[1] The generation process of whistler-mode chorus emissions is analyzed by both theory and simulation. Driven by an assumed strong temperature anisotropy of energetic electrons, the initial wave growth of chorus is linear. After the linear growth phase, the wave amplitude grows nonlinearly. It is found that the seeds of chorus emissions with rising frequency are generated near the magnetic equator as a result of a nonlinear growth mechanism that depends on the wave amplitude. We derive the relativistic second-order resonance condition for a whistler-mode wave with a varying frequency. Wave trapping of resonant electrons near the equator results in the formation of an electromagnetic electron hole in the wave phase space. For a specific wave phase variation, corresponding to a rising frequency, the electron hole can form a resonant current that causes growth of a wave with a rising frequency. Seeds of chorus elements grow from the saturation level of the whistler-mode instability at the equator and then propagate away from the equator. In the frame of reference moving with the group velocity, the wave frequency is constant. The wave amplitude is amplified by the nonlinear resonant current, which is sustained by the increasing inhomogeneity of the dipole magnetic field over some distance from the equator. Chorus elements are generated successively at the equator so long as a sufficient flux of energetic electrons with a strong temperature anisotropy is present.

[1] During magnetic storms, relativistic electrons execute nearly circular orbits about the Earth and traverse a spatially confined zone within the duskside plasmapause where electromagnetic ion cyclotron (EMIC) waves are preferentially excited. We examine the mechanism of electron pitch-angle diffusion by gyroresonant interaction with EMIC waves as a cause of relativistic electron precipitation loss from the outer radiation belt. Detailed calculations are carried out of electron cyclotron resonant pitch-angle diffusion coefficients D aa for EMIC waves in a multi-ion (H + , He + , O + ) plasma. A simple functional form for D aa is used, based on quasi-linear theory that is valid for parallelpropagating, small-amplitude electromagnetic waves of general spectral density. For typical observed EMIC wave amplitudes (1-10nT ), the rates of resonant pitch-angle diffusion are close to the limit of ''strong'' diffusion, leading to intense electron precipitation. In order for gyroresonance to take place, electrons must possess a minimum kinetic energy E min which depends on the value of the ratio (electron plasma frequency/ electron gyrofrequency); E min also depends on the properties of the EMIC wave spectrum and the ion composition. Geophysically interesting scattering, with E min comparable to 1 MeV, can only occur in regions where (electron plasma frequency/electron gyrofrequency) !10, which typically occurs within the duskside plasmapause. Under such conditions, electrons with energy !1 MeV can be removed from the outer radiation belt by EMIC wave scattering during a magnetic storm over a time-scale of several hours to a day.INDEX TERMS: 2716 Magnetospheric Physics: Energetic particles, precipitating; 2772 Magnetospheric Physics: Plasma waves and instabilities; 2471 Ionosphere: Plasma waves and instabilities; 2730 Magnetospheric Physics: Magnetosphere-inner; KEYWORDS: relativistic electrons, magnetic storms, EMIC waves, electron precipitation, outer radiation belt, strong diffusion scattering Citation: Summers, D., and R. M. Thorne, Relativistic electron pitch-angle scattering by electromagnetic ion cyclotron waves during geomagnetic storms,

Abstract.Resonant diffusion curves for electron cyclotron resonance with field-aligned electromagnetic R mode and L mode electromagnetic ion cyclotron (EMIC) waves are constructed using a fully relativistic treatment.

[1] Outer zone radiation belt electrons can undergo gyroresonant interaction with various magnetospheric wave modes including whistler-mode chorus outside the plasmasphere and both whistler-mode hiss and electromagnetic ion cyclotron (EMIC) waves inside the plasmasphere. To evaluate timescales for electron momentum diffusion and pitch angle diffusion, we utilize bounce-averaged quasi-linear diffusion coefficients for field-aligned waves with a Gaussian frequency spectrum in a dipole magnetic field. Timescales for momentum diffusion of MeV electrons due to VLF chorus can be less than a day in the outer radiation belt. Equatorial chorus waves (jl W j < 15 deg) can effectively accelerate MeV electrons. Efficiency of the chorus acceleration mechanism is increased if high-latitude waves (jl W j > 15 deg) are also present. Our calculations confirm that chorus diffusion is a viable mechanism for generating relativistic (MeV) electrons in the outer zone during the recovery phase of a storm or during periods of prolonged substorm activity when chorus amplitudes are enhanced. Radiation belt electrons are subject to precipitation loss to the atmosphere due to resonant pitch angle scattering by plasma waves. The electron precipitation loss timescale due to scattering by each of the wave modes, chorus, hiss, and EMIC waves, can be 1 day or less. These wave modes can separately, or in combination, contribute significantly to the depletion of relativistic (MeV) electrons from the outer zone over the course of a magnetic storm. Efficient pitch angle scattering by whistler-mode chorus or hiss typically requires high latitude waves (jl W j > 30 deg). Timescales for electron acceleration and loss generally depend on the spectral properties of the waves, as well as the background electron number density and magnetic field. Loss timescales due to EMIC wave scattering also depend on the ion (H + , He + , O + ) composition of the plasma. Complete models of radiation belt electron transport, acceleration and loss should include, in addition to radial (cross-L) diffusion, resonant diffusion due to gyroresonance with VLF chorus, plasmaspheric hiss, and EMIC waves. Comprehensive observational data on the spectral properties of these waves are required as a function of spatial location (L, MLT, MLAT) and magnetic activity.Citation: Summers, D., B. Ni, and N. P. Meredith (2007), Timescales for radiation belt electron acceleration and loss due to resonant wave-particle interactions: 2. Evaluation for VLF chorus, ELF hiss, and electromagnetic ion cyclotron waves,