Explicit structure-preserving geometric particle-in-cell algorithm in curvilinear orthogonal coordinate systems and its applications to whole-device 6D kinetic simulations of tokamak physics

Jianyuan XIAO (肖建元); Hong QIN (秦宏)

doi:10.1088/2058-6272/abf125

Plasma Science and Technology > 2021 > 23(5): 55102-055102. > DOI: 10.1088/2058-6272/abf125

Jianyuan XIAO (肖建元), Hong QIN (秦宏). Explicit structure-preserving geometric particle-in-cell algorithm in curvilinear orthogonal coordinate systems and its applications to whole-device 6D kinetic simulations of tokamak physics[J]. Plasma Science and Technology, 2021, 23(5): 55102-055102. DOI: 10.1088/2058-6272/abf125

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Explicit structure-preserving geometric particle-in-cell algorithm in curvilinear orthogonal coordinate systems and its applications to whole-device 6D kinetic simulations of tokamak physics

¹ School of Nuclear Science and Technology, University of Science and Technology of China, Hefei 230026, People's Republic of China
² Plasma Physics Laboratory, Princeton University, Princeton, NJ 08543, United States of America

Funds: J Xiao was supported by the the National MCF Energy R&D Program (No. 2018YFE0304100), National Key Research and Development Program (Nos. 2016YFA0400600, 2016YFA0400601 and 2016YFA0400602), and National Natural Science Foundation of China (Nos. 11905220 and 11805273). J Xiao developed the algorithm and the SymPIC code and carried out the simulation on Tianhe 3 prototype at the National Supercomputer Center in Tianjin and Sunway Taihulight in the National Supercomputer Center in Wuxi. H Qin was supported by the U.S. Department of Energy (DE-AC02-09CH11466). H Qin contributed to the physical study of the self-consistent kinetic equilibrium and the KBMs.

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Received Date: January 13, 2021
Revised Date: March 21, 2021
Accepted Date: March 22, 2021

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Abstract

Abstract

Explicit structure-preserving geometric particle-in-cell (PIC) algorithm in curvilinear orthogonal coordinate systems is developed. The work reported represents a further development of the structure-preserving geometric PIC algorithm achieving the goal of practical applications in magnetic fusion research. The algorithm is constructed by discretizing the field theory for the system of charged particles and electromagnetic field using Whitney forms, discrete exterior calculus, and explicit non-canonical symplectic integration. In addition to the truncated infinitely dimensional symplectic structure, the algorithm preserves exactly many important physical symmetries and conservation laws, such as local energy conservation, gauge symmetry and the corresponding local charge conservation. As a result, the algorithm possesses the long-term accuracy and fidelity required for first-principles-based simulations of the multiscale tokamak physics. The algorithm has been implemented in the SymPIC code, which is designed for high-efficiency massively-parallel PIC simulations in modern clusters. The code has been applied to carry out whole-device 6D kinetic simulation studies of tokamak physics. A self-consistent kinetic steady state for fusion plasma in the tokamak geometry is numerically found with a predominately diagonal and anisotropic pressure tensor. The state also admits a steady-state sub-sonic ion flow in the range of 10 km s⁻¹, agreeing with experimental observations and analytical calculations Kinetic ballooning instability in the self-consistent kinetic steady state is simulated. It is shown that high-n ballooning modes have larger growth rates than low-n global modes, and in the nonlinear phase the modes saturate approximately in 5 ion transit times at the 2% level by the E × B flow generated by the instability. These results are consistent with early and recent electromagnetic gyrokinetic simulations.
- curvilinear orthogonal mesh,
- charge-conservative,
- particle-in-cell,
- symplectic algorithm,
- whole-device plasma simulation

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Explicit structure-preserving geometric particle-in-cell algorithm in curvilinear orthogonal coordinate systems and its applications to whole-device 6D kinetic simulations of tokamak physics