Is an electron/proton gun possible? In the 1944 SF story “Off the Beam” by George O. Smith, an electron gun is constructed along the length of a spaceship. In order to avoid being constrained by a net charge imbalance, it is built to also fire the same number of protons in the other direction, dissipating the mass of the “cathode”.
With current knowledge, is this plausible? That is,


*

*Can a practical (i.e., not built with unobtanium insulators) electrostatic device like an electron gun separate and accelerate electrons and protons in this manner?

*Can it actually disassemble solid matter? If so, how does the composition of the cathode affect the difficulty?

 A: It would make far more sense to fire both streams of particles together so that you get a neutral particle beam. For starters, if the beam is uncharged it won't disperse due to coulombic repulsion. This is basically how ion engines work.
Additional: Whilst it is sci-fi, Orion's Arm has a fairly well thought out treatise on electron and proton beam weapons that's well worth comparing and contrasting with the story you mentioned.
[EDIT]: I seem to have misunderstood what you meant with 'disassemble solid matter'. As dmckee points out, all you really need to do is ionise some matter and accelerate the ions. In the simplest case, ionising hydrogen will allow you to make a proton beam. If a bulk material builds up enough charge it may disintegrate in a 'coulombic explosion'. This is the principle behind electrospray mass spec., where you dump enough negative charge into droplets of water for them to fly apart.
A: The general way of making proton beams is to ionize hydrogen and separate the protons and electrons with electric fields.
Notice that with an other material


*

*you have to get the protons out of a nuclear context, which requires much more energy (MeV rather than eV)

*you leave behind a increasingly neutron rich (i.e. unstable, AKA radioactive) material


Electron beams are generally extracted from metal cathodes or from silicon or germanium crystals (sometimes stressed if you want a polarized source), and the neutrality of the cathodes is maintained with an electric current.
There is nothing in principle to prevent you using both methods; take electrons from your cathode of choice, and protons from hydrogen, then use the spare electrons to balance the charge loss on the cathode.
A: Both electron gun and proton can be made but they don't work the way you want. Electrons or cathode rays flow from high potential region to a low potential region. To accelerate electrons you need high voltage. I agree with dmckee regarding protons. Protons are made by ionizing the Hydrogen gas because that's the easy way. When we use an electron gun in Electrodynamics applications, generally we have a vacuum tube and a very high potential difference and also we have an anode. Due to this the things work better. If there is no vacuum tube the electrons go to the shortest path to ground around it and in the way ionizes air. Practically if you have made an electron gun using thermionic emission or any other method, the electrons hit the ground immediately.
Its just like thunders. With huge potential difference and massive charge, they hit the highest point on earth. That's a deadly weapon. 
A: An example of a real-life electron/proton beam is the Neutral Beam Injector used in magnetically confined fusion devices. They're used to inject faster particles into the fusion plasma, raising the overall temperature. However an ordinary (charged) proton/deuteron beam will be bent away by the strong magnetic fields surrounding the plasma, so the beam has to be made neutral first. This is done by sending the ions through a gas where they can pick up electrons, then selecting only the neutral ones with another magnetic field.
