Ray trajectories in line-focused laser plasmas

The problem of radiation propagating along the axial direction of an elongated laser plasma is treated analytically and numerically. With the paraxial-ray equation, simple expressions for ray trajectories in such plasmas are derived that allow one to calculate beam trajectories in an expanding plasma. Linear, quadratic, exponential, and Gaussian electron-density distributions are considered for plane and curved targets. Several of the trajectories are exact solutions of the paraxial-ray equation; others are useful approximations that are compared with numerical solutions. This theory finds its main application in the field of x-ray lasers, in which it may be helpful to design targets for optimum beam propagation and to understand the effect of beam deflection on the effective gain and the beam divergence. Furthermore, with this theory, the maximum electron density at which there is gain can be estimated from the far-field deflection angle of an x-ray laser beam.