Two dimensional generalization of Raizer's analysis for the subsonic propagation of laser sparks

An extension to two dimensions of Raizer's analysis for the steady state, subsonic propagation of laser sparks is presented. A solution in closed form is obtained for a simplified, two dimensional energy equation, yielding both axial and radial temperature profiles as well as the relationship between incident laser intensity, laser radius and propagation velocity. The propagation mechanism is assumed to be thermal conduction and radiation losses are included in a phenomenological manner. The solution is obtained for a laser spark propagating in a channel and therefore can be used to investigate the effect of a boundary on spark propagation. The solution also allows calculation of the radial heat conduction parameter A introduced by Raizer for use in one dimensional approximations. Sample calculations are presented for air sparks of .15 and .50 cm radius.