A method of studying a non-equilibrium x-ray laser plasma is developed by extending the existing one-dimensional similarity equations to the case of two-dimensional plasma study in the directions perpendicular to the slab and along a focal line. With this method the characteristics of pre-plasma are optimized for transient neon-like Cr x-ray laser. It is found that when the duration and the intensity of 1.053μm pre-pulse are 1.2 ns and 6.5 TW/cm^2 respectively with a delay time of 1.5 ns, the temperature and the temperature discrepancy each approach a proper state, which will provide a uniform distribution of properly ionized neon-like Cr ions before the arrival of pumping pulse.
Based on the two-dimensional model, this paper compares the hydrodynamics of slab x-ray laser plasma produced by different nonuniform line focused irradiations. It finds that the average intensity and the duration of laser pulse and the overall shape of the intensity distribution in the focal line have different influences on the plasma. Calculations show that the evolution of temperature variation is more sensitive to the pulse duration and the electron density variation is more sensitive to the pulse intensity. Pulses with duration of 200 ps to 500 ps and with intensity of 0.2 TW/cm2 to 1.0 TW/cm2 are proved acceptable in slab x-ray lasers.
