Modification of classical Spitzer ion--electron energy transfer rate for large ratios of ion to electron temperatures

Corrections to the classical Spitzer heat transfer rate between ions and electrons are calculated for the case when the ion temperature Ti is significantly higher than the electron temperature Te. It is found that slow electrons are partially depleted by their interactions with the ions, resulting in a decrease in the heat transfer in comparison with the Spitzer rate, which assumes perfectly Maxwellian electrons. The heat transfer steadily decreases from the classical value as Ti/Te increases; for Ti/Te values of several hundred, the heat transfer rate drops to around 60%--80% of the Spitzer result. A useful expression for the heat transfer correction factor in the case when all of the ion species are at the temperature Ti is found to be Pie/(Pie)Spitzer ∼[1+(me/mi)(Ti/Te)]3/2 exp{-[3.5 summation i (Z2ini/ne)(me/mi) (Ti/Te)]2/3}. This expression is quite accurate for values of summation i (Z2ini/ne)(mp/mi)(Ti/Te) less than about 50 (where mp is the proton mass), although it underestimates the heat transfer rate for larger values of Ti/Te, and one must resort to the more accurate but more complex analytical results derived in the paper. (Abstract Truncated)