Theory of magnetospheric standing hydromagnetic waves with large azimuthal wave number: 4. Standing waves in the ring current region

Walker, A. D. M.; Pekrides, H.

doi:10.1029/96ja02701

Cited by 19 publications

(10 citation statements)

References 33 publications

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“…We make two other comments about Figures 3-6: (i) There are no fast modes in a thin filament because total pressure (particle and magnetic) does not change with time; (ii) close to the Earth and c 2 s ≪c 2 A , these waves have frequencies much higher than the slow modes and thus do not show up in Figures 3-6. A related approach to the physics of magnetospheric standing waves was developed by Southwood and Saunders (1985), Walker and Pekrides (1996), Walker (1987), Taylor and Walker (1987), and Klimushkin (1998) with a specific focus on the coupling of slow mode waves and Alfvén waves. There are clear similarities to the work presented in our paper.…”

Section: 1029/2019ja027516mentioning

confidence: 99%

“…A related approach to the physics of magnetospheric standing waves was developed by Southwood and Saunders (1985), Walker and Pekrides (1996), Walker (1987), Taylor and Walker (1987), and Klimushkin (1998) with a specific focus on the coupling of slow mode waves and Alfvén waves. There are clear similarities to the work presented in our paper.…”

Section: 1029/2019ja027516mentioning

confidence: 99%

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Buoyancy Waves in Earth's Nightside Magnetosphere: Normal‐Mode Oscillations of Thin Filaments

2020

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We derive a coupled pair of differential equations that describe linear oscillations of a thin magnetic filament that slides without friction through a stationary medium that is in equilibrium. Background field lines are assumed to be in the xz plane, and filament motion is confined to that plane. Sample eigenfunctions and eigenfrequencies are computed for a numerical equilibrium that approximately represents the average magnetosphere but departs from exact equilibrium due to finite grid spacing and other numerical inaccuracy. The most important result of the calculation is the value of the eigenfrequency of the lowest even mode for filaments that cross the equatorial plane at y = 0 and −18 < x < −2 R E . The characteristics of the lowest even mode depend on geocentric distances of the field line. For field lines that extend out in the plasma sheet, that mode is characterized as a buoyancy wave but, for the inner magnetosphere, it is best characterized as a long-wavelength slow mode.Plain Language Summary Bursty bulk flows often move sunward through the Earth's plasma sheet, coming to rest in the inner plasma sheet. Before coming to rest, they often exhibit damped oscillations with periods of a few minutes. These oscillations are very similar to oscillations of Earth's neutral atmosphere; if a small parcel of air is displaced downward a small distance, gravity causes the parcel to bob up and down, executing what atmospheric scientists call "buoyancy oscillations." The oscillatory motion observed in the plasma sheet is very similar to buoyancy oscillations in the neutral atmosphere, except that buoyancy force in the magnetosphere is caused by the curvature of magnetic fields rather than gravity. The theoretical analogy to the small parcel of air is a thin magnetic filament in the magnetosphere. This paper works out the theory of small amplitude oscillations of a thin magnetospheric filament and calculates the frequency lowest even mode for different field lines in an average magnetosphere. Out in the plasma sheet, these oscillations are best described as buoyancy waves, but in the inner magnetosphere it is a long-wavelength slow mode.

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Section: 1029/2019ja027516mentioning

confidence: 99%

Section: 1029/2019ja027516mentioning

confidence: 99%

Buoyancy Waves in Earth's Nightside Magnetosphere: Normal‐Mode Oscillations of Thin Filaments

2020

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“…Most papers address the longitudinal structure of high‐ m waves: recent work in this area is due to Walker and Pekrides [1996] and Denton [1998]. Significant attention has recently been given also to the structure of Alfvén waves in the direction across magnetic shells.…”

Section: Introductionmentioning

confidence: 99%

“…To save the situation, it is necessary to somehow increase the difference between the toroidal and poloidal eigenfrequencies. Finite plasma pressure does work in this direction [ Walker , 1987; Taylor and Walker , 1987; Walker and Pekrides , 1996; Denton , 1998].…”

Section: Introductionmentioning

confidence: 99%

Theory of azimuthally small‐scale Alfvén waves in an axisymmetric magnetosphere with small but finite plasma pressure

Mager

Klimushkin

2002

J.‐Geophys.‐Res.

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[1] An analytical and numerical study is made of the influence of plasma finite pressure on the structure of Alfvén waves with large numbers of the azimuthal wave number, m ) 1, as well as of the conditions under which the waves can be poloidally polarized. The study is based on using the axisymmetric model of the magnetosphere assuming the background plasma inhomogeneity along field lines and across magnetic shells, the curvature of field lines, and an equilibrium electric field. The poloidality condition of the mode can imply that in the region where many azimuthal wavelengths fit in the region where the propagation of the wave is possible (the transparent region). The broader is the transparent region, the less stringent conditions are imposed on azimuthal wave numbers of the poloidally polarized Alfvén wave. In this paper it is shown that with nonzero plasma pressure, the transparent region is much broader when compared with cold plasma case. For instance, if finite pressure for the second standing harmonic along a field line of the wave (N = 2) is accounted for, the width of the transparent regions several thousand kilometers, and poloidal Alfvén waves can exist when m ) 10. This is consistent with experimental data on radially polarized Pc4 pulsations in the magnetosphere which have m from 50 to 150, whereas in the case of zero pressure the transparent region does not exceed a few tens of kilometers; therefore, in b = 0 case, poloidally polarized waves must have too large values of m in excess of 1000, which is not observed. A further important result of this study implies that near the ring current maximum there must exist a cavity, and high-m oscillations enclosed within this cavity must be standing oscillations across magnetic shells.

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“…Leonovich andMazur, 1993, 1997;Walker and Pekrides, 1996;Vetoulis and Chen, 1996;Klimushkin et al, 2004;Klimushkin, 1998aKlimushkin, , b, 2000Mager and Klimushkin, 2002). However, MHD waves in the magnetosphere are generated by some transient, nonstationary processes; therefore, the monochromatic approximation does not appear to be quite realistic (although it can serve as the basis for the theory of nonstationary (impulse-generated in particular) waves).…”

Section: Introductionmentioning

confidence: 99%

The spatio-temporal structure of impulse-generated azimuthalsmall-scale Alfvén waves interacting with high-energy chargedparticles in the magnetosphere

Klimushkin

Mager

2004

Ann. Geophys.

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Abstract.It is assumed to date that the energy source of azimuthal small-scale ULF waves in the magnetosphere (azimuthal wave numbers m 1) is provided by the energetic particles interacting with the waves through the bounce-drift resonance. In this paper we have solved the problem of the bounce-drift instability influence on the spatio-temporal structure of Alfvén waves excited by a source of the type of sudden impulse in a dipole-like magnetosphere. It is shown that the impulse-generated Alfvén oscillation within a time τ ∼m/ T N (where T N is the toroidal eigenfrequency) is a poloidal one, and each field line oscillates with its own eigenfrequency that coincides with the poloidal frequency of a given L-shell. As time elapses, the wave becomes toroidally polarized because of the phase difference of the disturbance, and the oscillation frequency of field lines tends to the toroidal frequency. The drift-bounce instability growth rate becomes smaller during the wave temporal evolution, and the instability undergoes stabilization when the wave frequency coincides with the toroidal eigenfrequency. The total amplification of the wave can be estimated as eγ τ , whereγ is the wave growth rate at the beginning of the process, when it has its maximum value. The wave amplitude can increase only within a time ∼τ , when it is poloidally polarized. After this time, when the wave becomes to be toroidally polarized, it goes damped because of the finite ionospheric conductivity. This is in qualitative agreement with the recent radar experimental data.

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Theory of magnetospheric standing hydromagnetic waves with large azimuthal wave number: 4. Standing waves in the ring current region

Cited by 19 publications

References 33 publications

Buoyancy Waves in Earth's Nightside Magnetosphere: Normal‐Mode Oscillations of Thin Filaments

Buoyancy Waves in Earth's Nightside Magnetosphere: Normal‐Mode Oscillations of Thin Filaments

Theory of azimuthally small‐scale Alfvén waves in an axisymmetric magnetosphere with small but finite plasma pressure

The spatio-temporal structure of impulse-generated azimuthalsmall-scale Alfvén waves interacting with high-energy chargedparticles in the magnetosphere

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