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This +350 DC is used to charge a capacitor. When a trigger signal comes in, it will discharge. So I don't really need a constant high current. This is part of a portable instrument so I really want to save power. Thanks for your help.
Your problem could be solved with a flash circuit. They usually charge up 100-330uF electrolyte capacitor and then discharge to the photoflash tube.
You can see such circuit at many places in the internet but they usually work (by
default) from 1.5V battery. However there is here a circuit working from +9V:
I've built a few little charging circuits in my time, mainly for xenon strobes, coil guns...wire warping etc..
MikeOhio, good point! Many websites that have info on a CW multiplier contain tons of circuits. Cockroft-Walton multiplier alone is a good way to go, but only for doubling voltages, or multiplying by a small number. For 12-350v thats a factor of about 29. Which means, for the multiplier you would need 2 diodes, and 2 caps for each stage. Thats 4*29 components.
It also requires AC input. But hey, if you have a transformer that steps down 120 or 240v to 12v, then simply use it backwards. A simple 555 timer circuit could send pulsed DC to the transformer (experiment with frequency and mark-space ratio) and if the output of the transformer is too low (120-240v), use a few cockroft stages after it. Altohugh, I've never been to keen on using a multiplier in a cap charging circuit...to many things to blow with any back EMF you might create (if you connecto your large cap to a coil).
For a portable device, I guess the camera flash idea is the best. The circuit is small, efficient, and is specifically designed for charging large value caps. Those little transformers are a wonder in themselves. Driven at the correct frequency, with a feedback winding I've seen 93%+ efficiency.
Also, search google for 'boost converter' and 'direct drive inverter'. Both are quite efficienct and simple ways of stepping up voltage significantly. And the boost method, although I've read it can't do large scale factors (like a voltage gain of 10) I've got 400v from a tiny circuit before, using simple parts and the only wound component was an inductor. Alternatively, an easier method would be direct drive, using a hand-wound transformer. It may take a while (maybe half-an-hour) but it'll get you your voltage.
Although you siad current isn't really a big issue, I'm sure you are aware that, its directly related to charging time. But I guess, unless you're charging a 10000uf bank of caps, you won't have to wait too long with a 2-10ma supply.