Whistler attenuation by electrons with anE−2.5distribution

Abstract

We examine the thermal (Landau) attenuation of natural whistler radiation, assuming that the electron component has a velocity distribution of the (Cauchy) form ∼(υ2+a2)−3, which corresponds to an energy dependence of E−2.5 when ∣υ∣»a. It is found that a temperature of ∼105°K at R≃4Re geocentric is required to explain the observed cutoff at ω≃0.6ωc(0°), where ωc(0°) is the minimum cyclotron frequency along the path. The results are not appreciably different from those obtained previously by means of a Maxwell distribution. However, a simple algebraic expression is obtained for the electron temperature which makes the analysis of a large number of whistler traces feasible. The exact shape of the distribution and the concept of temperature are only relevant in the sense that they give the fraction of electrons that participate in the damping interaction at the Doppler-shifted phase velocity υ0(ω) = (ω - ωc)/Re k(ω). For a total density of 200 electrons/cm3 at R≃4Re, the thermal attenuation mechanism predicts an electron flux of ∼4×105 electrons/cm2 sec ev for energies near 250 ev.