I looked on the one I've got, no number, but they're commonly refered to as "mini-alternator". If you look on ebay for example, you'll see lots of them that match the one in the picture. From there you might get a number to look for one locally. Or check with a Kubota (maybe other manufacturers of small tractors as this unit is very common to them) dealer.

The nominal diameter (not counting the mounting ears) is 3 1/2".

The tractor ones are often 40 amp, though I've seen them also listed in 50 and 60 amp as well.