Chaotic particle motion in large amplitude whistler wave in the magnetosphere

The motion of a single charged particle in the large amplitude wave field is investigated. In the magnetosphere, energetic charged particles in the radiation belts are trapped by Earth's magnetic field. In the equatorial region where a symmetric mirror field may be assumed, these particles undergo bounce motion along the lines of force. When a large amplitude quasi-electrostatic whistler wave is present, the motion of the particles is expected to be perturbed, particularly when the wave frequency comes close to a harmonic or sub-harmonic of the bounce frequency. The nonlinear interaction due to the spatial dependence of field quantities is expected to cause the motions of some of the trapped particles to become chaotic. The authors initially restrict their attentions to the case of one dimensional motion along the magnetic field lines. The equations of motion for a single particle are integrated numerically, and the results investigated in a three dimensional phase space (z, pz, t), where z and pz are the components of position and canonical momentum along the geomagnetic field. This analysis lends itself well to the Surface of Section technique, which provides information on the location of fixed points, regions of regular orbits, and chaotic regions. In the chaotic regions the particle motion resembles that of a random walk. This can lead to particle diffusion into the loss cone, and thus particle precipitation along the magnetic field lines into the high latitude regions