The effect of the azimuthal angle φ of the wave vector k on the propagation characteristics of the superluminous L-O mode waves （together with a case of the R-X mode） during different geomagnetic activities using a three-dimensional （3D） ray-tracing method is investigated. This work is primarily an extension of our previous two-dimensional study in which the wave azimuthal angle was not considered. We present numerical simulations for this mode which is generated in the source cavity along a 70° night geomagnetic field line at the specific altitude of 1.5RE （where RE is the Earth＇s radius）. It is found that, as in the two-dimensional case, the trajectory of L-O mode starting in the source meridian plane （or the wave azimuthal angle φ = 180°） can reach the lowest latitude; whereas it basically stays at relatively higher latitudes starting off the source meridian plane （or φ=180°）. The results reveal that under appropriate conditions, the superluminous L-O mode waves may exist in the radiation belts of the Earth, but this remains to be supplemented by observational data.
The quasi-pure pitch-angle scattering of energetic electrons driven by field-aligned propagating whistler mode waves during the 9～15 October 1990 magnetic storm at L≈ 3 ～ 4 is studied, and numerical calculations for energetic electrons in gyroresonance with a band of frequency of whistler mode waves distributed over a standard Gaussian spectrum is performed. It is found that the whistler mode waves can efficiently drive energetic electrons from the larger pitchangles into the loss cone, and lead to a flat-top distribution during the main phase of geomagnetic storms. This result perhaps presents a feasible interpretation for observation of time evolution of the quasi-isotropic pitch-angle distribution by Combined Release and Radiation Effects Satellite （CRRES） spacecraft at L ≈ 3 ～ 4.
