The Marx Generator: Stacking Capacitors Into One Giant Pulse

Charge in parallel, fire in series

A Marx generator solves a hard problem: you want a pulse at, say, 1 MV, but capacitors and DC supplies rated for a full megavolt are enormous and costly. Marx's insight was to charge cheaply and discharge expensively. N identical capacitors are wired in parallel through high-value charging resistors and charged from a modest DC supply to a per-stage voltage V — a few tens up to roughly 200 kV. Between each stage sits a spark gap, an air or gas switch that stays open while the bank charges.

When the gaps close, those same capacitors are suddenly reconnected in series, and their voltages add:

V_out ≈ N · V

Ten stages at 100 kV become a 1 MV pulse; twenty stages, 2 MV. The charging resistors that set up the parallel path are deliberately large, so during the fast discharge they behave almost like open circuits and the current takes the low-impedance series route through the gaps. The generator has two personalities selected purely by the speed of the event: slow and parallel while charging, fast and series while firing.

The overvoltage cascade — why it fires itself

The dramatic moment is erection: the self-propagating collapse of every gap within nanoseconds. Only the first (bottom) gap needs a deliberate trigger, often a three-electrode trigatron. The causal chain is this — when gap 1 breaks down, the bottom plate of capacitor 2 is yanked from ground up toward +V. Its top plate is still held near its charged potential through a slow charging resistor, which cannot move charge on a nanosecond timescale, so the voltage across gap 2 is momentarily forced toward 2·V, well above its static breakdown level. Gap 2 flashes over; that hoists the next node toward 3V, overvolting gap 3, and so on up the column.

It is a positive-feedback avalanche — electrically a row of dominoes, where each firing raises the standing voltage on the gaps above it and guarantees they exceed breakdown. The whole stack erects in roughly 10–100 ns. Designers line the gaps up in sight of one another so ultraviolet light from each spark seeds electrons in the next, slashing the statistical time lag and jitter. The enabling condition is impedance separation, R_charge ≫ √(L/C), so almost no current leaks back through the charging resistors during the pulse.

The numbers: voltage, energy, current, power

Take a compact ten-stage generator: N = 10, stage capacitance C = 0.1 µF, charged to V = 100 kV. Erected output is ≈ 1 MV. Energy is where the "no free lunch" lives. Each stage stores ½·C·V² = ½ · 0.1 µF · (100 kV)² = 500 J, so the bank holds 10 × 500 J = 5 kJ. In series the stack looks like a single capacitor of C/N = 10 nF charged to 1 MV, storing ½ · 10 nF · (1 MV)² = 5 kJ — identical. Voltage is multiplied by N; the energy is merely rearranged.

Speed comes from the discharge loop. With a loop inductance of order L ≈ 1 µH, the surge impedance is √(L/C) = √(1 µH / 10 nF) ≈ 10 Ω, and the peak current into a low-impedance load is I ≈ V / √(L/C) ≈ 1 MV / 10 Ω = 100 kA. The instantaneous power V·I touches ~100 GW for a fraction of a microsecond — a torrent of power the little bank could never sustain, released in a single flash.

Shaping the impulse: the 1.2/50 µs standard

Most Marx generators in industry are not physics spectacles but referees: they apply the standardized 1.2/50 µs lightning impulse defined by IEC 60060-1 to prove that transformers, bushings, cables and switchgear survive a lightning-like overvoltage. The raw erected pulse would be far too abrupt, so two families of resistors shape it into a double exponential:

V(t) = V₀·(e^(−t/τ_tail) − e^(−t/τ_front))

A small series front resistor R_f, together with the load capacitance, sets the fast rising edge (front time ≈ 1.2 µs, the time to reach peak). A larger parallel tail resistor R_t discharges the bank slowly, fixing the time to fall to half value (≈ 50 µs). Switching-impulse tests use a slower 250/2500 µs shape. The real output never quite reaches N·V: stray capacitance to ground, loop inductance and the charging resistors cost a few to fifteen percent, so the voltage efficiency η = V_peak / (N·V) is typically 85–95%.

From test halls to the Z machine

Beyond the test hall, Marx generators are the front end of the world's biggest pulsed-power machines. Sandia National Laboratories' Z machine begins with dozens of Marx generators (originally 36) storing on the order of 20 MJ; after further pulse compression it drives roughly 20 MA through a wire array in about 100 ns, producing the intense X-ray bursts used for fusion and high-energy-density physics. Marx banks also power EMP simulators, high-power gas and excimer lasers, flash X-ray radiography, plasma sources, and the injectors of some particle accelerators.

The largest impulse-test generators reach several megavolts — the biggest exceed 6 MV and stand several stories tall. At the other extreme, modern solid-state Marx modules replace spark gaps with stacked IGBTs or MOSFETs, trading peak voltage for the ability to fire thousands of times per second with precise, low-jitter timing — the workhorse of medical linacs, water treatment, and repetitive pulsed-power research.

Conditions, limits, and staying alive

The design walks a tightrope. Charging resistors must be large enough to isolate the stages during the pulse, yet small enough that the RC charging time (seconds) is tolerable. Gap spacings are tuned so every gap self-fires reliably at the overvoltage but never prematurely from stray light or field enhancement. As N grows, stray capacitance to ground increasingly steals charge from the erection cascade, capping practical efficiency and stage count. Loop inductance limits how fast the front can rise, and every shot erodes the gap electrodes and fatigues the capacitor dielectric, so lifetime is finite.

Safety is not a footnote. A modest bench Marx already stores kilojoules at a million volts; the charged capacitors stay lethal after the supply is switched off, and a partial erection or a gap that fails to fire can leave unexpected charge trapped. Such machines carry grounding sticks and interlocks and are never approached without shorting each stage to ground. One misconception is worth killing: the Marx does not create or amplify energy, and it is not a Cockcroft–Walton multiplier. It only rearranges a fixed store of charge from parallel to series — trading current for voltage in one spectacular instant.

Marx generator vs. Cockcroft–Walton multiplier — two ways to reach very high voltages from a modest supply.

Feature	Marx generator	Cockcroft–Walton multiplier
Output form	Single fast high-voltage pulse (µs-scale)	Continuous / DC high voltage
Voltage relation	V_out ≈ N·V (series stacking of charged caps)	V_out ≈ 2N·V_peak (diode charge pump)
Switching element	Spark gaps (or stacked solid-state switches)	Rectifier diodes
Peak power	Very high — GW-class, but only for a brief flash	Low — limited by per-stage current
Typical use	Impulse testing, pulsed power, EMP simulators	X-ray tubes, accelerators, old CRT supplies
Inventor / era	Erwin Marx, 1924	Greinacher 1919 / Cockcroft–Walton 1932