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As the first step to analyze the orbit of the triton produced by the fusion reaction between the beam-injected deuteron and the deuteron in the bulk plasma, we developed the code to calculate the velocity and spatial profiles of the fusion products in the Large Helical Device (LHD) that properly treats the particle loss boundary and the velocity anisotropy of the triton at birth. The neutron emission and neutron counting rates calculated by the code were compared with experimental results. The experimental results are reproduced by the developed code when the bulk plasma density, including the impurity ion, was used.

In Large Helical Device experiments, independent low-order magnetic fluctuations due to the resistive interchange mode are commonly observed; investigating the characteristics of this instability is our ultimate goal. Two new methods for analyzing the single low-order instability in the stochastic region are developed. One method investigates it by constructing the initial single-mode perturbation. The other method investigates it by constructing a reference surface outside the last closed flux surface. The reference surface is necessary for constructing the coordinates that are used to extract the Fourier mode in the stochastic field line structure., source:https://doi.org/10.1585/pfr.8.2403157

In the previous 3D Cauchy-condition surface (CCS) method analysis to reconstruct the magnetic field profile in the Large Helical Device (LHD), one assumed an impractically large number of magnetic sensors, i.e., 440 field sensors and 126 flux loops. In the singular value decomposition (SVD) process employed in the CCS method, a gap is found in the magnitude of the singular values. The most accurate field results can be obtained if all the singular values smaller than the gap threshold are eliminated, independent of the number of boundary elements on the CCS and the number of sensors as well. With the reduction in the number of boundary elements, the required numbers of field sensors and flux loops are significantly reduced to 110 and 25, respectively, without losing the solution accuracy. They can be further reduced to 58 and 13 respectively if considering the symmetry of the field profile in the LHD. This result suggests the possibility of actual application to the LHD., source:https://doi.org/10.1585/pfr.8.1402134

As the first step to analyze the orbit of the triton produced by the fusion reaction between the beam-injected deuteron and the deuteron in the bulk plasma, we developed the code to calculate the velocity and spatial profiles of the fusion products in the Large Helical Device (LHD) that properly treats the particle loss boundary and the velocity anisotropy of the triton at birth. The neutron emission and neutron counting rates calculated by the code were compared with experimental results. The experimental results are reproduced by the developed code when the bulk plasma density, including the impurity ion, was used.

In boundary element methods, using double nodes at corners is a useful approach to uniquely define the normal direction of boundary elements. However, matrix equations constructed by conventional boundary integral equations (CBIEs) become singular under certain combinations of double node boundary conditions. In this paper, we analyze the singular conditions of the CBIE formulation for cases where the boundary conditions at the double node are imposed by combinations of Dirichlet, Neumann, Robin, and interface conditions. To address this singularity, we propose the use of hypersingular integral equations (HBIEs) for wave propagation problems that obey the Helmholtz equation. To demonstrate the applicability of HBIE, we compare three types of simultaneous equations: (i) CBIE, (ii) partial-HBIE where the HBIE is only applied to the double nodes at corners while the CBIE is applied to the other nodes, and (iii) full-HBIE where the HBIE is applied to all nodes. Based on our numerical results, we observe the following results. The singularity of the matrix equations for problems with any combination of boundary conditions can be resolved by both full-HBIEs and partial-HBIEs, and the partial-HBIE exhibits better accuracy than the full-HBIE. Furthermore, the computational cost of partial-HBIEs is smaller than that of full-HBIEs.