First, it needs to be pure sinewave and current limiting (meaning when under load, it lowers voltage instead of shutting off). Both of these properties are more important than actual output, but are typically not specified (particularly the current limiting part). **(edit to add:)**Modified sine wave inverters can cause excessive heat build up in the components of the flash, which can result in premature failure. Non-current liming inverters will shut down upon recharge of the flash caps. Alien Bees have an average 5A draw, but when recycling, draw 18A for a brief period. Multiple lights only exacerbate that problem. Current limited 120V inverters will drop voltage to about 40V until the initial surge is over, then raise back up to 120V. **
Higher output inverters will recycle the flash faster (up to maximum recycle speed), lower output inverters will reduce recycle time. For example: a 300W inverter will recycle a B800 (320Ws light) in about 1 second or so. A 150W inverter will take about 2 seconds. A 600W inverter will still take about 1 second, as the light simply cannot recycle any faster. But the 600W inverter can recyle 2-B800's in about 1 second, while a 300W inverter could take 2 seconds.
(The numbers above are for approximation purposes. Due to the nature of electronics and various designs in inverters, you will not always get an absolutely linear correlation in wattage and recycle times)
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