scholarly journals Standing Alfvén waves with m ≫ 1 in an axisymmetric magnetosphere excited by a stochastic source

1998 ◽  
Vol 16 (8) ◽  
pp. 900-913 ◽  
Author(s):  
A. S. Leonovich ◽  
V. A. Mazur
Keyword(s):  
White Noise ◽  
Broad Band ◽  
Alfven Waves ◽  
Statistical Properties ◽  
Wave Number ◽  
Alfvén Waves ◽  
Azimuthal Wave ◽  
Azimuthal Wave Number ◽  
Magnetic Shell

Abstract. In the framework of an axisymmetric magnetospheric model, we have constructed a theory for broad-band standing Alfvén waves with large azimuthal wave number m » 1 excited by a stochastic source. External currents in the ionosphere are taken as the oscillation source. The source with statistical properties of "white noise" is considered at length. It is shown that such a source drives oscillations which also have the "white noise" properties. The spectrum of such oscillations for each harmonic of standing Alfvén waves has two maxima: near the poloidal and toroidal eigenfrequencies of the magnetic shell of the observation. In the case of a small attenuation in the ionosphere the maximum near the toroidal frequency is dominated, and the oscillations are nearly toroidally polarized. With a large attenuation, a maximum is dominant near the poloidal frequency, and the oscillations are nearly poloidally polarized.

scholarly journals Spatial localization and azimuthal wave numbers of Alfvén waves generated by drift-bounce resonance in the magnetosphere

2005 ◽  
Vol 23 (12) ◽  
pp. 3775-3784 ◽  
Author(s):  
P. N. Mager ◽  
D. Yu. Klimushkin
Keyword(s):  
Spatial Localization ◽  
Energetic Particles ◽  
Alfven Waves ◽  
Wave Number ◽  
Alfvén Waves ◽  
Azimuthal Wave ◽  
Wave Numbers ◽  
Azimuthal Wave Number ◽  
Two Factors ◽  
The Waves

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.

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

2004 ◽  
Vol 22 (1) ◽  
pp. 267-287 ◽  
Author(s):  
D. Yu. Klimushkin ◽  
P. N. Mager ◽  
K.-H. Glassmeier
Keyword(s):  
Extreme Values ◽  
Second Harmonic ◽  
Alfven Waves ◽  
Wave Number ◽  
Mhd Waves ◽  
Alfvén Waves ◽  
Left Hand ◽  
Azimuthal Wave ◽  
Polarized Waves ◽  
Radially Polarized

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 ΩTN (ΩPN) 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 ∣ΩTN–ΩPN∣/ΩTN ≫ m–1 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 ΩPN 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, it has a resonance peak near the magnetic shell, the toroidal eigenfrequency of which equals the frequency of the wave. Key words. Magnetospheric physics (plasmasphere; MHD waves and instabilities) – Space plasma physics (kinetic and MHD theory)

scholarly journals Intermediate-<I>m</I> ULF waves generated by substorm injection: a case study

2010 ◽  
Vol 28 (8) ◽  
pp. 1499-1509 ◽  
Author(s):  
T. K. Yeoman ◽  
D. Yu. Klimushkin ◽  
P. N. Mager
Keyword(s):  
Phase Variation ◽  
Wave Activity ◽  
Wave Number ◽  
Ulf Wave ◽  
Azimuthal Wave ◽  
Azimuthal Wave Number ◽  
Source Particle ◽  
Phase Propagation ◽  
Field Lines

Abstract. A case study of SuperDARN observations of Pc5 Alfvén ULF wave activity generated in the immediate aftermath of a modest-intensity substorm expansion phase onset is presented. Observations from the Hankasalmi radar reveal that the wave had a period of 580 s and was characterized by an intermediate azimuthal wave number (m=13), with an eastwards phase propagation. It had a significant poloidal component and a rapid equatorward phase propagation (~62° per degree of latitude). The total equatorward phase variation over the wave signatures visible in the radar field-of-view exceeded the 180° associated with field line resonances. The wave activity is interpreted as being stimulated by recently-injected energetic particles. Specifically the wave is thought to arise from an eastward drifting cloud of energetic electrons in a similar fashion to recent theoretical suggestions (Mager and Klimushkin, 2008; Zolotukhina et al., 2008; Mager et al., 2009). The azimuthal wave number m is determined by the wave eigenfrequency and the drift velocity of the source particle population. To create such an intermediate-m wave, the injected particles must have rather high energies for a given L-shell, in comparison to previous observations of wave events with equatorward polarization. The wave period is somewhat longer than previous observations of equatorward-propagating events. This may well be a consequence of the wave occurring very shortly after the substorm expansion, on stretched near-midnight field lines characterised by longer eigenfrequencies than those involved in previous observations.

Concerning the Dynamics of Energetic Protons in Coronal Magnetic Loops: Dispersion Effects of Alfven Waves

1985 ◽  
Vol 107 ◽  
pp. 559-559
Author(s):  
V. A. Mazur ◽  
A. V. Stepanov
Keyword(s):  
Magnetic Field ◽  
Wave Dispersion ◽  
Alfven Waves ◽  
Alfven Wave ◽  
Wave Number ◽  
Alfvén Waves ◽  
Coronal Loops ◽  
Coronal Magnetic Loops ◽  
The Magnetic Field ◽  
Solar Coronal

It is shown that the existence of plasma density inhomogeneities (ducts) elongated along the magnetic field in coronal loops, and of Alfven wave dispersion, associated with the taking into account of gyrotropy U ≡ ω/ωi ≪ 1 (Leonovich et al., 1983), leads to the possibility of a quasi-longitudinal k⊥ < √U k‖ propagation (wave guiding) of Alfven waves. Here ω is the frequency of Alfven waves, ωi is the proton gyrofrequency, and k is the wave number. It is found that with the parameter ξ = ω2 R/ωi A > 1, where R is the inhomogeneity scale of a loop across the magnetic field, and A is the Alfven wave velocity, refraction of Alfven waves does not lead, as contrasted to Wentzel's inference (1976), to the waves going out of the regime of quasi-longitudinal propagation. As the result, the amplification of Alfven waves in solar coronal loops can be important. A study is made of the cyclotron instability of Alfven waves under solar coronal conditions.

scholarly journals Concerning the Dynamics of Energetic Protons in Coronal Magnetic Loops: Dispersion Effects of Alfven Waves

1985 ◽  
Vol 107 ◽  
pp. 559-559
Author(s):  
V. A. Mazur ◽  
A. V. Stepanov
Keyword(s):  
Magnetic Field ◽  
Wave Dispersion ◽  
Alfven Waves ◽  
Alfven Wave ◽  
Wave Number ◽  
Alfvén Waves ◽  
Coronal Loops ◽  
Coronal Magnetic Loops ◽  
The Magnetic Field ◽  
Solar Coronal

It is shown that the existence of plasma density inhomogeneities (ducts) elongated along the magnetic field in coronal loops, and of Alfven wave dispersion, associated with the taking into account of gyrotropy U ≡ ω/ωi ≪ 1 (Leonovich et al., 1983), leads to the possibility of a quasi-longitudinal k⊥ < √U k‖ propagation (wave guiding) of Alfven waves. Here ω is the frequency of Alfven waves, ωi is the proton gyrofrequency, and k is the wave number. It is found that with the parameter ξ = ω2 R/ωi A > 1, where R is the inhomogeneity scale of a loop across the magnetic field, and A is the Alfven wave velocity, refraction of Alfven waves does not lead, as contrasted to Wentzel's inference (1976), to the waves going out of the regime of quasi-longitudinal propagation. As the result, the amplification of Alfven waves in solar coronal loops can be important. A study is made of the cyclotron instability of Alfven waves under solar coronal conditions.

scholarly journals Nature and dynamics of overreflection of Alfvén waves in MHD shear flows

2014 ◽  
Vol 80 (5) ◽  
pp. 667-685
Author(s):  
D. Gogichaishvili ◽  
G. Chagelishvili ◽  
R. Chanishvili ◽  
J. Lominadze
Keyword(s):  
Shear Flows ◽  
Alfven Waves ◽  
Wave Number ◽  
Alfvén Waves ◽  
Transient Growth ◽  
Mean Velocity ◽  
Linear Dynamics ◽  
Linear Shear ◽  
Basic Physics ◽  
Cascade Processes

Our goal is to gain new insights into the physics of wave overreflection phenomenon in magnetohydrodynamic (MHD) nonuniform/shear flows changing the existing trend/approach of the phenomenon study. The performed analysis allows to separate from each other different physical processes, grasp their interplay and, by this way, construct the basic physics of the overreflection in incompressible MHD flows with linear shear of mean velocity, U0=(Sy,0,0), that contain two different types of Alfvén waves. These waves are reduced to pseudo- and shear-Alfvén waves when wavenumber along Z-axis equals zero (i.e. when kz=0). Therefore, for simplicity, we labeled these waves as: P-Alfvén and S-Alfvén waves (P-AWs and S-AWs). We show that: (1) the linear coupling of counter-propagating waves determines the overreflection, (2) counter-propagating P-AWs are coupled with each other, while counter-propagating S-AWs are not coupled with each other, but are asymmetrically coupled with P-AWs; S-AWs do not participate in the linear dynamics of P-AWs, (3) the transient growth of S-AWs is somewhat smaller compared with that of P-AWs, (4) the linear transient processes are highly anisotropic in wave number space, (5) the waves with small streamwise wavenumbers exhibit stronger transient growth and become more balanced, (6) maximal transient growth (and overreflection) of the wave energy occurs in the two-dimensional case – at zero spanwise wavenumber.To the end, we analyze nonlinear consequences of the described anisotropic linear dynamics – they should lead to an anisotropy of nonlinear cascade processes significantly changing their essence, pointing to a need of revisiting the existing concepts of cascade processes in MHD shear flows.

Sign in / Sign up

Export Citation Format

Share Document