhydrogen
i-1･
t
the ionization
's
HO(i)
recombination
the rate
are
in
quantum
all captured
sections
-51-
and
coefficients
coefficients
state
electrons
the temperature
end
i and
in
(including the
for charge
the
ion
the ground
areknown,
species
level
the rate
in
of
coefficients
For
be calculated.
a
can
symmetric
cylindrically
follows
plasma
(Ⅲ.50)
is to be
(an:/∂t)i.
where
sections
cross
integral
andもhe
the diLrusionflux
of
In practice,
to permit
precise
distributions
a
however,
species
in
this way
1S
A
limited
a
■
n12
a;
an
and
!
instrumental
considerable
At
fiuxes
=
is based
scale
problemfi
diffusion
present,
which
absolute
a;+Ion
component
to fit the
found
by
confirmed
of
impurity
for this particular
general
structure
component
radial
Eq.
of
uo
of
measure
Of interest, which
precisely
poses
still
the following
globally''in
manner
a
[F(r,u:･D⊥志望卜言
-
(Ⅲ･51,
"cylindrical''tokamak
as
tokamak
to describe
way
of IllZmay
(Ⅱ.51)
<
a
Eq.
(E[.51)
[12) and
withthe
structure
empirically
subsequently
findings.
in
be found
was
was
the experimental
for instance
is in.agreement
VIZ>
plasma.
ASDEX
in the
Choice
and
"more
determined
transport
reasons
to
expression
laboratories
other
not
=
rl(r,for the radial
sufficiently
are
necessary
prlnCipally
di瓜culties.
and
are
the emplrlCal
on
the region
over
region
of
●
is therefore
Since the data
It is in particular
reliable evaluation.
all
direcもexperimentaldetermination
radial
gone,
not
Provided,
the
and
Te,n言-ミnll
a;+lareknown
ne,
of
Tll2sha11 be detemined･
FZl(㍗)be determined･
and
impurity
an
to for which
aもtime
radial
be evaluated
can
possible.
taken
The
Refs･ [13-15]･
of Eq.
The
(Ⅱ. 48), with
,6he
by
approximated
(臥52'
(a, ;
vo･r--f(r,u:
Why'for
instanceI
The
ASDEX-team
もo be
Jetermined
the
vilue
All
toknmak
in
the
ease
for
uo*
Only
the gradient
has found
impurity
of obmie
<VZl,r--D⊥去誓(b,
to self-diffusion
i(r)uo'-D⊥2r/a2
experimentally).
and
due
0払er
groups
to be
determines
a
puり(rノ-
convenient
㍗/α and
<Vrl2>r
I
choice
chose
is not
clear･
(with only
D⊥
independently
D⊥.
transport
studies
yield approximately
the
same
values
for D_L and
uo'
beating:
D⊥記0･4-1
We
will consider
the eLrect of diffusion
on
-52-
the
radial particle
distributions.
The
Figure
8 showsもypicalradialdistributions
tokamaks･
from
1-D
a
Figure
The
distribution
9 shows
transport
is determined
been
has
a
diffusion
leads
recombination,
situation
lying
a
sign
between
to Figure
of
ne
Te
In
valid.
of Fez+
nFelZ
been
has
and
in medium-Sized
measured
distributions
diffusion
the particles
Figure
wider
diffuse
radialreglOnS,
inward
diuusion
and
completely
the Figures
=0)
The
a
retardation
m2/s
∼T
because
outward.
to
the ion
,
D⊥=1
with
●
over
obtained
coronal
9.a, diffusion
veloeiもy leadsもo
a
peaking
ofもbe
●
and
(Di
assumed
by assuming
ions
∂nl/∂r
inward
of
9.a.
inward
convective
of intrinsic
:
are
in ioni2:ation, the outward
retardation
a
they
as
the particles
spreads
negative
compared
Superimposing
distributions
to
no
to be
equilibrium
a
and
9.a,
Figure
●
positive
Te
and
by the localvalues
Diffusion
assumed･
ne
radial density
the
In
code.
ionization-recombination
has
of
9.a
recycling
and
-53-
9.b.
Impurities,that
means
radial
that
one
obtains
a
E=i=コ
[i]
l∈
こ至:
⊂己
b
二
⊂=亡=J
4)
く=
■■
■■■■■
i
lJ<
.
J
くロ
トー
fO
20
30
40
50
RAD(US(cm)
Figul･e 8.
Typical
radial
distributions
o( electron
rl･Om Ref. [16]
-54-
temperature
Te
and
electron
density
ne,
〟｢
l
∈
○)
-9
I■■●
ヽ_一
c).と
NLL
v;
⊂
≡
Q
rLrl
●∈
o1▲
●■垂
こ==コ
▼-■
)ト■
ヽ
C)
蒜
"CLL
:
fO
30
20
40
RAOIUS(cm)
Figure
9･
Lモadial distributions
iron
density
of
nlZ
for the Te･
ne
-distributions
zEn;e,l=1XIOllcm-3･
a
:
coronal
b
:
iollS Submitted
equilibrium
(D1=0)
to diffusion
･,
with
ATLcr血er. r167
-55_
D⊥=1
tn2/s.
of Fig･ 8･ with
the total
こi
Ji:.一
t
∽
さ亡j
l
≡
0
.e!
⊂⊃
▼■■■■■
ヽ_J■
∼
I
j5
10
15
MI'nor
Figure
LO･
Radial
TFR
distributions
discharge
Radius
r(cm)
or the particle nu又 densities
from
obtained
I-D transport
a
ions
rlZof intrinsic nickel
D⊥=0.4
code, with
m2/s
in
a
and
uo.=4m/s.
Full
indicate
arrows
impuriLies･
measuremenLs
limited
line
or charge
stages
elemclltS). One
and
uo.
in
ambiguous,
then
code
since
D⊥
reliability in proccsslng
localionand
the
pcaking,
"∼"
compares
LhcwidLh
an(I
and
a
uo+
or the
in pal･ticular
densiちy radial
broken
position,
ioni2T.aLion_recombination
coronal
radial pl･Orlle of
best
way･
delivered
from
is
in the
Te
by
case
The
diLTusion
data.
independently･
cocfrICicnt
indivi(lual dist.･ibutions nlZ(r)･
the
l･elative
conccntt･ations
-56-
stages
chord-
D⊥
The
of two
"
(o1-1y
By
high-Z
D⊥
modifying
method
Iiowever,
is
somewhat
is
thel･e
dcLermiーーCS Pnmaril.y
convccLive
wi(lely
a
cxperimcntally
-the
The
for
manner
"I
or medium-and
transporもcode･
fit to the experimental
be determined
charge
distributions
a
●
followltlg
Abel-inverted
nf(r)
to difrbrcnt
pertaining
ne,
i[l the
is perfornlCd
uo●
is considered
those
cannot
inもhis
and
for measul･ed
-
finds
one
the
inLensities
with
a;-distributions
the
when
0rD⊥
consLrucLs
o( spectral
number
determined
One
ion
maximum
【17】
determinatio[1
experimental
intrinsic
maximum
Rcr.
Artcr
assumcd.
The
this
indicate
arrows
the measured
tel･m
sepaI･'lLed
some
Lhc
inn.tcnces
ion
species. It is thus
vo+
For
non-intrinsic
and
D⊥
further
impurities,
be
can
to obtain
possible
determined
details the
for instance
from
introduced
to Refs.
reliable
for D⊥ and
values
by "laser-blow10ff",
the spatio-temporal
is refered
reader
ctモI.tainlimits
within
uo+.
the values
of the ion species.
evolution
[14, 15, 18] in which
the methods
of
For
havebeen
reviewed.
Figure
plasmas
10
calculated
measured
points
limiter
In
the stationary
once
the
and
center
the Eq.
state,
I.1k(r)isknown･
in Fig1 8･
ofもhe
discharge
inward
show
(Ⅱ. 51)
Neither
forces for the
driving
･
determination
Diffusion
from
lil.7
rate
to
relative
convection,
at
least
磨elds私r蝕e
only
somewhere
(Fli<o and
Ii>o)I
density.
be calculated
can
(r)
which
maximum
nuxes
(r) >
<w&1
:
(Ⅱ.53)
from
(Ⅱ. 51) has
a
point
as
to have
seems
Therefore
of view･
without
foundation.
intervene
ion species
of other
physical
theoretical
no
gradient
be discarded
not
should
for the heavier
impurity
of Convection
for the
particle
having
a
tested
really
as
a
II
an
whole.
To
equation
in pz:linciple. We
densities
from
origizlatir)ど
separate
for 7.
the two
electrons
For
radialne-distribl一tions.
are
also
D⊥,
vo'and
found.
are
species
yields only the entire nu又
nlZ
of two
effects
a
one
needs
should
Velocity 3o the
a
mass
column.
a
due
to
velocity
3o(T･)
equation.
second
permit
density常
density
to the
relative
Cylindricalplasma
the皿aSS
the nux
parts,
diqusion
･もwasfoundwhich
will8SSume
･T7L由温alcomponen七of
) and
Velocity
It iscomposed
system.
(deuterons
species, protons
plasma
the Llux density
and
Chaper
a
nil
for the totalimpurity
solved
the presence
measured
the laboratory
In
flux vector
a
the temperature
nor
(Ⅱ. 51) by using
as
equation
of the plasma
vo,
Eq.
Determination
The
-->
of the main
values
similar
density
for
or this method.
nuxes
determined
Also
(臥47)
whose
show
outward
expression
satisfactory
Eq･
Llo+=4m/s,
<VIZ>r=
gradient
nux.
is not
of FIZfrom
the potentiality
quite
diLrusion
This
IllZ(r)
on
noeLrect
tha七the
density
the proton-electron
be
can
flux velocity
the radial
like to emphasize
would
and
in TFR
and
Ions
have
ions
nickel
0.4m2/s
shown
<wzl(1･)>r=Vo,r+
We
D⊥=
with
intrinsic
･Lthose ions which
radially(I11Z>o), whereas
outward
the
the center
T;(r) for
of
code
to those
similar
towards
continuously
between
lD-transport
a
with
distributions
radial
Te-pro{11es
ne.
increases
the
shows
determination
The
of
Eq. (Ⅰ王.
57)
expression
(8t.54)
v.,r-志ほ芝.s･(享;hT$7s,ヰ芸k!(ns[警]c
157-
Again
1.
faced
are
we
The
with
Eq･
See
,
physical
The
(工r･88)･
of at least the ground
:
problems
for [∂Ts/∂t]cR COntains
expression
/at]cR
atomic
local
the
determination
0f all
density花言,1
state
lane/∂t]cR
productionrates
of these
quantities
chemical
species
【ane/∂t]cR aT2.a [∂EinE/∂t]cR in the radial region for which
Eq.
[aELnL
and
knowledge
re･quires the
…k''which
contribute
(Ⅱ. 54) is
to be
to
evaluated.
2･
The
of all flux densities
sum
determination
of this quantity
direction, ETk5,1(r)I must
relies in principle
theknowledge
on
also
be known･
The
data,
of atomic
Ⅱ. 6.
Chapter
see
in radial
●
Finally
3.
the
know
must
mean
the
A
we
ion charge
effective
density
Zen(r)
state
L2 forohmic
at
heating
radialposition
depends
which
Zen(r) is
r･
on
function
a
of
nkl,1(r)･
of the relevant
preciseknowledge
of the radial
and
the local power
ne
,
densities
Te-distributions
nh3, 1
at
should
(r)I tO be determined
least inprlnCiple
spectroscopically,
the determination
allow
of
uo.r･
A
We
favourable
particularly
the Eqs.
apply
the staもiQnary
situationarisesfor
(1Ⅰ.87, 88) and
the五q.
Then
State.
ap/a
holds.
t=O
(皿. 54) becomes
旦hTsr8)+0+R-[丁】cR
.虎ine
)
(Ⅲ.55)
.
.+
(∑2
v.,,一志G･
8
The
total ohmic
Te-distributions
ne,
be measured
can
power
it is thus
possible
Eq.
see
precisely,
to determine
an
Using
(臥37).
average
measrl_red
radial
of Zeufrom
value
JU
P
Z
eflP=
L
●
L21
where
is th･e calculated
I.7占1
densitywith
power
(Ⅱ
2汀rdr
●56'
<
Zeq=1･Assuming
Zed
to
be the
same
●
throughout
thus
the plasma,
determined
can
S2(r) in
Eq･
also be used
(Ⅱ･ 55) is known
for the calculation
for any
position
r･
The
of the bremsstrahlung
value
of Zeq
tosses in the
●
for R.
expression
at]cR appearing
The
of
the determinationof
poinもis
lane/∂t]cR
and
[aE紬/
(II. 55).
[anJ∂t]cR Could
for the
rp,e
(Ⅱ.Ll.a)
the crucial
in Eq.
calculation
conTlnement
to IEq.
Thus,
stationary
be by-passed
from
state
when
independent
oneknows
measurements･
the local
particle
since
according
:
TIS(r)
ーp,
=
e(r) lane / al]cR
-58-
(班.57)
I
However,
the determination
the atomic
physics
In皿q.
place.
It should
depend
on
lil. 8
Radiation
The
fusion
serious
than
a
D-T
a
D-D
a
Ⅰもwould
radii.
of the sign of uo,rもakes
reversal
the pinch
effect, since the r.h.s.
which
tosses due
energy
the Eqs.
Synchrotron
(ⅠⅠ.
77-8)).
it will probably
and
however,
reactor
reactor,
by
aregiven
be neglected
cases
play
will work
only
a
role in
minor
higher
aもmuch
to synchrotron
two
give
Figure
The
as
atom
coronal
function
a
To
which
obtain
to calculate
the power
excited
cascading
the
shows
gives
different
of
Te
electrons
back
return
to the
and
become
radiation
may
calculated
by many
loss
for the two
losses
the particle
densities
ground
losses.
In
case
without
has
one
in the
the limit
a
level
need
via
that
ground
-59-
loss in
the radiation
per
electron
is in the
state
the coronalexcitation
level･
of coronal
spontaneous
loss
the plasma
{1rSt tO Solve
be known.
not
increases
power
that
rates
diffusion.
to the
is particularly
radiation
ground
level
Diffusion
diffusion) and
the radiation
to the
the calculated
the assumption
(i.e.,no
been
9.b.
contributions
under
to bound-bound
shows
to the
compared
the radiation
loss due
9.a
of Figures
applicable.
equations
12
ll
Figure
examples.
of the plasma
part
radiation) have
(neglecting synchrotron
iron ion distributions
the central
used
inwhich
(1u･ 54･ 55)･
at different
values
(Ill.54, 55) contain
lost by radiation
For
tosses
We
authors.
iron
that Eqs.
different
Eqs･
the
problem.
Radiation
radial
for situations
seek
almosもall
reactors.
temperature
have
from
uo,r
of
to avoid
noもpossible
tosses
in
Can
determination
lt is thus
force."
densities
power
this relation･
on
the r.h.s.
on
be mentioned
the "pinch
radiation
D-T
terms
be interesも1ngもo
is based
rp,e
in the
problems
(班. 55) the
therefore
of
the
coupled
nk,1･
These
the
excitation,
simple,
system
and
per
of
is
model
of rate
densities
are
expression
for
since al) collisional1y
de-excitations･
Details
of the
ーニ
-:･-
【i二
∈
U
室
(LQ'
lo一l
●∝
u
≡
J
O
O
U
uJ
>
L====コ
ト
≦
⊂】
<
α:
20
RADIUS
(cmI
●
Figure
ll.
Power
given
density
RFe
in Figures
lost by
9.a
and
iron
radiation
for
9.b, after Ref. [16].
-60-
the
radial
iron iondistributions
5.6
6.0
6.L
6.8
7.2
76
8.0
8.(
)
(og1.Te(OK
●
Figure
12･
Power
densities
R/TLenFe
radiated
in coronal
a氏er Re￡
【191
_61'-
per
electron
and
equilibrium
at
per
iron atom
electron
by
temperature
a
plasma
Te.
皿. 9
Further
There
numerous
exist
information
obtain
large
1.
Applications
variety
other
processes
of atomic
determination
energy
spectrum
the neutral
localized
Doppler
and
essentially
in
diLrerent
direction
one
radii
When
Charge
2.
part
114.41
temperature
been
spectra
A
has
by
has
been
is obtained.
to
(leading
species
a
locally the particle density
measure
●
By
the Dopplerwidth
observlng
temperature
the nu又 velocity
and
The
in
is
movement
toroidaldirection
at
velocities information
rotation
shear
-
stressesintoroidal
are
species
present,
about
direction
charge
･
can
exchange
hydrogen
neutral
line intensities
in the
density
quantities
of the JIPP-TII
to conlPare
applied
determined
by
again
by
by using
a
using
●
u$1ng
U
been
The
Figure
Fe玉里主主星【24】.
tokamak
For
[21].
spectra
spectral
ratios
13 shows
a
obtained
lines
suitable
choice
of
fわr the
or
a
from
this
with
helium-like
purpose,
synthetic
of FeXXII
model.
the intensity
-62-
on
or
quantity.
the measured
the
density
the proton
is necessary
model
the desired
for instance
have
or
depends
to extract
and
to
oLrers the possibility
density,
the electron
or
of these
a
general,
been
the
line intensitie阜
one
of
determined
line of Fe墨茎星【23] and
When
measuringくw言>Q
ion
temperature,
was
l=117.17A,
to additionally
temperatures.
proton
be obtained･
to determine
temperatures
model
due
or
impurity
ion
Charge
plasma.
atoms
the
of
【20].
by plasmas
emitted
"a
can
the vicious
applied
measurement
density
and
In
electron
to
lines''the
sight (ts)
toknmak
lines.
of the
methods.
Zeu･
electron
l=
states
of impurity
core
local
with
addit号on to the toroidal
determination
Time-resolved
electron
charge
of the ratio of spectral
or spectral
interpretation
The
used
of the ratio of spectral
The
hot
sensitivity
canbe
determines
of the AIcator-C
temperature.
the
since
the measurement
on
(deuterium)
exchange
Hence･
￠･
number
has
either払e
titanium
ion
lineof
locally
measurement
determine
couples
limited
exchange
Al)Dlication
The
in
which
to determine
be applied
charge
"impurity
of the
obtains
a
only
to
physics
shall be mentioned,
is based
determine
can
species)
direction
>〆/∂r
<w;>￠a <w;
outer
of impurity
toroidal
list of application
is chopped,anincreased
shift of the emitted
the
long
a
hydrogen
one
species in diLrerent
<w;>ls in
few
".
of the impurity
case
beam-induced
excitation
of atomic
very
leavlngthe
neutrals
neutral
this latter
Additionalneutral
Only
application
(ion) temperature
exchange
beam
particle
the
on
lead to
would
tointrinsic
In
1相ected neutrals.
based
state.
of the proton
be due
Species
exchage
of charge
can
exchange
Atomic
methods
the plasma
about
At)I)1ication of charge
The
Using
the sensitivity
ones.
at
The
fわrbidden
a
proton
to
an
allowed
of the line
intensity
values
ratiowith
to the
respect
fbl･ the pl･Ot･On temperature
density
a
good
as
a
function
knowledge
of
of
ne
To
temperature.
(=n+)
get
reliable
is necessary.
′■ヽ
tn
Z
O
[::≡
′■ヽ
○
エ
a_
+<
くn
【i]
くn
≡
二
二
ヽ■■■
ヽ■■′
I.0
二
i:=ヨ
′
､
Eヨ
OD
ヽJ
㌫
ヽ-′
=
二
二
L===｣
=
二
二
巨:
>く
IL4I
o.6
0
二
ニ
ーー
<
∝
0.ち
>L=
●lll■ll●
tn
≡
tAJ
ト●
0.2
z
●■l■l●
200
000
400
T
Figui･e
I3.
IlltCnSity
ratio
or the forbidden
Fe茎り旦,
with
and
wiLhouL
1000
(eV)
(1=974･8ノi)
pl･OLon-i.･on
-63-
800
ion
Lo
the allowed
collisions･
^rter
line
(1=93･4^)
Iもc[･[24J
or
C且APTER.
1V
Applications_1ro BdgeMAnd
IV.1
this part,
some
There
discussed.
Interactions.
atomic
It is impossible
in
col)isions
【26】.F･dge plasma
and
treated
the
have
of articles
plasma
models
this particular
field.
cold molecular
been
lead
has
to
been
control
summarized
which
make
received
a
few
eV
in
the attention
a
plasma
processes
molecular
particle
been
main
and
in particular
concern
it merits
which
highdensity
of
which
Ref.
Our
●
reg10n,
and
and
respectively,
short.
plasma
in
of atomic
use
have,
be extremely
yet
of atomic
Ref. [27】. Neutral
experiments
diversiLy
the
concermng
[25].
field
complicated
and
not
numerous
extremely
reviewed
in the edge
of
of Plasma-Wall
physics
in
described
physics
Physics
The
optical methods
temperatures
gas
of Ref.
shall be
problems
impression
good
will therefore
molecular
The
a
has
for impurity
【29]. We
the
about
book
boundary
Molecularphysics
plasmas.
the
on
physics
in this broadand
will get
reader
p!asma
molecular
exhaustive
extensively
will be the treatmenもof
a
to be
The
in Refs. [28] and
朗vertor
amount
diagr7.OStics based
molecularproperties
transport
particular
of this {1eld in consulting
complexity
molecular
in
and
huge
a
exists
the presenもcontext.
within
by
Plasmas_
Introduction
ln
and
Divertor
in
in
surrounded
innuence
this type
Divertor
Plasmas
of
plasma.
Ⅳ2
In
a
Ⅱ
Chapter
lies inside
of
of Boundary
DeTlnition
we
defined
the magnetic
in
plasma
lies outside
the hot
the separatrix
and
magnetic
surface,
region
tha七is
Of the separatrix.
direction
to the
walls
and
The
which
of the (confined) plasma
is
that
as
14 shows
scrape-off
thought
to be
separatriⅩ.
scrape-off
forms
Layersand
the edge
layer
-64-
not
part
cut
(a)and
is that part
of the
conlined
The
boundary
from
by
that
toroidalplasma
a
of
poloidal
represented
extends
I)1asma.
a
layer
is magnetically
the magnetic
The
I)1asma
Figure
machine.
boundary
●
core
separatrix.
toroidal
a
Scrape-Off
and
to
a
a
top
plasma
closed
which
volume.
the outermost
The
closed
layer is situated
the separatrix
(b)
view
in radial
in the
spu ttering
reflectl'on
trqpplng
Cnd
a.
diffusion
rモモmlSSfOn
===I
=⇒■
r
一声
--一-◆
Figure
I4.
Definition
Charged
evoporotion
by
erosion
deposit ion
QrCS
particfes
neUtrafs
irnpurities
or boundaL･y
Rer. [30] for Fig. I4.a
and
(p(asma
contamination.
scrap-orr layers
in
wa((
a
Loroidal
an(I Re(. [31】for Fig. 14.b.
-65-
erosion)
plasma
device,
after
By
a
layer
the scrape10Lr
DOUBLET-班,
the target
at
region
When
plates.
highpressure
relative
Of the target
divertor
plasma
plates
is
which
capable
the
partly
as
energy
content
divertor
plasma
acts
field 一ines onto
Te
It is this
5
-
in
a
the
to 20
amounts
●
SCrape-Off
traLISformer"
plasma.
which
The
plates
divertor
a
and
a
part
it is
where
in
front
in
recycling
taken
of energy
The
strongly
from
thermal
transforms
energy
Pl(Ire
0('vertor PiQSmQ
Diver†or ThroQ†
Mul†ipole ⊂oiL
MQin
PIQSmQ
ChQmber
Scrape-Off
Lqyer
PLosmQ
divertor
conrlgul･aLion
-66-
of
the
ASDEX
tokamak,
the
recycling
ene_rgv.
Magnetic
the
high-density recycling
Tqrge†
15･
of
neutral
Oiver†o｢〔hql拍e｢
Figure
in
plasma
chamber,
strong
or
(e. ど.
is formed
eV
"closed"
plasma
inside
target
low-temperature
off huge
of radiating
"energy
placed
diverLor
the
place.
instreamlng
an
are
plates
surrounds
takes
or
thermal
radiation
target
to guide
ASDEX).
(DITE,
chamber
of temperature
I)1asma
the
plasma
it is possible
(Figure 15) situated
plates
the magnetic
along
divertor
cold
target
or
the main
outside
layer flows
A
neutralized.
or
fie一d structure
magnetic
to neutralizer
Pr,Ⅹ)
the scrape-oEr
gas
of the
suiとableぬiloring
after
Ref･ [32J･
in
lV･3
Formation
The
edge
plasma
is due
processes.
formation
far away
we
situation
limiter
that
hydrocarbon
Figure
along
The
and
or
16
other
notyet
clear
from
carbon
walls
a
molecules
shows
lines
pairs
how
or
of the
need
and
are
ends
The
neutrali21ed
main
In
order
to simplify
faces
main
charge
to the
is situated
plasma
of the
and
contribute
which
the
two
constituents
the
enter
a
to the
perpendicular
wall
the physical
from
far away
a
plasma
edge
metallic
wall
limiter
magnetic
(perpendicular
of the main
scrape-oぽ1ayer.
target
or
plate
field lines and
One
plasma,
part
mows
(parallel component).
hits the walls
where
component).
plasma
-
-separatrlX
≡:≡三コ =Eコ
I'甘,11盲
SCraPe-0
一ager
W{+{++1+a+1+7
′′′′′′′′′′
Figure
I6.
Diffusion
fluxes in the
so
be considered.
on
somewhere
layer
that
the separatriⅩ and
cross
processes
limiters.
carbon
assume
noももo
of the
10ni2;ation, recombination
scrape-off
Wewill
in front
molecular
the physicalprocesses.
pa.rt diffuses
the ion-electron
part
targeもplate.
any
layer
the scrape-off
Iもis
electrons,
tbe丘eld
in
Layer
to diffusion,dissociation,
will consider
any
protons
formation
plasma
chamber
transfer
Scrape-off
of the
scrape-off
layer
-67--
On
the wall,
e
numerous
●
incoTLllng
the
H+-e-
HO
The
atom.
palr
palr
formation
HO+HO+M-H20+M,
a
incomlng
the
●
+
H+-e-
●
For
become
and
processes
(II
do not
The
･7)･
Then
is then
1
HO
to form
1
the
on
adsorbed
to the
of 4.45
energy
an
wall
according
possible
1
I
lt
4
eV.
leaves
which
HO
aS
migrates
adsorbed,
H20
is absorbed
we
will
a
the wall
neutralatom,
reaction
M
be
can
the wall
as
on
a
reappears
and
moleculewith
later
much
equations
H+-e-
as
We
palrS.
they
have
parallel
for the atoms
and
an:
苛･-i2D-<w;,⊥言-
by
and
until
will
composition,
a
the edge
enter
this velocity
(This eLrect is treated
pairs
possible･
are
the neutrals
will keep
ion-neutral
the
neutrals.
that
and
field
magnetic
reactions
assume
<wO>1
ion-electron
the rate
as
Hx-Oy
many
change
of ions and
and戸ヱ.
+
atom
velocity
to the
which
equation
to encounter
whole.
l
palr
of oxygen,
mean
bound
distributions
HO.
atom
(retarded desorption).
of simplicity
some
with
a
J
is neutralizedand
molecule
presence
reasons
atoms
as
neutral
off the reaction
carries
+
_
H+-e-pair
thermal
Inthe
●
M
a
the chance
molecule
grid
4
Tlr
the incomlng
a
have
as
temperature.
the wall
as
Can
ofanH20
themetal
or
t
until it Tlndsanother
●
be reflected
where
atom
wall
Can
●
H+-e-
the incomlng
O
occur:
processes
are
influence
nux
perpendicular
ionized
exchange
the velocity
the Bolt2:mann
solving
electrons
they
neglect charge
only
as
plasma
COllision
i.e
vector,
write
(Ⅳ.∫.α)
cR=一九eSM
(N.1.b)
マ･弼･f;･苛⊥･叫箸】cR-･neSM
Electron-ion
has been
recombination
is permitted,
approximation
since
Also
per
of the total neutraldensity).
cent
neutral
in the collisional-radiative
the formation
event.
excited
neglected
have
atoms
been
of neutrals
omitted.
in the
scrape-off
(Their density
the eler,iron nu又 vectors
For
terms.
can
layer
This
is
represent
I7=ne<we>‡
Il-ne'we'⊥
1
ane
(N.2.b)
+D
neしu
0,⊥'
several
(Ⅳ.2.a)
ne
′
≡
rare
have
we
k(Te+T.)
≡
a
⊥n
ax
where
h(T+T)
e
(N.2.c)
e
帆+
is the
Eq.
ion acoustic
(N.I.a)
can
speed.
formally
On
the
r.h.s.
be solved
･,
ofEq.
(Ⅳ.2.b) we
obtain
we
-68-
made
use
ofEq.
(Ⅱ. 5I).
(Ⅳ.3)
n冨(x,-a;(o,
is the
where
nf(o)
(x)･
A:
depend
on
density
Theもwo
exp卜I
the
at
ne(x) is determined
wall.
must
equations
by Eqs.
be solved
simultaneously
(Ⅳ.7)
to
(Ⅳ.8) which
or
obtain
n10(x)and
ne(x).
one
define
can
an
n10(x) has decreased
which
length
aもtenuation
to
lO for the neutrals,
which
is that
length
for
x=AO
:
nP(o)/e
(Ⅳ･4'
<w;,i,血-1
I三=10(s:(x,
ne(x,/
wewi11
define
a
mean
temperature
electron
value
Te
10 by
in the edge
a
assumming
From
plasma.
mean
electron
Eq.
(N.4)
density7fe
a
and
mean
:
王0= <w?>l
言9言
vl're
where
is the
-a;
For
neutral
(<wl>⊥=
mean
2×
electron
neutral
To
atoms
ionization
●
hydrogen
104m/s)
density
for
coeLrlCient
atoms
and
leaving
entering
Teand
7fe=1×1013cm-3,
diffuse deeply
find the distribution
ne.
the walls
the edge
plasma
the
into the scrape-oLr
of the electron
(Ⅳ.古)
with
of
attenuation
laye1'and
density
across
a
kinetic
mean
of 2.6 eV'
Te=7eV
temperature
length
even
energy
is lO=
88cm.
into the mahl
the scrape-off1ayer
and
Thus,
the
Plasma.
we
put
(Ⅳ.♂)
The
Eq･
by
(N･1･b) thengives, with
(N･2･ b) :
the expression
Il;substituted
TL
(N.7)
蓋トevoi･D⊥登i-nes:a:一音
is determined
where
by Eq.
,i?(x)
are
approximations
is
uol
We
made.
that Di
to the
close
is constant
that
assume
negligible (whichwill
assume
(Ⅳ.3)･ An
wall
a2n
be
surely
layer.
Eq.
Then
further
when
velocity
We
hypothesis).
good
a
possible
convective
perpendicular
the scrape-off
across
l
the
is only
solution
analytic
further
(N.7) becomes
(Ⅳ.β)
1
-
ne
layer
first increases
term
The
-ヱニー-(トSM一切)
ar2
DJ_T1
ST(I)not(x)
(because of the
temperature
one
when
increase
from
proceeds
increases
which
the wall
Deep
into the scrape-off
Sf)
A
in the
scrape10ff
I
Sioixe'ncthhaengEe
1haiyge:･teSIo:xe'rnaPtix,'esd,?crLaes
the solution
-(a-x,仁許】-
(Ⅳ.9,
ne(x)=ne(a)
ne(a) is the electron
where
qualitative
has
the
energy
1n
has
feature
Owing
●
its energy
low
to the
ions is slow,
So
strong
from
radiation
the thermal
temperatures
Figure
x=a.
distributions.
To
17gives
a
T(x)
obtain
highthermalconductivity
be the
stays
higher
than
are
species
one
the electron
above
This
present.
ions,
and
Eq.(ⅠⅠ.88).
see
energies of electrons
Also
temperature.
temperature
the electron
the electron
atoms
of the electrons,
of the thermal
that
reason
of impurity
content
the equipartitioning
can
to be
ioni2;ation of the impurity
and
energy
the ion temperature
that
at
is often found
highconcentrations
when
in七he
its orlgln
takes
which
Particular
●
situated
temperature
and
temperature
theion
●
temperature,
the separatrix
equation.
layer,
the scrape-off
at
of the density
representation
to solve
In
density
e
is lower
and
a
than
the
ion temperature.
IV.4
Recycling
The
8
Coefficient
proton-electron
neutral
particle
nux
flux (TIJ/=T⊥+) onto
(Flo).
In
Ⅲ.5
Chapter
う
i
i
一
is
a
quantity
which
averages
●
streamlng
neutral
particle
out
f]uxes･
Ll
e
all poloidal
R
is
an
have
we
･･■
ro,R･dS=-R
R
the walls
partly
defined
a
back
recycling
to the
plasma
coefficient R
〟
-■
･dS=-R
toroidal
value
as
by
(N.10)
r
Pte
and
average
-70-
returns
for
variations
the whole
of tJhe back
inner
wall･
The
l
localvalue
of R
distribution
of time･
by
a
Ha
of
It is
be determined
can
Hp
or
even
discharges･
plasma-wall
interaction.
the Eqs.
ionization
volume
R
of gas
38.c,
changes
R-values
some
been
the
the
walls･
time
from
important
are
mean
for instancethe
R
for
R
isalso
better
a
function
a
to R>1
precedent
understanding
be expressed
can
radial
R<1
values
during
accumulated
40, 42) folliOWS that
【∂NJ∂l]cRand
rate
to
Close
after
has
which
of local
(Ⅱ. 38.a,
region
plasma
that
amounts
Measurements
From
the edge
conceivable
of huge
release
in
by measurlng
spectroscopically
by
the
of
total
:
confinemenもtime
`Ⅳ･11'
is the
Ne
total
also
equation
R若+￠o･G=[登】cR･警
number
No
of electrons,
the inwardly
that
shows
the
one
of neutral
directed
neutral
inthe
atoms
nux
particle
main
This
is the
plasma.
for the
source
ioni2:atioll Processes.
IV.5
Properties
Divertor
of Diverted
followed
by
reacts
with
the main
a
limiter
impurity
of the impurity
inもeraction''takes
Somewhere
must
contacもtakes
away
from
the main
Measurements
electron
Also
the
far away
density
neutral
from
layer
the divertor
target
Owing
interaction"
have
in the
gas
impurity
less
producing
shown
divertor
the divertor
plates, many
(H2
target
mean
with
molecules)
plates
a
intensely
limiter
to enter
into
between
[34].
source
of
plasma-chamber
material
wall
the interaction
that
there
electron
a
density
6e of the
non-1inearly
molecu一e
with
non-linear
density
with元e.
This
iO(see
in the
temperature
is
walls.
lengths
than
increases
hydrogen
-71-
In the
surface;
and
this
"edge
attenuaもion
relative low
[32, 35-39]
p一asma
reduction
plasma
plasma
contact"-
into contactwith
come
to the
sputtering
highprobability
less violent
reduced
atoms.
is also less violent
further
pressure
much
the separatrix
the main
plasma-1imiter
the
Only
exist.
plasma.
this "plasma-target
"main
The
the limiter
thin scrape-o打1ayer
very
(limiter surface) and
the scrape-off
on
place
not
a
a
strongly
interaction".
with
to metallic
abOmS) have
only
to
close
14) leading
or
-without
does
place
no
source
discharge
production
is
"plasma-1imiter
is very
which
is
plasma.
main
is in direct contact
plasma
(see Figure
there
the
[32, 33, 39J
shown
of carbon,
andalso
to reduced
(and/or carbon
atoms
because
diverted
due
have
contact"-
loss from
radiation
scrape-o打Iayer
surface
metallic
plasma,
the location
In
disI:harge, the main
the
The
erosion.
of the
species,
is mainly
concentrations
that llartOどthe
also
"plasma-1imiter
of metallic
decrease
noticeable
limiter
a
of
and
concentrat,ion
impuri'(y
of the
case
a
direct
witholl.i
experiments,
the impurity
that
Plasmas
Eq.
scrape-off
the
For
layer
limiter･
increase
main
Ⅳ.5)
of the
plasma･
instance,
of nf120--3× 1013cm-9
was
ASDl弓Ⅹ
measuredinthe
[36]. The
The
mean
increase
non-linear
by
Addiもion8l
discharges
a
[38, 40] did
(Te33 10eV) nearthe
divertor
diverted
with
features
Molecules
and
play
gas
intense
shell of the divertor
18
Figure
transitions
:
ionization
ions
plasma.
ASDEX
temperature
Of the plasma
-ne
temperature
that the
shown
in
the main
is
plasma
is attached
leads
The
plates.
of the
[32, 35, 38-40].
plasma
to strong
submitted
to the
are
conditions
are
properties
target
highdensities
to
recycling
such
is surrounded
plates
of the particle
nuxes
that
could
●
in particLi.1ar
plasma,
the plasma
molecules
■
In
at its perlPnery.
likely entirely
very
19,
shown,
molecule
Therefore
and
as
by radiative
a
Some
with
potential
the
same
the outer
determined
by
homo-nuclear
radiative
transitions
scale
belonglng
linear
top
take
(respecting the selectionrules).
vibration
transitions
represent
additional
take
place
radiation
lost
tO each
place
when
However,for
(rotational and
loss channels,
temperature.
-72-
no
thus
in
state
the molecule
vibrational
leading
H2+and
Fig.
18.
are
many
noもshown.
changes
its
many
bands).
They
decrease
The
H2
momont.
electronic
transition
electronic
a
H2+molecular
The
electric dipole
electronic
to
transfer
of radiation.
permanent
each
electronic
which
molecule,
electronic
has
molecule
only
in the form
for the H-atom
as
and
processes
main
for the H2
curves
energy
de-excitation,
the
are
important
the most
with
spantaneous
is then
which
energy
rotationallevels
by
recombination
energy
hydrogen
of atomic
followed
excitation
tointernal
Figu,e
are
the level system
electronic
followed
vibrational
state
target
plasma,
shows
energy
In
is
plasma
properties.
molecular
thermal
main
-ne.
Plasmas
which
role in the divertor
important
an
Divertor
highpressure
the
on
have
the divertor
that
plasma
at relative
recycling
of the
modesも1evel) of diverted
increasing
with
in Recycling
fact that the divertor
molecular
plasma
as
[32, 38, 40-42].
rV.6
a
the main
magnitude
the divertor
izICreaSe
noticeable
discharges
indications
are
the divertoL･ Chamber
The
a
same
of
with高e
from
in
plates.
within
by
to
densities
(at relatively
strongly decreases
plasma
These
lead
not
was
plasma
of radiation
heating
target
All experiments
the divertor
increase
beam
for -ne空6×1013cm-3
chamber
of the divertor
non-linear
neutral
in
density
electron
accompanied
divertor
of plasma
rotation-
e
Figul･e
+H(ls)
18･
Level
system
of atomic
hydrogen
2
1
some
with
3
collisionand
ムr(A)
internu､c.Itear dis.tQnCe
Figure
t9･
Potential
energy
curves
forthe
-73-
H2
,
H;and H22'molecules
radiation
processes
The
plasma
followed
curves
dissociation,
by dissociation･
the other
energleS
minus
temperatures
At
the transpor七of
depends
excited
levels and
could
the energy
on
dissociation
as
thermodynamically
ionization
and
from
L. T. E.
an
are
in Figure
shown
20
●
diLrerent
quantum
in divertor
the 00-atom
of H2
energy
stable
roもational states
The
020 and
of internal
a
with
and
whieb
The
energy･
2I
same
The
states
situation
is diuerent
deep
minimum
leading
potential
No
for
to
density
nitrogen,
curves
energy
electronic
structure
020-molecule･
stable
of
The
electronically
many
O言whichforms
large number
a
the
on
potential
ofもhe
state.
ground
function
partition
eventually
particular
of the electronic
electronic
The
removal.
22･
and
and
1013cm-3,
ne=5×
depends
not
Oxygen,
plasmas.
for energy
internal
or
role
The
are
02+ molecules
a
three
atom,
excited
stable
of vibrational
havealso
radiators.
excellent
for conducting
capabilities
is valid for N20and
N2+･
Figure
23
huge
amounts
their internal
shows
functions.
partition
Theformation
energy
removalof
internal
in the
far larger
a
for heat
of the H-atom
For
chosen.
is far
plasma
indication
an
the hydrogen
been
actually
tokamak
diversity
found･
curves
play
in Figures
is only
potential
has
be the
greater
been
mO)ecule
''stars"
a
have
J1=i'have
in
shown
yields
H{-molecule
states
are
numbers
oxygen
plasmas
0;
For
states
equilibrium
of the H2-mOleculeand
of temperature.
molecules
nH:/nH9
for 0,0, o2+and
energy
the H2
Whether
It is difficult to avoid
could
functions
in the
of quantum
divertor
be
transport
internal
energy
number
can
energy.
energy
capability.f
Althoughthe
function
partition
partition
function
a
be seenもhat
can
the H-atom.
ratio
as
function.
12eV,
i-) 1014cm-3,
of (local) thermodynamic
state
●
cut-oLr prlnClpal
i●--18･ It
than
internal
The
removalcapability.
the internal
state,
of 1013
of internal
The
energy.
in the
occupied
transp.,i
form
sam?.e
role in七he
certain
in
be stocked
can
which
the
atom
each
of the order
a
play
eventually
(IJ.T.E.) isgiven by the (internal) partition
away
to give
have
atoms
excitaもion to 9-
:
●
by two,
for
is used
These
atoms".
particle densities
and
internalenergy
energy
are
divided
energy
repulsive
energy
of 2.514eV/atom
in Eq. (ⅠⅠ.61).The
from苛･(EL･n13.+るInL)
(contribution
which
"Frank-Condom
in the range
of 5 to lOeV
the moleculeもo
of this thermalelectron
part
of 4.4eV,
energy
in exciting
to form
lie mainly
Which
dissociation
One
is used
part
●
kinetic
lose energyalso
electrons
energy)
of oxygenand
by
under
removalbecause
ions of
nitrogen
(and
radiation
conditions
to
probably
for which
iもis completely
higher
plasma
much
lesser
extent
not
further
a
hydrogen
ioni乞ed.
-74-
does
temperatures
by
still ensures
conduction
contribute
of
to the
and
1
2
3
4
5
6
7
T
Figure
20･
Internal
parLiLion
function
(or atomic
-75-
and
molecular
8
(104oK)
hydrogen
9
10
o(3p)
+q†(2DO)
22
o(Io) +o+(&sO)
o(3pl
+
0+(4sO)
J■ー
め
■ト●
二二
__
0-
t6
>
(=
O
L
【===コ
I4
O
4J
.巴
>-
l之
o(ID)+0(Is)
C)
0=
山
≡
tO
o(3p)+o((sl
LJ
＼､､--ユ.>一プ
■■
■∃
I
≦
ヽ__/_′
rIも
+0(tbI
o(3p)+o(ID)
･t
lヽ
卜
≡
o(lDI
J′
l
tlJ
ト
O
o(3p)
CL
+o(3p)
a(3p) +o-t2pO1
4
0;
0.4
0.8
暮.2
J.6
2.0
2.8
2.4
5.2
3.6
0
‡NTERNUCLEAR
DfSTANCE
l
Figure
211
Potential
energy
curves
for the
O2･
-76-
02- and
(A)､
O21･ molecules･
after Rer･ [43l･
Figure22･
Ⅰ'otcnLial energy
curves
for the
02- molecules,
-
771-
after
Rer･
[44】･
5
10
15
20
25
30
丁(103 oK)
Figure
23･ InLernal
partition
Rer･ [45)I The
functions
partition
P"･nL) for the
(unction
02
I
02+I N2
for II2 0r Fig.･ I9
-78-
is
I
and
showL
N2+mo]ecu]cs･
(or comparison･
artel･
Collisional-Radiative
rV. 7
All these
considerations
quantitatively
0nlyfor
i.T.B.
To
describe
a
●
Unfortunately,
qualitative.
role the molecules
the eLrect of molecules
ions and
indispensable
rather
and molecularions
and
is necessary
model
ions. To
atomic
both
to consider
which
ensure
forward
Stationary
Then
recombining
local thermodynamic
approaching
We
and
will consider
the following
consistency
backward
and
diatomic
be included
should
electronic
dissociationand
molecule,
ionization
states)
atom
in the model
:
recombination
3-body
and
≒A2十(kuJ)+2e-
A(i)+e
with
:
recombination
A2(nuJ)+e-
ionization
u)+2e-
≒A+
dissociation
A2(nvJ)+e-
:
→A2+. (kuJ)+2e-
1
rep ulsive
A+
(A2(nvJ)+eCharge
exchange
(l)+A(1)
(i)+A+
-A+
:
A+A+年A++A
A2+A+年A2++A
A2+A2+与A2++A2
Radiative
recombinationand
a
quantitatively,
atoms,
it is
model
to study
permits
for
the conditions
symbolically
･.
j
This
reactions.
A2+ (nuJ)+e一年A+(1)+A(i)+2e-
Electron-impact
plasmas.
plasmas
molecules,
of such
to investigate
plasmasand
homo-nuclear
i and
electrons,
couples
some
in divertor
A2('WJ)+e-与A(1)+A(i)+e-
Electron-impact
in divertor
play
be said
can
much
equilibrium.
reactions
vibrationalstates,
Electron-impact
a
ions
molecular
●
ionlZlng,
not
is their influenceknown.
plasmas
molecular
+
the
about
are
for Molecules
Models
:
photoionization
A++e一年A+hv
A2++e-
ち A2+hγ
-79-
∽+3e-)
designated
(TWJ designate
by A2.
electronic
ro-
Dissociative
:
recombination
A2++eAtomic
recombinat.ion
dissociation
and
→A+A
:
A++A+A串A2++A
A+A+A
The
reactions
these
reactions
reactionswithin
electronic
excitation
The
presence
e･
associations,
impurities
The
great
reactions
of carbon
g･ CxHyI
an
excited
CO,
OHI
atomic
and
reactions
in
excludes
an
play
plasma
task
●
most
prominant
reaction
To
test
calculationswith
a
properties.
Whether弓uCh
availability
and
heavy
simplified
larger
number
plasma
velocity
atomic
models,
of reaction
of the relevant
particle
edge
calculations
and
distributions
which
-80-
can
data
molecular
are
by charge
important
When
in the model.
to
numerous
molbculal･
transfer
in
reactions
ip. which
all
too
or
is thereforf,A the identification
dominate
the edge
many
of the
plasma
model
be performed.
should
be performed,
and/or
A2+-
role.
5t7dependent
processes
level.
spatial disもribuもions of metal
models
assuml17'.ど that they
processes,
The
influenced
important
leads
:
levels, and
ground
plasma
to
most
that is
accountl
be included
also
ions･
edge
taken
fromthe
must
species
into
ro-vibrational
and
hydrogen
a
is strongly
An
to be
In addition
state.
(and their ions), the
species
reabsorption
molecular
into account.
taken
have
CO皇, -andtheir
of reactions
their quantum
atomic
of electronic
oxygen
and
to
A+
and
eventual
environment
variety
are
A
the corresponding
in such
the
which
and
specified by
species
de-excitation
and
be formed,
can
be
possible
A2, A2,
de-excitations
Spontaneous
as
link molecular
which
important
ions
far
as
should
A2+A
*
rate
characteristic
or
not,
coefficients
for edge
depends
the
on
for electron
plasmas.
lV.8
AtomicAnd
Reliable
presence
model
data
molecular
Molecular
for the prominent
and
The
electronicstates.
the formation
the 02
molecular
should
be affected
The
ion H2
and
the
tO have
and
The
situation,
dissociation
SぐemS
of atomic
their ions.
complicates
2Ⅰ-g
by
three
the
since
ionization
and
of
direct innuence
a
fわr the al△g and
observed
02 molecular
of the
to
According
loweststates
ion which
edge
plasma
that
one
dominates
Refs.【46,471 thefo1lowing
of
elo告e to the walls
the
6eV
around
in
and
of
of 02
B3∑u-, l∑こ
11∑こ,
which
the divertor
excitation
states
A3∑u', A'3Au,
blEg!,
excitaもion energleS
or the
of the
electronic
●
have
bl∑g states
is the existence
O言states: Ⅹ3∑盲,
alAg,
intermediate
in払e
been
of this phenomenon
reason
state
levels.
the temperature
considerably
molecular
have
populations
resonance
lAu.
species
molecular
seJ(
minimum
role in the excitation,
of the
[46]. Theprobable
intermediate
a
require
ions.
ofH
molecule
ions
Plasmas
plasma
and
important
an
existence
Non-Fran￠k-Condom
and
atomic
molecular
levels play
ro-vibrational
02
for the edge
calculations
of molecules
for Edge
Data
to
corresponds
close to
plasma
the targeもplates.
This
exampleshows
data.
molecu王ar
edge
studies
data.
Only
The
in
Ref. [48] with
But
established.
finds
reader
for the H2
a
molecule
coupling
of the data
of the available
the H2
and
in the application
careful
discussion
a
review
data
of the presentlyknown
●
for fusion
requlrementS
data
base
of atomic
ion is the data
molecular
the
with
rate
emission
of Hq
atomic
and
Hp
and
base
plasma
molecular
relatively
to treat
aremissingwhichpermit
of the molecular
for insta_nee the photon
determines
to be
for this molecule
even
has
states.
This
which
i8 used
well
the
process
coupling
as
a
diagnostic
tool.
Theknown
molecular
compiled
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cross-sections
hydrogen
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for hydlogen,
the molecular
A
data
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the rate
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H:,H,7
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H3T)and
helium
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atomic
its ions
isgiven
to the
atomic
are
not
yetknown
states.
一番1
-
and
which
are
have
in Ref･
●
1mPOrtantCrOSS-Sections
and
necessary
been
[52】･As
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APPE
The
NDIX
mean
forany
i) >
<Q(i,
value
function
arbitrary
calculated
asfo1lows
+○)
･.
are
i)d3w
Q (iw)
n(r,i)
derivatives
by
i(Jw/,,
I:I:I
<Q6,i)>=⊥
The
Q(Jw,7,i) isgiven
+く○
川Q(a,冨#w-豊川Q(w,f(a,jrlt,d3w-孟
=ーW
divergence
The
of the
=
of a (+a)is obtained
moment
velocity
[･きコ
+oo
asfo1lows
+○〇
∫(''w)蒜F(1w,.r,
IIIQ(a,-F㌔w-守･
∫
∫
i)d3w=1v
a
t】○
-
The
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the
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with
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integration
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over詔
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because
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一
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forces
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:
:
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gradient
operator-ith
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to
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:
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aw
w
X
-86-
y
2
OF
LIST
辛
IPPJ-AM-I
=Cross
Sections
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H.
Tawara
fわrCharge
Range
Transfer
10 eV-10
of Hydrogen
Beams
in Gases
Vapors
and
keV"
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(1977)
REPORTS
Data
in Atomic
Nuclear
and
Data
22,
Tables
(1978)】
491
*
IPPJ-AM-2
Energy
IPPJ-AM
"Ionization
Excitation
and
or lons by Electron
Impact
or Empirical
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T. Kato
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IPPJ-AM-5
IPPJ-AM-6
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IPPJ-AM-7
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H. Narumi
T. Fujimoto
"Charge
l
Changing
from
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Positive
Atomic
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1940
"Charge
Changing
Cross
from
Sections
"Energy
for Excitation
and
Helium''
0.1 eVto
Okuno
in the Energy
Their
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for Heavy-Particle
10 MeV
N, Oand
ofC,
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Their
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and
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Y. Yamamura,
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II. Incidence
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Atomic
Or
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I. Incidence
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0.1 eVto
S. Nakazaki
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Cross
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"Charge
Born
IPPJ-AM-
Cross
Okuno
Kazuhiko
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Plasma
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Electroll
Kazuhiko
Range
IPPJ-AM-1
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Metal
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T. Iwai (1978)
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Range
10
Data
1977"
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Atomic
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Heavy
a
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M. MatstlZaWa
Elec'LrOn
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Y. Kaneko,
T. Arikawa,
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on
Interactions,
Itoh, 氏. Kamada
and
and
May
21
H. Tawara
(1984)
in Surface
Phenomena
23, 1984"
-
(1984)
【Published in Radiation
Efrects 89, I (1985)I
IPPJ-AM-36
=Equilibrium
Foils
through
K. Shima,
Nuclear
IPPJ-AM-37
Data
Nuclear
"Rate
IPPJ-AM-39
"Proceedings
TYleOry
and
IPPJ-AM-41
Data
and
Data
and
(Ⅰ986)I
of Atoms
M.
Ohnishi
lons by Electron
and
(1985)
[Published
lmpact"
in Atomic
Excitations
of C-like Ions"
(1985)
of the Japan-U.S.
Modeling,
Mar.
Y. Yamamura
and
the
Workshop
12
-
Impurity
on
and
Particle Control,
16, 1984"
(1985)
Sputterings
on
Passage
36, 167 (1987)I
"Low-Energy
"Data
(Zl ≧4) after
(1985) [Published in Atomic
for the Electron-Impact
Ed. by T. Kawamura
IPPJ-AM-40
and
Tables
Coemcients
Y. Itikawa
Sections
lons
or
after 1 972"
H. Tawara
34, 357
T. Kato
Data
Distributions
of Data
and
Tables
Cross
Tawara,
State
Compilation
-
T. Mikumo
"Ionization
H.
IPPJ-AM-38
Charge
the Monte
with
Y. Mizuno
Carlo
Program
ACAT"
(1985)
Backscattering
Coefficients
of
Light
Ions
from
Revision)"
R. Ito, T. Tabata,
N. Itoh, K. Morita,
-89-
T. Kato
and
H. Tawara
(1985)
Solids
(a
IPPJ-AM-42
"Stopping
Fusion
Power
Theories
Plasmas
(Emphasis
S.耳arashima, T.
IPPJ-AM-4
3
"The
Collected
Ed. by H. Tawara
IPPJ-AM-44
"Tokamak
5
Modelling
IPPJ -AM-4
6
Data
H･ Tawara,
Y･
IPPJ-AM-47
Ed･ by
Y･ Kanai
"Wavelengths
IPPJ-AM-49
T. Kato,
IPPJIAM-5
0
S. Morita
"Proceedings
of
action/High
Heat
IPPJ-AM-5
1
K.
and
at the
lOMW
Neutral
Miyahara,
Dependence
Y.
Base
5
Yamamura,
Facing
Neutral
IPPJ-AM-46
H. Tawara,
0.
Ignition
Materials
and
Steady
by
Hydrogen
of the IPP Nagoya"
Y.
Kaneko,
Sputtering
Y.
Kubota,
Oka
Yields or Monatomic
N. Itoh, H. Tawara
Flux
Components
-
and
Solids
Behaviour
T. Kawamura
and
of Metals
Experiments
and
Carbon
10 MW
at the
(1987)
Materials
Neutral
Beam
of the IPP Nagoya"
A. Miyahara,
Electron
State-Resolved
(n. O
"Atomic
Composite
Injection Test Stand
Kuroda,
the HighHeat
on
T. Kuroda
Capture
and
by
Y. Oka
(1987)
Charged
Multiply
Ions
Atoms"
N. Toshima,
N. Shimakura.
IPPJ-AM-5
C-C
on
Beam
T.
H. Bolt, C. D. Croessmann,
from
Step
Region"
Injection Test Stand
"Final
Next
lnter-
Material
(19只7)
or lon-Induced
Energy
ro† Plasma
IPPJ-AM-54
Plasma
on
(1987)
"Energy
"Data
P-92
for the
L. Wilson
Beam
N. Matsunami,
3
Workshop
30, 1987"
Experiments
A.
Ions (Proceedings)"
Needs
Flux
in the Low
IPPJ-AM-5
Data
-
Heat
Bolt,
H. Takagi,
(1987)
Japan-U.S.
Flux
by A. Miyahara
K. Sakurai
2
H. Tawara
the
S. Ohtani,
Iron Ions"
of
"High
H.
IPPJ-AM-5
(1986)
Jam. 26
State Devices,
Ed.
S. Ohtani
and
H. Nishimura,
(1986)
Charged
of K X-Rays
Plas皿aS=
Collisions''
of Highly
and
to Edge
(1986)
G. H. Dupn
and
Processes
"Dynamic
Relevant
in Electron-Ion
Effects
Ed. by 班. Tawara
IPPJ-AM-48
Yoshino
Collisions
T. ■Watanユbe (1986)
and
Y. 1toh, T. Kato,
M.
and
"Resonance
Processes"
in Ion-Atom
Hydrogens
Itikawa,
Takayanagi
Atomic
and
N. Tosbima
lnvolving
∼_K
(1985)
Nagoya"
Pro)'ect/IPP,
Transfer
N. Sbi皿akura,
"Atomic
Matters)"
H･ Tawara
and
lnertial Confinement
(1986)
of Electron
Ⅲ. Tawara,
in
(1985)
Plasma
Bibliography
Dense
and
T. Kato
of Nice
Ed. by T. Kawamura
IPPJ-AM-4
Hot
on
Watanabe,
Papers
Particles
for Charged
Data
for
T. Watanabe
Hydrogens
and
in Collisions
H. Tawara
with
(1987)
Electrons
"
Y. Itikawa,
H. Nishimura
-90-
and
M. Yoshino
(1987)
-
Addenda
to
IPPJ-AM-56
=Total
oq+
Models
K. Fujima
for Hot
Capture
H, H2 and
He
for Cq+
(q= 6-2)and
Atomsn
Dense
PlasmasH
(1988)
=Recommended
IPPJ-AM-59
fわr Electron
(1987)
uAtomic
IPPJ-AM-58
Sections
Ions in Collisionswith
(q=812)
H. Tawara
IPPJ-AM-57
Partial Cross
and
Data
for Excitation
Helium-Like
lons by Electron
T. Katoand
S. Nakazaki
"Atomic
Coemcients
Atoms
of口elium
and
lmpact"
(1988)
Molecular
and
Rate
Processes
in Edge
Plasmas
Hydrocarbon
Including
Molecules=
Ed. by 冗. Tawara
IPPJ-AM-60
"Theory
(1988)
or Tbresbold
Energy
or ‥on-Induced
Desorption
by
a
Few-Collision
ModelM
Y. Yamamura,
IPPJ-AM-61
"The
J. Bohdansky
Application
of
and
Atomic
E. Taglauer
and
(1988)
Molecular
Physics
in Fusion
Plasma
Diagnostics"
E. W. Drawin
Available
University,
upon
request
Nagoya
to
(1988)
Research
464, Japan,
Information
except
Center,
for the reports
-91-
Institute of Plasma
noted
with*･
Physics, Nagoya

IPPJ-AM-61(PDF 5421KB)

Transcription

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