A Marx generator is an electrical
circuit first described by Erwin Otto
Marx in 1924. Its purpose is to generate
a high-voltage pulse from a low-voltage
DC supply. Marx generators are used in
high energy physics experiments, as well
as to simulate the effects of lightning
on power line gear and aviation
equipment. A bank of 36 Marx generators
is used by Sandia National Laboratories
to generate X-rays in their Z Machine.
Principle of operation
The circuit generates a high-voltage
pulse by charging a number of capacitors
in parallel, then suddenly connecting
them in series. See the circuit above.
At first, n capacitors are charged in
parallel to a voltage V by a high
voltage DC power supply through the
resistors. The spark gaps used as
switches have the voltage V across them,
but the gaps have a breakdown voltage
greater than V, so they all behave as
open circuits while the capacitors
charge. The last gap isolates the output
of the generator from the load; without
that gap, the load would prevent the
capacitors from charging. To create the
output pulse, the first spark gap is
caused to break down; the breakdown
effectively shorts the gap, placing the
first two capacitors in series, applying
a voltage of about 2V across the second
spark gap. Consequently, the second gap
breaks down to add the third capacitor
to the "stack", and the process
continues to sequentially break down all
of the gaps. The last gap connects the
output of the series "stack" of
capacitors to the load. Ideally, the
output voltage will be nV, the number of
capacitors times the charging voltage,
but in practice the value is less. Note
that none of the charging resistors Rc
are subjected to more than the charging
voltage even when the capacitors have
been erected. The charge available is
limited to the charge on the capacitors,
so the output is a brief pulse as the
capacitors discharge through the load.
At some point, the spark gaps stop
conducting and the high voltage supply
begins charging the capacitors again.
The principle of multiplying voltage by
charging capacitors in parallel and
discharging them in series is also used
in the voltage multiplier circuit, used
to produce high voltages for laser
printers and cathode ray tube
televisions, which has similarities to
this circuit. The difference is that the
voltage multiplier is powered with
alternating current, and produces a
steady DC output voltage, while the Marx
generator produces a pulse.
Optimization
Proper performance depends upon
selection of capacitor and the timing of
the discharge. Switching times can be
improved by doping of the electrodes
with radioactive isotopes caesium 137 or
nickel 63, and by orienting the spark
gaps so that ultraviolet light from a
firing spark gap switch illuminates the
remaining open spark gaps. Insulation of
the high voltages produced is often
accomplished by immersing the Marx
generator in transformer oil or a high
pressure dielectric gas such as sulfur
hexafluoride.
Note that the less resistance there is
between the capacitor and the charging
power supply, the faster it will charge.
Thus, in this design, those closer to
the power supply will charge quicker
than those farther away. If the
generator is allowed to charge long
enough, all capacitors will attain the
same voltage.
In the ideal case, the closing of the
switch closest to the charging power
supply applies a voltage 2V to the
second switch. This switch will then
close, applying a voltage 3V to the
third switch. This switch will then
close, resulting in a cascade down the
generator that produces nV at the
generator output.
The first switch may be allowed to
spontaneously break down during charging
if the absolute timing of the output
pulse is unimportant. However, it is
usually intentionally triggered once all
the capacitors in the Marx bank have
reached full charge, either by reducing
the gap distance, by pulsing an
additional trigger electrode, by
ionising the air in the gap using a
pulsed laser, or by reducing the air
pressure within the gap.
The charging resistors, Rc, need to be
properly sized for both charging and
discharging. They are sometimes replaced
with inductors for improved efficiency
and faster charging. In many generators
the resistors are made from plastic or
glass tubing filled with dilute copper
sulfate solution. These liquid resistors
overcome many of the problems
experienced by more-conventional solid
resistive materials, which have a
tendency to lower their resistance over
time under high voltage conditions.
Short pulses
The Marx generator is also used to
generate short high-power pulses for
Pockels cells, driving a TEA laser,
ignition of the conventional explosive
of a nuclear weapon, and radar pulses.
Shortness is relative, as the switching
time of even high-speed versions is not
less than 1 ns, and thus many low-power
electronic devices are faster. In the
design of high-speed circuits,
electrodynamics is important, and the
Marx generator supports this insofar as
it uses short thick leads between its
components, but the design is
nevertheless essentially an
electrostatic one. 1 m diameter, it
requires around 10 wave reflections for
the field to settle to static
conditions, which restricts pulse
leading edge width to 30 ns or more.
Smaller devices are of course faster.)
When the first gap breaks down, pure
electrostatic theory predicts that the
voltage across all stages rises.
However, stages are coupled capacitively
to ground and serially to each other,
and thus each stage encounters a voltage
rise that is increasingly weaker the
further the stage is from the switching
one; the adjacent stage to the switching
one therefore encounters the largest
voltage rise, and thus switches in turn.
As more stages switch, the voltage rise
to the remainder increases, which speeds
up their operation. Thus a voltage rise
fed into the first stage becomes
amplified and steepened at the same
time.
The speed of a switch is determined by
the speed of the charge carriers, which
gets higher with higher voltage, and by
the current available to charge the
inevitable parasitic capacity. In
solid-state avalanche devices, a high
voltage automatically leads to high
current. Because the high voltage is
applied only for a short time,
solid-state switches will not heat up
excessively. As compensation for the
higher voltages encountered, the later
stages have to carry lower charge too.
Stage cooling and capacitor recharging
also go well together.
Stage variants
Avalanche diodes can replace a spark gap
for stage voltages less than 500 volts.
The charge carriers easily leave the
electrodes, so no extra ionisation is
needed and jitter is low. The diodes
also have a longer lifetime than spark
gaps.
A speedy switching device is an NPN
avalanche transistor fitted with a coil
between base and emitter. The transistor
is initially switched off and about 300
volts exists across its collector-base
junction. This voltage is high enough
that a charge carrier in this region can
create more carriers by impact
ionisation, but the probability is too
low to form a proper avalanche; instead
a somewhat noisy leakage current flows.
When the preceding stage switches, the
emitter-base junction is pushed into
forward bias and the collector-base
junction enters full avalanche mode, so
charge carriers injected into the
collector-base region multiply in a
chain reaction. Once the Marx generator
has completely fired, voltages
everywhere drop, each switch avalanche
stops, its matched coil puts its
base-emitter junction into reverse bias,
and the low static field allows
remaining charge carriers to drain out
of its collector-base junction.
Applications
One application is so-called boxcar
switching of a Pockels cell. Four Marx
generators are used, each of the two
electrodes of the Pockels cell being
connected to a positive pulse generator
and a negative pulse generator. Two
generators of opposite polarity, one on
each electrode, are first fired to
charge the Pockels cell into one
polarity. This will also partly charge
the other two generators but not trigger
them, because they have been only partly
charged beforehand. Leakage through the
Marx resistors needs to be compensated
by a small bias current through the
generator. At the trailing edge of the
boxcar, the two other generators are
fired to "reverse" the cell.
Marx generators are used to provide
high-voltage pulses for the testing of
insulation of electrical apparatus such
as large power transformers, or
insulators used for supporting power
transmission lines. Voltages applied may
exceed 2 million volts for high-voltage
apparatus.
See also
Cockcroft-Walton generator – a similar
circuit which has the same "ladder"
structure. CW generator produces a
constant DC.
Explosively pumped flux compression
generator – A solution to the opposite
problem of creating huge currents at
lower voltages
Transformer – An inductive circuit that
is analogous to using mechanical gears
to increase torque or speed. Can convert
AC from one voltage and current, to
another. Any increase in voltage will
result in a reduction in current. The
opposite is also true.
References
Further reading
M. Obara, "Strip-Line
Multichannel-Surface-Spark-Gap-Type Marx
Generator for Fast Discharge Lasers",
IEEE Conference Record of the 1980
Fourteenth Pulse Power Modulator
Symposium, USA, Jun. 3-5, 1980, pp.
201–208.
G. Bauer, "A low-impedance high-voltage
nanosecond pulser", Journal of
Scientific Instruments, London, GB, Jun.
1, 1968, vol. 1, pp. 688–689.
Graham et al., "Compact 400 kV Marx
Generator With Common Switch Housing",
Pulsed Power Conference, 11th Annual
Digest of Technical Papers 1997, vol. 2,
pp. 1519–1523.
S.M. Turnbull, "Development of a High
Voltage, High PRF PFN Marx Generator",
Conference Record of the 1998 23rd Int'l
Power Modulation Symposium, pp. 213–16.
R. Ness, et al. "Compact, Megavolt,
Rep-Rated Marx Generators", IEEE
Transactions on Electron Devices, vol.
38, No. 4, 1991, pp. 803–809.
Shkaruba et al., "Arkad'ev-Mark
Generator with Capacitive Coupling",
Instrum Exp Tech May-Jun. 1985, vol. 28,
No. 3 part 2, May 1985, pp. 625–628,
XP002080293.
I. C. Sumerville, "A Simple Compact 1
MV, 4 kJ Marx", Proceedings of the
Pulsed Power Conference, Monterey,
California, Jun. 11-24, 1989, No. conf.
7, Jun. 11, 1989, pp. 744–746,
XP000138799.
External links
"Marx Generator". ecse.rpi.edu.
Jochen Kronjaeger, ""Marx generator".
Jochen's High Voltage Page, 2003.
Jim Lux, "Marx Generators", High Voltage
Experimenter's Handbook, 3 May 1998.
"The 'Quick & Dirty' Marx generator".
Mike's Electric Stuff, May 2003.
