Abstract
In the theoretical investigation of the dynamic stabilization of a current-carrying plasma filament by a high-frequency multipole magnetic field it is usually assumed that the cross section of the filament has a circular form in equilibrium [1, 2]. This considerably simplifies the calculations but it does not correspond to reality, since the surface of the plasma must be fluted in the multipole field. An attempt to estimate the influence of the deformation of the filament cross section on its stability against bending in the special case of quadrupole field was made in [3], in which the parameters were determined of the elliptical cross section corresponding to a plasma filament with current in a quadrupole field and an expression was found for the electrodynamic force acting on the filament in the case of long-wavelength kink perturbations. However, this force was calculated incorrectly in [3]. In the present paper a study is made of the equilibrium and stability of a current-carrying plasma filament against kink perturbations in the general case of a multipole stabilizing field. Under the assumption that the flute depth is small, the equilibrium form of the cross section of the current-carrying plasma filament in the multipole magnetic field is found and the components of the force exerted by the field on the perturbed filament are calculated. It is shown that the external field interacts with the current in the perturbed filament only in the case of a quadrupole field. The results are discussed in connection with the problem of multipole dynamical stabilization of a z pinch against kink perturbations.
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S. M. Osovets, “Dynamics stabilization of a plasma coil,” Zh. Éksp. Teor. Fiz.,39, No. 2 (1960).
M. L. Levin and M. S. Rabinovich, “Strong focusing method for stabilization of straight and toroidal discharges,” Zh. Tekh. Fiz.,33, No. 2 (1963).
F. L. Ribe, Effect of an Oscillating Quadrupole Field on Kink Modes of a Screw Pinch, Los Alamos Rept. 1081-MS (1969).
M. G. Nikulin, “Stabilization of a plasma filament with alternating current by a quadrupole magnetic field,” Prikl. Mekh. Tekh. Fiz., No. 6 (1968).
D. V. Orlinskii, “Interaction of a straight plasma filament with an alternating magnetic field of quadrupole configuration,” At. Énerg.,18, No. 4 (1965).
P. R. Forman, A. Haberstich, H. J. Karr, J. A. Phillips, and A. E. Schofield, “Dynamic stabilization of a linear z pinch by a magnetic quadrupole,” Phys. Fluids,14, No. 3 (1971).
S. M. Osovets and V. I. Sinitsyn, “Dynamic stabilization of a plasma filament,” Zh. Éksp. Teor. Fiz.,48, No. 4 (1965).
G. Berge, “On the problem of dynamic stabilization,” Plasma Phys. and Controlled Nucl. Fusion. Res., Vol. 2, Vienna (1969).
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, No. 1, pp. 23–29, January–February, 1974.
I thank S. M. Osovets and M. L. Levin for discussing the paper.
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Nikulin, M.G. Equilibrium and stability of a z pinch in a multipole magnetic field. J Appl Mech Tech Phys 15, 18–23 (1974). https://doi.org/10.1007/BF00850722
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DOI: https://doi.org/10.1007/BF00850722