Discrete Calderon's projections on parallelepipeds and their application to computing exterior magnetic fields for FRC plasmas

Authors:
E. Kansa;U. Shumlak;S. Tsynkov
Affiliations:
Computational Sciences, LLC, 8000 Madison Blvd., Madison, AL 35758-2035, USA;Computational Sciences, LLC, 8000 Madison Blvd., Madison, AL 35758-2035, USA and Aerospace & Energetics Research Program, University of Washington, Box 352250, Seattle, WA 98195, USA;Computational Sciences, LLC, 8000 Madison Blvd., Madison, AL 35758-2035, USA and Department of Mathematics, North Carolina State University, Box 8205, Raleigh, NC 27695, USA
Venue:
Journal of Computational Physics
Year:
2013

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Abstract

Confining dense plasma in a field reversed configuration (FRC) is considered a promising approach to fusion. Numerical simulation of this process requires setting artificial boundary conditions (ABCs) for the magnetic field because whereas the plasma itself occupies a bounded region (within the FRC coils), the field extends from this region all the way to infinity. If the plasma is modeled using single fluid magnetohydrodynamics (MHD), then the exterior magnetic field can be considered quasi-static. This field has a scalar potential governed by the Laplace equation. The quasi-static ABC for the magnetic field is obtained using the method of difference potentials, in the form of a discrete Calderon boundary equation with projection on the artificial boundary shaped as a parallelepiped. The Calderon projection itself is computed by convolution with the discrete fundamental solution on the three-dimensional Cartesian grid.