Time-dependent Boltzmann kinetic model of x rays produced by ultrashort-pulse laser irradiation of argon clusters

The Boltzmann equation and a detailed collisional-radiative model are solved simultaneously as a function of time to model the time-integrated x-ray spectra of the transient plasma produced by a high intensity ultrafast laser source. Level populations are calculated by solving the rate equations as a function of time using rate coefficients corresponding to a time varying electron energy distribution function (EEDF) determined by the solution to the Boltzmann equation. Electron-electron interactions are included through the solution of the Fokker-Planck equation. It is assumed that all the ions are initially in the Ne-like ground state due to the laser prepulse and that all free electrons have high energy (5 keV) from the fast laser deposition. The collisional-radiative model included over 3000 levels in the Ne-like through H-like ion stages of argon. The results are in agreement with highly resolved F-like to He-like K-shell emission spectra recorded recently during ultrashort laser experiments with argon cluster targets in Japan. The calculated time scale for emission is consistent with estimates of cluster decay times for these conditions. The calculations also show that the typical Li-like and Be-like satellite structure, sometimes attributed to a hot-electron component in the EEDF, can also be due to transient effects in a high-temperature ionizing plasma.