[1] Electron acceleration inside the Earth's magnetosphere is required to explain increases in the $MeV radiation belt electron flux during magnetically disturbed periods. Recent studies show that electron acceleration by whistler mode chorus waves becomes most efficient just outside the plasmapause, near L = 4.5, where peaks in the electron phase space density are observed. We present CRRES data on the spatial distribution of chorus emissions during active conditions. The wave data are used to calculate the pitch angle and energy diffusion rates in three magnetic local time (MLT) sectors and to obtain a timescale for acceleration. We show that chorus emissions in the prenoon sector accelerate electrons most efficiently at latitudes above 15°for equatorial pitch angles between 20°a nd 60°. As electrons drift around the Earth, they are scattered to large pitch angles and further accelerated by chorus on the nightside in the equatorial region. The timescale to accelerate electrons by whistler mode chorus and increase the flux at 1 MeV by an order of magnitude is approximately 1 day, in agreement with satellite observations during the recovery phase of storms. During wave acceleration the electrons undergo many drift orbits and the resulting pitch angle distributions are energy-dependent. Chorus scattering should produce pitch angle distributions that are either flat-topped or butterfly-shaped. The results provide strong support for the wave acceleration theory.

[1] We present a new computer code (PADIE) that calculates fully relativistic quasi-linear pitch angle and energy diffusion coefficients for resonant wave-particle interactions in a magnetized plasma. Unlike previous codes, the full electromagnetic dispersion relation is used so that interactions involving any linear electromagnetic wave mode in a predominantly cold plasma can be addressed for any ratio of the plasma-frequency to the cyclotron frequency w pe /jW e j. The code can be applied to problems in astrophysical, magnetospheric, and laboratory plasmas. The code is applied here to the Earth's radiation belts to calculate electron diffusion by whistler mode chorus, electromagnetic ion cyclotron (EMIC), and Z mode waves. The high-density approximation is remarkably good for electron diffusion by whistler mode chorus for energies E ! 100 keV, even for w pe /jW e j % 2 but underestimates diffusion by orders of magnitude at low energies ($10 keV). When a realistic angular spread of propagating waves is introduced for EMIC waves, electron diffusion at $0.5 MeV is only slightly reduced compared with the assumption of field-aligned propagation, but at $5 MeV, electron diffusion at pitch angles near 90°is reduced by a factor of 5 and increased by several orders of magnitude at pitch angles 30°-80°. Scattering by EMIC waves should contribute to flattening of the distribution function. The first results for electron diffusion by Z mode waves are presented. They show that unlike the whistler and EMIC waves, energy diffusion exceeds pitch angle diffusion over a broad range of pitch angles less than 45°. The results suggest that Z mode waves could provide a significant contribution to electron acceleration in the radiation belts during storm times.Citation: Glauert, S. A., and R. B. Horne (2005), Calculation of pitch angle and energy diffusion coefficients with the PADIE code,

Abstract.Intense interest currently exists in determining the roles played by various wave-particle interactions in the acceleration of electrons to relativistic energies during/following geomagnetic storms. Here we present a survey of wave data from the CRRES Plasma Wave Experiment for lower band (0.1-0.5fce) and upper band (0.5-1.0fce) chorus, fce being the electron gyrofrequency, to assess

[1] Electromagnetic ion cyclotron (EMIC) waves which propagate at frequencies below the proton gyrofrequency can undergo cyclotron resonant interactions with relativistic electrons in the outer radiation belt and cause pitch-angle scattering and electron loss to the atmosphere. Typical storm-time wave amplitudes of 1-10 nT cause strong diffusion scattering which may lead to significant relativistic electron loss at energies above the minimum energy for resonance, E min . A statistical analysis of over 800 EMIC wave events observed on the CRRES spacecraft is performed to establish whether scattering can occur at geophysically interesting energies ( 2 MeV). While E min is well above 2 MeV for the majority of these events, it can fall below 2 MeV in localized regions of high plasma density and/or low magnetic field ( f pe /f ce,eq > 10) for wave frequencies just below the hydrogen or helium ion gyrofrequencies. These lower energy scattering events, which are mainly associated with resonant L-mode waves, are found within the magnetic local time range 1300 < MLT < 1800 for L > 4.5. The average wave spectral intensity of these events (4-5 nT 2 /Hz) is sufficient to cause strong diffusion scattering. The spatial confinement of these events, together with the limited set of these waves that resonate with 2 MeVelectrons, suggest that these electrons are only subject to strong scattering over a small fraction of their drift orbit. Consequently, drift-averaged scattering lifetimes are expected to lie in the range of several hours to a day. EMIC wave scattering should therefore significantly affect relativistic electron dynamics during a storm. The waves that resonate with the $MeV electrons are produced by low-energy ($keV) ring current protons, which are expected to be injected into the inner magnetosphere during enhanced convection events. INDEX TERMS: 2730Magnetospheric Physics: Magnetosphere-inner; 2772 Magnetospheric Physics: Plasma waves and instabilities; 7867 Space Plasma Physics: Wave/particle interactions; 2716 Magnetospheric Physics: Energetic particles, precipitating; KEYWORDS: EMIC waves, relativistic electrons, wave/particle interaction, outer radiation belt Citation: Meredith, N. P., R. M. Thorne, R. B. Horne, D. Summers, B. J. Fraser, and R. R. Anderson, Statistical analysis of relativistic electron energies for cyclotron resonance with EMIC waves observed on CRRES,