* Corresponding author. Tel.: #81-720-31-0709; fax: #81-7210-31-0596. E-mail address: sasaki@apr.jaeri.go.jp (A. Sasaki) Journal of Quantitative Spectroscopy & Radiative Transfer 65 (2000) 501}509 Development of a collisional radiative model of X-ray lasers Akira Sasaki*, Takayuki Utsumi, Kengo Moribayashi, Toshiki Tajima, Hiroshi Takuma Advanced Photon Research Center, Kansai Research Establishment, Japan Atomic Energy Research Institute, 25-1 Miiminami-cho, Neyagawa-shi, Osaka 572-0019, Japan Abstract A theoretical model of plasma hydrodynamics and atomic kinetics of X-ray lasers is developed to investigate the mechanism of lasing in 4d}4p transition of Ni-like ions at short wavelength by the transient pumping scheme. The model is designed for calculations of the ion abundance and soft X-ray gain in the short pulse laser-irradiated plasmas. We develop a compact collisional radiative model which combines the detailed level structure of Ni-like ion using atomic data calculated by HULLAC, with averaged levels over a wide range of charge states using the screened hydrogenic model. The ion abundance and soft X-ray gain are calculated by postprocessing the temperature and density of the laser-produced plasma obtained by the hydrodynamics code. It is found that a large abundance of Ni-like ion can be maintained in the plasma produced from an exploding foil target showing its usefulness as a gain medium of transient collisional X-ray lasers. For improvement of the model, sensitivity of the gain and averaged charge to the level structure included in the model are discussed.  2000 Elsevier Science Ltd. All rights reserved. 1. Introduction Recently, signi"cant progress in collisional X-ray lasers has been reported as in Refs. [1}4]. Using a combination of pre- and main-laser pulses to irradiate the target to produce a plasma with an optimized density and temperature pro"le, high gain of more than 30/cm and saturated ampli"cation have been obtained with small pump energies [1]. Since in short pulse laser- produced plasmas, the laser absorption, heat conduction, hydrodynamics expansion, atomic kinetics and radiative transfer are coupled, the computational model of X-ray lasers should solve these processes together. Di$culty in the modeling also arises from the complex atomic structure of 0022-4073/00/$ - see front matter  2000 Elsevier Science Ltd. All rights reserved. PII: S 0 0 2 2 - 4 0 7 3 ( 9 9 ) 0 0 0 9 2 - 8