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Publication# Stability of the N = 1 Ideal Internal Kink for Large Aspect Ratio Shafranov Equilibria

Abstract

Stability limits for the ideal internal kink mode are calculated analytically for the Shafranov current profile using the large aspect ratio expansion. For equilibria with q(a) > 2 and circular cross-section, the maximum stable poloidal beta is below 0.1. In the absence of a conducting wall, an equilibrium with q(a) < 2 is unstable at arbitrarily small positive poloidal-beta or shear inside the q = 1 surface. The effects of non-circularity are discussed and quantitative results are given for elliptic cross-sections.

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Plasma stability

The stability of a plasma is an important consideration in the study of plasma physics. When a system containing a plasma is at equilibrium, it is possible for certain parts of the plasma to be disturbed by small perturbative forces acting on it. The stability of the system determines if the perturbations will grow, oscillate, or be damped out. In many cases, a plasma can be treated as a fluid and its stability analyzed with magnetohydrodynamics (MHD).

Cross section (geometry)

In geometry and science, a cross section is the non-empty intersection of a solid body in three-dimensional space with a plane, or the analog in higher-dimensional spaces. Cutting an object into slices creates many parallel cross-sections. The boundary of a cross-section in three-dimensional space that is parallel to two of the axes, that is, parallel to the plane determined by these axes, is sometimes referred to as a contour line; for example, if a plane cuts through mountains of a raised-relief map parallel to the ground, the result is a contour line in two-dimensional space showing points on the surface of the mountains of equal elevation.

Conic section

A conic section, conic or a quadratic curve is a curve obtained from a cone's surface intersecting a plane. The three types of conic section are the hyperbola, the parabola, and the ellipse; the circle is a special case of the ellipse, though it was sometimes called as a fourth type. The ancient Greek mathematicians studied conic sections, culminating around 200 BC with Apollonius of Perga's systematic work on their properties. The conic sections in the Euclidean plane have various distinguishing properties, many of which can be used as alternative definitions.

Ontological neighbourhood

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2018