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Parametric instability of the m = 1 mode in the dynamic stabilization of a plasma filament

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Journal of Applied Mechanics and Technical Physics Aims and scope

Abstract

We consider the parametric excitation of long-wave magnetohydrodynamic oscillations of the m = 1 type in a cylindrical plasma conductor with an alternating, longitudinal, high-frequency current. The plasma cylinder is placed in a constant longitudinal magnetic field and is enclosed in a conducting case. The problem is solved on the basis of the flexible filament model under the assumption of ideal conductivity of the plasma and the case. Hill's method is used to study the stability of the equation with periodic coefficients that describe the oscillations of the filament. Results of computer calculations of the stability increments of oscillations in the first four resonance zones for various values of the parameters of the system are given.

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Literature cited

  1. M. G. Nikulin, “Dynamic stabilization of a plasma filament in a longitudinal magnetic field,” Zh. Tekh. Fiz.,39, No. 12 (1969).

  2. M. G. Nikulin, “Parametric excitation of helical instability of a θ-pinch by a high-frequency longitudinal current,” Zh. Prikl. Mekhan. i Tekh. Fiz., No. 2 (1970).

  3. F. L. Ribe and W. B. Riesenfeld, “Unstable, transverse-displacement mode of a bumpy plasma column and its possible stabilization,” Phys. Fluids,11, No. 9 (1968).

  4. M. A. Vasilevskii, I. M. Roife, and E. V. Seredenko, “Investigation of the stability of a toroidal plasma filament with a high-frequency current in a longitudinal magnetic field,” International Conference on the Containment of Plasma in Closed Systems, Dubna (1969); Collection of Annotated Proceedings, Moscow (1969).

  5. E. T. Whittaker and G. N. Watson, A Course of Modern Analysis, Part 2, Cambridge (1946).

  6. V. D. Shafranov, “Stability of a cylindrical gaseous conductor in a magnetic field,” Atomnaya Énergiya, No. 5 (1956).

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Authors and Affiliations

  1. Moscow

    V. N. Beloozerov, V. V. Zhukov & M. G. Nikulin

Authors
  1. V. N. Beloozerov
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  2. V. V. Zhukov
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  3. M. G. Nikulin
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Additional information

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 42–46, July–August, 1972.

In conclusion the authors thank M. L. Levin for helpful discussions of the work.

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Beloozerov, V.N., Zhukov, V.V. & Nikulin, M.G. Parametric instability of the m = 1 mode in the dynamic stabilization of a plasma filament. J Appl Mech Tech Phys 13, 468–471 (1972). https://doi.org/10.1007/BF00850386

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  • DOI: https://doi.org/10.1007/BF00850386

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