Drive current from a pulse

How much current is actually flowing in the drive coil by the end of the pulse?

I1 = \frac{V}{R} \left( 1 - e^{-T1 / τ} \right)

Method

1. The final current is the supply voltage over the coil's resistance — Ohm's law, once the inductance has stopped mattering.
2. The time constant is the inductance over the resistance. Divide the pulse's on-time by it to see how many time constants the pulse lasts.
3. The current at the end of the pulse is the final current times (1 − e^(−T₁/τ)): 63 % after one time constant, 86 % after two, 95 % after three.
4. If a supply current limit is given and the current would exceed it, the supply holds the current at the limit from the moment it gets there, which is at t = −τ·ln(1 − I_lim/I_∞). From then on the drive is a current source, which is what a bench supply in constant-current mode is.
5. The stored energy is half the inductance times the square of the current, and the resistive power is the square of the current times the resistance.

Assumptions

• Constant L and R over the pulse. A ferromagnetic medium in the tube that saturates during the pulse lowers L as it goes, so the real current rises faster toward the end than the exponential says.
• The switch is ideal: it drops nothing while on and turns on instantly. A MOSFET's on-resistance belongs in R; a transistor's saturation voltage comes off V.
• The current starts from zero. At a high repetition rate the coil may not have discharged by the next pulse, and the current then ratchets up over several pulses toward the final value — or, with a freewheel diode, decays through it at its own L/R.
• The resistive power is taken at the end-of-pulse current and is therefore an upper bound on the mean over the pulse; for a pulse many time constants long the two are the same.
• Nothing here is Meyer's. The estate's pulse figures for the EPG are given as voltages and timings; this page exists because a coil turns a voltage into a current on its own schedule, and the field follows the current.