Toroidal and poloidal Alfvén waves with arbitrary azimuthal wavenumbers in a finite pressure plasma in the Earth's magnetosphere

Abstract

Abstract. In this paper, in terms of an axisymmetric model of the magnetosphere, we formulate the criteria for which the Alfvén waves in the magnetosphere can be toroidally and poloidally polarized (the disturbed magnetic field vector oscillates azimuthally and radially, respectively). The obvious condition of equality of the wave frequency ω to the toroidal (poloidal) eigenfrequency T N ( P N ) is a necessary and sufficient one for the toroidal polarization of the mode and only a necessary one for the poloidal mode. In the latter case we must also add to it a significantly stronger condition, where m is the azimuthal wave number, and N is the longitudinal wave number. In cold plasma (the plasma to magnetic pressure ratio β = 0) the left-hand side of this inequality is too small for the routinely recorded (in the magnetosphere) second harmonic of radially polarized waves, therefore these waves must have nonrealistically large values of m. By studying several models of the magnetosphere differing by the level of disturbance, we found that the left-hand part of the poloidality criterion can be satisfied by taking into account finite plasma pressure for the observed values of m ∼ 50 − 100 (and in some cases, for even smaller values of the azimuthal wave numbers). When the poloidality condition is satisfied, the existence of two types of radially polarized Alfvén waves is possible. In magnetospheric regions, where the function P N is a monotonic one, the mode is poloidally polarized in a part of its region of localization. It propagates slowly across magnetic shells and changes its polarization from poloidal to toroidal. The other type of radially polarized waves can exist in those regions where this function reaches its extreme values (ring current, plasmapause). These waves are standing waves across magnetic shells, having a poloidal polarization throughout the region of its existence. Waves of this type are likely to be exemplified by giant pulsations. If the poloidality condition is not satisfied, then the mode is toroidally polarized throughout the region of its existence. Furthermore, itCorrespondence to: D. Yu. Klimushkin (klimush@iszf.irk.ru) has a resonance peak near the magnetic shell, the toroidal eigenfrequency of which equals the frequency of the wave.

Field-aligned structure of poloidal Alfvén waves in a finite pressure plasma

“…A possibility of this effect for an azimuthally large-scale (toroidal) mode needs a special consideration, but most probably it is to be much less pronounced. But it can be observed also in the compressional component of the magnetic field b which is coupled with electric field in a finite-pressure plasma as Klimushkin et al, 2004). This component is often measured with satellites.…”

“…Furthermore, if the poloidal Alfvén mode is considered, the problems of finding the parallel and transverse structure of the wave field can be treated separately, as described by Leonovich and Mazur (1993), Vetoulis and Chen (1996) and Klimushkin et al (2004). An equation describing the field-aligned structure of Alfvén waves in a finite pressure plasma may be written as follows (Denton, 1998;Denton and Vetoulis, 1998;Mager and Klimushkin, 2002;Klimushkin et al, 2004) …”

Giant pulsations as modes of a transverse Alfvénic resonator on the plasmapause

“…Besides, the maximum of the poloidal component in the field line resonance occurs at the same location as the maximum of the toroidal component, while for the giant pulsations the maximum of the poloidal component corresponds to the dip of the toroidal component (Chisham et al, 1997). A possible solution is suggested by the strong compressional magnetic field component of giant pulsations which is an indicator of the role of finite plasma pressure in ULF wave formation (Klimushkin et al, 2004). Indeed, Pgs are a subclass of the poloidal Alfvén wave, but the poloidal eigenfrequency is very sensitive to plasma pressure (e.g., Klimushkin, 1997;Mager and Klimushkin, 2002;Agapitov and Cheremnykh, 2011;Mazur et al, 2012).…”

“…Trapping of energy across magnetic shells may provide a natural explanation for the strong latitudinal localization of the poloidal modes. Under very general assumptions, the resonator can be situated on the outer edge of the plasmapause (Klimushkin et al, 2004), which may explain the location of the giant pulsations in that region. The purpose of this paper is to explore this suggestion, consider a possible generation mechanism of the wave in the resonator, and compare with observations.…”

“…A necessary (although not sufficient: Klimushkin et al, 2004) condition for the Alfvén waves to be poloidally polarized is a high azimuthal wave number value, |m| 1. Indeed, direct measurements confirm that Pgs are moderately high-m waves, |m| = 15-40.…”