Components of the Magnetic Field from Interior and Exterior Sources in Toroidal Geometry

by Lazanja, David, Ph.D., COLUMBIA UNIVERSITY, 2011, 233 pages; 3451931


A fundamentally important problem of magnetically confined plasmas is to understand how changes in the external currents influence the physics inside the plasma volume. For plasmas confined to the shape of a torus, the total magnetic field on the outermost plasma surface has contributions due to exterior currents and due to interior plasma currents. This thesis proposes several methods to uniquely separate each contribution from the total field on the plasma surface. In the context of plasma physics, the separated information is useful in determining the linear plasma response. The methods are based on a solution to Laplace’s equation for the magnetic potential in general toroidal geometry, which is valid in the annular region outside the plasma where there are no currents. All methods are based on a Green’s function integral equation approach. The first method entails a direct evaluation of integral equation solutions for the magnetic potential and normal field component. The integrals contain singular integrands, and therefore a regularization procedure is required to achieve accurate solutions. The second method is an inverse method that requires the evaluation of the Dirichlet-to-Neumann map on a given toroidal surface. The method also requires the evaluation of singular integrals and, additionally, requires a matrix inversion. Finally, the third method is another integral equation inverse method. It is based on extending the solution for the potential due to exterior sources into the exterior annular region of the plasma, where boundary conditions are specified on the plasma. This is known to be an ill-posed problem in the sense of Hadamard [30]. The direct method provides the most robust approach and is the main contribution of this thesis, although the inverse methods may be useful under appropriate conditions.

Source TypeDissertation
SubjectsElectromagnetics; Plasma physics
Publication Number3451931

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