New RADIOM algorithm using inverse EOS

The RADIOM model, [1-2], allows one to implement non-LTE atomic physics with a very low extra CPU cost. Although originally heuristic, RADIOM has been physically justified [3] and some accounting for auto-ionization has been included [2]. RADIOM defines an ionization temperature Tz derived from electronic density and actual electronic temperature \textit{Te}. LTE databases are then queried for properties at \textit{Tz} and NLTE values are derived from them. Some hydro-codes (like FAST at NRL, Ramis' MULTI, or the CRASH code at U.Mich) use inverse EOS starting from the total internal energy \textit{Etot} and returning the temperature. In the NLTE case, inverse EOS requires to solve implicit relations between \textit{Te}, \textit{Tz}, $<$Z$>$ and \textit{Etot}. We shall describe these relations and an efficient solver successively implemented in some of our codes. \\[4pt] [1] M. Busquet, \textit{Radiation dependent ionization model for laser-created plasmas}, Ph. Fluids B 5, 4191 (1993).\\[0pt] [2] M. Busquet, D. Colombant, M. Klapisch, D. Fyfe, J. Gardner. \textit{Improvements to the RADIOM non-LTE model}, HEDP 5, 270 (2009).\\[0pt] [3] M.Busquet, \textit{Onset of pseudo-thermal equilibrium within configurations and super-configurations}, JQSRT 99, 131 (2006)