PARAXIAL WAVE-OPTICS SIMULATION OF X-RAY LASERS

Paraxial wave-optics models of x-ray lasers include diffraction, time dependence, a stochastic description of spontaneous emission, two-way waves coupled by a saturable nonuniform gain, and refraction due to a nonuniform charge density. Standard algorithms for this modeling tax t he speed and storage of a supercomputer. Recent work, using such algor ithms on an overly coarse grid, has very distorted near fields, too wi de far fields, and an optimistic estimation of spatial coherence. This paper develops axial shooting-secant iterations that feature coarse-g rid storage of fields, refined-axial-step standard-algorithm shooting between coarse-grid data, and improved coarse-grid approximations via secant estimation. Such calculations, effective when the charge densit y and gain vary much more transversely than axially, save time and muc h storage. High-accuracy integral Hermitian methods for the transverse discretization are also introduced and provide several advantages in comparisions with standard finite differences, discrete Fourier transf orms, and Gauss-Hermite or Gauss-Laguerre expansions. Several well-con verged x-ray-laser calculations are presented. A slightly greater gain along certain curved paths contributes much less than refraction to p rominent maxima in the far-field wings. Discrete computation inherentl y underestimates diffraction and thereby overestimates power output. R efraction enhances the evolution of single-mode-like intensity whereas saturation of the gain inhibits this process. The fields are sensitiv e to the transverse profiles of the charge density and small-signal ga in. Although refraction leads to many more transverse modes, it improv es spatial coherence.