Let me show you how the "frequencies combine and begin to feed themselves" creating more power in the process, or rather receiving more power.
I did this derivation elsewhere, but here it will have a new twist because now this will not be DC excitation. The setup is a basic loop for receiving an external magnetic field, however there is a local oscillator that oscillates in phase with the external magnetic field.
The instantaneous power delivered to a resistor 'R' depends on the voltage squared, as follows:
P =1/R [ V^2 = (v1 + v2)^2 ]
If we let v1=V1 sin(wt), and v2 = V2 sin(wt), both of the same frequency, where v1 is perhaps the voltage induced in the loop from the external fields, and v2 a locally generated in phase signal, we obtain the following:
P = 1/R [ ( V1 sin(wt) + V2 sin(wt) )^2 = V1^2 sin(wt)^2 + V2^2 sin(wt)^2 + 2 V1 V2 sin(wt)^2]
These three instantaneous power terms, when integrated over one period, give us the AVERAGE power delivered to the load (BTW, this is how we go from INSTANTANEOUS to AVERAGE) So, after integrating over one period, we obtain:
P_avg = 1/R [ (0.5 V1^2) + (0.5 V2^2) + (V1 V2) ]
Because the local signal is IN PHASE with the external signal, notice that now the 3rd power term no longer averages to zero as was the case with DC excitation. This is a very powerfull result. It shows that EXTRA POWER appears from the interaction of two signals. Notice that this 3rd power term can be a lot larger then what can be received with the loop alone, if V1 < 1. Assume we are receiving a week signal where V1=1 mV, and our driving signal V2 = 1. Then, the first power term would be equal to 0.5 micro watts, but the third power term would be 1 mW, which is 2000 times larger! So this is the beauty of regeneration, but in this case we are not using the signal itself and feeding it back in phase, but instead we have an oscillator running in phase. The trick is staying IN PHASE! This is not a simple problem because the external field is swamped out by the local oscillation, if our local oscillator amplitude is orders of magnitude larger, which normally it is when dealing with weak received signals.
EM
PS, If we don't want a local oscillator, then we have to feed some of the power received back, and we need tuned circuits to start the process, however, it's very hard to tune to low frequencies, and that's where this whole heterodyne principle comes in, or mixing frequencies. I believe SM did it both ways, because he said some of the TPUs had batteries in them, while others did not. So what TPU will you build, and more importantly what magnetic frequency will you tune into?
