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 tau Negative discharges are shown to propagate only if u > mu E-b, where mu, is electron mobility and E-b is the breakdown field, positive discharges propagate only if the channel preconductance exceeds similar to 6 X 10(-11) m/Omega The axial electric field E is shown to spike up to several times E-b and then relax to similar to E-b for as long as the gas remains cold In this streamer region, the channel conductance, current, and potential all increase linearly with tau 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 [doi 10 1063/1 3494160]