Chaotic Scattering of Energetic Electrons in Magnetospheric Radiation Belts by Whistler Waves

Summary form only given. In the magnetospheric radiation belts, very energetic electrons (in MeV level) trapped by the Earth´s dipole magnetic field have strong impact on passing satellites. An approach using a large amplitude whistler wave to precipitate those energetic electrons is explored. The trajectories of electrons are shown to fall in a three-dimensional phase space. Thus, a surface of section technique is used to examine graphically the chaoticity of the electron-wave system. The pitch angle time function is also plotted to verify if the electron can be scattered into the loss cone. Once the electron wanders into the loss cone, it can precipitate 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. The commencement of chaotic behavior in the electron trajectory for a given electron energy and region (i.e., a L value) requires the whistler wave to have a proper frequency and to exceed a threshold level. Moreover, the threshold requirement also depends on the initial pitch angle of the electron and the loss cone angle that varies with the L value. The dependency of the optimal wave frequency on the electron energy and L value are determined in general way through a semi-empirical relation deduced from the numerical results. The threshold condition is determined for the specific case that trapped electrons are located in Lles1.5 regions. Thus, the loss cone is about 30deg and the most proper pitch angle of the trapped electrons is about 60deg. The dependence of the threshold whistler wave field on the electron energy is determined. The results show that the threshold wave magnetic field is in the range of about 0.2% of the geomagnetic field for those energetic electrons having kinetic energies larger than 500 keV, i.e., gamma₀>2