A spark gap doesn't produce pulses, the HV source does. A gap may produce a spark if fed a high enough voltage.The 1kV pulse is provided by a spark gap connected to a HV source.
That's probably going to be the challenge - to not leak the power away faster than it's being produced. Cool project, thanks for writing up the details.It outputs about 1kV in the microamp range.
I was thinking of that also, but I thought leakage might exceed the battery's output, which might be down in the nanoamps range. Maybe the key here is to identify a suitable capacitor. You might have to put some in series to get enough voltage.... a high voltage capacitor...
There are pulse transformers being manufactured that might work. He needs a transformer with a turns ratio of ≈1000:1. Most are designed to convert a low voltage pulse to a high voltage, but you should be able to turn them around. A current transformer might also work (in reverse), but I suspect that the secondary inductance (was primary) might be too low.The problem with a transformer is that it's an AC device; nothing happens except when the current through it changes. You're battery makes a constant and tiny current. You do get a sudden current burst when it's finally able to jump the spark gap, though, so maybe the transformer will allow capturing a bit of that. It will give you more current at a lower voltage, and reasonably efficiently.
You'll want reduce the spark gap to a voltage that the transformer can survive, unless you can find an old TV flyback transformer that can handle high voltage without arcing.
I agree.1kV is so low that you are unlikely to need any specialised type of winding.