The ballooning instability in space plasmas

Hameiri, Eliezer; Laurence, Peter; Mond, M.

doi:10.1029/90ja02100

Cited by 98 publications

(84 citation statements)

References 42 publications

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“…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. General approach to the 3D case with account for the gravity and plasma rotation effects was outlined by Hameiri et al (1991). Our analysis of 2D configuration is given in another form.…”

Section: Mhd Plasma Equilibrium and Linearized Dynamic Equationsmentioning

confidence: 99%

“…The system (4) is a special case of the system (71) from (Hameiri et al, 1991). It can be re-written in the following form (Klimushkin, 1998) …”

Section: Mhd Plasma Equilibrium and Linearized Dynamic Equationsmentioning

confidence: 99%

“…A theoretical approach to the study of the ballooning instability is based on a complicated system of coupled equations for the poloidal Alfven waves and slow magnetosonic (SMS) modes in a finite-pressure plasma, immersed in a curved magnetic field B (e.g., Southwood and Saunders, 1985;Walker, 1987;Hameiri et al, 1991;Klimushkin and Mager, 2008). Favorable conditions for the instability growth emerge at a steep plasma pressure drop held by curved field lines.…”

Section: Introduction: Ballooning Instability Of Nearearth Plasma As mentioning

confidence: 99%

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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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Section: Mhd Plasma Equilibrium and Linearized Dynamic Equationsmentioning

confidence: 99%

“…The system (4) is a special case of the system (71) from (Hameiri et al, 1991). It can be re-written in the following form (Klimushkin, 1998) …”

Section: Mhd Plasma Equilibrium and Linearized Dynamic Equationsmentioning

confidence: 99%

Section: Introduction: Ballooning Instability Of Nearearth Plasma As mentioning

confidence: 99%

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Ballooning modes and their stability in a near-Earth plasma

2013

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“…2 In magnetic confinement devices and space plasma, when a pressure gradient exists at a location where the magnetic field has an unfavored curvature, the configuration is RT unstable, and gives rise to the ballooning mode. [16][17][18] These RT and MRT processes, despite their diverse geometries and causes, share a common feature that the (effective) gravity g is perpendicular to the interface. In this sense, the interfaces can be approximately treated as planar.…”

Section: Introductionmentioning

confidence: 99%

A hybrid Rayleigh-Taylor-current-driven coupled instability in a magnetohydrodynamically collimated cylindrical plasma with lateral gravity

Zhai

Bellan

2016

Physics of Plasmas

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We present an MHD theory of Rayleigh-Taylor instability on the surface of a magnetically confined cylindrical plasma flux rope in a lateral external gravity field. The Rayleigh-Taylor instability is found to couple to the classic current-driven instability, resulting in a new type of hybrid instability that cannot be described by either of the two instabilities alone. The lateral gravity breaks the axisymmetry of the system and couples all azimuthal modes together. The coupled instability, produced by combination of helical magnetic field, curvature of the cylindrical geometry, and lateral gravity, is fundamentally different from the classic magnetic Rayleigh-Taylor instability occurring at a two-dimensional planar interface. The theory successfully explains the lateral Rayleigh-Taylor instability observed in the Caltech plasma jet experiment [Moser and Bellan, Nature 482, 379 (2012)]. Potential applications of the theory include magnetic controlled fusion, solar emerging flux, solar prominences, coronal mass ejections, and other space and astrophysical plasma processes.

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“…At sufficiently high beta the stability of MHD ballooning modes needs to be examined. The high beta MHD stability limit has been examined by several authors [5,6,7] in the magnetospheric context. For the magnetospheric problem it is necessary to consider rotation, anisotropy (p ⊥ = p ) as well as the boundary condition where the field lines enter the conducting regions near the planetary poles.…”

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confidence: 99%

Magnetohydrodynamic stability in a levitated dipole

1999

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Plasma confined by a magnetic dipole is stabilized, at low beta, by magnetic compressibility. The ideal magnetohydrodynamic (MHD) requirements for stability against interchange and high-n ballooning modes are derived at arbitrary beta for a fusion grade laboratory plasma confined by a levitated dipole. A high beta MHD equilibrium is found numerically with a pressure profile near marginal stability for interchange modes, a peak local beta of β ∼ 10, and volume averaged beta of β ∼ 0.5. This equilibrium is demonstrated to be ballooning stable on all field lines.The dipole magnetic field is the simplest and most common magnetic field configuration in the universe. It is the magnetic far-field of a single, circular current loop, and it represents the dominate structure of the middle magnetospheres of magnetized planets and neutron stars. The use of a dipole magnetic field generated by a levitated ring to confine a hot plasma for fusion power generation was first considered by Akira Hasegawa [1,2]. In order to eliminate losses along the field lines Hasegawa suggested the use of a levitated ring. He postulated that if a hot plasma having pressure profiles similar to those observed in nature could be confined by a laboratory dipole magnetic field, this plasma might also be immune to anomalous (outward) transport of plasma energy and particles.The dipole confinement concept is based on the idea of generating pressure profiles near marginal stability for low-frequency magnetic and electrostatic fluctuations. From ideal MHD marginal stability results when the pressure profile satisfies the adiabaticity condition [3,4], δ(pV γ ) = 0, where p is plasma pressure, V is the flux tube volume (V ≡ d /B) and γ = 5/3. This condition leads to dipole pressure profiles that scale with radius as r −20/3 , similar to energetic particle pressure profiles observed in the Earth's magnetosphere. This condition limits the peak pressure i.e. p peak ≤ p edge (V edge /V peak ) γ and a relatively low pressure at the plasma edge requires a large flux expansion, i.e. V edge /V peak 1.At low beta the magnetic field in the plasma will closely approximate the vacuum field. At finite beta the equilibrium field can be determined from a solution of the Grad-Shafranov equation. At sufficiently high beta the stability of MHD ballooning modes needs to be examined. The high beta MHD stability limit has been examined by several authors [5,6,7] in the magnetospheric context. For the magnetospheric problem it is necessary to consider rotation, anisotropy (p ⊥ = p ) as well as the boundary condition where the field lines enter the conducting regions near the planetary poles. Chan et al.[7] utilize a low beta equilibrium expansion in the ballooning calculation and their results are suspect at high beta [8].As a laboratory approach to controlled fusion a circular magnet that is located within a plasma will generate a dipole configuration. To avoid losses on supports the ring needs to be superconducting and be magnetically levitated within the vacuum cha...

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The ballooning instability in space plasmas

Cited by 98 publications

References 42 publications

Ballooning modes and their stability in a near-Earth plasma

Ballooning modes and their stability in a near-Earth plasma

A hybrid Rayleigh-Taylor-current-driven coupled instability in a magnetohydrodynamically collimated cylindrical plasma with lateral gravity

Magnetohydrodynamic stability in a levitated dipole

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