Influence of ionospheric conductivity on the ballooning modes in the inner magnetosphere of the Earth

Cheremnykh, O. K.; Parnowski, A. S.

doi:10.1016/j.asr.2005.01.073

Cited by 27 publications

(20 citation statements)

References 12 publications

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“…This statement is additionally proven by this article, as it shows that in the case of curved magnetic field lines, the transversal amplitude of flute perturbations deviates from the constant and is accompanied by significant longitudinal displacements. The stability criterion derived in the paper by Cheremnykh and Parnowski (2006a) and later improved in the paper by Cheremnykh and Parnowski (2006b) is by about one-third less than the Gold criterion (∼4.25 against ∼6.67). Given the problem that radial pressure gradients in the magnetosphere (Lui and Hamilton, 1992;DeMichelis et al, 1999) are insufficient to break the Gold criterion, it is crucial to determine which instabilities can be triggered in the magnetosphere.…”

Section: Introductionmentioning

confidence: 96%

“…Then we cast the dipole magnetic field into them and rewrite them for an individual magnetic field line, taking into account that ballooning perturbations are fieldline-driven. After that, we rewrote them in a dimensionless form (Cheremnykh and Parnowski, 2006b) 2 c 6 b …”

Section: The Equations Of Small Oscillationsmentioning

confidence: 99%

“…|B| 2 is the plasma displacement vector, ξ =ξ ∇ψ is the poloidal displacement (Alfvén), η=ξ [B∇ψ] |∇ψ| 2 is the toroidal displacement (Alfvén), τ =ξ B is the longitudinal displacement (slow magnetosonic), λ is the polarization parameter (Cheremnykh and Parnowski, 2006b;Dewar and Glasser, 1983), α=− L p dp dL is the pressure profile, β=γpB −2 0 is the plasma beta taken on the equatorial plane, γ =5 3 is the ratio of specific heats, B 0 =ML −3 is the value of the magnetic field at the equator, M is the magnetic dipole momentum of the Earth, T 0 =γ pdivξ is the compressibility of the perturbations, ρ is the mass density of plasma, p is the plasma pressure.…”

Section: The Equations Of Small Oscillationsmentioning

confidence: 99%

“…We omit the derivation of the equations for the sake of brevity; those interested should consult either Cheremnykh et al (2004) or, preferably, Cheremnykh andParnowski (2006b). We would, however, indicate that this derivation was identical in the sense that we did not use any nonidentical operators, except for the ballooning approximation, so we believe that the eigenmode spectrum of our equations coincides with that of the original MHD equations for ballooning perturbations.…”

Section: Introductionmentioning

confidence: 99%

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Eigenmode analysis of ballooning perturbations in the inner magnetosphere of the Earth

Parnowski

2007

Ann. Geophys.

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Abstract. We analyze coupled Alfvén and slow magnetosonic eigenmodes in a dipole geomagnetic field with different ionospheric conductivities in the framework of ideal magnetic hydrodynamics (MHD) with finite pressure. We use numerical and, if possible, analytical methods to describe eigenmode frequencies, growth rates and eigenfunctions. The spectrum of Alfvén and slow magnetosonic modes is discrete and equidistant. The frequencies of the first Alfvén and slow magnetosonic eigenmodes are estimated as ∼1 Hz and ∼1 mHz, respectively. In the case of finite conductivity, periodic and aperiodic modes are separated and their interaction analyzed. It was shown that periodic and aperiodic perturbations can mutually transform into each other. A new flute stability criterion is derived (α∼4.25), which is stricter than the Gold criterion (α=20/3). Here, as usual, α=−L/p dp/dL. For flute perturbations, the deviations of transversal displacement from a constant are calculated. An approximation for longitudinal displacement is derived. We determined the position of the main longitudinal peak, which can be responsible for nonlinear structures observed by Freja. An influence of nonlinear terms in pressure is estimated as well.

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Section: Introductionmentioning

confidence: 96%

Section: The Equations Of Small Oscillationsmentioning

confidence: 99%

Section: The Equations Of Small Oscillationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Eigenmode analysis of ballooning perturbations in the inner magnetosphere of the Earth

Parnowski

2007

Ann. Geophys.

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“…Therefore, influence of the ionospheric boundaries on the ballooning mode properties can be neglected, assuming that the growing disturbances are localized in the near-equatorial region of the nightside magnetosphere. The influence of the ionospheric boundary conditions on the ballooning modes was considered in many papers (e.g., Cheremnykh and Parnowski, 2006). 2.1 Asymptotic theory of transverse small-scale disturbances For small-scale in the transverse (across B) direction disturbances the linearized MHD equations of a finite pressure plasma can be simplified and reduced to a system of ordinary differential equations for coupled Alfven and SMS modes.…”

Section: Mhd Plasma Equilibrium and Linearized Dynamic Equationsmentioning

confidence: 99%

Ballooning modes and their stability in a near-Earth plasma

2013

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As a possible trigger of the substorm onset, the ballooning instability has been often suggested. The ballooning disturbances in a finite-pressure plasma immersed into a curved magnetic field are described with the system of coupled equations for the Alfven and slow magnetosonic modes. The spectral properties of ballooning disturbances and instabilities can be characterized by the local dispersion equation. The basic system of equations can be reduced to the dispersion equation for the small-scale in transverse direction disturbances. From this relationship the dispersion, instability threshold, and stop-bands of the Alfvenic and slow magnetosonic modes have been determined. The field-aligned structure of unstable mode is described with the solution of the eigenvalue problem in the Voigt model. We have also analyzed in a cylindrical geometry an eigenvalue problem for the stability of ballooning disturbances with a finite scale along the plasma inhomogeneity. The account of a finite scale in the radial direction raises the instability threshold as compared with that in the WKB approximation.

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