It's not really my area, so no specific part numbers, sorry.
For 50V use I'd be looking at one with at least 100V VDS rating, to have a chance of coping with inductive turn-off spikes. I'll assume the board layout keeps these down to a minimum and that any spikes are suppressed by TVS diodes or similar if necessary. If not, consider improving the layout and suppression first, but if that's not an option, a 200V transistor might be a better bet. It'll have higher gate capacitance and/or higher RDSon, though.
22kHz is quite slow, so you could go for a device with higher than average gate capacitance in order to achieve lower RDSon. Conduction losses are I^2R, so if I = 10A, I^2 is 100, so that's 1W per 10mOhms resistance.
As a first guess, I might look at this one:
http://www.vishay.com/docs/71141/SUP85N10.pdf100V rating, 12mOhm RDSon @ VGS=4.5V, continuous drain current rating 60A. It has a high capacitance, but since it's being switched quite slowly that shouldn't be the end of the world. Provided the device driving it is up to the job, it should do nicely with a small heat sink.