Relativistic Kinematic Effects in the Interaction Time of Whistler-Mode Chorus Waves and Electrons in the Outer Radiation Belt

Abstract

Whistler-mode chorus waves propagate outside the plasmasphere. As they interact with energetic electrons in the outer radiation belt electrons, the phase space density distribution can change due to energy or pitch angle diffusion. Calculating the wave-particle interaction time is crucial to estimate the particle’s energy or pitch angle change efficiently. Although the wave and particle velocities are a fraction of the speed of light, in calculating the interaction time, the special relativistic effects are often misleading, incomplete, or simply unconsidered. In this work, we derive an equation for the wave-particle interaction time considering the special relativity kinematic effect. We solve the equation considering typical magnetospheric plasma parameters, and compare the results with the non-relativistic calculations. Besides, we apply the methodology and the equation to calculate the interaction time for one wave cycle in four case studies. We consider wave-particle resonance conditions for chorus waves propagating at any wave normal angle in a dispersive and cold plasma. We use Van Allen Probes for in situ measurements of the relevant wave parameters for the calculation, the ambient magnetic field, and energetic electron flux under quiet and disturbed geomagnetic conditions. Thus, we use a test particle approach to calculate the interaction time for parallel and oblique propagating waves. Also, we evaluate the variation of pitch angle scattering for relativistic electrons interacting with whistler-mode chorus waves propagating parallel to the ambient magnetic field. If the relativistic effects are not taken into account, the interaction time can be ∼ 30 % lower for quiet periods and a half lower for disturbed periods. As a consequence, the change in pitch angle is also underestimated. Besides, the longest interaction time occurs at wave-particle interaction with high pitch angle electrons, with energy ∼ 100′ s of keV, interacting with quasi-parallel propagating waves. Additionally, the change in pitch angle depends on the time of interaction, and similar discrepancies can be found when the time is calculated with no special relativity consideration. The results described here have several implications for modeling relativistic outer radiation belt electron flux resulting from the wave-particle interaction. Finally, since we considered only one wave-cycle interaction, the average result from some interactions can bring more confident results in the final flux modeling.