AC causes engine to stall (2002 MX-5)

My 2002 mx5, 64000 miles, stalls when using the ac. Could be 30 minutes but with the ac on the engine just chokes out. Engine cranks when trying to restart. Won't start. Turn off ac, Wait 10 minutes, and the engine catches, runs rough for a few seconds and then it's running fine again.
Anybody had this experience?
 
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