High-current capable (±250A) AC power-supply, sine wave/square wave (±20V)
Look for programmable power supplies with 5000W (5kW) peak rating.  Something might come up on Google.  

Trying to make one on the cheap from random parts might work but may not give repeatable results for characterising parts.  

A DC coupled 5kW servo/audio/lab power amplifier connected to a programmable arbitrary pulse/signal generator might be the DIY direction to investigate.

For the load resistor you can look up Shunt resistors, that should be the easy part.  Make sure you use robust cables and bus-bars for the connections so you do not have volt drops in unexpected places. The frequency of 3kHz will not require you to have too much concern about inductance but you will need to keep the cables short.  Check out welding and car starter motor cables for ideas and then decide if the volt drop is acceptable, your cabling may be enough of a resistor to dispense with the separate load.

EDIT:
Corrected my hasty calculations.  

Continuous power likely not required to be at the peak rating as the tests are short in duration but impressive apparatus in any event.  

Finding a used bit of gear from a Diode manufacturers lab would likely be the best if you want to keep it simple.  Making a resonant capacitor discharge circuit that has only passive power components might be the cheapest DIY solution requiring only good quality measuring methodology.