Vol. 1, No. 1, 2006

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Bifurcated equilibria and magnetic islands in tokamaks and stellarators

Paul R. Garabedian

Vol. 1 (2006), No. 1, 79–89

The magnetohydrodynamic variational principle is employed to calculate equilibrium and stability of toroidal plasmas without two-dimensional symmetry. Differential equations are solved in a conservation form that describes force balance correctly across islands that are treated as discontinuities. The method is applied to both stellarators and tokamaks, and comparison with observations is favorable in both cases. Sometimes the solution of the equations turns out not to be unique, and there exist bifurcated equilibria that are nonlinearly stable when other theories predict linear instability. The calculations are consistent with recent measurements of high values of the pressure in stellarators. For tokamaks we compute three-dimensionally asymmetric solutions that are subject to axially symmetric boundary conditions.

magnetic fusion, plasma physics, equilibrium and stability
Mathematical Subject Classification 2000
Primary: 82D10, 70K50, 82C40
Received: 16 August 2005
Revised: 21 December 2005
Accepted: 23 December 2005
Published: 8 May 2007
Paul R. Garabedian
Courant Institute of Mathematical Sciences
New York University
New York, NY 10012
United States