The following formula can be used to calculate the dynamic resistance of a spark gap:
R = R0 * (1 - exp(-t / tau))
where:
??? R is the dynamic resistance of the spark gap at time t
??? R0 is the initial resistance of the spark gap (when t = 0)
??? tau is the time constant of the spark gap
The time constant of a spark gap for nitrogen at 1 atmosphere with a gap of 3mm is approximately 100 nanoseconds. This can be calculated using the following formula:
tau = 1.5 * d^2 / p * k
where:
??? tau is the time constant in nanoseconds
??? d is the gap spacing in millimeters
??? p is the gas pressure in atmospheres
??? k is a constant that depends on the gas composition
