Thinking about John Larkin's problem of discharging a capacitor fast in an LCR network, I was reminded of a scheme that I lucked onto where an inductor that was mostly saturated did what was needed in the brief intervals it was out of saturation.
John's problem is that discharging through a resistance is purely exponential, and thus too slow.
My suggestion was to add an inductor and chose the resistance and inductance to set up a critically damped circuit which has a shorter tail.
An inductor that won't get saturated by the peak current is big, but if we choose a smaller inductor that will saturate early in the discharge we can probably live with with the consequences - even a simple RC will lose a lot of energy early on. Once the current has dropped to the point where it doesn't saturate the inductor, you will have a critically damped LCR circuit which would then give the critcally damped discharge, but only at the end of the discharge where it would get rid of the last of the energy rather faster than a simple RC would.
The wire still has to be heavy enough to carry the peak discharge current, so it still has to be a bulky inductor, but we can use an ungapped high permeability core and get the desired inductance - say 5H
- with fewer turns than you'd need on a gapped core - and in a smaller volume.
It would need to be very high permeability core - Waldek Hebisch seems to have had an iron core in mind and his core got 5H with a 1cm air gap with just 1727 turns. Without the airgap he would have needed fewer turns, so we could probably get the 5H with a few less turns on a somewhat smaller core.
The aim has to be to get the inductor coil resistance high enough to damp the LCR - perhaps somewhere around 10R - with enough wire in the inductor that 4kJ won't get it hot enough to soften the insulating enamel on the wire.