Author(s)

M. Itagaki, T. Ishimaru & K. Watanabe

Abstract

An efficient boundary element technique has been proposed to deal with a problem when geometry and boundary conditions have a rotational symmetry. In this technique, no boundary elements need to be defined on the symmetry surface. This idea has been applied to a problem of magnetic field in nuclear fusion plasma. A useful \“linear transformation” for the rotational symmetry in the toroidal direction has been derived in terms of the x-, y- and z-components of vector potential in a 3-D Cartesian coordinate system. Applying this linear transformation to the discretized set of boundary integral equations, one can drastically reduce the size of matrix, the number of unknowns and then computing cost. Also, accurate solutions can be expected. Results of test calculations demonstrate the validity of the present formulation. Keywords: boundary element method, rotational symmetry, vector potential, linear transformation, nuclear fusion plasma, Cauchy condition surface method, magnetic sensor. 1 Introduction The present work is a part of the authors’ research plan to develop an inverse analytic technique to identify the boundary shape of nuclear fusion plasma from signals of magnetic sensors located outside the plasma. For this purpose, the Cauchy condition surface (CCS) method [1] has already been established for a tokamak-type fusion device. The geometry of tokamak plasma is axisymmetric so that the analysis can be made in a 2-dimensional (2-D), r-z system. On the other hand, 3-D analyses are required for non-axisymmetric plasma, e.g., in a helical type device such as the Large Helical Device (LHD). The application of

Keywords

boundary element method, rotational symmetry, vector potential, linear transformation, nuclear fusion plasma, Cauchy condition surface method, magnetic sensor