Theory of quasi‐monochromatic whistler wave generation in the inner plasma sheet

Abstract

Nonlinear interactions between plasma sheet electrons and nearly monochromatic whistler wave packets are studied. The theory applies to the generation of chorus emissions from quasi‐monochromatic wavelets observed in the plasma sheet at the top of the ELF/VLF hiss band. The hiss‐triggered chorus is produced by step‐like deformations that develop in distribution functions at the boundaries between resonant and nonresonant electrons. Equations are obtained describing the wave amplitudes and frequency‐time characteristics for propagation at small angles with respect to the geomagnetic field. The linear resonant interactions leading to wavelet generation are investigated. The resonant wave frequencies change along the field lines to compensate for geomagnetic field inhomogeneities. If the electric fields exceed the amplitudes of those in the background plasmapheric hiss (≫ 10−6 V/m), electrons become trapped in phase space, and their distribution functions develop plateaus whose extents are proportional to the square roots of electric field amplitudes. Nonlinear currents generated by the trapped electrons are studied to obtain analytical representations of the growth rates and frequency spreads. Numerical examples are presented to illustrate our theoretical analysis.