It is almost certain that the starting surge for the compressor is causing the voltage to drop below the minimum that your plasma machine needs. Moving the compressor to a different outlet may help, but make sure it is on a different breaker.
If both pieces of equipment are running on 120V make sure they are on differents legs of the incoming 240 supply to balance the load; if you are running both on 240 they are balanced of course.
If they can be wired to run on 240V, wire them this way to reduce the current draw.
An open mind is a virtue...so long as all the common sense has not leaked out.