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.
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