Abstract

The stability of a cylindrical plasma with an axial magnetic field and confined between conducting walls is investigated by solving, for small oscillations about equilibrium, the linearized Boltzmann and Maxwell equations. A criterion for marginal stability is derived; this differs slightly from the one derived by Rosenbluth from an analysis of the particle orbits. However, Rosenbluth’s principal results on the possibility of stabilizing the pinch under suitable external conditions are confirmed. In the appendix a dispersion relation appropriate for plane hydromagnetic waves in an infinite medium is obtained; this relation discloses under the simplest conditions certain types of instabilities which may occur in plasma physics.

Keywords

PinchDispersion relationPhysicsStability (learning theory)PlasmaMagnetic fieldMarginal stabilityInstabilityClassical mechanicsMechanicsMagnetohydrodynamicsPlane (geometry)MathematicsCondensed matter physicsGeometryQuantum mechanicsComputer science

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Publication Info

Year
1958
Type
article
Volume
245
Issue
1243
Pages
435-455
Citations
219
Access
Closed

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Cite This

S. Chandrasekhar, Allan N. Kaufman, Kenneth Watson (1958). The stability of the pinch. Proceedings of the Royal Society of London A Mathematical and Physical Sciences , 245 (1243) , 435-455. https://doi.org/10.1098/rspa.1958.0094

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DOI
10.1098/rspa.1958.0094