A new Monte Carlo code based on particle tracing using real coordinates has been developed to properly treat the re-entering particles that repeatedly pass in and out of the last closed flux surface (LCFS). The particle loss due to the charge-exchange reaction has also been taken into account in this code. We apply this new code to the analysis of high-energy particles produced by tangential neutral beams (NBs) of the large helical device (LHD). It is confirmed that reasonable solutions of distribution functions are obtained for particles produced by the tangential-NBs. It is also confirmed that the effect of the particle orbit and the charge-exchange loss on the distribution function is properly included. The shapes of the distribution functions of particles, produced by the tangential-NBs in two temperature cases (1 keV and 0.1 keV), are the same. It is found that the re-entering particles play an important role in the analyses of the distribution function of particles produced by the NBs.

High-energy particles in a finite beta plasma of the Large Helical Device (LHD) are numerically traced in a real coordinate system. We investigate particle orbits by changing the beta value and/or the magnetic field strength. No significant difference is found in the particle orbit classifications between the vacuum magnetic field and the finite beta plasma cases. The deviation of a banana orbit from the flux surfaces strongly depends on the beta value, although the deviation of the orbit of a passing particle is independent of the beta value. In addition, the deviation of the orbit of the passing particle, rather than that of the banana-orbit particles, depends on the magnetic field strength. We also examine the effect of re-entering particles, which repeatedly pass in and out of the last closed flux surface, in the finite beta plasma of the LHD. It is found that the number of re-entering particles in the finite beta plasma is larger than that in the vacuum magnetic field. As a result, the role of reentering particles in the finite beta plasma of the LHD is more important than that in the vacuum magnetic field, and the effect of the charge-exchange reaction on particle confinement in the finite beta plasma is large.

The three-dimensional (3-D) Cauchy condition surface (CCS) method code, 'CCS3D', is now under development to reconstruct the 3-D magnetic field profile outside a non-axisymmetric fusion plasma using only magnetic sensor signals. A new "twisted CCS" has been introduced, whose elliptic cross section rotates with the variation in plasma geometry in the toroidal direction of a helical type device. Independent of the toroidal angle, this CCS can be placed at a certain distance from the last closed magnetic surface (LCMS). With this new CCS, it is found through test calculations for the Large Helical Device that the numerical accuracy in the reconstructed field has been improved. Further, the magnetic field line tracing indicates the LCMS more precisely than with the use of the axisymmetric CCS. A new idea to determine the LCMS numerically has also been proposed.

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 nonaxisymmetric 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.

A new type of boundary element method has been applied to solve the Grad-Shafranov equation and to give a distribution of magnetic flux function in a Tokamak nuclear fusion device. The quantity