It would have to be trial and error I'm afraid as there's no basic electronic circuit available which is tailormade for this antenna, not that I can see anyway.
If one could assume that the frequencies involved which activates the antenna, for energy collecting purposes then, lies in the range of say a few tens or hundreds of kilohertz, then by all means, switch it on and off using a variable frequency generator, much like the way you would use it in a step up converter.
That way you wouldn't risk blowing the whole circuit up should you actually hit some sweet spot, provided you use say a optocoupler between the generator and the power transistor that is.
I guess you have to decide which way you'd like to go from the start here, either using a frequency generator which you yourself control the output frequency with or if you'd like to use a self resonating circuit homing in on the natural resonance frequency for the antenna itself, which is by far the most inexpensive way to drive the antenna while also leaving the circuit exposed to all kinds of dangers with regards to high voltages and so on.
Also, by using a frequency generator you could find interesting anomalies along the way as you crank up the frequency, chances are that the "sweet spot" frequency is nowhere near the natural self oscillating frequency of the antenna, you never know.