Abstract
Abstract. 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.
Highlights
The paper is devoted to studying drift-bounce instability which is suggested as a generation mechanism of azimuthally small-scale, ultra-low frequency waves in the magnetosphere
The following questions arise: How strong is the dependence of the growth rate on m and L for the given distribution function? In particular, how sharply are the poloidal Alfven waves generated by the instability localized across magnetic shells? And what values of the azimuthal wave numbers m can these poloidal Alfven waves have?
For the fundamental harmonic of poloidal oscillations (N=1), the azimuthal wave number m can be determined with greater accuracy: for the distribution function with =10 keV, mL is determined with the accuracy of ±5 and mtot with the accuracy of ±10, but the region of their localization with observed values |m|∼50−100 is located in the distant part of the magnetosphere with L>9 RE
Summary
The paper is devoted to studying drift-bounce instability which is suggested as a generation mechanism of azimuthally small-scale, ultra-low frequency waves in the magnetosphere (azimuthal wave numbers m 1). It should be noted that in writing the observed value as m± m, the error m is usually attributed to the measurement rather than to the nature of the waves, tacitly implying that the real m number of the wave has a well-defined value It should be mentioned, that the resonance condition Eq (1) is important only as a part of the growth rate expression,. The instability does not select any particular m value, and the whole logic comparising the drift-bounce resonance theory with the experiments fails To elucidate this issue, it is necessary to perform the integration over the velocity space and to calculate the growth rate as a function of the azimuthal wave number. The following questions arise: How strong is the dependence of the growth rate on m and L for the given distribution function? In particular, how sharply are the poloidal Alfven waves generated by the instability localized across magnetic shells? And what values of the azimuthal wave numbers m can these poloidal Alfven waves have?
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
