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Solution of Grad–Shafranov equation by the method of fundamental solutions

Published online by Cambridge University Press:  19 February 2014

D. Nath  and
M. S. Kalra
D. Nath*
Affiliation:
Nuclear Engineering and Technology Program, Indian Institute of Technology Kanpur, Kanpur 208 016, UP, India
M. S. Kalra
Affiliation:
Nuclear Engineering and Technology Program, Indian Institute of Technology Kanpur, Kanpur 208 016, UP, India
*
†Email address for correspondence: dnath@iitk.ac.in
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Abstract

In this paper we have used the Method of Fundamental Solutions (MFS) to solve the Grad–Shafranov (GS) equation for the axisymmetric equilibria of tokamak plasmas with monomial sources. These monomials are the individual terms appearing on the right-hand side of the GS equation if one expands the nonlinear terms into polynomials. Unlike the Boundary Element Method (BEM), the MFS does not involve any singular integrals and is a meshless boundary-alone method. Its basic idea is to create a fictitious boundary around the actual physical boundary of the computational domain. This automatically removes the involvement of singular integrals. The results obtained by the MFS match well with the earlier results obtained using the BEM. The method is also applied to Solov'ev profiles and it is found that the results are in good agreement with analytical results.

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Type
Papers
Information
Journal of Plasma Physics , Volume 80 , Issue 3 , June 2014 , pp. 477 - 494
Copyright
Copyright © Cambridge University Press 2014 

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