Electron precipitation caused by chaotic motion in the magnetosphere due to large‐amplitude whistler waves

Abstract

In the magnetosphere, energetic electrons in the radiation belts are trapped by Earth's magnetic field and undergo bounce motion about the geomagnetic equator. When a large‐amplitude whistler wave is present, the motion of the electrons becomes perturbed. It is shown that the nonlinear interaction due to the spatial dependence of the field quantities causes the motion of some of the trapped particles to become chaotic. Contrary to considering a gyroresonant interaction, this chaotic scattering does not have a directional preference and may therefore offer a plausible explanation of the simultaneous observation of the electron precipitation into the upper atmosphere at geomagnetically conjugate regions due to a single lightning flash [Burgess and Inan, 1990]. After simplifying the dipole configuration of the geomagnetic field, a Hamiltonian formulation is used to study the dynamics of a single, trapped electron on the L = 3 shell, subjected to a large amplitude 13.7 kHz whistler wave. A canonical transformation is introduced to remove the time dependence from the test electron's Hamiltonian. The chaotic behavior of the electron motion is investigated with surface of section and Lyapunov exponent techniques. To show that this chaotic behavior can lead to particle precipitation, the temporal evolution of the equatorial pitch angle of the electron is computed. Considering electrons with an initial pitch angle of 88°, the results are found to be qualitatively independent of the bounce frequency. They show that the equatorial pitch angle of a chaotic electron varies wildly and often dips below 25°, the minimum loss cone angle one would expect to find for a charged particle in the magnetosphere. Therefore the electrons may escape the geomagnetic trap and be precipitated into the upper atmosphere.