A conducting limiter brings about equilibrium of a toroidal plasma by anchoring magnetic field lines. Charge separation arising from the curvature effect can be short circuited by the limiter. This way of achieving equilibrium is not possible if the charge separation current exceeds the maximum ion saturation current to the limiter. Experiments with the Model C stellarator are consistent with this model. An observed instability is related to the loss of equilibrium due to the excess charge separation current.
Kruskal and Tuck 1 (in a paper hereafter referred to as KT) have examined the influence of a longitudinal magnetic field on the instabilities of the pinch effect. The pinch effect is the confinement of a thin column of plasma by means of the magnetic field due to a high current discharge along the column. Instabilities in the form of lateral "buckling" of the column (in the absence of a longitudinal field) have been predicted theoretically 2 and are well known experimentally. In KT it was noted that when there is a uniform externally imposed longitudinal field much larger than the field of the discharge current, one should expect instabilities in the form of a lateral displacement of the plasma column into a helix of large pitch. At the wavelength of fastest growth the e-folding time approximates the time it takes a sound wave in the plasma to traverse the radius of the plasma column. In successive sections we (a) re-examine this problem under the conditions which might be expected to occur in the stellarator during ohmic heating, including the presence of external conductors; (6) apply this theory to the stellarator; (e) show that the external conductors are in fact unimportant; (d) discuss the important effects due to the finite length of the machine; (e) consider the effects of more general current distributions; and (/) give the relevant experimental results.It should be emphasized that the considerations of this paper apply only to stellarators in which the rotational transform 3 results from the large scale geometry of the tube (such as a Figure 8 shape) rather than from small local perturbation coils (such as helical windings). It is perhaps worth noting that the theoretical results of the following four sections are given in less condensed form elsewhere; 4 the appearance of instability and the dependence of the critical current, both on the confining field and on the direction of the plasma current, were predicted in this earlier work well in advance of the experimental confirmation. INFINITE CYLINDER THEORYWe start with the analysis of pinch instability under the conditions considered in KT, but now additionally taking into account the effect of a thin cylindrical sheet conductor coaxial with the plasma. Familiarity with KT is assumed.The material pressure, density and velocity of the plasma are denoted by p, p, and v, the magnetic and electric fields by В and E, the current and charge densities by j and e, the permeability and permittivity of space by щ> and «o. and the ratio of specific heats by y. (We employ MKS units throughout.) The equations we use for the interior of the plasma (treated as infinitely conductive) are Eqs. (1) through (8) of KT.At an interface between plasma and vacuum, n denotes the unit normal to the surface, directed into the plasma; ¡i, the normal velocity of the surface; j* and e*, the surface current density and surface charge density; brackets, the jump in the enclosed quantity upon crossing the surface from the vacuum into the plasma; a bar under a quantity, the arithmetic...
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