Hydromagnetic Instability in a Stellarator

Abstract

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...

Effect of a Limiter on Ohmic Discharges in the Heliotron D

“…10 ' 11 Qualitative agreement is found between the experiment and the theory of the kink mode. 9 Quantitatively, however, the experimental results for 7 0i/ * are lower than the theoretical values except for the m ~ Fig. 4, where the hatched regions indicate the unstable regions of the theory.…”

“…A similar phenomenon was observed in the Stellarator C with the I-3 winding. 9 Another feature of the experimental results is that the instability for [t F (a L )+ t QH (a L )]/2ij % i is not observed appreciably. This result is different from the experimental results obtained on the Wenderstein-IIb which has almost no shear.…”

Stability: multi-dimensional configurations

“…To answer this question one basically has to include the line bending j∂X/∂lj 2 term that was neglected in the evaluation of W. Sinclair et al (1965) have carried out such a calculation, the result being a generalized form of Suydam's criterion. To answer this question one basically has to include the line bending j∂X/∂lj 2 term that was neglected in the evaluation of W. Sinclair et al (1965) have carried out such a calculation, the result being a generalized form of Suydam's criterion.…”

Структура Магнитных Флуктуаций Плазмы В Торсатроне Ураган-3м При Редких Частотах Соударений

“…Кроме того, возможно возбуждение геодезических акустических мод GAM [2], тороидально индуцированных альфвеновских ТАЕ [3], различного типа бета-индуцированных альфвеновских BAE [4] и дрейфово-акустических BTG-мод [5], параметрических неустойчивостей, связанных с нагревом плазмы [6] и т. д. Также методы нагрева влияют на возбуждение дрейфовых волн [7], которые при конечных значениях β (отношение энергии плазмы к энергии удерживающего магнитного поля) могут сопровождаться флуктуациями магнитного поля. Наличие продольного тока в стеллараторной магнитной конфигурации может сопровождаться возбуждением токовых неустойчивостей (kinkи tearing-мод) [8].…”