Electrostatic and electromagnetic gyroharmonic emissions due to energetic electrons in magnetospheric plasmas

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Abstract
Growth rates are calculated for perpendicularly propagating electrostatic and electromagnetic waves with frequencies between harmonics of the electron gyrofrequency. The source of free energy for these emissions is diffuse, power‐law distributed energetic electrons (E >10 keV) which possess a distribution function with a loss cone feature and a shoulder. This shoulder is defined as a hardening of the distribution function, that is, a less rapid decrease with increasing energy, in a given energy range as compared to energies outside of this range. Such shoulders have been observed experimentally to occur in conjunction with electrostatic gyroharmonic emissions. This available free energy is then coupled to waves supported by the background thermal plasma (T ≈ 1 keV) via the velocity dependence of the electron gyrofrequency. For electrostatic waves, both spatially homogeneous and inhomogeneous energetic electron distributions are considered. For the homogeneous case the calculated growth rates are consistent with observations of so‐called ‘n + 1/2’ electrostatic gyroharmonic emissions located between electron‐cyclotron frequency harmonics in the earth's magnetosphere. The additional free energy of the energetic electron gradient allows excitation without a shoulder in the inhomogeneous case. The electromagnetic emissions are modeled by the ordinary mode. For this case it is shown that either (1) the allowed coupling energies are less than 10 keV, and hence the source of energetic electron free energy is inaccessible or (2) when coupling is possible, the resulting growth rates are small compared to those for electrostatic emissions. This is consistent with the observations that the observed gyroharmonic emissions are electrostatic. From this study, it is concluded that electrostatic gyroharmonic excitation is possible without the cold component of plasma which is often postulated in the existing literature.