9V to 400V DC-DC Converter
Here's a reputable one that runs from 5 volts and uses an inductor to get initial voltage magnification then a cockcroft-walton multiplier: -



Maxim article that gives more detail. Use a voltage regulator to drop the 9 volts to 5 volts and because you are using a battery I'd urge you to use a buck regulator to prolong battery life.

There is also this that runs from a 555 timer and uses an LT700 audio transformer: -



Full details here. But google really is your friend on this and you can find many images of circutis on-line.