Edge-only differential drive: screening-failure transient gradient, plus a zero-i_c dwell window that measures Faradaic leakage directly

DRIVE SCHEME: plate B lags plate A during the RISING EDGE ONLY; both plates common-mode for the remainder of the pulse. Differential across the gap exists only in the lag window.

1. TORQUE vs TENSION (the correct premise). Dipole in a UNIFORM field: torque tau = p x E is non-zero, net force F = (p.grad)E is ZERO. Alignment only — this is the nanovolt rung. Net translation/elongation requires a field GRADIENT. Consistent with my own wording in The Birth of New Technology, Capacitance (Cd): applied potential "causes and sets up Molecular Polarization Alignment (617) via electrical molecular ROTATION."

2. COAXIAL GEOMETRY ALREADY SUPPLIES THE GRADIENT. E(r) = V/(r*ln(b/a)). Worked at 600 V, 0.5 in inner tube (r=6.35mm) in 0.75 in outer (r=9.53mm): E_inner = 233 kV/m, E_outer = 155 kV/m. Dielectrophoretic force ~ grad(E^2) ~ 1/r^3, so pull at inner electrode = 3.38x the outer. Tube-in-tube IS an asymmetric geometry; inner-tube radius is a design lever, not packaging. Same reason the taper injector works: constant .010 in annulus wrapped on a .080 in tip.

3. NEW RESULT — EDGE TIMING ADDS A GRADIENT THE GEOMETRY CANNOT. Dielectric relaxation time of the water, tau = eps_r*eps_0/sigma:

   • lab distilled, sigma ~ 1e-4 S/m -> tau = 7.1 us
   • ultra-pure, sigma ~ 5.5e-6 S/m -> tau = 129 us If the differential window is SHORTER than tau, ions cannot redistribute and no screening double layer forms. The field penetrates the BULK on the geometric 1/r profile instead of collapsing into two ~1 um wall layers. That field distribution does not exist in steady state at all. Water keeps up easily: Debye reorientation ~8.3 ps, so alignment and elongation complete well inside even a 100 ns edge. The molecule responds; the screening does not. => Edge duration is a first-class design parameter set against tau, i.e. against water purity.

4. NEW RESULT — THE COMMON-MODE DWELL IS A FREE FIGURE-8 MEASUREMENT WINDOW. During the dwell dV/dt = 0, therefore i_c = C_dldV/dt = 0 BY CONSTRUCTION. Any current measured in that window is pure Faradaic leakage i_f = ksqrt(v). No capacitive term to subtract, no deconvolution. This gives a direct per-level measurement of k as the drive climbs the amplitude ladder — exactly the applied-potential-vs-amp-leakage split of Figure 8, US 4,798,661, obtained by timing rather than by curve fitting. Converts a qualitative "leakage ~ zero" into a hard number per level.

5. CURRENT MODULATION IS REAL AND SEVERE. i_c = C*dV/dt. For C = 98 nF to 600 V: 1 us edge -> 58.8 A; 10 us -> 5.88 A; 100 us -> 0.588 A. A 30 V rail cannot source 58 A, so the achieved edge rate is set by source impedance and choke L, not by the gate command. Back the true dV/dt out of measured current to learn the ACTUAL lag window.

6. FAILURE MODE TO CHECK FIRST. "Common mode" is ambiguous and the two cases are opposite: (a) plates EQUALISE through some path -> cell discharges, field off, edge work relaxes in ~ps, dwell is dead time AND the leakage window reads the discharge path instead of i_f. (b) plates rise together with the differential FROZEN (blocking diode holding charge) -> field persists at full strength through the dwell. This is the step-charge condition and the one that makes items 3 and 4 valid. Test: scope BOTH plates single-ended to a common ground, not differentially. If gap voltage decays during the dwell, case (a).