How to generate 100 A at 20 kHz?
The simplest solution will be to resonate your magnetic coil with a capacitor, to be resonant at about 20kHz, then drive it from an amplifier at resonance.

The amplifier will only need to supply sufficient power to make up for losses in the LC circuit. These will principally be resistive losses in the coil and in the capacitor's ESR.

Finding a capacitor you can use at 100A will be interesting. I suggest you think about using several metal film polycarbonate types in parallel. Calculate the voltage needed, or measure it at low current, before committing to a final build, you might find you need a lot of voltage to slew 100A through your inductance. It might be appropriate to build a second lower inductance coil for your AC work if the required voltage is too high.

You have a choice of topology, depending on your amplifier. You can use a high voltage low current amplifier driving them in parallel. Alternatively, you could use a high current low voltage amplifier to drive them in series. 

Your 'amplifier' does not need to have a sinewave output, though a large audio amplifier would be one obvious choice. A FET H-bridge would be a perfectly reasonable driver, as the coil current will be dominated by the resonance, barely distorted by your drive waveform. At 20kHz, a ferrite matching transformer would be straightforward to use to match whatever AC source you had to hand to the appropriate impedance level for your LC resonator.