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 T i is significantly higher than the electron temperature T e . 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 T i /T e increases; for T i /T e 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 T i is found to be P ie /(P ie )Spitzer ≊[1+(m e /m i )(T i /T e )]3/2 exp{−[3.5∑ i (Z 2 i n i /n e )(m e /m i ) (T i /T e )]2/3}. This expression is quite accurate for values of ∑ i (Z 2 i n i /n e )(m p /m i )(T i /T e ) less than about 50 (where m p is the proton mass), although it underestimates the heat transfer rate for larger values of T i /T e , and one must resort to the more accurate but more complex analytical results derived in the paper. In the event that the ion distribution is non‐Maxwellian, T i in the correction factor should be replaced by 2〈E i 〉/3, where 〈E i 〉 is the mean ion energy.