The effect of electron and ion temperature on the refractive index surface of 1–10 kHz whistler mode waves in the inner magnetosphere

Whistler mode waves in the magnetosphere play an important role in the energy dynamics of the Earth’s radiation belts. Previous theoretical work has been extended to include ions in the fully adiabatic warm plasma theory. Using a finite electron and ion temperature of 1 eV, refractive index surfaces are calculated for 1–10 kHz whistler mode waves in the inner magnetosphere (L≲ 2.5). For the frequencies of interest, a finite ion temperature is found to have a greater effect on the refractive index surface than the electron temperature and the primary effect is to close an otherwise open refractive index surface. Including a finite ion temperature is especially important when the wave frequency is just above the local lower hybrid resonance frequency. For wave frequencies more than ∼1 kHz above the local lower hybrid resonance frequency, including the ion temperature has a negligible effect on the refractive index surface calculation. The results are used to assess previous conclusions on whether in situ whistler mode sources can be realistically used to precipitate energetic electrons. It is found that the number of in situ sources needed to illuminate the inner plasmasphere (L≲ 2.5) with whistler mode energy may be greater than previously predicted.