UCRL-ID-120238
Final Report on the LLNL Compact
Torus Acceleration Project
J. Eddleman, J. Hammer, C Haxtman,
H. McLean, and A. Molvik
March 19,1995
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This U an informal report intended primarily for internal or limited external
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Work performed under the auspices of the U.S. Department of Energy by the
Lawrence Iivermore National Laboratory under Contract W-7405-Eng-48.
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document.
Final Report on the LLNL Compact Torus Acceleration
Project
March 19,1995
James Eddleman, James Hammer, Charles Hartman, Harry McLean, and
Arthur Molvik
Introduction
In this report, we summarize recent work at LLNL on the compact torus
(CT) acceleration project. The CT accelerator is a novel technique for projecting
plasmas to high velocities and reaching high energy density states. The accelerator
exploits magnetic confinement in the CT to stably transport plasma over large
distances and to directed kinetic energies large in comparison with the CT internal
and magnetic energy. Applications range from heating and fueling magnetic fusion
devices, generation of intense pulses of x-rays or neutrons for weapons effects and
high energy-density fusion concepts.
Beginning in 1986, we conducted experiments with the Ring Accelerator
Experiment (RACE) accelerator at LLNL to establish proof-of-principal for the
concept. The accelerator concept and early modeling studies are found in
references 1 and 2. The first experiments on CT acceleration are described in
reference 3 and experiments on slow formation and compression in references 4
and 5. Applications are discussed in references 2, and 6-8. More recent RACE
experiments that demonstrated the predicted feature of magnetic flux compression
during CT focusing are described in section 1 below. The last experimental series
from 1992 to 1993 studied the effects of drag on the CT from wall-evolved gases
and potential ways of reducing the drag through heating the electrodes. Drag
effects strongly limited the operating regime in the precompressor/accelerationfocusing geometry. Recent analysis of data from these experiments shows that the
drag was primarily due to snowplow of the CT through gas filling the accelerator
tube. The gas was apparently produced during the formation stage of the CT. These
results are reported in section 2.1. Modeling of wall plasma effects is described in
section 2.2.
From 1993 to 1994, we collaborated with the Air Force Phillips Laboratory
on the MARAUDER device in a program of accelerator studies, improvements
and CT stagnation experiments at higher energy than available on RACE.
Experimental results and modeling of MARAUDER are summarized in section 3.
Finally, we describe two recently-conceived variants of the accelerator concept that
may offer advantages for some applications, including a low-voltage driver scheme
9
DISTRIBUTION OF THIS DOCUMENT IS UNUSED
13
in section 4.1, and a radial/ non-self similar accelerator in section 4.2. We conclude
with a discussion of possible techniques for extending the operating regime of the
CT accelerator to higher energies and energy densities.
1. Focusing and Flux Compression Experiments, on RACE
In this section we report the three-fold compression in radius and length and
five-fold increase in the magnetic field of a CT in the 7.4 m-long coaxial-cone
geometry in RACE. This compression follows a two-fold quasistatic compression,
reported previously , for a six-fold total compression. A CT, shown in Fig. 1.1, is
a toroidal, or doughnut-shaped, plasma configuration similar to a tokamak plasma.
The plasma in a CT is an electrically conducting, ionized gas heated to a few tens
of eV. A magnetic field is produced by currents flowing in the plasma and forms a
set of nested surfaces to confine the particles, so a CT can be used as a container to
hold plasma during acceleration.
4,3
Compression of magnetically confined plasmas has generally been used for
the purposes of increasing the plasma temperature! and density by compressing in a
time short compared with an energy or density confinement time. The experiments
described here differ in that increasing the thermal energy of the plasma is not
necessarily desireable, instead our goal is to increase the velocity and kinetic
energy of a compact torus and compress it to a small cross section and short length
so as to deliver a higher power density in a shorter time. This is an alternative to
the electrical pulse compression techniques usually used in pulsed power.
We calculate the scaling of the poloidal magnetic field Bp with the plasma
major radius R assuming that poloidal flux, ^ p , is conserved. This can be written
as
V =JB dA
p
p
= const.
(1.1)
where A is the area of the poloidal cross section. A is approximately the product of
Ap, the thickness of the flux layer, and 2rcR, the circumference of the outer
electrode. For a CT in axial force balance, A is proportional to A, the rip between
the inner and outer coaxial electrodes. A is proportional to R for the seL imiiar
electrodes for which Rinner is proportional to Router, so we obtain
P
V
= 2jcRApB ~ R B
(1.2)
2
?
P
?
from which the scaling of Bp is apparent
Bp-HVR
(1.3)
2
2
If toroidal flux is also conserved, i.e.
4^ ~ B L(A-2A ) - B LR
T
P
(1.4)
T
where L is the length, then
B -4VLR.
(1.5)
T
In magnetic pressure balance, B = B , and if B « 1, as expected for plasma near
the Taylor minimum energy state, then we have
2
2
T
P
L ~ R ~ A.
(1.6)
That is, when forced to compress self similarly in radius, the compact torus also
compresses self similarly in length.
In previous experiments, we demonstrated CT formation and
precompression as well as acceleration in straight coaxial electrodes. Some of the
earlier straight acceleration experiments, without a precompression cone, were
followed by a focusing cone. Resilient, stable magnetically-confined rings were
formed and accelerated to velocities as high as 3 x 10^ cm/s in the straight system.
Focusing, or compression, to smaller radii was observed when a CT entered a cone
at high velocity, but the CT magnetic field did not scale as R"2. If the cone were
too short, with too steep an angle, the CT stopped or bounced without significant
compression. We investigated many aspects of the dynamics of CT ring
acceleration, including the limits on the accelerating force, ring shaping in
response to acceleration, and the balance of CT equilibrium forces with the
4
accelerating force in the precompressor cone. In those experiments, we achieved
good correspondence with two-dimensional (2D) magneto-hydrodynamic (MHD)
and other models, especially for the precompression cone experiments where we
found excellent agreement between our observations and 2D simulations using the
TRAC code .
10
The configuration of the RACE facility, during the experiments described in
this section, is shown in Fig. 1.2. For these experiments, we installed a new set of
electrodes combining all four phases: formation, precompression, acceleration, and
focusing. As in the previous experimental runs, the CT is formed at the muzzle of a
magnetized, coaxial plasma gun and is initially captured in the precompression
section. The precompression section consists of two coaxial metal cones. The
cones have an outer diameter of 0.32 m (inner diameter of 0.14 m) that converges a
factor of 2 over an axial distance of 0.43 m. The electrode geometry is self-similar
3
throughout; i.e., the ratio of inner to outer electrode diameters is independent of
position along the accelerator. If the accelerator bank is not fired, the C'" -emains
at the large-radius end of the precompressor and persists as a stable-syr etric
structure, decaying within about 100 \is.
When the accelerator bank is fired, the CT is slowly compresse relative to
the Alfven time which is the order of 1 (is) over a period of 10 (is, di ;g which
the acceleration force approximately balances the expansive force o le CT in the
precompressor cone. The expansive force is similar to the force on... oalloon that
has been inserted into a smooth, conical tube. The balloon, or CT, exerts a pressure
against the walls of the tube, which results in a net force toward the side end of the
cone. During this time, accelerator field energy is inductively stored behind the
CT.
1
The CT is compressed the factor of two in an axial distance of 0.43 cm, then
it enters the acceleration/focusing section. This section is also conical; the outer
diameter shrinks another factor of three from 0.1(5 to 0.053 m over an axial
distance of 7.4 m. The cone angle is much shallower than it is in the
precompression section, so the expansive force plays a smaller role. In fact, the
cone angle was made as small as possible, by making the length of the cone equal
to the length of the accelerator, to preclude the bouncing or non-flux-conserving
behavior that had been previously observed. The acceleration force is mainly
balanced against the acceleration of the CT and any drag forces. At the smalldiameter end, the CT exits the accelerator and is allowed to expand.
The electrodes are constructed from aluminum to minimize the magnetic
skin depth, and faced with refractory metals to reduce sputtering. The inner
electrode is coated with plasma sprayed tungsten to a thickness of about 0.05 cm.
The outer electrode is covered with 0.025 cm thick tantalum sheet that has been
hydroformed to conform tightly to the aluminum structure. The outer electrode is
interrupted at approximately 0.7 m intervals with rings that provide penetrations
for diagnostics. These rings are also coated with plasma sprayed tungsten to a
thickness of about 0.05 cm.
The major diagnostic used for the discussion in this section is tr. e magnetic
loop probe system that measures the axial (poloidal) and theta (toroidal
components of the magnetic field at 11 axial locations on the inner wall of the
outer electrode, after the precompressor. At most locations, 2 pairs of probes are
installed with toroidal separations of 180°. Other diagnostics include HeNe
interferometers located at three axial locations, a visible light spectrometer to
measure the time dependence of oxygen impurity lines, and X-ray diodes and
photo diodes to measure VUV emissions at several axial locations.
4
The trajectory of a moving compact torus is displayed by a family of time
plots of magnetic field in Fig. 1.3. The vertical spacing of the plots is proportional
to the axial spacing of the magnetic probes. The characteristic signature of a
moving CT is a localized poioidal field signal as the CT passes over a probe
location. The slope of a line fitted to the time of peak field gives its velocity. In this
example the CT accelerated to 5.9 x 10? cm/s, although we have observed
velocities up to 1.5 x 108 cm/s in this configuration of RACE.
The trajectory line shown is from the zero-dimensional (0D) RAC code .
For this calculation, we varied the CT mass to give the best fit, resulting in a mass
of 62 |ig and a kinetic energy of 11 kJ (the accelerator bank energy was 65 kj).
From the interferometer measurement of the chord-averaged electron density, we
obtain a mass estimate an order of magnitude lower, assuming hydrogen as the
dominant constituent. The difference may be due to the carbon and oxygen
impurities that we observe spectroscopically. If oxygen is the dominant CT
constituent, the interferometer-based estimate would be much closer to the
dynamically based estimate. The difference may also be due to anomalous drag
from interaction of the plasma with gas evolved from the walls. Additional drag
would reduce the mass needed in the RAC code to fit the experimental CT
trajectory.
2
Of particular note for the shot shown in Fig. 1.3 is the increase in magnetic
field as the CT is compressed. During acceleration, the CT passes a given point
more quickly, both because it is becoming shorter and because its velocity is
increasing. Both of these observations will be quantified for comparison with
MHD theory in subsequent figures.
To compare the observed magnetic field amplification during compression
with that predicted for flux conservation, we plot the poloidal magnetic field vs the
reciprocal of the outer electrode radius in Fig. 1.4. We see that the magneticfieldis
decaying, or constant, for the first 3 m (the first five data point sets) of axial
distance. After that, the magnetic field increases. For comparison a (1/R)2 line is
fit to this part of the data. We conclude that conservation of poloidal flux is a good
approximation during the final 4 m of acceleration over which the magnetic field
increases by a factor of five. This result is consistent with ideal (zero electrical
resistivity) MHD theory.
We determine the length of the CT in two ways. First, we measure the full
width (in us) at half maximum of each of the probe locations shown in Fig. 1.3,
and multiply this by the local velocity to get the CT length as it passes that
location. The length is found to be approximately proportional to the radius as
shown in Fig. 1.5a. A second method is to find a shape and length for the plasma at
5
each time by fitting a profile to signals simultaneously present on two to f
probes. The length obtained in this way is plotted vs axial position in Fig.
along with a line with its length proportional to radius for comparison. T
line is an approximate fit to the data between 5 and 7 m. We find that th
prediction that length of a C T is proportional to the radius is approxima
satisfied.
ir
5b,
atter
H*D
Good agreement with flux-conserving M H D theory is obtained iy during
the final 4 m of acceleration. The initial decay m a y indicate ohmic decay at
electron temperatures of 3-5 eV. The C T magnetic field following the
precompression stage and at the beginning of the acceleration/focusing stage is
irregular, suggesting that the drive magnetic field at that time was excessive. High
drive field causes the "blowby" effect where accelerating field blows past the CT,
either partially or completely disrupting the C T . T h e robustness of the C T
geometry is indicated by the coalescence of multiple peaks into a single peak as the
C T is accelerated.
2 Drag and Heated Electrode Studies
2.1 Experiments
2.1.1 Drag measurements and phenomenology
Drag is generally associated with the exchange of CT momentum with
plasma or gas evolved from the walls either before or during the passage of the CT.
Classical resistive drag with the electrodes is small in the RACE operating regime.
Some OMA (optical multi-channel analyzer) data from the RACE long-cone
accelerator snowed the light emission peaking at the front of the CT, rather than at
the back where the density peaks. In addition, the emission shows a transition from
predominately singly ionized oxygen at early times to triply ionized as the rear end
of the CT sweeps past a location. An example, Shot 12054, is shown in Figs. 2.12.3. These data suggest that gas at a significant density exists in the gap between
electrodes, and that the CT is ionizing and sweeping up the gas as the C ~ transits
the accelerator.
We examine the hypothesis that sufficient gas exists between the e rodes
to cause the drag that prevents the compact torus from accelerating. From :*.
2.2a, we see that the density at 194 cm has a nearly constant density foot t lending
from the front of the B magnetic field at 25 \x& to the density peak at the t ck of
the CT, beginning at 31.2 us. At the CT velocity of 14.6 cm/u^, Fig. 2.3a, the foot
has a line density of 3.5 x 10*6 cm-3, more than enough to completely ionize any
gas in front of the CT. We conjecture that the density of the foot is composed
completely of gas, swept up from in front of the CT, which would allow us to
z
6
equate the electron density in the foot to the neutral density before the CT. The
momentum balance is given by
F
(2.1.1)
~~H
or
BJA yn./KAz)^
(212)
=
2U
At
0
since (Az/At) = VCT, and assuming that the gas fills the gap so that the areas, A,
cancel, we obtain
"o = ^ - V
(2.1.3)
Evaluating B as the change in the toroidal field pressure between the front
and back of the CT, and assuming that the gas is water from the walls with a total
mass of 18 AMUs and results in 2 singly charged hydrogen and 1 doubly charged
oxygen (From Fig. 1, OIII which is doubly charged dominates except at the front
of the CT where Oil dominates and the back where OIV dominates.) yielding and
average ion mass of 4.5 AMUs. With these assumptions, we compute an electron
density of 6.5 x 1014 cm-3, which is of the same order of magnitude as the
measured electron density of 4.6 x 10*4 cm-3 at 194 cm.
2
T
We apply this same analysis to shots 12045-12062. In Fig. 2.4, we plot the
measured electron density in the front foot of the CT vs no from Eq. 3 at an axial
position of 194 cm. In Fig. 2.5, we show the same plot at 120 cm, but using the
measured electron density at 194 since we did not have an interferometer at 120
cm. In both figures, a unity slope line is shown for comparison. The computed
neutral density required to prevent acceleration of the CT is somewhat greater than
the measured electron density in both cases. Closer agreement can be obtained by
using an average mass of 6 (for singly charged oxygen) rather than 4.5 AMU,
however, the spectroscopic data indicate that 4.5 is the better value.
Two classical processes would also reduce the neutral density required for
the sum of all drag processes to create a constant velocity CT. These are the drag
due to the magnetic field soaking into the electrodes and the back force on the CT
due to the conical electrodes. Both of these effects are predicted to be small.
We now discuss the source of the gas. Vacuum systems generally have the
order of 100 monolayers of gas adsorbed on the walls , which can be readily
desorbed by plasma ions incident on the wall at energies the order of 100 eV .
Many neutrals per incident ion may be released, depending on the surface
13
14
7
conditioning. We observe that a prepuise plasma frequently extends i-2 m down
the accelerator for a period of 10's of us before trie CT traverses the accelerator.
This plasma is very apparent on Langmuir probes, and is also seen with marnetic
probes, VUV's, VUV monochromators, and to a slight degree with interfer leters.
Langmuir probe data from a probe inserted to 1.0 cm, is shown in Fig. 2.oa from
Shot 12218. The Langmuir probe is shielded by a tantalum cap with a pinhole to
admit plasma. The probe was at z = 120 cm, with the pinhole facing towards the
gun. Fig. 2.6b shows the accumulation of poioidail magnetic field at the entrance to
the precompressor at z = 12 cm. Three spikes of plasma emission are seen in the
Langmuir probe current between 1 and 7 jis, which is near the peak poloidal field
buildup at 12 cm. The CT passes the Langmuir probe between 20 and 30 u,s, which
gives a much smaller ion current.
Rotating the Langmuir probe to look away from the gun eliminates the spikes, as
shown in Fig. 2.7 for Shot 12214, indicating that the prepuise ion flux is directed
downstream from the gun. Surprisingly, the CT current at 27-30 [is is several times
larger than the upstream signal of shot 12218, indicating that the plasma ions near
the wall may be flowing in the direction opposite to the CT.
In Fig. 2.8., the probe is inserted another 0.5 cm to 1.5 cm, and faces the gun,
Shot 12221. Here, the prepuise ion current is smaller, the CT ion current is larger.
From Figs. 2.6-8, we conclude that fast prepuise ions are due to emission from the
plasma gun, and that they are close to the wall. This may be appropriate for ions
resulting from charge exchange or ionization of cold gas in front of the CT. The
gas is concentrated near the electrodes because in -20 us it can move only a short
distance given by
dr(cm) = v<Sr = 1 0 * c m / / - j E™(eV)2 x W's = 1.1cm
0
UJ
(2.1.4)
where we assume that the desorbed neutrals are H2O at a temperature of 300 K.
The electrode gap was in the range 1.5 to 4.4 cm, so even gas at 300 K can fill at
least half of the gap. Higher energies are possible, since the ions impinge at
glancing incidence on the walls, and could impart a significant fraction of »• .sir
energy to the H2O.
To estimate the ion velocity and energy, we look at the time of flight from
other diagnostics.
UV diagnostics are shown in Figs. 2.9-11. Fig. 2.9 shows a UV
monochromator signal at 28 cm (within the precompressor cone that extends from
8
z = 16 to 38 cm). Fig. 2.10 shows a VUV (XRD secondary emission detector) at 46
cm, just after the precompressor. Spikes are seen in both detectors, that appear
correlated with those in the Langmuir probe current. The large spike in Figs. 2.9
and 2.10 is associated with the passage of the CT. Fig. 2.11 shows another VUV
detector at z = 194 cm, which exhibits very small spikes or noise, between 0 us and
the CT arrival at 28 us, that may correlate with other diagnostics. Deriving
velocities from these data, we obtain 2.1-3.7 x 10^ cm/s between 28 and 46 cm,
and 2.4 -3.4 x 10^ cm/s between 46 and 194 cm.. Helium ions moving at 2.4 3.4 x 10? cm/s have an energy of 1.1-2.3 keV.
Magnetic probes measuring the poloidal field at z = 43, 120, and 194 cm are
shown in Fig.s 2.12-14 respectively. These signals do not show the strong spikes
seen on the previous diagnostics, but do show 5-20% modulation of the signal that
may correlate with the spikes. The initial rise of the signal propagates from 43 to
120 cm in about 1 us, but takes 5.2 us to reach 194 cm, implying a velocity
between 120 and 194 cm of 1.4 x 10? cm/s or a helium energy of 400 eV.
The dominant signal from the magnetic probes shows a poloidal magnetic
field extending along the accelerator shortly after a CT begins to form in the
precompressor, as seen in Figs. 2.12-14 and Fig. 2.15, for Shots 5877 and 5333.
The prepulse magnetic field is generally stronger, closer to the precompressor
(which extends from 0.12 m to 0.43 m), decaying to smaller values by z = 1-2 m.
One possibility is that the magnetic field carries little plasma, but pushes prepulse
ions against the electrodes. Also, doubly-ionized helium ions at 400 eV (if this
represents a temperature as well as a directed velocity) would have a gyroradius of
order 3 cm in the ~ lkG pre-pulse magnetic field and a high probability of
intercepting an electrode. The presence of the pre-pulse field in the accelerator
implies plasma within the field to carry the self-consistent currents, and either
needs excess Bthcta or the momentum of fast ions to balloon the Bpoioidal field
axially.
2.1.2 Heated electrode experiments
We modified RACE to test the importance of volatile gas emission from the
electrodes by installing a set of accelerator electrodes which can be operated at
high temperature. The modified electrodes are shown schematically in Fig. 2.16.
Data from the experimental run from February - March 1993 indicates that
high temperature (-400° C) bakeout has little effect on CT dynamics for some
experimental conditions, but may significantly increase the CT velocity for other
conditions. Impurity line emissions measured with the OMA were reduced. Fig.
2.17 shows the CT velocity calculated from the transit time between two axially9
offset interferometers vs. shot number. Three different experimental conditions
were tested before, during, and after bakeout. There is a large amount of shot-toshot scatter, but the mean velocity for high inductance, 40 and 50 kV acce! -ator
voltage shots increased by about 30% for the hot or post-bakeout tests in
comparison with the pre-bakeout tests. Low-inductance, 70 kV shots she :d no
measurable change in velocity with bakeout. The 70 kV shots show a m a
greater difference in velocity when compared with earlier, non-bakeabk ^old
plated, perforated aluminum electrodes.
In addition, we extended the high-inductance operation to 70 and 80 kV
accelerator voltage (80 kV is the present upper limit on bank operation) with the
electrodes hot and observed velocities greater than 50 cm/p.s. Previous cold
operation in this parameter range yielded velocities of order 20 cm/ps. Fig. 2.18
shows the CT trajectory (axial distance vs. time) for a 70 kV high inductance shot
as indicated by peak signals on various diagnostics.
These electrodes had a stagnation region at the end of the accelerator. Data
from soft x-ray diodes and silicon photodiode bolometers indicates a strong burst
( - ps duration) when the CT impacts the stagnation region, followed by a lower,
decreasing intensity over 10's of ps. This may indicate a long lived post-shock
heated plasma.
2.2 Modeling of Instability of the Wall Plasma Layer in a Coaxial Accelerator
The dense plasma layer generated by desorption from electrode surfaces is
also of concern because this material may become distributed across the
interelectrode gap and cause current shunting and reduced power flow to the load.
The magnetic pressure of the accelerator is presumed to play a role in the dynamics
of the wall-derived plasma. As described by J. Degnan , during the current ramp
up phase magnetic field diffuses into the plasma and pins it against the wall due to
magnetic pressure. During the current decay phase the flux in the wall plasma is at
least partly "frozen in" and the plasma expands into the gap as the magnetic
pressure drops.
If the current rises and falls slowly enough, we expect the wall plasma to be
in near magnetic pressure balance with the field in the gap, where we assume a
much lower density plasma exists. Under these conditions, and for sub-Alfvenic
flow in the low density region, there is the possibility of instability due to the
Venturi effect. If the surface of the dense wall plasma develops aripple,then the
flow of low density plasma becomes locally constricted. In the constriction the
pressure drops (for sub-Alfvenic flow) which causes the wall plasma to expand
and enhance the ripple. In the low Alfven Mach number (incompressible) limit
10
this goes over to the Kelvin-Helmholtz instability. For Mach numbers close to
unity, the instability grows rapidly.
A simple ideal MHD analysis of a high aspect ratio coaxial accelerator is
given in the following. Estimates for the most unstable modes (shortest wavelength
modes consistent with approximations, i.e., wavelength ~ few x gap ) give growth
times in the few - 10 jis range, depending on wall plasma density , thickness, etc.
The instability may place more severe limits on wall plasma evolution or
acceleration time than the expansion during current decay described above.
The interelectrode region (see Fig. 2.19) is divided into a dense wall layer
with density, p„ axial velocity, v,, and thickness 5„ and a low density channel
with corresponding quantities p , v , 5 . A uniform (in the high aspect ratio limit)
azimuthal field fills the gap and the plasma pressure is assumed to be negligble. A
sharp boundary is assumed to exist between regions and the electrodes and plasma
are taken to be perfect conductors In this case we can write the nozzle flow
equations for either region 1 or 2:
2
2
2
a (p5)/a t + a (p5v)/a z = o.
(2.2.1)
a (pv5)/a t + a (p5v )/a z = - s a (B /2)/a z
(2.2.2)
(3/3t + v8/3z)B/p
(2.2.3)
2
B, = B
2
= 0
(2.2.4)
2
5, + 5 = constant = interelectrode gap
(2.2.5)
2
We look for perturbations around a steady flow state, uniform in z,t. The
unperturbed flow velocity near the wall, v„ is taken to be 0. For region 2 we
assume that the perturbations have a frequency co « k v^, kv , where v^ = B/p
and k is the axial wavenumber. In both region 1 and 2 the perturbations are
proportional to exp( - ioa t + ik z). In the low frequency case we can neglect the
time derivatives in equations 2.2.1-3 . Equations 2.2.1 and 2.2.3 can then be
integrated directly with the results substituted into 2.2.2, giving the familiar nozzle
equation:
1/2
2
2
2
(vj'-v^ ) a p / a z + p v /5 a 5 / a z = o
2
2
2
2
2
2
(2.2.6)
For small perturbations, p = p + Ap ,5 = o^, - %, we have
2
Ap /p
2
20
2
= AB/B = ( v / ( v - v
2
20
2
2
2
2
11
2
A 2
))$/8
2 0
(2.2.7)
For region 1 the linearized equations, with 5, = S + ^, are:
t0
Ap,5 + ^ p
I0
1 0
+ p 5 3 v,/3 z = 0
1 0
(2.2 •)
1 0
PioS v, = - 5 B a A B / a z
(2.: 0
AB/B = A p , / p
C ..10)
I0
10
I0
The region 1 equations reduce to
(0) - k B /p )AB + c o B $ / S
2
2
2
= 0
2
I0
10
(2.2.11)
Equation 2.2.11 can be combined with equation 2.2.7 to give a dispersion relation:
co = -k v (5 /5 )(p /p.o)/(l-v Vv (l4-5 /5 )).
2
2
2
(2.2.12)
2
2
10
20
20
2
A2
10
20
This expression indicates instability for all sub-A lfvenic flows with
V /
2
= M < M ^ = l / ( l + S /S )
l0
V A 2
(2.2.13)
l/2
20
The growth rate diverges as M -> M^, however ithe assumption o « kv breaks
down at this point. For Mach numbers, M, not close to M the assumption will
usually be satisfied since 8 /8 , pa/Pu, are « 1 for cases of interest. The fastest
growing modes are at the shortest wavelength. The growth rate is unbounded as k
becomes large, a consequence of the nozzle flow, sharp boundary approximations.
In practice, the largest k consistent with the approximations is of order the
(interelectrode gap)' . For the CT accelerator the flow in the low density region is
typically sub-Alfvenic (if not, most of the accelerator energy will go into
accelerating the plasma in the channel rather than the CT) so the instability is
usually present. For example if we assume M « 1 and take v = 10 cm/sec, k = .1
cm' , p, = 10 p , and 8, = .1 8 , we obtainy= 10 sec' . Growth times are then of
order typical acceleration times.
2
ehKt
10
20
1
8
2
1
3
s
6
1
2
3 MARAUDER Experiments and Modeling
The LLNL CT acceleration program has included a collaboration with the
Air Force Phillips Laboratory in Albuquerque, New Mexico on the MARAUDER
experiment. One configuration of the MARAUDER formation/acceleration
electrodes are shown schematically in Fig. 3.1. The goal of these experiments is to
demonstrate CT acceleration at the megajoule energy scale and test the CT x-ray
source concept. We have predicted that stagnation of plasmas with intermediate to
high atomic numbers against a barrier should lead to strong shock heating of the
7
12
CT and an intense source of multi-keV x-rays, appropriate for a weapons effects
simulator.
Our efforts in the collaboration have concentrated on deployment of
diagnostics and modeling of CT acceleration, compression and stagnation. We
deployed a 16 channel detector to measure the space and time-resolved vacuum
UV emission during acceleration, giving an indication of how the plasma is
distributed. The detector, shown in Fig. 3.2, views different radial chords at a fixed
axial location. The data are Abel inverted, assuming axial symmetry, to give the
radial dependence. Fig. 3.3 shows the emitted power as a function of radius and
time for a MARAUDER shot. This shot, employing neon gas in the CT formation,
produced significant keV x-ray yield at stagnation. The data are collected about
halfway along the acceleration/focusing cones, between the formation and
stagnation regions. Most of the emission comes after the passage of the CT and is
localized near the electrodes, as expected for plasma produced from electrodedesorbed gases. Spectroscopic observations suggest that the wall plasma is largely
composed of carbon and oxygen, which are common contaminants. The
localization near the electrodes is consistent with current and voltage
measurements that show the accelerating current is flowing at the moving CT
rather than being "shorted out" in the following plasma.
We also deployed a data acquisition system similar to the RACE system,
Langmuir probes to sample the edge plasma density, visible light framing and
streak cameras to view the stagnation region, and new magnetic probes, flush
mounted in the electrode surface, to allow measurements toward the muzzle of the
accelerator. The probes allow us to obtain better data on the CT trajectory and
field structure without the probe ablation and perturbative effects of the existing
insertable probes.
We have used the two dimensional TRAC2 magnetohydrodynamics code to
model CT dynamics in MARAUDER. We have used the code to evaluate different
designs for the transition between conical and straight electrodes. The code
predicts that a geometry with a gradual transition, the "gentle corner" design
,should greatly reduce the non-adiabatic heating in comparison with earlier abrupt
transitions. Excessive plasma heating at a transition can have severe effects on the
acceleration process, such as disruption of the CT or ablation of wall material from
the resulting intense x-ray pulse.
The sharp/gentle electrode geometries are sketched in Fig. 3.4. For all
simulations, a CT in the Taylor state is initialized in the region just upstream of the
comer with varying velocities. The CT parameters are mass = .9 mg, length = 20
cm, magnetic energy = 3.5 kJ, thermal energy = I kJ, peak magnetic field = 10 kG,
electron temperature = ion temperature = 30 e V, atomic mass = 20, X = 4.
M
13
The calculations, summarized in table 3.1 below, do not include self
consistent ionization balance, ohmic losses or radiation. Hie non-adiabatic mating,
AU , is the sum of the artificial viscosity and energy conservation terms. ich
are of comparable magnitude. Shock heating is manifested in the artificL
viscosity terms in MHD numerical calculations. The increase in therma ergy,
AU^j, is the sum of non-adiabatic and PdV terms. The change in energy -aken at
a time after the CT rounds the comer when the kinetic energy is minim
(subsequent expansion of the CT can convert some of the thermal ener into
kinetic energy).
NA
;
fc
Table 3.1
Sharp
v (cm/\is)
20.
30.
40.
50.
Gentle
AUTO/UKIN
AUTO/UKIN
.020
.010
.006
.005
.046
.040
.040
.035
Sharp
Gentle
AU /U,
AIWUKD,
NA
.021
.028
.033
.023
.0014
.0012
.0013
.0020
The sharp corner calculation shows heating roughly as expected if the radial
part of the CT kinetic energy is converted to heat, i.e., AV /U = ( V ^ ^ L / V ) =
.05. This type of "inelastic collision" with the electrodes while preserving the axial
momentum was seen in earlier TRAC2 runs.
2
rH
K]N
We have also used LASNEX to model x-ray output at stagnation. These
calculations are ID with the CT compression ratio (initial/final radius), length,
density, magnetic field, and velocity taken from slug model predictions of CT
parameters at the muzzle of the accelerator. Calculations of x-ray output in various
spectral energy ranges are shown in fig. 3.5 for MARAUDER and a hypothetical
50 MJ facility. Only the lowest velocity example has actually been achieved on
MARAUDER. Longer acclerator geometries than have been currently tested would
berequiredto reach high velocity (> 40 cm/us). Predicted spectra for son .2 of the
parameters in Fig. 3.5 are shown in Fig. 3.6
4 Accelerator Variants
4.1 Radial CT Accelerator
It may be possible to reach high velocities (-100 cm/|is) and high power
densities (10-100 TW/cm ) without using a long acceleration stage, but instead a
pure radial compression geometry. This could be an advantage forreducingwall
2
14
effects since the electrode area is small. The concept is based on inductive storage
behind the CT in non-self-simiiar electrode geometry and radiation clamping of the
CT temperature.
We have usually considered self-similar geometry (g =interelelectrode gap /
mean radius ^constant) for the CT accelerator although MARAUDER has
employed non-self-similar electrodes in one series of experiments . There may be
an advantage to some types of non-self-similarity, e.g., the inductance of the
accelerator can increase rapidly with distance if g increases, allowing efficient
transfer of inductively stored energy to CT kinetic energy in a short accelerator.
Another aspect of non-self-similarity is the different variation of the CT magnetic
energy with radius. In the approximations usually employed in OD models such as
the RAC code , (CT length « electrode length, g « 1, (3 « l ) the CT magnetic
energy varies as (electrode gap) and hence inversely with radius for selfsimilarity. If the radius decreases but the gap does not change, however, there is no
change in the CT magnetic energy and no corresponding restoring force, to first
order in the approximations mentioned above.
9
2
l
A purely radial geometry is interesting for exploiting non-self-similarity
since it is less prone to blow-by as g increases (there is no difference in magnetic
pressure between inner and outer electrodes). Fig. 4.1b shows one example where
conically converging electrodes transition to electrodes with constant gap. The
behavior of the accelerator, based on OD model calculations, is similar to other
MARAUDER geometries. The circuit used in these calculations, representing the
SHIVA-star bank, is shown in Fig 4.1a. The calculations show a period of 5-10 us
of current build-up with the piston force nearly balancing the equilibrium force of
the CT, followed by a rapid increase in inductance and transfer of inductive energy
to kinetic energy. We have done a OD calculation for full energy MARAUDER
(9.4 MJ) with the circuit and electrode geometries of Fig. 4.1a,b. Since the voltage
climbs to 3MV as the CT implodes, most of the inductance should be on the
vacuum side of the insulator. The model neglects drag and finite beta and assumes
a magnetic decay time proportional to the square of the gap distance. The decay
model is consistent with constant, radiatively clamped electron temperature. The
CT parameters were: mass=l.e-3 grams, magnetic energy = 100 kJ, iength=l5 cm
and initial magnetic energy decay time of 20 us.
The CT reaches a kinetic energy of 660 kJ and a radial velocity of 115 cm/
us at CT mean radius, R = .2 cm, where the calculation is arbitrarily stopped.
The efficiency is only 7%. It is hard to do better than this with the series resistance
shown in Fig 4.1a. Lowering the series resistance, reducing external inductance
and optimizing the geometry should improve efficiency substantially. The CT
geometry is strongly distorted at a radius of .2 cm and the OD model
approximations are no longer valid. More accurate calculations will require 2D
CT
15
MHD simulations. Essentially, the CT implosion transitions to a (possibly
stabilized) z-pinch implosion.
If the CT is too small in radial extent, magnetic tension forces car
I :he
CT away from the electrodes. The CT length (CT radial extent in this ge etry)
varies approximately proportional to R , so at small enough radius, the igth
equals the gap distance. If the length becomes shorter than the gap dis ,e, the
CT will also contract axially, possibly causing detachment of the curr
heet and
blowby. For our example, the length would equal the gap distance at
= 6.7 cm.
The time to pull away from the electrodes is roughly the gap distance . er the
Alfven velocity ~ 2 cm / 40 cm/^is ~ .05 |is. This is comparable to the remaining
time to implode ~ 6.7 cm / 115 cm/|is ~ .06 u.s, so detachment may be an issue in
the final phase. The tendency toward detachment could be countered by
introducing axial magnetic flux crossing the gap that reconnects with the CT flux
as it implodes. If all of the CT flux were reconnected in this fashion, the final
configuration would resemble a B stabilized z-pinch . Alternatively, a CT with
sufficiently large initial length could be used to prevent detachment. The final
stagnation phase of the CT on axis should be dynamically similar to z-pinch
implosions where the plasma kinetic energy is converted to thermal energy and
radiation.
CT
12
r
4.2 Low voltage/long drive pulse CT accelerator
Part of the appeal of the CT accelerator concept has been the comparatively
low voltage power sources (few hundred kV) that can be used by exploiting
inductive storage and precompression. We usually assume that the limitation on
the inductive storage time is the CT lifetime. In this section we consider the
possibility of using a sustained CT during the current build-up phase to decouple
the inductive storage time from the CT lifetime, thereby allowing very low voltage
drivers (~ 10 kV).
The scheme works as follows: a CT can be formed and sustained at the
beginning of the precompression cone for long periods, based on the su ainment
experiments at LANL . Pump-out holes/slots would be necessary to a\ 1 buildup of plasma or neutrals (see Fig. 4.2). The accelerator current is then i oed up
over an extended time, e.g., 1 msec, with the minimum drive voltage set the
resistive loss of the CT, typically ~ 10 ohms based on plasma resistivity 10 eV
and a CT radius of 50cm. The gun current and helicity injection rate alsc jnp up
to maintain sufficient magnetic energy in the CT to keep it from compress g. Fig
4.3 shows typical waveforms for the accelerator current and CT flux (~
proportional to the gun current). Near peak current the gun is turned off and the CT
begins to decay. Slightly later the CT starts to compress since its equilibrium force
is no longer sufficient to resist the accelerating farce at the precompressor breech.
12
5
16
The CT continues to decay and compress until it "rounds the comer" and takes off
down the accelerator tube. This type of behavior was observed on many RACE
shots in the precompressor geometry where the initial rise of the accelerator current
was insufficient to compress the CT (at high initial CT field or low accelerator
voltage) and the CT was found to compress slowly during its decay with the
accelerator current crowbarred.
The power losses for this scheme are dominated by the gun, although an
"anomalous" accelerator loss comparable to the gun loss might be expected since
the accelerator bank coupling to the CT is similar to the gun (see Fig. 4.2). We can
estimate the gun voltage and power from C. Bames empirical gun impedance
formula ,
13
V = r (Ia - I ) ,
G
G
r ~.5/R
c
G
(4.2.1)
where V is in volts, I is the gun current in amperes and R is the gun radius in cm.
I is the critical current for overcoming field line tension within the gun,
G
G
c
Ic = ^G/MO ¥G-
(4.2.2)
\}/ is the gun poloidal flux and X is the Taylor eigenvalue for the gun, XQ ~ rc/Ao,
where A is the gun interelectrode gap. If steady-state balance between gun
injection and CT magnetic decay exists, then we can use helicity injection
concepts
to find the CT magnetic energy. Defining the CT helicity as K we
have
G
G
G
16,17,11
Helicity input rate = 2 V \y = Helicity decay rate = K/x^y
G
G
(4.2.3)
The CT magnetic energy is related to the helicity through the Taylor eigenvalue for
the formation region, X - it/A, with A the formation region interelectrode gap.
Making use of equations 4.21-3, we have the CT magnetic energy given by
U = A/(2m) K = ^
M
T ^ r Ic( Ic - Ic )
G
(4.2.4)
The magnetic energy is optimized by operating the gun with poloidal flux such that
I = IQ 12. At optimum the magnetic energy is then
c
U - X / ^ T , r I / 4 =X/^ T ^ V c I c / 2
2
M
DM
y
G
G
(4.2.5)
For this scheme the CT magnetic energy must be sufficient to "plug" up the
accelerating field during current rise. Approximate force balance is given by
U /1*,. = L' W / 2, L' = 2 x l a In ( R ^ , / R ^ )
9
M
17
(4.2.6)
with 1 ^ the length of the precompressor cone, L' the inductance per unit I :gth of
the accelerator, and I the accelerator driving current, liquations 4.2.5/ low us
to relate the gun power to the accelerator drive current,
drive
P = V I = Z,,,, W ,
G
G
Z
G
l0iI
= (XJX) L' 1 ^ / x ^
(
. 7)
where Z^, is an effective impedance. For example, if Xo/X =2, L' = K ^ = 100
= 200 \xs then Z^ = 10 ohms. At accelerator drive volta i below
cm and x
Z ,I the energy losses in the gun will exceed the inductively stored energy, e.g.,
if the accelerator drive current is 10 amperes with 2. - 10' ohms, the accelerator
drive voltage should exceed 10 kV.
We can also relate the gun current to the accelerator drive current through
equations 4.2.1 and 4.2.7, since P = r I /2 = Z,,,,, I .
3
Xitcty
l0i
b
Mt
drive
7
3
Xott
2
G
I = (2 Z
G
l0M
/r )
G
m
I
drive
G
2
G
drive
,
(4.2.8)
For example, if the gun radius is 50 cm, then r ~ 10" ohms from equation 4.2.1
and if Z,.,. = i a then I ~ .45 I ..
2
G
3
G
dIive
One concern with this scheme is the prepulse plasma described in section 2
above. Millisecond drive pulses will allow plenty of time for prepulse-driven
desorbed gasses to cross the interelectrode gap. On the positive side, the long pulse
may give adequate time for pumpout of the gas.
Conclusions
Neglecting wall effects, one can use the point model or 2D MHD codes to
find a wide variety of possible accelerator geometries that lead to a tightly focused,
high velocity, high energy density CT at the accelerator output. Our experience
with RACE and MARAUDER, however, suggests; that wall effects place severe
constraints on accelerator operating regimes. Unfortunately, determining the
source and distribution of wall-evolved material is not very amenable to first
principles" modeling since it is dependent on conditioning of surfaces a the
interaction of low density pre-pulse plasma with the surfaces. Once the t ribution
of material is known, the effect on the CT can be calculated as discussed i section
2 above. While a fundamental understanding of the wall effects remains e ive,
some empirical "rules of thumb" can be drawn from the experiments, whit we list
here:
The inter-electrode gap during acceleration should be sufficiently large.
Sufficiendy large means of order 10 cm for formation/acceleration times of order
10 us. Desorbed gas moves at a velocity of order 10 cm/s, so a gas/plasma layer
s
IS
of order a cm in thickness can form in IOJIS. The gap should be large compared to
this distance. The high velocity CT's observed in earlier RACE and MARAUDER
experiments had an electrode gap of 15 cm. Focusing to small size should take
place after the CT is at high velocity ( ~ 10 cm/sec) as well as down stream from
any prepulse plasma associated with formation. At high velocity, material desorbed
during the time of CT passage (eventually « 1 JIS) should remain close to the
surface.
8
Fast (<10us) is better than slow (~100ns) formation. Our last series of
experiments on RACE employed slow formation, which produce symmetric,
quiescent CT's, but also sent low density (< 10 cm' ) plasma streaming down the
accelerator tube. We believe this plasma is responsible for desorbing gas that
essentially filled the accelerator tube, as discussed in sec. 2 above. The exception
may be formation on very long time scales ( > 1 ms) where plasma streaming down
the accelerator may pump out the desorbed gas, as in discharge cleaning
techniques.
13
3
Discharge cleaning and electrode heating helps. There was ample evidence for
conditioning of the accelerator in RACE experiments. Subsequent shots at identical
conditions would often show a gradual improvement in CT velocity and trailing
plasma - sometimes followed by a gradual worsening. RF glow discharge aided
recovery after an air cycle, but did not clearly improve the CT dynamics after the
initial conditioning phase. Heating the electrodes to 400° C in order to drive off
weakly bound gases gave some indications of improvement on RACE, and was
found to have very beneficial effects in the CT acceleration experiments at the
California Institute of Technology . The RACE heated electrodes, as well as
perforated, gold-plated electrodes that were tested, were observed to reduce the
"snow plow" through gas seen with the OMA.
18
Acknowledgements
We thank Aaron Jones, Richard Green, and Dennis Wilson for operation of the
RACE. Richard Cross, Robert Rego, and Jeffery Van Lue with John Delapena,
developed hydroforming techniques for expanding tantalum tubes to fit tightly
against the aluminum outer electrode. Donald Bubp, Dave Cummings and Dewey
Ravenscroft provided capable design and engineering support. Dave Cummings
and Marco DiCapua ably assisted with program administration and technical
discussions. We gratefully acknowledge the support of J. H. Nuckolls, R. J.
Former, and J. F. Holzrichter. This work was performed under the auspices of the
19
U.S. Department of Energy at Lawrence Livermore National Laboratory under
Contract No. W-7405-Eng-48.
References
1. C. W. Hartman and J.H. Hammer, Phys. Rev. Lett. 48,929 (198? .
2. C. W. Hartman and J.H. Hammer, "Acceleration of a Compact oru^ Plasma
Ring, A Proposed Experimental Study," Lawrence Livermore National Laboratory
Report No. LLL-PROP-191,15 April 1984. See AIP Document No. PAPS PFBPE03-2236-180 for 180 pages of the RACE experimental Proposal.
3. J. H. Hammer, C.W. Hartman, J.L. Eddleman and H.S. McLean, Phys. Rev.
Lett. 61, 2843 (1988).
4. A. W. Molvik, J. L. Eddleman, J. H. Hammer, C. W. Hartman, and H. S.
McLean, Phys. Rev. Lett. 66,165 (1991).
5. J. H. Hammer, J. L. Eddleman, C. W. Hartman, H. S. McLean and A. W.
Molvik, Phys. Fluids B 3,2236 (1991).
6. C. W. Hartman, W. L. Barr, J. L. Eddleman, M. Gee, J. H. Hammer, S. K. Ho,
B. G. Logan, D. J. Meeker, A. A. Mirin, W. M. Nevins, L. J. Perkins, D. E.
Shumaker, A. W. Leonard, P. B. Parks, H. McLean, E. Morse and D. R. Solvin, in
Plasma Physics and Controlled Nuclear Fusion Research, 1988 (IAEA, Vienna,
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C. W. Hartman, J. L. Eddleman, J. H. Hammer, B. G. Logan, H. S. McLean, and
A. W. Molvik, Fusion Technol 20,776 (1991).
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Zimmerman and J. F. Holzrichter, Bull. Am. Phys. Soc. 33,1925 (1988).
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Dearborn, D. Dietz, M. R. Douglas, S. E. Englert, T. J. Englert, K. E. Hackett, J. H.
Holmes, T. W. Hussey, G. F. Kiuttu, F. M. Lehr, G. J. Marklin, B. W. Mullins, D.
W. Price, N. F. Roderick, E. L. Ruden, C. R. Sovinec, P. J. Turchi, G. Bird, S. K.
Coffey, S. W. Seiler, Y. G. Chen, D. Gale, J. D. Graham, M. Scott, and W.
Sommars, Phys. Fluids B, 5,2938 (1993).
10. J. L. Eddleman, J.H. Hammer, C. W. Hartman, A. W. Molvik, and H. S.
McLean, Bull. Am. Phys. Soc. 34,2051 (1989).
20
11. T. R. Jarboe, I. Henins, A. R. Sherwood, C. W. Barnes, and H. W. Hoida, Phys.
Rev. Lett, 51, 39, (1983).
12. R. B. Baksht, A. V. Luchinsky, and A. V. Fedyunin, Zh. Tekh. Fiz., 62, 165
(1992).
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14. R. A. Langley, et al., "Data Compendium for Plasma-Surface Interactions,"
Nuclear Fusion Special Issue, 1984.
15. C. W. Barnes, T. R. Jarboe, G. J. Marklin, S. O. Knox, and I. Henins, Phys.
Fluids B, 2,1871 (1990).
16 J. B. Taylor, Phys. Rev. Lett. 33,1139 (1974). and J. B. Taylor, Rev. Mod.
Phys., 58,741 (1986).
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Hartman, D. S. Prono, and J. Taska, Phys. Fluids, 26, 1965 (1983).
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M. R. Brown, P. K. Loewenhardt, J. Yee, D.R. Derkits, and P. M. Bellan, Bull.
Am. Phys. Soc, 39, 1596 (1994).
Figure Captions
Fig. 1.1 A compact torus is a magnetically confined toroidal plasma in near forcefree equilibrium (j // B).
Fig. 1.2 The RACE apparatus consists of a magnetized plasma gun, a
precompression cone, and an acceleration/focusing stage.
Fig. 1.3 The axial magnetic field at the outer electrode vs time is shown at various
axial locations. Each trace is offset vertically by an distance proportional to the
axial location. The solid line shows the trajectory predicted by the RAC code,
assuming a CT mass of 62 u,g. The axial magnetic field peaks at 8.7 kG.
Fig. 1.4 The peak axial field of the CT vs 1/R, where R is the CT radius. The line
shows the predicted scaling 1/R2 for comparison.
21
Fig. 1.5 Ca) The CT length at each time from fitting the signals on up to 4 magnetic
probes. The line shows the predicted scaling L °c R for comparison, (b)' e CT
length at each location from the full-width (in time) -at-half-maximum fl i vs 1/R.
The line shows the predicted scaling L <* R for comparison.
Fig. 2.1 (a) Time-dependent optical multichannel analyzer signals for C (dashed
curve), Oin (solid and dotted curves) and OIV (dot-dashed curve) emi *on for
shot 12054. Oil is observed earliest, followed by OQI and OIV. The spectrometer
views a radial chord at z = 120 cm. (b) Time-dependent axial magnetic field (B ) at
z=l 20 cm and for eight azimuthal positions for shot 12054. The primary CT field
shows good symmetry, but the low-field front has; a strong n=l asymmetry. The
OIV emission peak approximately coincides with the peak of the CT magnetic
field.
z
Fig. 2.2(a) Time-dependent, chord-averaged electron density and axial magnetic
field (BJ at z = 194 cm for shot 12054. (b) Same at z = 264 cm.
Fig. 2.3(a) The axial magnetic field at the outer electrode vs time is shown at
various axial locations for shot 12054. Each trace is offset vertically by an distance
proportional to the axial location. The straight line through the times of peak axial
field gives a CT velocity of 14.55 cm/us. (b) Axial (dotted curve) and azimuthal
(solid curve) magnetic field vs. time at z = 12,43,120,194 and 264 cm for shot
12054.
Fig. 2.4 The vertical axis is the chord-averaged electron density at the front of the
CT measured with the interferometer. The horizontal axis is the neutral density
inferred from momentum balance. The straight line has unity slope. Quantities are
measured at z = 194 cm.
Fig. 2.5 The vertical axis is the chord-averaged electron density at the front of the
CT measured with the interferometer. The horizontal axis is the neutral density
inferred from momentum balance. The straight line has unity slope. Quantities are
measured at z = 120 cm, except the interferometer which is at z = 194cm.
Fig. 2.6 (a) Time-dependent Langmuir probe current for shot 12218. The probe is
inserted 1 cm from the outer electrode at z = 120 cm and faces the gun. (b) Timedependent poloidal magnetic field in the precompressor, z = 12 cm, for shot 12218.
Fig. 2.7 Time-dependent Langmuir probe current for shot 12214. The probe is
inserted 1 cm from the outer electrode at z = 120 cm and faces away from the gun.
22
Fig. 2.8 Time-dependent Langmuir probe current for shot 12221. The probe is
inserted approximately 2 cm from the outer electrode at z = 120 cm and faces the
gun.
Fig. 2.9 Time-dependent VUV monochrometer signal at z = 28 cm for shot 12218.
The (negative going) signal shows emission at 1639 angstroms.
Fig. 2.10 Time-dependent x-ray diode signal at z = 43 cm for shot 12218.
Fig. 2.11 Time-dependent x-ray diode signal at z = 194 cm for shot 12218.
Fig. 2.12 Time-dependent axial magnetic field signal at z = 43 cm for shot 12218.
Fig. 2.13 Time-dependent axial magnetic field signal at z = 120 cm for shot 12218.
Fig. 2.14 Time-dependent axial magnetic field signal at z = 194 cm for shot 12218.
Fig. 2.15 (a) The axial magnetic field at the outer electrode vs time is shown at
various axial locations for shot 5877. Each trace is offset vertically by an distance
proportional to the axial location, (b) Same for shot 5333.
Fig. 2.16 Schematic of RACE bakeable electrodes.
Fig. 2.17 Velocity of CT's in RACE as calculated from the transit time between
chordal-view interferometers at z = 50 cm and z = 124 cm in the bakeable
electrode section. The velocity is plotted vs. shot number with different markers
denoting gun/accelerator bank voltage and electrode condition.
Fig. 2.18 Trajectory (axial distance vs. time) of the CT for RACE shot 15020. Each
marker shows the time of peak signal at different diagnostics located along the
accelerator. The maximum velocity apparently exceeds 50 cm/p.s.
Fig. 2.19 Interelectrode region divided into low density channel( region 2) and
dense wall plasma (region 1).
Fig. 3.1 Schematic MARAUDER configuration.
Fig. 3.2 Geometry of 16 channel x-ray photodiode detector array.
Fig. 3.3 Power density of the emitted VUV radiation in kilowatts/cm as a function
of radius and time for a MARAUDER shot.
3
23
Fig. 3.4 CT and electrode geometry for TRAC2 simulations of a "gentle comer"
vs "sharp corner" transition in the MARAUDER accelerator.
Fig. 3.5 Lasnex predictions for x-ray output in different spectral bins on
MARAUDER and a 50 MJ accelerator. Comp. is the compression ratio.
Fig. 3.6 Lasnex output spectra for different CT parameters
Fig. 4.1 (a) Circuit and (b) geometry for MARAUDER-driven radial CT
accelerator.
Fig. 4.2 Long-pulse, sustained CT acclerator
Fig. 4.3 Accelerator current and CT magnetic flux waveforms for long-pulse,
sustained CT accelerator.
24
Compact torus
Conducting walls
• it is maintained in radial equilibrium by an external field or by
induced currents in conducting walls
• the compact torus is a state of low free energy
with observed rugged stability and long lifetime
Fig. 1.1
(X.
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p
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3
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t
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KE (MJ) V(cm/|is) Comp. Species
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30
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4
b) Geometry
»
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Fig. 4.1
R=
50 cm
R=
25 cm
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Perforated for
pumpout during
sustainment
R
Insulator
C/L
Fig. 4.2
*
Accelerator
Current and
CT Flux ~ Gun
current before
shutofT
Accelerator
Current
Fig. 4.3
The gun is ramped up so
that the CTfluxis
proportional to the
accelerator current during
the current rise/inductive
storage phase
i±
Time ->
t, = Gun shutoff time ~ 1 msec
ti = CT begins to compress at ~ t, + IOJIS due to flux decay
r, = CT enters straight accelerator following flux decay
/quasistatic compression at ~ tj + 30|is
t4 =CTexits accelerator at ~ t + 5ps
3
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