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ptonsparky:
If it truly turns on with a very fast rise, and a somewhat slower fall, then it is probably a load with an SCR or equivalent device that is turned on at the leading edge of the current, is charging a capacitor, and turns off when the current thru the SCR drops to near zero. This is approximately when the supply voltage equals the capacitor voltage. This will be somewhat near the source voltage peak.
If it were simply a diode rectifier feeding a large capacitor with a resistive load that produced only a small amount of capacitor voltage ripple, then the leading edge would be slower and nearly like the trailing edge. Generally this looks a little like a short duration half sine wave perched on top of the other normal AC current from other resistive loads.
You are probably looking for some sort of electronic equipment.
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