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Annales Geophysicae


The strong increase in the ̄ux of relativistic electrons during the recovery phase of magnetic storms and during other active periods is investigated with the help of Hamiltonian formalism and simulations of test electrons which interact with whistler waves. The intensity of the whistler waves is enhanced signi®cantly due to injection of 10±100 keV electrons during the substorm. Electrons which drift in the gradient and curvature of the magnetic ®eld generate the rising tones of VLF whistler chorus. The seed population of relativ- istic electrons which bounce along the inhomogeneous magnetic ®eld, interacts resonantly with the whistler waves. Whistler wave propagating obliquely to the magnetic ®eld can interact with energetic electrons through Landau, cyclotron, and higher harmonic reso- nant interactions when the Doppler-shifted wave fre- quency equals any (positive or negative) integer multiple of the local relativistic gyrofrequency. Because the gyroradius of a relativistic electron may be the order of or greater than the perpendicular wavelength, numerous cyclotron, harmonics can contribute to the resonant interaction which breaks down the adiabatic invariant. A similar process di􏰀uses the pitch angle leading to electron precipitation. The irreversible changes in the adiabatic invariant depend on the relative phase between the wave and the electron, and successive resonant interactions result in electrons undergoing a random walk in energy and pitch angle. This resonant process may contribute to the 10±100 fold increase of the relativistic electron ̄ux in the outer radiation belt, and constitute an interesting relation between substorm-generated waves and en- hancements in ̄uxes of relativistic electrons during geomagnetic storms and other active periods.