Where could one find small capacitors to build a small demonstrational railgun?

By "small" I presume you mean in actual size, because I should think that the capacitance values must be high even for a small railgun. Probably what you want are called "supercaps" with values on the order of one farad -- an unthinkable amount for a single device just a few decades ago. You can combine devices by connecting them in parallel for more current, or in series for more voltage.

I'd also assume you know what you're doing, as the capacitors are acting as energy storage devices, thus can 'pack a wallop' if you mishandle them or don't use properly designed circuitry. Try websites for (1) Digi-Key (2) All Electronics (3) Jameco (4) Mouser Electronics. Those are all reputable hobbyist-oriented sources of components (among many others).

More.

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