Modal analysis of x-ray laser coherence

Abstract

We present a modal analysis of the paraxial wave equation for plasma x-ray lasers. Gain guiding and refractive antiguiding are identified as the essential mechanisms which influence the coherence of the output radiation. Scaling laws for the number of guided modes and the coherence are given, depending on three parameters: the gain-dependent Fresnel number, the strength of refraction relative to gain, and the amplification length. The importance of controlling excess spontaneous emission to obtain coherence is identified. We suggest an experimental effort to verify various guiding regimes and to produce coherent output in the range between 45 and 200 Å.