WFC design session v22: reasoning

Lab note, 2026-07-10

This sweep confirms what I suspected: pushing water_ppm down toward ultrapure (0.1-1ppm) and varying surface_factor from 0.25× to 2× barely moves the needle on the figure of merit that matters — the four top candidates (#1-4) are bit-for-bit identical in geometry, R, C_eff, resonance, and cell voltage. Surface_factor only rescales C_dl (1.1µF→8.7µF), which doesn't touch the tank math because displacement current dominates at 98.9% anyway — the double-layer is along for the ride, not driving resonance. That's a useful negative result: surface treatment is not a lever for hitting the Paschen window at this geometry; it's decoupled.

The real lever is ppm/temperature, which sets bulk R and shifts f_r. #5 (1ppm, 3°C) drops f_r to 289kHz and lands at 717V — just under the 719V Paschen threshold, sub-breakdown. #1-4 (0.1ppm, 60°C) push f_r to 329kHz, 745V, and cross into townsend-avalanche at 297Td — inside my 80-250Td target only at the edge, and I'm not thrilled about that; it's borderline CGDE, not comfortably centered.

Adopting #3 (surface ×1, the "neutral" untreated case) since surface_factor is confirmed inert here — no reason to claim credit for ×0.25 or ×2 when they're numerically identical. But every candidate this round violates the 1-100kHz practical band by 3×. Next session: hold ppm/temp near #1-4's values (they're the only ones crossing into avalanche) and sweep geometry (rod/tube diameter, length) specifically to pull f_r down under 100kHz without losing the Td window — that's the real unsolved constraint, not surface finish.