I am looking to charge a larger capacitor to a 'high voltage' somewhere in the realm between 50-400 volts.
Yes, I know capacitors are dangerous in regards to electric shock, explosion, line faults, etc... I have and continue to use safety protection and protocol when working around this equipment, so please don't bash me before for inexperience before hearing me out.
My supply voltage is DC 1.5-15 volts (output to capacitor is between 50-400 volts).
From my research it looks like a DC-DC boost circuit is the most approachable method.
In theory this will work. 50V should be doable, but once you start getting into the 400V range you have to carefully consider the voltage ratings of your components. For example, your switch transistor has to withstand 400V, and definitely a little bit more for headroom. Same with your diode, inductor coils, etc. Theory goes a little bit out the window as the voltages climb (or, more accurately, you have to be very aware of component ratings and parasitic properties, like the capacitance of your inductor).
Also research the "flyback converter" topology, as that might be a bit safer for your Arduino and you will get a natural voltage boost from the transformer.
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The Ruggeduino: compatible with Arduino UNO, 24V operation, all I/O's fused and protected
I wouldn't use that sort of circuit, it's not isolated. Instead I would get a 6v mains (240v) transformer and drive the secondary with 12v switched from a H-bridge. Then out of the mains side would come 480v RMS, which will give you what you need when you have rectified it.
Look at circuits to drive GM tubes.
Get hold of a "disposable, single use" cheapo camera with inbuilt flash and take it apart to recover the inverter unit. This will generate around your 400 volts from a AA battery. If you talk nicely to your local photoshop they may have a stock of these in their rubbish bin.
Sounds like you need your own DC/DC converter then. Chop up the 12V, run backwards thru a 120V to 24V transformer, filter to get back to DC.
Check out hammond manufactuting, they make all kinds of transformers for tube amplifiers.