My comment to a blog found here.
A very common way of boosting voltage does not use an inductor. Instead it uses a ‘charge pump’ or switched capacitor, or flying capacitor.
You can buy the Fair-Rite 2673002402 core for $0.12 (U.S.) apiece, and 12 turns of 24 AWG (0.5mm) insulated telephone wire can be scrounged from old scraps. The BC337-25 makes an excellent JT transistor.
The efficiency of a conventional JT is around 40 to 60 percent. Not all that good, but it’s simple and it does work.