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Author(s):
C.C. Hegna and N. Nakajima
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Title:
On the Stability of Mercier and Ballooning Modes in Stellarator Configurations
Date of publication:
Oct. 1997
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Key words:
ballooning modes, Mercier criterion, Stellarators
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Abstract:
The stability properties of pressure driven ballooning and Mercier modes in general stellarator configurations are studied. A method originally introduced to study tokamak stability by J.M. Greene and M. S. Chance [Nucl. Fusion 21, 453 (1981)] is generalized to three-dimensional systems. This method introduces a way to examine various stability physics mechanisms by using a perturbation theory. Variations in equilibrium quantities are introduced to a localized region whose amplitude is small but whose cross field derivative is large. Consistent with this ordering, changes in the magnetic coordinates and metric elements are calculated using Boozer coordinates. In the general case, the set of equilibria are characterized by two free functions, which are usually chosen to be the local variation of pressure and rotational transform profiles. In this way, a stability space for Mercier and ballooning modes is generated which is parameterized by the average shear and pressure gradient at the magnetic surface of interest. If an additional currentless constraint is imposed, the change in the local rotational transform profile and the local pressure gradient are related; in this limit only one free function parameterizes the set of equilibria. A different way to view the stability information is plot the stability curves in a space parameterized by the local pressure gradient and the field-line-averaged parallel current. When viewed using these plots, it's possible to show that a second stability regime always exists for Mercier modes at sufficiently large pressure gradient.
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