Spontaneous initiation, radiation propagation, and gain buildup in hot-plasma x-ray lasers

Abstract

A three-dimensional, time-dependent theory for spontaneous initiation, radiation propagation, and gain buildup in hot-plasma x-ray lasers is presented. The temporal and spatial evolution of the radiation field and atomic polarization is governed by a set of Maxwell-Bloch equations with an additional Langevin-force term which accounts for stochastic processes. The model equations are solved, in the limit of small signal and large Fresnel numbers, by the ray-tracing technique yielding formulas for the field intensity, autocorrelation function, complex degree of coherence, and the power spectrum in terms of the solution of a set of coupled ray equations. A specific two-dimensional (r,z) numerical example, demonstrating the capacity of the method, showing the transition from the spontaneous stage through a transient buildup stage to steady state is presented.