0.25 mm Taylor-plug gap: usable Td ladder is 370 V to ~1.2 kV, hard ceiling at Paschen 1,298 V

Scotchn's segmented (Taylor) flow through a 0.25 mm annulus: the gas plug spans the channel, so discharge length = gap, removing the guessed-sheath-thickness unknown.

At 1 atm / 300 K, 1 Td = 245 V/cm, so E = V/0.025 cm gives:

• 370 V -> 60 Td (below the 80-250 Td cold-chemistry window; good for N2/H2O vibrational pumping, not for bond breaking)
• 490 V -> 80 Td (window floor)
• 735 V -> 120 Td (dissociative attachment, e + H2O -> H- + OH, peak sigma near 6.5 eV)
• 980 V -> 160 Td
• 1,225 V -> 200 Td
• 1,530 V -> 244 Td: alpha = 269.6 /cm, alphad = 6.74, M = gamma(e^(alphad)-1) = 25.3 at gamma = 0.03. Self-sustained Townsend glow, NOT streamer, but the sub-critical corner is lost.

Paschen breakdown for water vapour at p*d = 1.9 Torrcm is 1,298 V (Paschen minimum 214 V at 0.74 Torrcm). M = 1 crossing at gamma = 0.03 lands near 1.25 kV. So the usable ladder for this geometry is 370 V to ~1.2 kV; L5 at 1,225 V is the top rung.

Contrast case, same 1.5 mm gap earlier in the thread: at 125 psi / 20 kV it is 56 Td, M = 6.4e-5 (dead); at 1 atm / 20 kV it is 532 Td, alpha*d = 284, deep streamer. Amplitude alone is not the lever - the ratio V/d against pressure is.

Per-molecule cross-check (series micro-capacitor treatment): 0.25 mm = 925,930 molecules; 490 V = 529 uV/molecule (top of polarization band); 926 V = 1 mV/molecule (elongation threshold). The vibrational ladder is what gets past elongation without paying 926 V of Faradaic leakage.

Thin-film variant for the same 370 V measured drive: 150 um film = 98 Td, M = 6e-4; 70 um film = 211 Td, alpha*d = 1.07, M = 0.057. Raising gamma from 0.03 to 0.10 by cathode surface treatment puts M = 0.19, inside the 0.1-0.5 target band, without raising volts.