WFC design session v23: reasoning

Lab notebook — geometry sweep at fixed chemistry (0.1ppm Na+, 60°C)

This sweep confirms what I suspected: holding the water chemistry at the avalanche-crossing point locks the vapor-film physics, so geometry only moves f_r and the breakdown margin, not the Townsend number. Every top candidate lands 121-129 Td — dead inside the 3-6 eV cold-chemistry window — because cell voltage stays pinned near 320V by the tank Q (~27) and the 12V drive. That's the key coupling: Td tracks cell voltage, and cell voltage is set by Q, not by rod diameter. Enlarging the rod OD and tube ID barely touched C_eff (0.65-0.73nF) because the wider gap offsets the larger area — the log-ratio geometry is self-compensating. So I cannot pull f_r below ~93kHz this way without either shrinking the gap (raising C, risking breakdown margin collapse) or adding turns to the choke (more wire, more AC loss).

Trade-off is clean: higher Q buys me the 320V I need to light the film, but it also lets series current climb toward the 130mA I'm seeing — still comfortably under the 1A restriction, so I have headroom to push Q harder next time.

I'm adopting #4: 12mm rod in 28mm tube × 150mm, single cell. Same 0.548 score as #1-3 but the longer single electrode is mechanically simpler than 3 parallel cells (#3) and gives the largest breakdown margin (×1000+) in a buildable form.

Next session: sweep choke inductance to break the 93kHz floor, and probe gap-narrowing to trade breakdown margin for lower f_r — watch the Paschen 719V ceiling.