Buildup of the radiation power spectrum in hot plasma x-ray lasers

Abstract

A three‐dimensional quantum theory of hot plasma x‐ray lasers, which takes into account general transverse profiles of electron density and gain, is presented. Maxwell–Bloch equations, including a fluctuation source term, are used to obtain the buildup of stimulated gain from spontaneous emission. Radiation propagation and amplification equations, which depend only on the average fluctuation fields, are obtained. These equations are appropriate to describe diffraction effects for Fresnel numbers F∼1 and refraction effects for F≫1. In the refraction case a multiple‐mode treatment is presented and analytical solutions for the steady‐state power spectrum and time‐dependent intensity are obtained. The steady‐state power spectrum under low‐gain (spontaneous) and high‐gain (stimulated) conditions is compared and found to be in good agreement with the predictions of the phenomenological photon rate equation.