Linear and Nonlinear Whistler Wave Propagation in the Magnetosphere Based on Plasma Density Models from IMAGE Spacecraft Data

From the radio plasma imager on the IMAGE satellite, spatial profiles of electron density in the inner magnetosphere were constructed [B.W. Reinisch {\it et al}, Geophys. Res. Lett., {\bf 28}, 1167 (2001)]. We use these profiles and the dipolar magnetic field model to analyze the propagation of whistler waves. We compute the dispersion characteristics of wave packets from the 2D $\omega(kx,kz,n, B)$ dispersion function, showing wave energy focusing into low phase velocity regions. We add model growth rates from S. Sazhin, {\it Whistler-mode waves in a hot plasma} (Cambridge U. Press, Cambridge, 1993) and nonlinear terms from Horton {\it et al} [W. Horton {\it et al}, Nonlinear Dynamics of the Electromagnetic Ion Cyclotron Structures, Firehose and Whistlers, preprint, Nonlin. Processes Geophys.] to determine saturation levels of whistler chorus waves and associated coherent structures. We explore NLS, DNLS and vortex models, consistent with experiments by Stenzel {\it et al} [R.L. Stenzel {\it et al}, Plasma Phys. Control. Fusion {\bf 50} 074009 (2008)].