Partial electron velocity spectrums from cyclotron absorption of whistler power

A method is proposed for the determination of partial electron velocity spectrums from the power spectrums of whistler signals at their upper cutoff. It is assumed that the only frequency-dependent attenuation of the signal is cyclotron resonance absorption by the nonthermal electron component (around 1 kev) in the magnetosphere. According to the theory, the differential density is related by an integral equation to the power loss L(ω) of each whistler, where v∣∣ is the velocity component parallel to the local geomagnetic field, u is the resonance speed, and ω is the propagation frequency. The equation is too difficult to solve analytically for F, but over a narrow frequency band ω1 ≤ ω ≤ ω2 at the cutoff, where L is measurable, an approximate solution is obtained in the form F = Au−n in the range u1 ≤ u ≤ u2. The power spectrum of whistlers has not been measured accurately yet, but the sharp cutoffs observed on sonograph traces suggest that n ≥ 9. The results are compared with previous applications of the theory.