I was looking for a photo of a tiny cyclotron that I saw at the Smithsonian. I didn't find it, but I think that this is better:
This is the first cyclotron, invented by E.O. Lawrence. The tiny evacuated device was inspired by description of an odd device in a German electrical engineering journal. Read about it here:https://www.aip.org/history/exhibits/lawrence/first.htm
This device, the direct predecessor of today's gigantic super colliders, accelerated charged particles, i.e. hydrogen nuclei, which are single protons, around a circular path. To do this required pulses of magnetism around the circular path, which had to be pulsed at radio frequencies to time to the particles' motion as it approached the speed of light. The article suggests that these high frequency currents were produced by a Tesla coil.
You may remember a line from the film Ghostbusters describing the Proton Pack as an "unlicensed nuclear accelerator". It was small cyclotrons like this that Dan Aykroyd had in mind when he wrote that line.
If you prefer steampunk props that actually look like functional devices, you might consider building your gun around a replica of this device.