Nonresonant optogalvanic laser-induced signals in prebreakdown gas discharges. I. Simplified model for time dependence of metastable atom density changes

Electrical responses of low-biased noble gases irradiated by medium-intensity, nonresonant, short laser pulses can be described by a limited number of internal processes. Simplified rate equations for the main processes are solved analytically. It is assumed that (1) a four-level model describes the gas energy states and (2) metastable levels (the most populated excited levels) are the principal source for free-electron concentration change. The solution in the form of a series of time-varying exponentials represents the behavior of the metastable atom density perturbed by laser pulse illumination. Although this polynomial type of representation of discharge behavior is typically assumed empirically, here it is derived analytically, and coefficients in such polynomials are related to actual quantum processes within the discharge and initial laser-induced perturbation