Taper injector gap is a PARALLEL 0.254 mm (.010 in) annulus proven by two dimension pairs; at 20 kV it reaches the elongation rung, and the elongation threshold coincides with the Townsend sub-critical corner

GEOMETRY — THE GAP IS PARALLEL, NOT TAPERED IN SPACING. From Memo WFC 423 DA Fig 2-1/2-2 detail crops:

• Probe: stainless steel T304, .156 DIA (-.001), with an .080 DIA polished tip surface, .993 exposed length.
• Plug housing: conical inner surface, .176 DIA inlet hole (polished), .100 DIA exit port. Annulus at inlet = (.176 - .156)/2 = .010 in. Annulus at tip = (.100 - .080)/2 = .010 in. Both surfaces taper together, so the radial gap is CONSTANT at .010 in = 0.254 mm from inlet to exit. "Taper resonant cavity" means tapering DIAMETER at constant SPACING. Confirmed independently by Scotchn as "parallel 0.25 mm". CONSEQUENCE: the .010 in quenching-slot dimension (Fig 2-3, six slots .010 W x .010 D) and the polarization field gap are THE SAME DIMENSION. This supersedes the caution in notebook #3372 item 3 — Townsend/Td work at 0.25 mm does apply to the cavity gap.

PER-MOLECULE LADDER AT THIS GAP (0.254 mm, N = 940,740 molecules at 2.7 A each):
1 nV/molecule (alignment) at 0.00094 V applied
1 uV/molecule (polarization) at 0.94 V
1 mV/molecule (elongation) at 940.7 V
1 V/molecule (ionization scale) at 940,740 V
At the Fig 4-15 figure of "typically 20K volts applied": 21.3 mV per molecule — the ELONGATION band. For comparison, a 1.57 mm wet tube at 370 V yields 63.6 uV/molecule, polarization only. The injector runs two rungs higher.

CONVERGENCE (the eureka): the applied voltage for 1 mV/molecule at 0.254 mm is 941 V. Working independently from gas-discharge physics, the sub-critical Townsend corner at the same gap (80-250 Td, below Paschen breakdown of ~1384 V for water vapour) is roughly 500-1380 V. The elongation threshold sits in the middle of that window. Two unrelated criteria — molecular electrostatics and Townsend avalanche — identify the same operating corner.

WHY 20 kV IS NOT A GAS-PHASE NUMBER. Treating the 0.254 mm gap as water vapour at 20 kV: E = 787 kV/cm, E/N = 3,140 Td, alpha = 7,468 /cm, alpha*d = 190 (streamer criterion is 18.5), M = gamma(e^(alpha*d) - 1) ~ 5e19, Paschen exceeded ~14x. Regime: streamer. Therefore 20 kV must stand across a gap FILLED WITH LIQUID WATER AND MIST, not vapour.
This explains the Fig 4-25 firing order: WATER INJECT TRIGGER (START) -> PULSE DELAY ADJUST (OUT 1) -> (HI) VOLTAGE TRIGGER (OUT 2). Water is metered in before the HV edge arrives.
It also justifies sub-100 ns rise, low duty and the unipolar constraint that the Fig 4-5 "ADJUST (T2) TO COMPENSATE MAGNETIC FIELD OSCILLATION OF (VIC) PRI/SEC. COILS TO PRODUCE UNIPOLAR PULSE-FREQ." trim exists to maintain: past the Raether limit the pulse must terminate before the avalanche thermalises into an arc. Firing this gap dry at 20 kV with a long pulse yields an arc, not fuel.

BENCH RULE: (1) water present in the gap before the HV edge, never fire dry; (2) short, unipolar, fast-edged pulse; (3) if targeting the sub-critical VAPOUR regime instead, use 500-1380 V at this gap, not 20 kV.
The .010 in geometry serves double duty: it sets the field gap and acts as the restricted orifice preventing flashback (quenching circuit, US 5,149,407).