calculation · Water Fuel Cell · computed
WFC design session v47: best candidate (Q=24.4, 94.6kHz)
Sweep: Deliberately detune Q (larger rod OD + wider annular gap → lower magnification) crossed with gamma_se and low peak_v/low-duty drive to slide V_cell into the 80-250 Td sub-critical CGDE corner (M 0.1-1) instead of overshooting into avalanche, keeping Faradaic leakage quenched with cold/pure water.
Cell: 24mm rod in 28.0mm tube × 50mm, 1 cell(s) parallel → C_eff = 1.41nF, bulk water R = 30097Ω. Water/electrodes (Randles): 0.5ppm Na+ @ 25°C, surface ×0.5 → λ_D 106nm, C_dl 6.7µF, cell series R 47.0Ω, displacement current 96.2%, breakdown margin ×128. Fig-8 voltammetry (4,798,661): τ_EDL 200324.4µs (18953.2 carrier cycles to charge), Faradaic leakage at peak 99.0mA (leak score 0.50 — keep amp leakage inhibited while voltage climbs the ladder). Vapor-film discharge (CGDE onset, 975V across 0.1mm film): regime townsend-avalanche, film Paschen 778V, 389 Td — OUTSIDE the 80-250 Td cold window. Townsend α/γ: γ = 0.003 (electrode lever), criterion M = γ(e^{αd}−1) = 90.187 → self-sustaining (M≥1) — γ feedback closed, heading for thermalization. Per-molecule (series micro-capacitor chain): 7.41M molecules across 2.00mm → 131.66 µV/molecule (polarization (µV band)). Chokes: 2 × 0.001H (200 turns, AWG 18, 24m wire, AC R 0.9Ω each). At resonance f_r = 94.61kHz: Xl = 1189Ω, Xc = 1189Ω, tank Q = 24.4, coil Q = 690.5. Cell voltage 975V from 40V drive (×24.4). Tank current 0.82A circulating (CW upper bound — rate wire/switch for this); average input 16mA at 2% duty. No hard violations (band, wire length, dielectric). Average current is scored, not gated. Score 0.614.
Basis
- Confidence
- 0.70
- Method
- townsend-v5
- Recorded
- Published
- 30 Aug 2026
- Device
- Water Fuel Cell
- Component
- cell
- Source Ref
- design session v47
- Notebook Id
- 1637
design-loop Q resonance