Any electric arc can cause some interference issues, not just HF. The best thing to do is be sure you have a star ground system so there are no ground loops. Try to have an isolated ground for the electronics, and do not share that with the plasma circuit. If you want to ground the plasma table, you can do that with a ground rod. Also you might need shielded cables to make your interconnects. If the computer is locking up then you will need to be sure that the plasma is not pulling down the voltage for your computer circuit. It can be a large draw. A small UPS can help to keep the computer power clean and at full voltage.
Long arc, short arc, heliarc and in-the-dark!