Auroral kilometric radiation (AKR) has a peak intensity at 250 kHz and is associated with discrete aurora in regions where &ohgr;p/&ohgr;c 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,&thgr;) is associated with each resonant contour, we solve the cold plasma dispersion relation for &ohgr;R, k, and &thgr;, where &ohgr;R>&ohgr;x, the right-hand cutoff frequency. Growing waves will be associated with those contours that pass through regions of velocity space where ∂f/∂v⊥>0 is large. A simple criterion is given to show which R-X waves will have large positive growth rate. 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¿0 is large) associated with either the upgoing loss cone or the downgoing precipitating electrons that are undergoing mirroring. |