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)].