Quantifying ionization in hot dense plasmas

Ionization is a problematic quantity in that it does not have a well-defined thermodynamic definition and yet it is a key parameter within plasma modeling. One still therefore aims to find a consistent and unambiguous definition for the ionization state. Within this context we present finite-temperature density functional theory calculations of the ionization state of carbon in CH plasmas using two potential definitions: one based on counting the number of continuum electrons, and another based on the optical conductivity. Differences of up to 10% are observed between the two methods. However, including “Pauli forbidden” transitions in the conductivity reproduces the counting definition, suggesting such transitions are important to evaluate the ionization state.

Figure 1

Mean ionization state of CH ($N/N_{\mathrm{CH}}$) calculated using different methods. The red circles represent the MIS using $N=N_{\mathrm{eff}}$ as suggested in Ref. [23]. The green triangles use $N=N_{\mathrm{eff}}+\mathrm{\Delta }{N}_{\mathrm{eff}}$. The blue squares denote the counting definition, $N=N_{\mathrm{cond}}$.