ex jump pilot,
When talking about the power of a radar, it's customary to be talking of the peak power during the pulse. The average power is much less - by the duty cycle.
Assume you want to see out to 40km. That means the time between pulses is a minimum of 266microseconds. If you want resolution to 300 metres, the maximum pulse length is 1 microsecond. This gives a duty cycle of 1/266 or .00375. So a radar giving 50kW peak at the transmitter would actually be only 187.5 watts average.
I also said 'effective radiated power'. This is the power of the transmitter multiplied by the gain of the antenna. A 2 foot dish at 5Ghz will give around 20dB, so my example of the 50kW ERP is actually 500 watts (peak) of RF, and with a duty cycle of .00375, is only a few watts. In all probability, a magnetron based thing will run at around 20 or so watts average, and quite likely around 20kW peak. So the power requirements are well within the aircraft generator capabilities - unlike the start of WW2, where things like Whitleys and Blenheims reportedly had only about 500 watts for everything!
I agree that it's not a good idea to stand in front of one while it's working, though. Incidentally, although it's never as far as I know been formally studied, it is apparently well known amongst engineers working on high power microwave transmitters that when they father children, it's almost always daughters........