Putting the rise time issue aside one interesting solution to high power problem could be having multiple resonance circuits and connecting them in serial/parallel manner to increase voltage/current. You could take 40 circuits with 1000 volts to get 40kv voltage. The multi-million amperage seems more of an issue.
The question is how do you control such a large number of circuits precisely? This project seems worth of ITER challenge, but the small testing circuits connected a mini-dpf could be worked on by students on an university level.