Approximately analytical model for inner-shell photoionization x-ray lasers in low-Z elements art. no. 033809

A model employing five energy levels and a fit linear rising photopumping r ate of x-ray source is proposed to analyze the gain of inner-shell photoion ization (ISPI) x-ray lasers when the lasing medium is irradiated with a fil tered approximate blackbody source. The deduced analytical expressions for the time of the onset of the peak gain and its peak value reveal the effect s of Auger decay, electron-impact ionization, the density of lasing medium, and the increase rate of pumping rate on the duration and the peak value o f the laser gain. Also the requirements on the intensity of the driving ult rashort pulse laser can be estimated. The model is generally suitable for a nalyzing ISPI x-ray lasers in low-Z elements from carbon to neon although c arbon is analyzed in details as a representative to verify the validity of the model. K alpha x-ray lasing at 3.2 nm in nitrogen is also discussed as an attractive candidate for experimentally implementing a "water window'' I SPI x-ray laser.