Finite pressure ballooning mode stability in toroidal equilibria
We examine the effect of finite pressure on the ballooning instability in toroidal MHD equilibria of steep boundary stellarators and tokamaks. Ballooning modes tend to arise near the place where the local shear vanishes and the normal curvature (the curvature component perpendicular to the flux surface, pointing away from the magnetic axis) is negative. We will show how the pressure gradient determines the position of the shearless points, and demonstrate in detail how this effect explains the existence of second stability in tokamaks. For large aspect ratio circular cross-section tokamaks the second stability condition is found to scale as ..cap alpha.. = const S/sup 1.25/. Stellarators are inherently more stable, due to the negative vacuum shear which at moderate pressure gradients allows the zero shear point to localize on the inner side of the flux surface. However, at high pressure gradients the Pfirsch-Schlueter current produces a positive mean shear when the total toroidal current on a flux surface is zero. This causes the zero shear point to localize on the outer edge, near the vertical extremes of the flux surface. This causes the zero shear point to localize on the outer edge, near the vertical extremes of the flux surface. This effect, together with helical contributions to the helical curvature, allows for ballooning instability to arise. At higher pressure gradients, with zero net toroidal current, an unstable ballooning mode which localizes to within a helical period always arises where the normal curvature is unfavorable.
- Research Organization:
- Texas Univ., Austin (USA). Inst. for Fusion Studies
- DOE Contract Number:
- FG05-80ET53088
- OSTI ID:
- 6957113
- Report Number(s):
- DOE/ET/53088-263; IFSR-263; ON: DE87004483
- Resource Relation:
- Other Information: Portions of this document are illegible in microfiche products
- Country of Publication:
- United States
- Language:
- English
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