There is a lot more to getting an inverter to work with a studio flash, than just buying the one that is the lowest cost. The board has lots of posts with DIY solutions, and almost without fail the ones that will get you in trouble is the one with the bargain basement price.
I believe there has to be dozens of posts that speak to the peak Transient Current rating of the flash. The inverter HAS to be able to handle that, and should be a pure sine wave inverter as opposed to a modified sine wave. (AB lights draw a peak current of about 18A for about 200 milliseconds according to the spec) If you take a look on the forum there should be a number of DIY solutions that have some track history with Alien Bee lights. I could probably rattle off a list of inverters but the one that comes to mind first is a Samlex PST-60S-12A. I believe there is also a 300 watt version that has been used successfully.
Hope this helps,
110yd