Gain Guided X-Ray Beams

It is shown that with gain and index profiles of typical x-ray laser experiments the x-ray beam is guided by the gain profile rather than defocussed by the refractive index distribution. An arbitrary beam generated within the medium or injected into the medium is quickly transformed into a ’matching’ beam, propagating without change. The effective gain of the matching beam is somewhat, lower than the gain at the maximum of the gain distribution. If the gain distribution exhibits a small curvature in direction of beam propagation the effective gain is dramatically reduced.