Investigation of amplified spontaneous X-ray laser radiation using the equation for the transverse correlation function of the field

A physical model, based on the solution of the quasi-optics equation for th e transverse correlation function (TCF) of the field amplitude, is develope d for investigating the brightness, angular divergence, and spatial coheren ce of the amplified spontaneous emission in a laboratory X-ray laser. The m odel takes account of the spontaneous source of radiation, diffraction, reg ular refraction, regular amplification taking account of saturation, nonres onance absorption, scattering by small-scale fluctuations of the electron d ensity and the gain, and scattering by random hose-like deviations of the e xtended plasma medium of the X-ray laser. It is established that the TCF me thod makes it possible to obtain the final result much more quickly than th e basic Monte Carlo method for the parabolic equation for the field amplitu de. As a result of the statistical linearization of the equation for the tr ansverse correlation function in the presence of gain saturation, this meth od overestimates the absolute values of the average intensity of the amplif ied spontaneous radiation, but the maximum overestimation does not exceed 1 0%. It is found that fluctuations of the optical parameters of the medium o f the X-ray laser degrade the quality of the amplified spontaneous radiatio n beam, and they are the analog of the nonresonance absorption from the sta ndpoint of the effect on the brightness of the laser and therefore decrease the observed gain. For the characteristic conditions of an X-ray laser wit h a quasistationary generation scheme, the contribution of small-scale gain fluctuations and random hose-like deviations of the plasma filament of the laser to the scattering of the amplified spontaneous radiation is much sma ller than the contribution of small-scale density fluctuations. Calculation s of the amplified spontaneous radiation in an X-ray laser, which is produc ed by unilateral irradiation of a curved target and possesses an asymmetric plasma electron density profile in the gain zone, are performed. It is sho wn that in the gain saturation regime the coherence length and the coherent power of the amplified spontaneous radiation can be substantially increase d, realizing in the gain zone a convex electron density profile instead of a typical concave profile. It is found that this improvement of the coheren ce occurs only under conditions such that the characteristic depth of the s mall-scale density fluctuations does not exceed several percent of the typi cal regular values of the density in the gain zone. (C) 2000 MAIK "Nauka/In terperiodica".