General concepts on the generation of auroral kilometric radiation

Abstract

Auroral kilometric radiation (AKR) has a peak intensity at 250 kHz and is associated with discrete aurora in regions where ωp/ωc < 0.2. There are two high‐frequency electromagnetic wave modes in which AKR could propagate, the L mode and the R mode. Observations of AKR are inconsistent with the characteristics of L mode radiation. However, the characteristics of the upper frequency branch of the R‐X mode are consistent with AKR observations. We therefore look at the following free‐energy sources in the auroral electron distribution functions as possibilities for exciting the R‐X mode: (1) the accelerated, precipitating electrons, and (2) the upgoing loss cone associated with the electrostatically trapped electrons. Solving the relativistic resonance condition exactly gives contours in velocity space that are elliptical. Diffusion of precipitating electrons, which develop ∂f/∂υ⊥ > 0 because of the magnetic mirroring force, and diffusion of trapped electrons in the upgoing loss cone with R‐X waves are toward decreasing energies, so that wave growth is possible. To determine which frequency and wave vector (k, θ) is associated with each resonant contour, we solve the cold plasma dispersion relation for ωR, k, and θ, where ωR > ωx, the right‐hand cutoff frequency. Growing waves will be associated with those contours that pass through regions of velocity space where ∂f/∂υ⊥ > 0 is large. A simple criterion is given to show which R‐X waves will have large positive growth rates. Finally, we calculate the group velocity of R‐X waves and show that R‐X waves with large, positive growth rates also have small group velocities (Vg/c ≪ 1), implying a very small convective growth length ∼10 m. The intense wave generation should occur at wave frequencies just above the right‐hand cutoff frequency and have wave normal angles 75° < θ ≲ 105°. Wave growth maximizes in regions where ωp/ωc is small (≲0.06) and where there exists sufficient free energy (∂f/∂υ⊥ > 0 is large) associated with either the upgoing loss cone or the downgoing precipitating electrons that are undergoing mirroring.