Chaotic scattering of trapped relativistic electrons in the magnetosphere by whistler waves

In the magnetosphere, energetic electrons in the radiation belts are trapped by the Earth's dipole magnetic field and undergo bouncing motion about the geomagnetic equator. Those very energetic electrons (in MeV level) have strong impact on passing satellites. The behaviors of the trajectories of these electrons interacting with a large amplitude whistler wave are explored, with the electron energy and wave amplitude as variable parameters. A surface of section technique is used to examine the chaoticity of the system graphically. Once the trajectory of an electron becomes chaotic, it can wander into the loss cone and subsequently, precipitates into the ionosphere and/or the upper atmosphere. The bouncing motion of the electron is a key factor to cause chaotic behavior in the interaction. However, the commencement of chaotic behavior in the electron trajectories also requires the whistler wave field to exceed a threshold. The threshold wave magnetic field for the onset of chaos can be as low as 0.25% of the geomagnetic field for those energetic electrons having kinetic energies larger than 250 keV, i.e., γ ₀ > 1.5. Waves with amplitudes at this level have been observed propagating between hemispheres. This threshold increases slightly with γ ₀ ∼ 3, i.e., for those MeV energetic electrons.