Wave dispersion in a plasma with complex orbits

Using the technique of integration along particle orbits, we construct the plasma response function for electrostatic waves in the vicinity of a strong dipole magnet. A large number of particle orbits are integrated numerically using a second-order symplectic integrator with adjustable time-step. A significant measure of the particle orbits are chaotic, many are also regular and either trapped or untrapped. Some orbits undergo chaotic scattering from the dipole field. Along each orbit a weighted average of E*v is compiled keeping track of the contribution a field of basis modes (spherical Bessel functions) to the eventual phase-space perturbation over a set of discritized spatial points. These point are the final locations of sets of particle orbits. The conditilon of self-consistency between the perturbed orbits and the phase space perturbations is used to construct either a dispersion relation or a solution to the scattering of an ion acoustic plane wave incident in the far-field. The goal is to provide a point of comparison for experiments of ion acoustic wave scattering from a magnetic dipole. Further extension of the work is planned to address the scattering of the CVK spectrum instead of just the acoustic wave.