Whistler mode waves that propagate through the magnetosphere exchange energy with energetic electrons by wave-particle interaction mechanisms. Using linear theory, a detailed investigation is presented of the resulting amplitude variations of the wave as it propagates. Arbitrary wave frequency and direction of propagation are considered. A general class of electron distributions that are nonseparable in particle energy and pitch-angle is proposed. Comparison with data is obtained by computing the total amplitude variation between two locations along the wave ray path. It is found that the proposed distribution model is consistent with available whistler and particle observations. In particular, this model yields insignificant amplitude variation over a. large frequency band, a feature commonly observed in whistler data. This feature of the data implies e certain equilibrium between waves and particles in the magnetosphere over a wide spread or particle energy, at least during certain (magnetically quiet) times, and is relevant to plasma injection experiments. Application of our analysis for monitoring the distribution of energetic electrons in the magnetosphere is discussed.
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