High Voltage Power Supply Design
There are ICs specifically designed for this, typically marketed as capacitor charger controllers. For instance, the LT3750. They're commonly used for photographic flashes.

One thing to bear in mind is the leakage specification of your capacitor banks; make sure it's very very low, or you'll spend a lot of energy just topping them up continuously. Photographic flash caps are specifically designed with low leakage for just this reason.