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A simple method for predicting maximum electron density in microwave air breakdown

The electron density in air breakdown reaches the maximum level, when the transmitted electric field decreases to the critical value at which electron ionization balances electron loss. This paper reports a simple method based on the wave equation in nonuniform plasma to fast predict the maximum electron density in air breakdown by plane microwave, when the electron density profile is known. The wave equation is solved numerically by the finite difference method, and the obtained transmitted electric field is consistent with the “exact” solution from the scattered-field finite difference time domain method. When the electron density profile is assumed to be a parabolic distribution in the direction of wave propagation, the effects of air pressure, incident field strength, wave frequency, and plasma thickness on the maximum electron density are investigated. The maximum electron density as a function of air pressure from our simulation shows the same trend as the solutions of Maxwell-plasma equations as well as the experiment.