Steam Resonator design session v4: reasoning

This sweep chased a specific hypothesis: decouple edge-rate from the fundamental. Keep the drive slow (100 kHz) so the bulk field fully establishes, then dump all the Debye loading through sub-100 ps edges to reach up the 57 GHz relaxation tail. Ten thousand candidates, and the top five are effectively one design wearing different dead-times and edge-rates: coaxial T-304, 2 mm gap, 1000 V, 100 kHz bipolar switchover, resistive pickup and choke restricting leakage to ~3.47 A. Winner scores 0.516 at 3.826 kg/hr.

Physically the field story is clean. τ_bulk is 183 ns and the on-time is far longer, so ⟨E⟩ of 495 kV/m establishes to 100% — a real, fully-formed field across the gap. The double layer is genuinely frozen out: 0.03% charge per phase, τ_EDL near 15 ms, orders of magnitude slower than the drive. That part of the amp-restriction concept is working exactly as intended.

But I have to be straight about the heat budget, because it damns the design. Cavity heat is 2754 W. Of that, dielectric relaxation — Stan's "particle impact," the term we actually care about — is 1.76 milliwatts. Not watts. Milliwatts. The other 2754 W is split evenly between double-layer cycling (1377 W) and ohmic leakage (1377 W). That is 0.0% non-ohmic. This design makes steam by pushing 3.47 A of leakage current through resistive water and calling the I²R a kettle. The sharp edges bought nothing: at 100 kHz fundamental we sit at 1.76e-4% of the 56.9 GHz loss peak, and the harmonic comb only reaches 3.18 GHz — still four orders below where ε'' lives. Establishing the field slowly and dumping edges into the tail did not couple to the relaxation; it just heated resistively.

The finding that matters: edge-rate alone cannot reach the Debye peak from a 100 kHz base. Next session I raise the fundamental itself — sweep 1–100 MHz — so real cycles land inside the loss band, and I hunt for the regime where dielectric relaxation exceeds ohmic leakage even by 1%. Score the non-ohmic fraction directly, not yield. Until that fraction moves off zero, we are boiling water with a resistor.