calculation · Water Fuel Cell · computed
WFC design session v49: best candidate (Q=86.6, 95.4kHz)
Sweep — Slide V_cell into the 80-250 Td sub-critical corner (M 0.1-1) by softening tank Q with cold/pure water while trimming gamma_se and peak_v together — the water/thermal path, not more magnification.
- Cell — 12mm rod in 14.0mm tube × 50mm, 1 cell(s) parallel → C_eff = 1.55nF, bulk water R = 106752Ω.
- Water/electrodes (Randles) — 0.1ppm Na+ @ 5°C, surface ×0.5 → λ_D 228nm, C_dl 1.7µF, cell series R 10.9Ω, displacement current 99.0%, breakdown margin ×13.
- Fig-8 voltammetry (4,798,661) — τ_EDL 180201.1µs (17183.1 carrier cycles to charge), Faradaic leakage at peak 263.7mA (leak score 0.29 — keep amp leakage inhibited while voltage climbs the ladder).
- Vapor-film discharge (CGDE onset, 5197V across 0.1mm film) — regime streamer, film Paschen 797V, 2072 Td — OUTSIDE the 80-250 Td cold window.
- Townsend α/γ — γ = 0.002 (electrode lever), criterion M = γ(e^{αd}−1) = 10369411057174145024.000 → self-sustaining (M≥1) — γ feedback closed, heading for thermalization.
- Per-molecule (series micro-capacitor chain) — 3.70M molecules across 1.00mm → 1.40 mV/molecule (elongation (mV band)).
- Chokes — 2 × 0.0009H (180 turns, AWG 18, 21m wire, AC R 0.8Ω each).
- At resonance f_r = 95.36kHz — Xl = 1078Ω, Xc = 1078Ω, tank Q = 86.6, coil Q = 693.6.
- Cell voltage 5197V from 60V drive (×86.6). Tank current 4.82A circulating (CW upper bound — rate wire/switch for this); average input 96mA at 2% duty.
- No hard violations (band, wire length, dielectric). Average current is scored, not gated.
- Score 0.687.
Basis
- Confidence
- 0.70
- Method
- townsend-v5
- Recorded
- Published
- 30 Aug 2026
- Device
- Water Fuel Cell
- Component
- cell
- Source Ref
- design session v49
- Notebook Id
- 1642
design-loop Q resonance