Spatial localization and azimuthal wave numbers of Alfvén waves generated by drift-bounce resonance in the magnetosphere
Spatial localization and azimuthal wave numbers m of poloidal Alfvén waves generated by energetic particles in the magnetosphere are studied in the paper. There are two factors that cause the wave localization across magnetic shells. First, the instability growth rate is proportional to the distribution function of the energetic particles, hence waves must be predominantly generated on magnetic shells where the particles are located. Second, the frequency of the generated poloidal wave must coincide with the poloidal eigenfrequency, which is a function of the radial coordinate. The combined impact of these two factors also determines the azimuthal wave number of the generated oscillations. The beams with energies about 10 keV and 150 keV are considered. As a result, the waves are shown to be strongly localized across magnetic shells; for the most often observed second longitudinal harmonic of poloidal Alfvén wave ( N=2), the localization region is about one Earth radius across the magnetic shells. It is shown that the drift-bounce resonance condition does not select the m value for this harmonic. For 10 keV particles (most often involved in the explanation of poloidal pulsations), the azimuthal wave number was shown to be determined with a rather low accuracy, -100< m<0. The 150 keV particles provide a little better but still a poor determination of this value, -90< m<-70. For the fundamental harmonic ( N=1), the azimuthal wave number is determined with a better accuracy, but both of these numbers are too small (if the waves are generated by 150 keV particles), or the waves are generated on magnetic shells (in 10 keV case) which are too far away. The calculated values of γ/ω are not large enough to overcome the damping on the ionosphere. All these have cast some suspicion on the possibility of the drift-bounce instability to generate poloidal pulsations in the magnetosphere.