Three-dimensional Cauchy-condition surface method to identify the shape of the last closed magnetic surface in the Large Helical Device

Abstract

Kurihara's Cauchy-condition surface (CCS) method, originally developed for axisymmetric tokamak plasma, has been expanded to reconstruct the 3-D magnetic field profile outside the non-axisymmetric plasma in the Large Helical Device (LHD). The boundary integral equations (BIE) in terms of 3-D vector potential for magnetic field sensors, flux loops and points along the CCS are solved simultaneously. In the BIE for a flux loop, the portions related to the fundamental solution are integrated along the loop. The rotational symmetry of the plasma is incorporated into the formulation to reduce the number of unknowns. The reconstructed magnetic field caused only by the plasma current agree fairly well with the reference solution for the LHD, while a good agreement is observed when adding the coil current effect to the magnetic field. The magnetic field line tracing using the reconstructed field indicates the plasma boundary (the outer surface of the stochastic region) precisely and the last closed magnetic surface agrees fairly well with the reference one