Traveling wave model for laser-guided discharges

We present an easily solvable 1D traveling wave model for laser-guided discharges. By assuming constant propagation speed u, the hydro/electrodynamic/chemistry equations are reduced to ordinary differential equations in retarded time τ. Negative discharges are shown to propagate only if u>μEb, where μ is electron mobility and Eb is the breakdown field; positive discharges propagate only if the channel preconductance exceeds ∼6×10−11 m/Ω. The axial electric field E is shown to spike up to several times Eb and then relax to ∼Eb for as long as the gas remains cold. In this streamer region, the channel conductance, current, and potential all increase linearly with τ. The transition to the leader stage, where E is much smaller, occurs in two steps: excitation of vibrational and low-lying electronic states, then gas heating. The propagation range decreases as a function of initial radius and (for given maximum voltage) of the voltage rise rate. Expansion of the hot channel is shown to increase the range.