One- and two-dimensional hybrid simulations of whistler mode waves in a dipole field
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We simulate whistler mode waves using a hybrid code. There are four species in the simulations, hot electrons initialized with a bi-Maxwellian distribution with temperature in the direction perpendicular to background magnetic field greater than that in the parallel direction, warm isotropic electrons, cold inertialess fluid electrons, and protons as an immobile background. The density of the hot population is a small fraction of the total plasma density. Comparison between the dispersion relation of our model and other dispersion relations shows that our model is more accurate for lower frequency whistlers than for higher frequency whistlers. Simulations in 2-D Cartesian coordinates agree very well with those using a full dynamics code. In the 1-D simulations along the dipole magnetic field, the predicted frequency and wave number are observed. Rising tones are observed in the one-fourteenth scale simulations that have larger than realistic magnetic field spatial inhomogeneity. However, in the full-scale 1-D simulation in a dipole field, the waves are more broadband and do not exhibit rising tones. In the 2-D simulations in a meridional plane, the waves are generated with propagation approximately parallel to the background magnetic field. However, the wavefronts become oblique as they propagate to higher latitudes. Simulations with different plasma density profiles across L shell are performed to study the effect of the background density on whistler propagation.