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.
Primary result on the impact of the latitudinal distribution of whistler-mode chorus upon temporal evolution of the phase space density （PSD） of outer radiation belt energetic electrons was presented. We evaluate diffusion rates in pitch angle and momentum due to a band of chorus frequency distributed at a standard Gaussian spectrum, and solve a 2-D bounce-averaged momentum-pitch-angle Fokker-Planck equation at L = 4.5. It is shown that chorus is effective in accelerating electrons and can increase PSD for energy of ～1 MeV by a factor of 10 or more in about one day, which is consistent with observation. Moreover, the latitudinal distribution of chorus has a great impact on the acceleration of electrons. As the latitudinal distribution increases, the efficient acceleration region extends from higher pitch angles to lower pitch angles, and even covers the entire pitch angle region when chorus power reaches the maximum latitude λm = 45°.
