Resonant enhancement of relativistic electron ̄uxes during geomagnetically active periods

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 relativistic 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 resonant interactions when the Doppler-shifted wave frequency 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 enhancements in ̄uxes of relativistic electrons during geomagnetic storms and other active periods. Key words. Magnetospheric physics (energetic particles, trapped; plasma waves and instabilities; storms and substorms). 1 Introduction Magnetic storms cause some of the largest geomagnetic ®eld deformations. The source of these strong perturbations originates at the Sun and they are believed to be triggered by a persistent southward interplanetary magnetic ®eld. Generally, a magnetic storm is characterised by an enhancement in the ring current, due to the injection of ions by strong convective electric ®eld. An additional important storm characteristic is the behaviour of energetic electrons during di€erent phases of the storm. The evolution of relativistic electrons in the outer radiation belt depends on the time scale of magnetic perturbations and on the di€erent characteristic frequencies of electron dynamics. If the perturbation time scale is much longer than that of the quasiperiodic motion of a particle in geomagnetic ®eld, the corresponding adiabatic invariant is conserved. Conservation of the three invariants during the main phase of the storm together with Liouville's theorem requires that the enhanced ring current, which decreases the inner magnetospheric magnetic ®eld, causes a decrease in the electron ̄ux as the electrons move to higher L shells. The resulting decrease in relativistic electron ̄uxes at this phase has been observed by numerous satellites like SAMPEX, WIND and POLAR (Baker et al., 1997; Reeves et al., 1998). At the recovery phase one observes an increase up to two orders of magnitude in the ̄ux of relativistic electrons (Li et al., 1998; Reeves et al., 1998). During active times the ̄ux increase of very energetic electrons …>3MeV† at lower L shells often precede the increase of electrons with the same ®rst and second adiabatic invariant at higher L and results in a peak of the distribution f …L† around L ˆ 4:5 (Selesnick and Blake, 1997). The decay phase is characterised partly by adiabatic behaviour, as well as by radial di€usion (which violates the third invariant) and by pitch angle scattering (which violates the ®rst two adiabatic invariants) (e.g., McIlwain 1996; Li et al., 1998). The increase in the relativistic electron ̄ux during active times and in the storm recovery phase is Correspondence to: I. Roth Ann. Geophysicae 17, 631±638 (1999) Ó EGS ± Springer-Verlag 1999