Here are some waveforms measured between ground and the cathode of my water cell. Was using a signal generator without DC bias, going into a diode / inductor / water-cell / inductor circuit. I'm posting these to show what the charging choke does.
First one is with the ferrite rod wound with two layers of 150 turns for the two inductors:
You can see the spikes there caused when the inductor field collapses but gets blocked by the diode.
Next is the same thing with a sine wave:
So a sine wave works too.
When frequency is turned up so that the square wave 'swallows' the 3rd, and 4th "bounces" of the charging choke's flyback spike, it looks like this:
And if turned up further to also swallow the 2nd, I got this, where the flyback spike is highest of all the frequencies:
Is this what is meant by achieving "charging choke resonance"?
You can do the same for the sine wave:
Then with a 250 mH inductor:
Larger inductor makes for wider flyback peaks, peaks farther apart, and somewhat higher voltage.
For this larger inductor, the max flyback peak with sine waves happens here:
I have not yet gotten the "doubling of frequency" that Meyer talked about. Sure, in that last image above there is a sine peak and then a spike, so both together make for double frequency of input, but Meyer's diagrams showed what looked like a full-wave rectified sine wave coming out of the diode or resonant charging choke. Instead, these peaks I have are too narrow, higher than the surrounding square/sine peaks, and not centered between them either.