Comparing different charge-state models with experimental data of ion beams penetrating fully and partially ionized plasmas

Abstract

In the present work, we have conducted a study to investigate the validity of three different charge-state models of ion beams penetrating plasma targets through a comparison with a total of five experiments from the literature. We have applied two alternative theoretical approaches. On the one hand, we have used a further extension of our cross-sectional model (CSM) code based on projectile electron loss and capture cross sections (rate equations) that was developed previously [Morales et al., Phys. Plasmas 24, 042703 (2017); R. Morales, Ph.D. thesis (Universidad de Castilla-La Mancha, 2019)]. On the other hand, we also used two charge-state models based on a semi-empirical formalism adapted to the plasma case: the Kreussler model [Kreussler et al., Phys. Rev. B 23, 82 (1981)] and the Gus'kov model [Guskov et al., Plasma Phys. Rep. 35, 709 (2009)]. Specifically, we present the predictions and the interpretation of the charge state of light to heavier ions at high, intermediate, and low velocities in Z-pinch and laser-produced partially and fully ionized plasmas. We are showing that experimental data support our new CSM code based on the cross-sectional formalism. In contrast, the framework based on semi-empirical formulas is less accurate for a precise charge-state prediction, but it can be applied for a reasonable stopping power calculation. Overall, results denote that the Gus'kov model is better suited to stopping power calculations at low projectile velocities and the Kreussler model fits better the energy loss data at intermediate velocities. Additionally, we propose a simple non-equilibrium charge model, derived from the semi-empirical framework, as a function of the ion path and equilibrium charge state.