Hope you're planning on smoothing out that PWM if you're going to be > 20 khz. The alternator field windings behave like an inductor and if you try to apply PWM to them you'll burn up the switching transistor before you know it from the switching spikes.
Essentially you'll be building a variable-voltage DC-to-DC if you want to use those kinds of switching frequencies. Which is possible and not a bad idea.
If you run PWM at lower rates, around 100 hz, you will in fact be able to get the field to turn on and off that fast, though there will be some spikes you have to smooth out.
Good luck, sounds like a cool
project.