I have a Hyperthern 45 XP and a HD Husky Pro compressor with a 3.2 hp motor, and output of 10.2 SCHM. The Hypertherm needs a minimum of 85 psi even when the compressor is restarting. I mounted an air pressure gauge at the input of the 45 xp as recommended by Jim Colt and I see a lowest pressure of 90 psi then the compressor starts to refill the tank. That was after adjusting the pressure switch to turn on at 120 psi. Normal input pressure at the plasma cutter is 120 psi. I have been cutting some 3/8" and 1/2 " plate recently and that works the plasma cutter hard. After a 30 amp cutter i really love the 45 XP! It’s strong and cuts very well. If you are using a different cutter your air supply needs may be less.
Bottom line: get at least a 60 gal 230 volt compressor at minimum and a 3 hp with more SCFM if possible.
I plan to build a silencing cover for my compressor to reduce the noise when it’s running.