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Analysis of self-consistent nonlinear wave-particle interactions of whistler waves in laboratory and space plasmas

AuthorCrabtree, Chris; Ganguli, Gurudas; Tejero, Erik;
KeywordsDispersion relations; Electron beams; SingingEigenvalues; Van Allen Probes; Whistler waves
AbstractWhistler mode chorus is one of the most important emissions affecting the energization of the radiation belts. Recent laboratory experiments that inject energetic electron beams into a cold plasma have revealed several spectral features in the nonlinear evolution of these instabilities that have also been observed in high-time resolution in situ wave-form data. These features include (1) a sub-element structure which consists of an amplitude modulation on time-scales slower than the bounce time, (2) closely spaced discrete frequency hopping that results in a faster apparent frequency chirp rate, (3) fast frequency changes near the sub-element boundaries, and (4) harmonic generation. In this paper, we develop a finite dimensional self-consistent Hamiltonian model for the evolution of the resonant beam of electrons. We analyze a single wave case and demonstrate that the instability occurs due to a Krein collision, which manifests as a coupling between a negative and positive energy mode. This analysis revealed that the nonlinear evolution of the spectrally stable fixed-points of the self-consistent Hamiltonian develop a sub-packet structure similar to that of space observations. We then analyze the case of two whistler waves to show that the model reproduces the nonlinear harmonic generation and leads to a hypothesis for the closely spaced frequency hopping observed in laboratory experiments and space data.
Year of Publication2017
JournalPhysics of Plasmas
Number of Pages056501
Date Published03/2017