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Author(s):
N. Nakajima, K. Ichiguchi, M. Okamoto and R.L. Dewar
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Title:
Ballooning Modes in Heliotrons/Torsatrons
Date of publication:
Sep. 1996
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Key words:
ballooning, local shear, local curvature, heliotron, torsatron
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Abstract:
The characteristics of the high-n ballooning modes and the corresponding beta ( = kinetic pressure/magnetic pressure) limit are discussed in a planar-axis L = 2/M = 10 heliotron/torsatron with a large Shafranov shift ( L and M are the polarity and toroidal pitch number of helical coils, respectively). The exact incompressible high-n ballooning mode equation for three-dimensional equilibria is solved in the covering space (psi, eta, alpha) where psi and alpha are the labels of the flux surface and the magnetic field line, respectively, and eta is the coordinate along the magnetic field line (-infty < eta < infty). In three-dimensional equilibria, the eigenvalue generally depends on alpha: omega^2 = omega^2 (psi, theta_k, alpha) with theta_k the radial wave number. From the analyses of the local magnetic shear associated with the toroidal force balance, the physical mechanism is clarified why the high-n ballooning modes can be unstable even in the region with stellarator-like global magnetic shear. Such high-n modes have strong alpha-dependence of omega^2 for a peaked pressure profile giving Mercier stable equilibria. In contrast, a broad pressure profile allows high-n modes with weak alpha-dependence of omega^2. The relationship between the high-n and low-n ballooning modes and the related beta limit are also considered through the alpha-dependence of omega^2.
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