The Nature of Magnetospheric Electron Velocity Distribution Functions from Wave Observations

It is often assumed, as a first approximation, that the electron velocity distribution function is Maxwellian when calculating the dispersion of magnetospheric plasma waves. Data from the relaxation sounder on the GEOS-1 satellite were used to relate natural emissions between the harmonics of the electron cyclotron frequency fce, often referred to as “(n+1/2)fce” waves, to sounder-stimulated plasma resonances (known as the Qn resonances due to Bernstein-mode waves); it was recognized that a proper interpretation of the observations would require a non-Maxwellian plasma [Christiansen et al., Nature, 1978]. A detailed theoretical investigation indicated that the observations could often best be described by using the superposition of two finite-temperature Maxwellian distributions, one hot and one cold, in the dispersion equation [Belmont, Planet. Space. Sci., 1981]. Later theoretical work, directed toward explaining the frequency spectrum of the Qn resonances stimulated by the Radio Plasma Imager (RPI) on the IMAGE satellite in the magnetosphere, indicated that the RPI observations were in better agreement using a kappa distribution with κ near 2, rather than a Maxwellian distribution, in the dispersion equation [Viñas et al., JGR, 2005]. This result indicated a significant departure from Maxwellian since the kappa distribution closely corresponds to a Maxwellian distribution only when κ is greater than about 10 (the two distributions are the same when κ → +∞). Here we extend the kappa-distribution approach, which has the advantage of requiring fewer parameters than a bi-Maxwellian to describe the physical problem, by calculating the Qn frequencies for a variety of κ values from 1.6 to 10.0 for fpe/fce = 1.00 to 9.75 in intervals of 0.25, and for Qs from Q1 to Q9 where fpe is the electron plasma frequency. Q1 was generated for fpe/fce = 1.00, 1.25, 1.50, 1.75 by the Kappa distribution, but not by the Maxwellian distribution (for comparison, the Qn frequencies were calculated using a Maxwellian distribution for fpe/fce = 1 to 9.75 in intervals of 0.25). These calculations will enable information on the nature of the magnetospheric electron-velocity-distribution function to be determined from magnetospheric sounders such as RPI once accurate fpe/fce values are determined from other sounder-stimulated plasma resonances and wave-cutoffs.