Compression of Compact Toroids in Conical

COMPRESSION OF COMPACT
TOROIDS IN CONICAL-COAXIAL
C^ f— f j Iwl p T p Y
E X P E R I M E N T A L DEVICES
KEYWORDS: compact toroid,
compression, conical-coaxial
J. H. DEGNAN, G. P. BACA, D. E. BELL, G. BIRD,* A. L. CHESLEY,
S. K. COFFEY,t M. E. DEARBORN,t M. R. DOUGLAS,
S. E. ENGLERT, T. J. ENGLERT, D. GALE,J J. D. GRAHAM,J
K. E. HACKETT, J. H. HOLMES,§ T. W. HUSSEY, G. F. KIUTTU,
F. M. LEHR, G. J. MARKLIN, || B. W. MULLINS,# R. E. PETERKIN, Jr.,
D. W. PRICE, N. F. RODERICK, E. L. RUDEN, M. SCOTT,J
S. W. SEILER,* W. SOMMARS,f and P. J. TURCHI
Phillips Laboratory, High Energy Plasma Division
Kirtland Air Force Base, New Mexico 87117-5776
Received May 5, 1994
Accepted for Publication September 19, 1994
Experiments to form, compress, and accelerate compact toroids are described. A 1-m-diam, two-stage, puffed
gas, magnetic field embedded coaxial plasma gun is
used. Emphasis is on conical compression. Discharges
were in the several mega-ampere, few microsecond rise
time range. Magnetic probe data suggest that l/(r-br)
compression of the toroid field is achieved, consistent
with theoretical prediction. The magnetic field pulse
and electron density pulse due to the compact toroid
correlate in space and time. The compact toroid species is the injected gas species and precedes electrode
plasma by several microseconds. The poloidal magnetic
field precedes the azimuthal magnetic field. The time
of arrival of the axial magnetic field compared with the
axial position is consistent with the mean current axial
position trajectory obtained from inductance growth.
INTRODUCTION
The Phillips Laboratory magnetically accelerated
ring to achieve ultrahigh directed energy and radiation
•Current address: Physical Sciences, Inc., Alexandria,
Virginia.
tCurrent address: U.S. Air Force Academy, Colorado
Springs, Colorado.
tCurrent address: Maxwell Laboratories, Inc., Albuquerque, New Mexico.
§Current address: Bosque Farms, New Mexico.
||Current address: Houston, Texas.
(MARAUDER) compact toroid program is studying
the formation, compression, and acceleration of compact toroids. This effort was inspired by the Lawrence
Livermore National Laboratory RACE compact toroid
acceleration effort. 1 Compact toroids are magnetized
toroidal plasmas with linked poloidal (axial-radial) and
toroidal (azimuthal) closed magnetic field surfaces. The
magnetic field distribution is nearly force free, and in
a relaxed compact toroid, the free energy is minimum
for a given helicity, a conserved quantity.
The helicity is K = f A x Bd (volume), where B =
V x A. The helicity is approximately a product of
the poloidal and toroidal magnetic flux. This is a measure of the linkage of the poloidal and toroidal magnetic flux. The relaxed state is referred to as the
Woltjer-Taylor state, or the Taylor state. The Taylor
state magnetic field distribution depends on the confining electrode geometry, called the flux conserver
geometry. 2
The compact toroid is resilient and has considerable
stability under acceleration and compression by magnetic pressure, provided the accelerating field is less
than the compact toroid magnetic field. The ability to
accelerate and compress compact toroids without fluid
instability growth may have important applications to
fusion, including magnetized target fusion 3 and inertial
confinement fusion. This stability under compression
and acceleration enables much longer compression/
acceleration times and distances than in ordinary Z
pinches, the latter being limited by instability growth
to —0.1 /zs and a few centimetres 4 versus many microseconds and metres for compact toroids. Thus, much
easier, less expensive pulse power may be used with compact toroids, enabling less expensive scaling to higher
energy.
#Current address: SAF/AQ, Pentagon, Washington, D.C.
107
FUSION T E C H N O L O G Y
VOL. 27
M A R . 1995
Degnan et al.
COMPRESSION OF COMPACT TOROIDS
RESULTS AND DISCUSSION
We are forming and accelerating compact toroids
with a two-stage coaxial plasma gun. The first-stage discharge into a magnetic field embedded gas puff forms
the compact toroid. The second-stage discharge compresses and accelerates it. The formation occurs when
the magnetized toroidal plasma bubble pushed into the
expansion region by the first-stage discharge undergoes
reconnection of the poloidal field (PF) lines in its neck.
When energetically favorable, such reconnection occurs
when the diffusion time across the PF (reversal) scale
length becomes approximately as short as the Alfven
time for that scale length. The duration of this reconnection process is roughly the geometric mean of the
Alfven transit time and the diffusion time for the field
reversal layer.
The Phillips Laboratory full-energy (9-MJ) design
concept, intended to be driven by the Shiva Star capacitor bank 5 (1300 /xf, 120 kV) is illustrated in Fig. 1.
Compression of the formed compact toroid in the early
stages of the acceleration increases the compact toroid
fields to enable stronger acceleration fields, while retaining stability and avoiding blowby of the accelerating fields past the toroid.
To the extent that the compact toroid poloidal and
toroidal magnetic field fluxes are conserved, and to the
extent that compact toroid compression is self-similar,
the compressed toroid field should scale as B 0 ro/r 2 ,
where B0 is the initial toroid field ( - 0 . 5 T) and r0 is the
CF = 110 jiF
1/2 CFVF02 = 500 kJ
CA = 1300yiF
1/2 CAVAo2 = 9 MJ
initial toroid major radius ( - 5 0 cm). For full energy
(9-MJ acceleration/compression capacitor bank energy), we intend a factor 10 to 20 compression. For this
compression range, the expected toroid fields are 50 to
200 T, or 0.5 to 2 MG.
Thus far, we have formed 1-m major diameter,
18-cm minor diameter, 1- to 2-mg compact toroids with
argon, N 2 , and H 2 . We have performed low-energy (a
few hundred kilojoules) acceleration experiments in
straight coaxial geometry,6 and we have done megajoulerange, factor 3 compression experiments.
In that first-stage portion, we inject gas with an array of 60 fast (pulsed-solenoid) valves. Transient gas
distributions have been measured in situ with Penning
ionization gauges and piezoelectric pressure probes.
More detailed auxiliary experiments with single valves
include careful mass injection measurements with a
theta discharge closure of a copper injection tube.7 Gas
distributions are also calculated by using two-dimensional hydrodynamics. In this first-stage portion of the
gun, we inject 0.1 to 0.2 T of radial-axial magnetic field
by using a pair of pulsed solenoids. The solenoids are
driven by a 15-mF, 1.7-kV, 10-ms rise time discharge.
Field distributions are measured with Hall probes and
calculated with two-dimensional magnetohydrodynamics
(MHD), including diffusion effects.
The prototoroid formed and trapped in the expansion region relaxes toward the Woltjer-Taylor minimum
free-energy state, with the closest approach —15 /xs after
the start of formation (first-stage) discharge.6 The toroid
BCT~1/R2
^PISTON ~ 1/R
ACCELERATION/FOCUSING
REGION
R - 15 cm
B ~ 5-10 7
R - 50 cm
~ BT ~ BP ~ 0.5-1 T ~ \
/ /
/ /
I COMPRESSION REGION
f
(3X COMPRESSION)
\
/
EXPANSION/FORMATION
REGION
« — GAS INJECTION
CFVF
FIELD INJECTION
SOLENOIDS
Fig. 1. Full-energy design concept for compact toroid formation, compression, and acceleration using a two-stage coaxial
plasma gun.
108
FUSION TECHNOLOGY
VOL. 27
MAR. 1995
Degnan et al.
can be accelerated intact with the few mega-amperes,
— 5-/xs rise time acceleration/compression discharge
starting — 7 /xs after the start of formation discharge.6
The charging and triggering for Shiva Star has been
made adjustable so that 3, 6, 12, or all 36 of its fast capacitor bank modules can be used. We have conducted
compact toroid conical compression experiments using
6 modules (220 /xf) and using 12 modules (440 /xf) to
drive the acceleration/compression discharge.
Our initially installed conical compression electrodes have an axial offset. That is, the inward turn of
the inner electrode is downstream of the inward turn
of the outer electrode. This is to avoid two-dimensional
MHD-predicted blowby of the second-stage discharge
piston magnetic field past the compact toroid. While
this works, it prevents us from having a continuously
self-similar compression geometry. By continuously
self-similar, we mean a constant ratio of conical electrode gap to mean radius. A superior design employs
compound corners and enables avoidance of blowby
while retaining self-similar compression geometry, according to two-dimensional MHD predictions.
For the initially installed design, the predicted scaling for a compact toroid magnetic field compression
is oc(r-5r)~ l . A comparison of simple theory, twodimensional MHD prediction, and experimental results
of Bz versus r is shown in Fig. 2 for 220-/xf, 60-nH,
75-kV driven compression. For higher energy (440-/xf,
60-nH, 60-kV) driven compression, the peak compressed Bz observed is —4 T.
The correlation in space and time of the axial magnetic field pulse associated with the compact toroid and
the initial sharp electron density peak suggests that this
peak is due to the compact toroid. This is illustrated in
Fig. 3. The electron density data are obtained by HeNe
2.5
2<1)
03
1.5
C
U)
cz
COMPRESSION OF COMPACT TOROIDS
laser interferometry. This density peak is considerably
larger in conical compression experiments than in lower
energy straight coaxial geometry experiments, as expected. We do not yet have data at enough different positions to confirm 1/r 3 scaling of the density (or, 1/
[(r-5r)r] for our current geometry), but the data we
have are promising.
The large-density pulse following the initial density
spike is believed to be due to electrode plasma-based
partly on time and space-resolved optical spectroscopy
and partly on the fact that various measures of the inertial mass (1 to 2 mg) approximately agree with experimental and two-dimensional MHD information on
injected mass ( - 2 mg) and efficiency of incorporating
injected mass into the toroid ( - 7 0 % ) . The large, late
density apparently has little velocity and does not appear to be dynamically coupled to the toroid.
Time and space-resolved optical spectroscopy was
obtained by using an optical multichannel analyzer
(OMA), fiber-optic lines, and collimation/collection
optics. Axially, time-resolved OMA data for a nitrogen compact toroid experiment is shown in Fig. 4. It
is evident that the injected species (nitrogen) precedes
the contaminant species (carbon, silicon) by several microseconds. The spectroscopy evidence for nitrogen is
time and space correlated with magnetic probe and interferometer evidence for the compact toroid. Chordal
view optical spectroscopy indicates that the contaminant plasma is concentrated near the electrodes. 8 The
silicon is believed to be attributable to the glass envelopes protecting the magnetic probes.
In Fig. 5, we show acceleration/compression current / and axial position Z of the current versus time
t for a higher energy, 440-/xf, 60-nH, 60-kV, 800-kJ
second-stage discharge with factor 3 conical compression geometry. The injected mass was 1.5 to 2 mg of
nitrogen. The injected field was - 0 . 2 T, with a radialto-axial ratio of —2 to 1. The formation discharge parameters were 110 /xf, —30 nH, 70 kV, and —2 MA with
an — 3-/xs rise time. Here, Vis the voltage at the capacitive divider voltage probe position, i.e., outside the
vacuum-solid insulator interface. The nominal secondstage discharge resistance is 3.3 mfi, and L is obtained
from /, V by using
IR)dt
"to
"5
'o
oL
C
0.5
40
50
60
70
80
90
100
Axial Height (cm)
Fig. 2. Poloidal field compression data compared with simple theory and two-dimensional MHD calculations
(MACH2) for 220-/*F, 70-kV, second-stage discharge.
109 FUSION TECHNOLOGY
VOL. 27
MAR. 1995
To obtain good agreement between experiment zerodimensional calculations at this operating energy, one
must consider the motion of the second-stage discharge
return current path. This return current path position
starts near the second-stage discharge annular feed slot.
Data from magnetic probes located between the gas injection and second-stage discharge feed slot locations
indicate that this current return path moves almost halfway to the lower gun baffles. This current return path
motion starts - 3 /xs into the second-stage discharge.
Degnan et al.
COMPRESSION OF C O M P A C T TOROIDS
8
10
12
Time (jus)
Fig. 3. Poloidal magnetic field, radially averaged electron density compared with time in conical compression cone.
The motion lasts - 2 . 5 ns. The inductance growth associated with this motion is - 5 nH.
The times of arrival of the B-d (azimuthal magnetic
field) signal peaks correspond well to the mean current
position obtained from inductance growth obtained
from the current and voltage data. The zero-dimensional
prediction of compact toroid mass centroid motion correspond well with the times of arrival of the Bz (axial
magnetic field) signal peaks. This correspondence is optimum for zero-dimensional model parameters with
>
>
350
1200
r
O
1000
c
(a)
13
O
o
j
<D
O
CD
800
600
400
O
O
200
J
4500
4550
4600
wavelength
4650
(A)
4700
_JL_
-200
4450
4500
4550
4600
wavelength
4650
4700
(A)
Fig. 4. Optical spectra for nitrogen compact toroid acceleration/compression. Toroid species precedes electrode plasma
species.
110
FUSION TECHNOLOGY
VOL. 27
MAR. 1995
Degnan et al.
COMPRESSION OF COMPACT TOROIDS
Time ^s)
Fig. 5. Current, mean current axial position compared with time; poloidal and azimuthal magnetic field peak times of arrival. For magnetic probe locations (close to electrodes), PF time of arrival should correspond to toroid, and azimuthal field time of arrival should correspond to discharge current flowing through toroid.
2-mg toroid mass. The assumed initial toroid magnetic
energy is 10 to 20 kJ. Varying the toroid magnetic energy Wm in that range has little predicted effect. This
initial toroid magnetic energy is the magnetic energy
density for the trapped, relaxed toroid (Be ~ 0.5 T,
Bpoioidai ~ 0-4 T) times the toroid volume
105 cm 2 ).
The compression of the toroid causes a force opposing
rr
compression of Fm = dWm/dr. Since W
m=
—wm0 r0/r9
F,„ = —WQ r0/r . The analogous rotational (Wroty0 ~
100 J, Fro, ~ 1 /r3) and internal energy (Winty0 ~ 100 J)
forces are negligible. Magnetic diffusion drag forces are
not negligible but are small compared with magnetic
compression forces. The diffusion drag forces are not
considered in the current zero-dimensional model. They
may need to be considered for higher compression
experiments.
Figure 6 shows a 200-ns exposure micro channel
plate (MCP) tube photo of a compact toroid that has
been compressed a factor of 3 within conical-coaxial
electrodes and has inertially compressed another factor of —2, after extraction from the conical electrodes
111 FUSION TECHNOLOGY
VOL. 27
MAR. 1995
Fig. 6. Computer-enhanced, gated MCP tube camera image
of compact toroid after exiting factor 3 compression
conical electrodes.
Degnan et al.
COMPRESSION OF COMPACT TOROIDS
into a 1-m-diam, 1-m-long vacuum vessel. The mean
diameter is —15 cm. Contained compression to — 7-cm
mean diameter, or smaller, is required for our current
compact toroids to achieve megagauss fields.
Candidate applications at several megajoule accelerator capacitor bank energy include intense X-ray generation (requiring compressions to 5- to 10-cm mean
diameter), intense neutron generation/fusion research,
and high-quality plasma flow switching (requiring compressions to 20- to 30-cm mean diameter). This is a potentially reusable, nondestructive device. Experiments
at the megajoule, 3-MA, factor of 3 compression level
are nondestructive.
4. T. W. HUSSEY, N. F. RODERICK, and D. A. KLOC,
"Scaling of MHD Instabilities in Imploding Plasma Liners,"
J. Appl. Phys., 51, 1452 (1980).
5. R. E. REINOVSKY, W. L. BAKER, Y. G. CHEN, J.
HOLMES, and E. A. LOPEZ, "SHIVA Star Inductive
Pulse Compression System," Proc. 4th IEEE Int. Pulsed
Power Conf., Albuquerque, New Mexico, June 6-8, 1983,
p. 196, M. F. ROSE and T. H. MARTIN, Eds., Institute of
Electrical and Electronics Engineers (1983).
6. J. H. DEGNAN et al., "Compact Toroid Formation
Compression and Acceleration," Phys. Fluids, B5, 2938
(1993).
REFERENCES
1. C. W. HARTMAN and J. H. HAMMER, "New Type of
Collective Acceleration,"Phys. Rev. Lett.,48,14, 929(1982).
2. J. B. TAYLOR, "Relaxation of Toroidal Plasma and
Generation of Reverse Magnetic Fields/' Phys. Rev. Lett.,
33, 1139 (1974).
3. I. LINDEMUTH and R. KIRKPATRICK, "Parameter
Space for Magnetized Fuel Targets in Inertial Confinement
Fusion," Nucl. Fusion, 23, 263 (1983).
7. E. L. RUDEN, J. H. DEGNAN, T. W. HUSSEY, M. C.
SCOTT, J. D. GRAHAM, and S. K. COFFEY, "Time Resolved Mass Flow Measurements for a Fast Gas Delivery
System," Rev. Sci. Instrum64, 1740 (1993).
8. T. J. ENGLERT, G. F. KIUTTU, and S. VIGIL, "Spectral Evidence of Heating and Confinement of Compressed
and Accelerated Compact Toroids," Bull. Am. Phys. Soc.,
37, 1474 (1992).
James H. Degnan (BS, physics, St. Joseph's University, 1969; MS, 1972,
and PhD, 1973, physics, University of Pittsburgh) has a research background
that includes experimental nuclear physics, high-energy-density plasmas, and
high-current pulsed power.
G. P. Baca No biography was available at publication time.
David Bell (BS, physics, University of Texas-El Paso, 1986; MS, engineering physics, 1987, and PhD, plasma physics, 1993, Air Force Institute of
Technology) has research interests that include computational physics and application of evolutionary strategies to physics simulations.
Geoffrey D. Bird (AAS, electromechanical technology, Washington Technical Institute, 1972) has worked in pulsed power, high-power microwave, highenergy plasma, and electron beam systems design and development. He is
currently with Physical Sciences, Inc.
Allen L. Chesley [MS, physics (atmospheric), Iowa State University, 1978;
BA, chemistry and physics, Coe College, 1975] has a special interest in optical and X-ray image processing and in data acquisition systems.
Sean K.Coffey (BSME, 1981, and MSNE, 1985, University of New Mexico) has a research background that includes steady-state and pulsed magnetic
field diagnostics, fast photography, data acquisition, and pulsed radiography
in hostile environments.
M. E. Dearborn No biography was available at publication time.
Melissa Rae Douglas (PhD, physics, University of New Mexico, 1994) has
research interests that include computational radiation hydrodynamics. She
is currently investigating hazardous waste removal by using silent discharge
plasmas.
Sue E. Englert (PhD, physics, University of Wyoming, 1986) studied acoustics and signal processing. Her research background also includes fast photography, data acquisition, and image processing.
112
FUSION TECHNOLOGY
VOL. 27
MAR. 1995
Degnan et al.
COMPRESSION OF COMPACT TOROIDS
Thad J. Englert (BS, physics, University of Northern Colorado, 1962; MS,
physics, Iowa State University, 1964; PhD, physics, University of Wyoming,
1983) has research interests that include quantum electrodynamics, spectroscopy, and electro-optics.
Donald G. Gale (BSME, California Polytechnic Institute-San Luis Obispo,
1976) has technical experience that includes structural design and stress analysis (in the nuclear power industry), vacuum vessel and electrode design for highcurrent pulsed power and high-voltage applications, and numerous fabrication
techniques.
Jack D. Graham is a pulsed power engineer for Maxwell Laboratories, Inc.
He leads the Shiva Star operations team and has extensive high-energy capacitor bank and pulsed power coupling design, development, and operations
experience.
Kirk E. Hackett (BA, physics, Dartmouth, 1977; PhD, physics, Massachusetts Institute of Technology, 1983) has a research background that includes
high-energy-density plasmas and high-power microwave sources.
J. H. Holmes No biography was available at publication time.
Thomas W. Hussey (PhD, University of Florida, 1974) is the chief of the
Phillips Laboratory High Energy Plasma Division. He has been active in the
area of high-energy-density plasma radiation sources and is best known for
his theoretical and computational work on the hydromagnetic Rayleigh-Taylor
instability in fast Z pinches.
Gerald F. Kiuttu [BS, engineering science, Arizona State University, 1975;
MS, 1980, and PhD, 1986, nuclear engineering (plasma physics), University
of New Mexico] has done research work that includes X-ray spectroscopy and
plasma diagnostics, plasma accelerators, hollow Z pinches, charged-particle
beams, high-power microwaves, compact toroids, and pulsed power.
F. Mark Lehr (PhD, electrical engineering, Texas Tech University, 1990)
is currently a research physicist in the Phillips Laboratory High Energy Plasma
Division, where he leads the advanced pulsed power research program.
G. J. Marklin No biography was available at publication time.
B. W. Mullins No biography was available at publication time.
Robert E. Peterkin, Jr. (BS, physics, Boston College, 1976; PhD, physics and astronomy, University of North Carolina-Chapel Hill, 1983) studied
elementary particle physics, general relativity, and quantum gravity. His subsequent research has been in theoretical and computational plasma dynamics
and high-performance computing.
David W. Price (BS, engineering physics, University of Tulsa, 1975; MS,
nuclear engineering, 1977, and PhD, engineering, 1988, University of New
Mexico) since 1984 has been a research physicist with the U.S. Air Force
(USAF), where he has been involved with nonperturbative high-energy plasma
diagnostics.
Norman F. Roderick (BS, USAF Academy, 1962; MSE, 1968, and PhD,
1971, aerospace engineering, University of Michigan) is now an Intragovernmental Personnel Act employee (IPA) at Phillips Laboratory and a professor
in the University of New Mexico Chemical and Nuclear Engineering Department. His research background includes propulsion, pulsed power, particle beams, plasma physics, theory, and computational modeling of plasma
phenomena.
Edward L. Ruden (BS, physics, Case Western Reserve University, 1982;
PhD, physics, University of California, Irvine, 1988) has experience with
plasma diagnosis and theory, Z pinches, compact toroids, and other plasma
geometries. He is currently working in the Phillips Laboratory High Energy
Plasma Division.
Michael C. Scott (BS, electrical engineering, Texas Tech University, 1986)
has experience that includes pulsed power research and development for plasma
physics and high-power microwave experiments. He has done specialized work
in high repetition, high average pulsed power generators.
113 FUSION TECHNOLOGY
VOL. 27
MAR. 1995
Degnan et al.
COMPRESSION OF COMPACT TOROIDS
Steven W. Seiler (BA, physics, Cornell University, 1972; PhD, physics,
Princeton University, 1977) has experience in high-energy physics, plasma physics, pulsed power engineering, electromagnetic and electrothermal guns, and
nuclear weapons effects. He is currently with Physical Sciences, Inc.
Wayne Sommars (BSEE, Southern Illinois University, 1979; MSEE, Air
Force Institute of Technology, 1983) has technical experience that includes communication electronics, operational testing, and pulsed power engineering.
Peter J. Turchi (BSE, 1967; MA, 1969; and PhD, 1970, aerospace and mechanical sciences, Princeton University) is currently an IPA at Phillips Laboratory and a professor in the Ohio State University Aerospace Engineering
Department. His research background includes high-energy-density plasma
physics, high-current pulsed power, and propulsion.
114
FUSION TECHNOLOGY
VOL. 27
MAR. 1995