Inductance needed for a target frequency

What choke do I need to make this cell resonate where I want it?

L = \frac{1}{4\pi^{2} \cdot \left(f\right)^{2} \cdot C}

Method

1. Convert the frequency to hertz and the capacitance to farads. Everything below is SI.
2. Square the frequency. This is the step that makes the answer sensitive: halving the target frequency quadruples the inductance you have to wind.
3. Multiply by 4π² — about 39.48 — and by the capacitance.
4. Take the reciprocal. The result is the total series inductance in henries.
5. If the design uses two chokes in series, each needs half of this, because inductances in series add.
6. Check the characteristic impedance √(L ÷ C) before winding anything: it tells you the reactance the drive has to push against, and a number in the hundreds of kilohms means very little current will flow.

Assumptions

• The chokes are ideal inductors. A real coil with the henries this calculation asks for has substantial resistance and its own self-capacitance, and both pull the actual resonance below this figure.
• The capacitance is what you think it is. Cell capacitance moves with temperature, with gas in the gap, and with how much of the electrode is actually submerged.
• Series connection, with the chokes adding. Coils wound on a shared core couple to each other, and mutual inductance can add or subtract depending on winding sense — the total is then not simply the sum.
• The result must be below the chokes’ own self-resonant frequency to mean anything. A coil driven above its SRF behaves as a capacitor, and no amount of turns will fix that.