Generation of Impulse Currents and Triggering

Chapter 13 reproduced the voltage of a lightning surge. But a stroke is equally a current event — a channel carrying tens of kiloamperes for a few microseconds. Two classes of equipment exist precisely to survive that current, and both must be tested with it. A surge arrester clamps an overvoltage by suddenly conducting, diverting the lightning current safely to earth; it must absorb that current without shattering. An earthing system must carry the same current into the ground without its potential rising dangerously. To certify either, we need a source that delivers a controlled, repeatable high-current pulse.

As with voltage, the waveshapes are standardised so results compare worldwide. The everyday workhorse is the 8/20 µs current impulse, used to rate arrester discharge behaviour; a sharper 4/10 µs wave serves high-current withstand tests; and long rectangular currents of hundreds to thousands of microseconds test the thermal and energy endurance of arrester blocks. The generator that makes them is, at heart, the dual of the voltage circuit: where the impulse-voltage generator emphasised resistance and capacitance, the current generator turns on inductance.

An impulse current is defined just like an impulse voltage: a front time \(T_1\) (the rise, again taken from the steep 10–90% portion) and a time to half-value \(T_2\) on the tail. So "8/20" means an \(8~\mu\mathrm{s}\) front and a \(20~\mu\mathrm{s}\) time to half-value. The crucial extra requirement is that the wave be unidirectional — the current must not swing back through zero by more than a small allowed amount, or it would no longer represent a lightning surge.

Keeping the wave unidirectional turns out to be the whole design challenge, and it comes down to one circuit parameter — the damping. Get the damping wrong and the current rings back and forth like a struck bell; get it right and it makes a single clean pulse. To see why, we need the circuit.

The impulse-current generator is a capacitor bank \(C\), charged to \(V_0\), that is discharged through a series inductor \(L\) and resistor \(R\) into the test object. The inductance is no accident — it is the deliberate ingredient that controls the rate of rise and limits the peak, and the whole circuit is a textbook series RLC loop. When the switch (a triggered gap) closes, the capacitor drives a current governed by

This is the dual of the voltage generator: there, a capacitor charged a smaller capacitor through a resistor; here, a capacitor drives a current through an inductor. Its behaviour — and whether the output is the clean unidirectional pulse we need — is decided entirely by how the three elements balance, which is the story of damping.

Solving the RLC loop gives a current whose character depends on a single comparison: the circuit resistance \(R\) against the surge impedance \(\sqrt{L/C}\). When \(R\) is small the discharge is underdamped and the current is a decaying sinusoid that swings negative; when \(R\) is large it is overdamped and sluggish; between them lies critical damping. The underdamped solution makes the oscillation explicit:

The boundary between ringing and not ringing is critical damping, which occurs when the resistance equals twice the surge impedance:

For a lightly damped circuit the first peak of the current is reached after about a quarter-cycle, and its size follows from the surge impedance directly — the stored voltage divided by \(\sqrt{L/C}\):

This formula is a design map. To reach a higher peak current we want a small surge impedance — a large capacitance and a small inductance. Capacitance is increased the obvious way: by connecting many capacitors in parallel. Here is the pleasing symmetry with the last chapter. The Marx generator chases voltage, so it charges capacitors in parallel and fires them in series; the impulse-current generator chases current, so it simply discharges its capacitors in parallel. The inductance, meanwhile, is kept low by short, wide, coaxial busbars — every nanohenry of stray inductance steals peak current.

Both impulse generators — voltage and current — depend on a switch that connects the charged store to the load at a single, sharp instant. So far that switch has been "a sphere gap that fires when the voltage reaches its breakdown value." That is enough to make a pulse, but it is useless for real testing, because the firing instant is uncontrolled: the gap goes whenever the voltage happens to reach breakdown, scattered by humidity, dust and statistics.

Serious work needs the generator to fire on command, at a chosen moment, for three reasons. First, synchronisation: the measuring oscilloscope must be started a known instant before the pulse arrives, or the fast wave is missed. Second, chopped-wave tests: to test insulation against a surge truncated by a nearby flashover, a second gap must chop the wave at a precise time. Third, and most important, multistage erection: a Marx generator's stages must be made to fire together reliably, which means the first gap must be fired deliberately rather than left to chance. All three demand a gap that holds the voltage off and then breaks down the instant it is told to.

The solution is to add a third electrode to the gap. The two main electrodes are set a little wider than their natural breakdown spacing, so the gap holds off the applied voltage indefinitely. A small trigger pulse applied to the third electrode then tips the gap over the edge — either by distorting the field to raise the local stress, or by injecting a burst of initiatory electrons and ultraviolet light that seeds the discharge. The main gap collapses within nanoseconds of the trigger, and the firing instant is now under our control.

The most successful design of this kind is the trigatron. A small metal pin is set into a hole bored through the centre of one main electrode, separated from it by a thin annular gap. A trigger pulse drives a spark across that small annulus; the ultraviolet light and ionised gas it produces flood the main gap with the electrons it needs to break down, and the main discharge follows immediately. The trigatron is compact, fires reliably over a wide range of main-gap voltages, and has very little jitter — which is why it became the standard triggered switch in impulse and pulsed-power systems.

Now the loose end from Chapter 13 can be tied. A Marx generator is fired by building its first gap as a trigatron. While the stages charge in parallel, every gap — including the first — sits just below its breakdown voltage, holding the column inert. To fire, a trigger generator (usually a small pulse transformer) sends a sharp pulse to the trigatron pin in the bottom gap. That gap collapses on command, and its collapse over-volts the second gap, which fires the third, and so on up the stack in a self-propagating cascade — the erection we described before, now started at a precise instant of our choosing.

This is why the controlled first gap matters so much: it converts the Marx from a device that fires whenever its charging voltage drifts up to breakdown into one that fires exactly when the experiment requires, synchronised with the oscilloscope and repeatable shot after shot. The same trigatron principle, scaled and refined, runs through modern pulsed-power machines, where banks of triggered gaps — or fast solid-state switches doing the same job — must close within nanoseconds of one another to add their contributions cleanly.

For each item, first identify what it tests — the waveshape, the surge impedance, the peak-current formula, the damping condition, or the triggering principle — then apply it. Difficulty rises down the list.