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An arc discharge is primarily a low voltage load with the current thru it largely determined by the external circuit.
From "Fundamentals of Engineering Electronics", by William G. Dow. p456, and 552.
An approximate empirical formula for an arc voltage drop is:
Va = A + B / Ia^N
where A, B, and N are empirically determined constants.
Va is the arc drop, including both electrodes, and
Ia is the arc current.
N is a function of the anode material.
If you have a constant source impedance at say 100 ohms at 10,000 V, then the short circuit current is 100 A, and assume 50 V for the arc drop. Then the power dissipated in the arc is 5000 W.
Use a transformer to step this down to 100 V, then the approximate source impedance is 100 / (100 * 100) = 0.01 ohms. Assuming the arc drop remained the same, then the approximate arc power would be 50 * 50 / 0.01 = 250,000 W. In reality the arc drop will be higher and the current lower, but there will still be vastly more energy in this arc than the high voltage one.
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