Electron acceleration in the magnetosphere by whistler-mode waves of varying frequency

Acceleration of relativistic electrons in an inhomogeneous geomagnetic field during their resonant interaction with longitudinally propagating whistler-mode waves of varying frequency has been considered. Specific features of acceleration of electrons trapped by the wave field have been studied. Previous estimates of the efficiency of such acceleration have been generalized with regard to relativistic effects, and the simple formula for energy gain in a wide range of initial energies has been obtained. It has been indicated that the energy gain during a single interaction between electron and a whistler-mode wave packet, with typical parameters of an element of chorus emissions in the Earth’s magnetosphere, can reach several keV. The conditions of this acceleration mechanism realization are discussed. Specifically, it has been found that, in the case of chorus emissions in the Earth’s magnetosphere, this mechanism can be effective for electrons with perpendicular energies several times as high as such an energy of electrons generating chorus.