Linearized one-dimensional model of optical plasmatron operation

An analysis is made of a steady-state optical discharge in a stream of gas, sustained by a focused cw CO₂ laser beam. By means of a series of simplifications the complex equations of the process are reduced to a second-order ordinary inhomogeneous differential equation with variable coefficients, which is linear in each of the characteristic regions of the optic axis. The equation is solved analytically by means of Kummer functions which are transformed into combinations of Bessel functions. The positions of the discharge boundaries are determined as a function of the laser power, the flow velocity, and the focusing angle. The regime with no gas flow is also considered.