Physics and technology of
high-voltage pulsed plasmas
Bob Merlino
Plasma Physics Seminar
April 5, 2010
1
outline
1. Controlled thermonuclear fusion
2. Early work (1950’s)
a)
b)
c)
d)
Stellarators at PPPL
Linear (Z) pinch
Toroidal pinch
Magnetic mirrors
3. High voltage linear q pinch
a) Implosion or shock heating
b) Pulsed power technology
4. HV toroidal q pinch
2
controlled thermonuclear fusion
D + T   (3.5 MeV) + n (14.1 MeV)
reaction rate (cm3/s)
• heating
• confinement
• Lawson criterion
for ignition:
nt > 1014 cm3 s
 n is the plasma density
 t is the confinement time
ion temperature (keV)
3
ITER – Cadarache, France
4
early work in magnetic fusion
• Project Matterhorn begun in 1951 at Princeton University
as a classified project
• Problem with toroidal devices is that magnetic field is
non-uniform (stronger on inner radius than outer radius)
 ultimately this leads to plasma moving outward
• loss of confinement “pump-out”
• First experiments at PPPL studied confinement in
Stellarators – toroidal magnetic field with rotational
transform i
2
i
1
minor cross section
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Lyman Spitzer, Jr.
CONFIDENTIAL: Such material would cause damage
or be prejudicial to national security if publicly available.
- US Atomic Energy Commission – AEC
- US Energy Research and Development Administration (ERDA)
- US Department of Energy (DOE) 1977
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Model A Figure 8 Stellarator 1954
Spitzer invited Van Allen to come to Princeton in 1953-54 to initiate an
experimental program. It was Van Allen’s idea to start with a table-top
device to demonstrate the Stellarator concept.
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Racetrack Stellarator
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Plasma heating in a linear (Z) pinch
HV capacitor
bank
JxB
• Pass a large current
through a gas making a
linear discharge
• JxB force causes pinching
• Current heats the plasma
• if dI/dt large enough,
plasmas with keV
temperatures can be
formed
• how fast? dI/dt ~ 1013 A/s
• Since V = L dI/dt, very
high voltages and low
inductances are required
• Problem is that linear pinch
is unstable to sausage and
kink instabilities
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Toroidal pinches
• Even if the linear pinch were
stable, it could never be a
viable fusion device because
the electrodes introduce
impurities that would cause
the plasma to radiate away a
large fraction of its energy
• Must consider closed
magnetic configurations with
no internal electrodes
• Zeta in UK
• Perhapsotron at Los Alamos
• These are “stabilized” pinches
due to presence of toroidal
magnetic field
ZETA - toroidal pinch
Atomic Energy Research
Establishment, Harwell, UK
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Other Plasma heating devices
• work at Los Alamos. the
Naval Research Lab in
DC and the Univ. MD
concentrated on methods
of producing hot plasmas
in linear q pinch devices
• groups at Oak Ridge
National Lab and
Lawrence Livermore
National Lab investigated
heating and confinement
in magnetic mirrors
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q pinches
• simple straight solenoidal magnetic field
line devices
• magnetohydrodynamically stable
• produce very hot plasmas  Ti ~10 keV
• very high efficiency for conversion of
electrical energy into plasma energy
• inherently a pulsed device
• confinement limited by plasma squirting
out the ends
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Maryland High Voltage q Pinch
one-turn solenoidal coil
pre-ionized plasma
Pyrex or quartz
vacuum vessel
Main
capacitor bank
• solenoid coil was 1m long by 46 cm id
• plasma formed in H2 or D2 at P ~ few mtorr
• preionization done by discharging capacitor ringing at 150 kHz
• initial plasma “fully ionized” at n ~ 1013 cm3 with +/- 400 G bias field
• main bank: 250 kV, dI/dt rises in < 10 nsec giving dB/dt ~ 1010 G/s
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q pinch physics
Bo
BMain
induced current
in plasma sheath
radially inward
J x B force
• plasmas are diamagnetic, so
currents are induced on the surface
• the J x B force makes plasma implode,
causing it to be heated – shock or
implosion heating  snowplow model
to exclude field penetration
• plasma resistivity allows magnetic
field to penetrate
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pulsed power technology
• how do you produce voltage pulses of
hundreds of kA with currents of
hundreds of kA in fractions of
microseconds?
• there are no commercially available
devices that can provide this
• pulsed power technology developed in
US and UK (R. A. Fitch) for Radar in
WW II
• in US, main development program was
at Sandia National Lab
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q pinch HV technology
oil
2500 g H2O + CuSO4
3 mm polyethylene
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Marx generator
charge capacitors in parallel then switch to
series to get voltage multiplication
output switch
L
O
A
D
DC
inversion switch (spark gap)
with crowbar
I
with out crowbar
t
crowbar switch
Marx output voltage
= N x # capacitors
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Magnetic field diagnostics
d
induced voltage : V 
dt
   B  dA
B
probe area , A
B
dB
V  NA , N  # turns
dt
1
B(t ) 
 V (t )dt
NA
4 mm
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B
Magnetic field profiles
B
Main implosion
field antiparallel
to initial bias field
0
Main implosion
field parallel to
initial bias field
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Reconnection and tearing in q pinch
20 cm
reversed or antiparallel
field configuration
t = 440 ns
0
J. H. Irby, J. F. Drake, and
H. R. Griem, Phys. Rev. Lett.
42, 228 (1979)
-20 cm
-70 cm
0
+70 cm20
confinement in q pinch
• limited by end loss
• e.g., L = 1 m, Te = 1 keV, tconf ~ L/Cs,
Cs = 2x105 m/s  tconf ~ 5 ms
• suppose density was ~ 1016 cm-3, how long
would a q pinch have to be to satisfy
n tconf > 1014 cm-3 s ?  tconf = 0.01 s
 L ~ 2 km
• LANL tried plugging the ends with solid plugs
of quartz or lithium-deuteride
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MD High Voltage Toroidal q pinch
• goal was to study implosion heating in a toroidal device
• determine if Te  Ti when fast electron endlosses were eliminated
• compliment to SCYLLAC at LANL
tank with
water + CuSO4
HV generator
in transformer
oil
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THOR
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THOR electrical schematic
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HV pulsers: swinging LC generators
• Charge capacitors in series
• use inductors and switches
across every other capacitor
module to reverse polarity
• gives voltage multiplication
• use 6 generators connected
to toroidal coil with parallelplate transmission lines
• Total energy: 600 kJ*
• output voltage: 580 kV
• output current: 3 MA in < 1 ms
• dI/dt = 6.0 x 1012 A/s
• built by Maxwell Labs
* 3400 lbs moving at 65 mph
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Neutron and x-ray emission
Coil current
Neutron emission
soft x-ray emission
thick Al filter
soft x-ray emission
thin Al filter
time (ms)
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Magnetic field profiles in toroidal q pinch
Antiparallel
Parallel
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toroidal q pinch: conclusions
• Electrons attain higher temperatures as
compared with linear q pinch, now Te  Ti
• Implosion, shock or turbulent heating
processes remain effective in toroidal
geometry
• However, attempts to achieve MHD
equilibrium through the use of vertical
fields and toroidal currents failed
• Plasma abruptly drifts to outer wall after
implosion phase
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