Experimental study of the relationship between energetic electrons and ELF waves observed on board GEOS: A support to quasi‐linear theory

Abstract

The interaction between energetic electrons (E > 15 keV) and whistler mode ELF/VLF waves (0.2–2 kHz) is studied experimentally in the light of the quasi‐linear pitch angle diffusion theory. This work is carried out with data from the European magnetospheric satellites GEOS 1 and GEOS 2. A method is given to calculate from the data in a complete manner the particle anisotropy A and the temporal growth rate of the waves, γ, as defined by Kennel and Petschek (1966), A and γ being frequency dependent. The data are averaged over 5 min, which is slightly less than the minimum lifetime of the electrons. Therefore the temporal evolution of weak diffusion cases can be studied. The calculated anisotropy is compared to the critical anisotropy AC, which is the minimum anisotropy needed for wave growth, and to the measured wave spectrum. In the presence of waves, A is greater than AC and roughly follows AC in the frequency range of wave emission. The difference [A‐AC] is smallest during strong diffusion but remains positive, as expected from pitch angle diffusion in a steady state situation. The behavior of A does not change considerably between the geomagnetic equator (GEOS 2) and latitudes of about 20° (GEOS 1). The normalized wave growth rate γ/ωce varies between ∼10−4 and 10−2 at the equator, leading to the generation of more or less intense waves and thus to strong or weak electron pitch angle diffusion. Conversely, the constant level of γ/ωce (∼10−5) at a latitude of 20° indicates that the diffusion is most efficient at lower latitudes. A very detailed discussion in terms of the quasi‐linear theory of wave‐particle interactions shows that this theory is applicable for the explanation of the observations. The discussion includes a consideration of the conditions for the existence of a steady state emission in terms of a minimum level of the integrated spatial growth rate needed to compensate for the wave losses at the ionosphere.