Kinetic Theory of Drift-Dissipative Instabilities of a Plasma

Rukhadze, A. A.; Silin, V. P.

doi:10.1070/pu1969v011n05abeh003740

Cited by 63 publications

(22 citation statements)

References 9 publications

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“…Lifshitz and Pitaevskii 1980). The first term has been given previously by Rukhadze and Silin (1960). Note that non-relativistically only 4 of the Pauli paramagnetic spin susceptibility is cancelled by the diamagnetic contribution from the orbital motion, whereas in the extreme relativistic limit, the purely paramagnetic part, xp = (ai42) p(p2 -1)1'2, is almost completely cancelled.…”

Section: Magnetisationmentioning

confidence: 96%

Magnetic susceptibility of a neutron star crust

Blandford

Hernquist

1982

J. Phys. C: Solid State Phys.

108

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Abstract. The magnetic susceptibility of the degenerate free electrons in the crust of a neutron star is computed for a range of densities, temperatures, and field strengths. It is shown that when the temperature is low enough (typically less than 10' K for densities of about 1O'g and 10" G fields), the susceptibility undergoes large de Haas-van Alphen oscillations. The crust is then unstable to the formation of layers of domains of alternating magnetisation. Associated with these domains are magnetic field fluctuations of a few per cent amplitude and anisotropic magnetostrictive stresses which may be large enough to crumble the crust. It is argued that these domains are unlikely to directly influence the surface properties of the neutron star but may possibly be coupled indirectly to observable effects.

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Section: Magnetisationmentioning

confidence: 96%

Magnetic susceptibility of a neutron star crust

Blandford

Hernquist

1982

J. Phys. C: Solid State Phys.

108

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“…The model viscosity tensor component ÜÝ for ½ is necessary for such problem, where is the ion collision frequency, Ü is the radial coordinate counted from the resonant magnetic surface, and Ý is the direction perpendicular to Ü and to the equilibrium magnetic field. Following [86,87], this value can be taken in the form…”

Section: Polarization Current and Viscosity Sustention Mechanism Of Imentioning

confidence: 99%

Theory of magnetic islands in tokamaks with accenting neoclassicaltearing modes

Mikhaǐlovskiǐ

2003

Contrib. Plasma Phys.

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Key aspects of existing theory of magnetic islands in tokamaks are overviewed. The threshold models of neoclassical tearing modes (NTMs) are discussed. It is found that though the NTM theory is often used for interpreting MHD data observed in experimental devices and for designing next-step machines, the existing NTM theory is imperfect and the use of it is questionable. The main reason for such conclusion is a tangle of problems related to polarization current effect. Analytical approaches in the magnetic island theory are presented. Contents

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“…In contrast to the simpler case of Krook's collision integral, the collision term in such a form instantaneously conserves the number of particles, the momentum and the energy of the particle (Griv & Chiueh 1997). According to Pitaevskii (1963), Rukhadze & Silin (1969), Bhadra (1971) and Griv et al (1997), however, quantitative and qualitative corrections to the Bhatnagar et al model may be very large sometimes.…”

Section: Basic Equations and Equilibriummentioning

confidence: 99%

“…Lin & Bertin 1984). Reviews of plasma kinetic theory, in which the integrals for elastic particle collisions were considered in detail, are given by Rukhadze & Silin (1969), Mikhailovskii (1974) and Alexandrov et al (1984). The right-hand side of the Boltzmann equation (1), (∂ f /∂t) St , is the so-called collision integral, as yet unspecified.…”

Section: Ba S I C E Q Uat I O N S a N D E Q U I L I B R I U Mmentioning

confidence: 99%

On the stability of Saturn's rings: a quasi-linear kinetic theory

Griv

Gedalin

Yuan

2003

Monthly Notices of the Royal Astronomical Society

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A self‐consistent system of the Boltzmann kinetic equation and the Poisson equation is used to study the dynamical evolution of Saturn's main A, B and C rings composed of discrete mutually gravitating particles. The simplified case of relatively rare collisions between identical particles, when the collision frequency is smaller than (compared with) the orbital frequency, is examined. Equations describing the quasi‐linear stage of Jeans instability of small‐amplitude gravity perturbations in Saturn's rings are derived and solved analytically. Conditions under which the quasi‐linearization of the Boltzmann equation can be used to describe a wave–particle interaction are calculated with reference to the excitation of Jeans‐type perturbations. The theory, as applied to Saturn's rings, predicts for several features, such as numerous irregular Jeans‐unstable wakes, with size and spacing between them of the order of 2πh≤ 100 m, where h is the typical thickness of the system. The interaction of particles with these almost aperiodically growing gravity perturbations increases both the radial spread of the disc and random velocities of particles in a very short time‐scale of only two to three disc orbital revolutions. The latter leads to an eventual stabilization of the system, unless some effective cooling mechanism exists, reducing the magnitude of the relative velocity of particles. It is suggested that inelastic (dissipative) interparticle impacts provide such a cooling mechanism, leading to the recurrent density waves activity. We predict that the high‐resolution images from the forthcoming (2004) Cassini spacecraft will reveal this fine‐scale recurrent ∼100 m or even less spiral structure in low and moderately high optical depth regions (τ≤ 1, where τ is the normal optical depth) of Saturn's main rings.

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Kinetic Theory of Drift-Dissipative Instabilities of a Plasma

Cited by 63 publications

References 9 publications

Magnetic susceptibility of a neutron star crust

Magnetic susceptibility of a neutron star crust

Theory of magnetic islands in tokamaks with accenting neoclassicaltearing modes

On the stability of Saturn's rings: a quasi-linear kinetic theory

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