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One of the fundamental features of space plasmas is the observation of non-Maxwellian particle velocity distributions. In the present study, we observe electron velocity distributions in the Earth's magnetosphere at times when the electron density is low, typical of cusp values, and when it is enhanced as a result of disturbances by the solar wind. We find that electron distributions are flat-topped and have two populations: one cold and one hot. We fit the observed electron distributions by a generalized $( {r,q} )$ distribution, and derive and plot expressions for the real frequency and growth rate using fitted and observed parameters. We show that enhancement in the density of hot electrons enhances the growth rate of whistler waves, which play an important role in energy transport in the Earth's magnetosphere.

Lion roars are low-frequency (∼100 Hz) whistler waves frequently observed in the Earth's magnetosheath. By analyzing both wave and electron data from the Cluster spacecraft, and comparing with linear Vlasov kinetic theory, Masood et al. (2006) investigated the underlying cause of the lion roar generation. However, the analysis based upon the bi-Maxwellian distribution function did not adequately explain the observations qualitatively as well as quantitatively. This outstanding problem is revisited in the present paper, and a resolution is put forth in which, the flat-top non-Maxwellian distribution function with a velocity power law energetic tail, known as the (r,q) distribution, or the generalized kappa distribution is employed. Upon carrying out the linear stability analysis of the (r,q) distribution against the whistler wave perturbation, and upon comparison with the Cluster data, good qualitative and quantitative agreements are found between theory and data.