Page 11 - Electrostatic quasi-neutral formulation of global cross-separatrix particle simulation in field-reversed configuration geometry

Physics of Plasmas ARTICLE
FIG. 10. Comparisons of three different mesh operations are shown: (a) the partial derivative with respect to the radial coordinate R, (b) the partial derivative with respect to the axial coordinate Z, and (c) the Laplacian. A test function of form f ðw; SÞ / cosðkw wÞ cosðkS SÞ is shown in the real space mesh (top left) and in the field-aligned mesh (top right). A mesh operation is calculated in the cylindrical mesh and is shown in the real space mesh (mid-left) and in the field-aligned mesh (mid-right). The same mesh operation is calculated in the field-aligned mesh and is shown in the real space mesh (bottom left) and in the field-aligned mesh (bottom right).
support of the Norman Rostoker Fellowship (Grant No. TAE- 200441). Further development and simulations used the resources of DOE Office of Science User Facilities: National Energy Research Scientific Computing Center (DOE Contract No. DE- AC02–05CH11231) and Innovative and Novel Computational Impact on Theory and Experiment (INCITE) program at Argonne Leadership Computing Facility at Argonne National Laboratory (DOE Contract No. DE-AC02–06CH11357).
APPENDIX: FIELD-ALIGNED MESH OPERATION BENCHMARKS
A. Grid operations
Using test functions, comparisons are made for the mesh oper- ations in the field-aligned and regular meshes. The results for the
field-aligned mesh operations are from ANC directly while the results from the regular mesh operations are from Python using the NumPy library.
In Figs. 10(a) and 10(b), the partial derivatives with respect to the radial and axial directions, respectively, are shown. These partial derivatives are used for the calculation of the electric field from the self-consistently solved electrostatic potential, which is then used to push simulation particles. The field-aligned mesh operations agree with the regular mesh operations both qualita- tively and quantitatively.
In ANC, either the full Laplacian or the perpendicular Laplacian can be used to solve for the self-consistent electrostatic potential from the quasi-neutrality equation. In Fig. 10(c), the full Laplacian is shown. The field-aligned mesh operation agrees with the regular mesh operations both qualitatively and quantitatively.
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Phys. Plasmas 27, 082504 (2020); doi: 10.1063/5.0012439 Published under license by AIP Publishing
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