Electron temperature effects in the linear proton mirror instability

It is shown that when the electron temperature T e is of the same order of the proton temperature parallel to the background magnetic field, the growth rate of the proton mirror mode in the long‐wavelength limit is reduced by the presence of a longitudinal electric field. The field is due to the electron pressure gradient which builds up when T e ≠ 0, because the electrons are dragged by nonresonant protons which are mirror accelerated from regions of high into regions of low parallel magnetic field flux. In return, the longitudinal electric field causes the density of nonresonant protons with a perpendicular velocity smaller than a strongly T e ‐dependent critical velocity υ ⊥,crit to increase (decrease) at maxima (minima) of the parallel magnetic field flux. These nonresonant protons thus behave differently from the “circulating” protons described by Southwood and Kivelson (1993) in the cold electron limit. Although the instability threshold is only weakly affected by changes in T e , quantities like the growth rate, the compressibility, the polarization, and the angle between wave vector and magnetic field for the most unstable mode, as well as the structure of the perturbed proton distribution itself, are strongly modified by variations in the electron temperature. The predictions of the model are shown to agree well with numerical solutions of the full Vlasov dispersion relation, indicating that most long‐wavelength aspects of the proton mirror instability are included in the model.