Theoretical study on charge-state evolution of carbon ions passing through hydrogen plasma

In this paper, the charge state evolution behavior of carbon ions interacting with hydrogen plasma is systematically investigated based on a cross-sectional model. First, the influence of introducing a “shifted” Maxwellian velocity distribution on the dielectronic recombination rate coefficients is investigated within the range of carbon ion incident energies from 1 keV/u to 100 MeV/u and hydrogen plasma electron temperatures of <inline-formula><tex-math id="M6">\begin{document}$k{T_{\text{e}}} = 1$\end{document}</tex-math></inline-formula>–1000 eV. The rate coefficient data for this system are provided. On this basis, this research specifically solves the equilibrium rate equations by taking into account various ionization and recombination processes for projectile carbon ions with an energy of <inline-formula><tex-math id="M7">\begin{document}${0}{\text{.5 MeV/u}}$\end{document}</tex-math></inline-formula>, plasma electron temperatures of <inline-formula><tex-math id="M8">\begin{document}$k{T_{\text{e}}} = 3{\text{ eV}}$\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M9">\begin{document}${\text{8 eV}}$\end{document}</tex-math></inline-formula>, and electron densities ranging from <inline-formula><tex-math id="M10">\begin{document}${1}{{0}^{{18}}}{\text{ c}}{{\text{m}}^{{{ - 3}}}}$\end{document}</tex-math></inline-formula> to <inline-formula><tex-math id="M11">\begin{document}${1}{{0}^{{20}}}{\text{ c}}{{\text{m}}^{{{ - 3}}}}$\end{document}</tex-math></inline-formula>. The results show that the abundance of both non-equilibrium and equilibrium charge states of carbon ions passing through hydrogen plasma varies with plasma thickness, revealing how plasma conditions such as temperature and density, along with projectile ion energy and initial charge states, influence the evolution of the ion charge states. Furthermore, a comparison of the dynamic behaviors of carbon ions in hydrogen plasma and neutral gas (hydrogen) shows that the unique effects of the plasma environment on ion charge exchange are elucidated. The mean equilibrium charge state of projectile ions exhibits a positive correlation with electron temperature and a negative correlation with electron density. It is particularly important that the calculated equilibrium charge states in hydrogen gas targets are notably lower than those in plasma environments. As the initial charge state of projectile ions approaches its equilibrium value, the equilibrium thicknesses for all charge states demonstrate a decreasing trend, accompanied by a corresponding reduction in the mean equilibrium thickness. This phenomenon is consistently verified in both plasma and gas targets, with the mean equilibrium thickness values in gas targets being significantly smaller than those in plasma environments. Most importantly, when the initial charge state of projectile ions exceeds the equilibrium value, these ions display more pronounced energy loss characteristics in non-equilibrium regions. This study will provides important references for investigating the dynamic evolution and energy transport characteristics of ion-plasma interactions in the field of high-energy-density physics.