A self-consistent theory of magnetospheric ELF hiss

A self-consistent solution of the equation of wave generation and particle diffusion is obtained for gyroresonant interactions between ELF waves (a few hundred hertz) and medium-energy electrons (a few tens of kev). A dynamic equilibrium is considered in which new particles are continuously injected and ultimately lost in the atmosphere through diffusion inside the loss cone; meanwhile, waves are generated continuously, but only a fraction of them is reflected by the ionosphere. By an iterative process the wave spectrum can be computed in shape as well as in amplitude; the distribution function of the trapped particles is also obtained. Some of the concepts that were introduced by Kennel and Petschek (1966) are more precisely defined, and attention is drawn to possible misapplications of these concepts. In particular, it is established that the so-called limiting flux does not have a unique value and that it in fact depends upon the source strength: enhancements by factors of up to 20 can be achieved in very disturbed conditions (Kp ≥ 6). It is also demonstrated that the particle distribution function, in an equilibrium configuration, does not depend on the cold plasma density, a conclusion that is of great geophysical importance. A comparison with experimental data shows a reasonable agreement with the theory and establishes its interest for interpreting ELF hiss and equilibrium particle distributions, at least inside the plasmasphere.