Design a VIC: cell, choke, Q and step charging

Given this tube, this water and a target frequency, what choke does it need, how sharply will it ring, and will it step-charge?

The formula

L = \frac{1}{{(2 π f)}^{2} C}

LaTeX

L = \frac{1}{(2\pi f)^2 \cdot C}

Work it out

Fill from a part the library

w Water

What is in the cell.

T Temperature

°C

The water's temperature under load.

a Inner tube outer diameter

The inner electrode's outside diameter.

b Outer tube inner diameter

The outer electrode's inside diameter. The gap is half the difference.

l Tube length

The overlapping length of the two tubes.

f Target frequency

kHz

Where the drive will run. The choke is designed to ring the cell here.

R Series resistance

Everything resistive in the loop — choke DCR, cell ESR, wiring.

V Drive voltage

The amplitude driving the resonant loop.

v Pulse amplitude

The height of each gated pulse for step charging.

n Pulses per gate

How many pulses arrive before the gate closes.

p Pulse period

µs

Time between pulses.

k Cell leak resistance

kΩ

The resistance the charge leaks away through between pulses — the water's conductance across the gap.

or see a worked example with typical numbers

Find the cell's capacitance from the two tube diameters, the overlap length and the water's permittivity at temperature — the coaxial capacitance calculation.
Find the choke that rings that capacitance at the target frequency: L = 1 ÷ ((2πf)² C) — the required inductance calculation.
With that choke, that cell and the series resistance, find the Q and the resonant voltage rise — the Q factor calculation.
Ask what the water is doing at that frequency: its Cole-Cole loss tangent. A cell full of tap water at a few kilohertz is a resistor with a capacitor attached, and the Q above is optimistic by however much this says.
Run the pulse train against the cell and its leak resistance: does the charge accumulate into a staircase, or drain away between pulses — the step charging calculation.
Each step is its own calculation with its own page. Every formula is shown below with these numbers in it, and each links to that page pre-filled, so any step can be checked alone.

Every assumption of every constituent applies. In particular: the cell is an ideal coaxial capacitor with no end effects; the choke is lossless and its self-capacitance is ignored; the water's permittivity follows the linear temperature fit and the Cole-Cole relaxation; the step-charge pulses are ideal.
The series resistance and the leak resistance are two different things and are entered separately. The first is what damps the ring — choke wire, cell ESR, wiring; the second is what drains the cell between pulses — the water's conductance across the gap.
The loss tangent step is diagnostic, not fed forward. The Q reported is the lossless-dielectric figure from the series resistance alone; a loss tangent near or above 1 means the real Q is far lower, and the page says so rather than blending the two.
This is standard physics chained together. What is Meyer's is the claim about what the cell is — a water capacitor to be rung, not an electrolytic cell to be driven — and that claim lives in the sources, not in the arithmetic.