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Whistler mode chorus waves are particularly important in outer radiation belt dynamics due to their key role in controlling the acceleration and scattering of electrons over a very wide energy range. The efficiency of wave-particle resonant interactions is defined by whistler wave properties which have been described by the approximation of plane linear waves propagating through the cold plasma of the inner magnetosphere. However, recent observations of extremely high-amplitude whistlers suggest the importance of nonlinear wave-particle interactions for the dynamics of the outer radiation belt. Oblique chorus waves observed in the inner magnetosphere often exhibit drastically nonsinusoidal (with significant power in the higher harmonics) waveforms of the parallel electric field, presumably due to the feedback from hot resonant electrons. We have considered the nature and properties of such nonlinear whistler waves observed by the Van Allen Probes and Time History of Events and Macroscale Interactions define during Substorms in the inner magnetosphere, and we show that the significant enhancement of the wave electrostatic component can result from whistler wave coupling with the beam-driven electrostatic mode through the resonant interaction with hot electron beams. Being modulated by a whistler wave, the electron beam generates a driven electrostatic mode significantly enhancing the parallel electric field of the initial whistler wave. We confirm this mechanism using a self-consistent particle-in-cell simulation. The nonlinear electrostatic component manifests properties of the beam-driven electron acoustic mode and can be responsible for effective electron acceleration in the inhomogeneous magnetic field.

Plain Language Summary We consider the effects of induced scattering of the electromagnetic whistler wave to the electrostatic electron acoustic wave (observed as field-aligned electric field bursts). The main discussed effect is based on the coupling of the slightly oblique whistler wave and a beam-driven electron acoustic wave observed as ''nonlinear whistler waves''. The wave interaction as the result produces the whistler wave and the rapidly steepening acoustic electrostatic wave with the same phase (and the same k and frequency). Then, because the two different modes are the result of the interaction, the following dynamics of the waves in the inhomogeneous magnetic field is different: the whistler wave phase velocity depends on the background magnetic field magnitude but the acoustic mode propagate with the constant phase velocity. This dynamics leads to the waves phase differences and explains the fact that the observed in the experiment whistler and electrostatic bursts usually have actually random phase shift. To confirm this, we studied the dynamics of these waves in the inhomogeneous magnetic field system making use of the particle-in-cell simulation, reproduced all steps of the modes conversion, and confirmed that the dynamics in the inhomogeneous plasma system leads to the observed effects.