A comparison of time-dependent ionization models for laser-produced plasmas

Abstract

Models for calculating time-dependent ionization are compared in simulations of a germanium plasma for conditions which are relevant to collisionally pumped X-ray lasers. A simple two-level model, which treats each ion stage with a ground state and single excited state, is compared with the collisional radiative model in the hydrogenic approximation and the time-dependent average atom model in simplified single Lagrangian test cell problems. A method for determining ionic populations from average atom level populations (Djaoui and Rose 1992) is investigated. The results show good overall agreement between the three models, but indicate that the two-level model underestimates stepwise ionization via excited states. The importance of this limitation is considered in more detail in full simulations of a collisionally pumped system with a 1.5D hydrodynamic code. The two-level model is tested against the hydrogenic collisional radiative approach and the importance of detailed modelling of the sodium- and neon-like ion stages is also considered. The simulations indicate that the discrepancies between the two-level and hydrogenic models are small. A detailed description of the neon-like ion stage, considering both enhanced ionization from the metastable levels and dielectronic recombination, is found to be more significant when evaluating the neon-like population.