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Application of Lie Algebra in Constructing Volume-Preserving Algorithms for Charged Particles Dynamics

Part of: Hamiltonian and Lagrangian mechanics Lie algebras and Lie superalgebras Lie groups

Published online by Cambridge University Press:  17 May 2016

Ruili Zhang ,
Jian Liu ,
Hong Qin ,
Yifa Tang ,
Yang He  and
Yulei Wang
Ruili Zhang*
Affiliation:
Department of Modern Physics and School of Nuclear Science and Technology, University of Science and Technology of China, Hefei, Anhui 230026, China
Jian Liu*
Affiliation:
Department of Modern Physics and School of Nuclear Science and Technology, University of Science and Technology of China, Hefei, Anhui 230026, China
Hong Qin*
Affiliation:
Department of Modern Physics and School of Nuclear Science and Technology, University of Science and Technology of China, Hefei, Anhui 230026, China Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08543, USA
Yifa Tang*
Affiliation:
LSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
Yang He*
Affiliation:
Department of Modern Physics and School of Nuclear Science and Technology, University of Science and Technology of China, Hefei, Anhui 230026, China
Yulei Wang*
Affiliation:
Department of Modern Physics and School of Nuclear Science and Technology, University of Science and Technology of China, Hefei, Anhui 230026, China
*
*Corresponding author. Email addresses:rlzhang@ustc.edu.cn (R. Zhang), jliuphy@ustc.edu.cn (J. Liu), hongqin@ustc.edu.cn (H. Qin), tyf@lsec.cc.ac.cn (Y. Tang), heyang14@ustc.edu.cn (Y. He), wyulei@mail.ustc.edu.cn (Y. Wang)
*Corresponding author. Email addresses:rlzhang@ustc.edu.cn (R. Zhang), jliuphy@ustc.edu.cn (J. Liu), hongqin@ustc.edu.cn (H. Qin), tyf@lsec.cc.ac.cn (Y. Tang), heyang14@ustc.edu.cn (Y. He), wyulei@mail.ustc.edu.cn (Y. Wang)
*Corresponding author. Email addresses:rlzhang@ustc.edu.cn (R. Zhang), jliuphy@ustc.edu.cn (J. Liu), hongqin@ustc.edu.cn (H. Qin), tyf@lsec.cc.ac.cn (Y. Tang), heyang14@ustc.edu.cn (Y. He), wyulei@mail.ustc.edu.cn (Y. Wang)
*Corresponding author. Email addresses:rlzhang@ustc.edu.cn (R. Zhang), jliuphy@ustc.edu.cn (J. Liu), hongqin@ustc.edu.cn (H. Qin), tyf@lsec.cc.ac.cn (Y. Tang), heyang14@ustc.edu.cn (Y. He), wyulei@mail.ustc.edu.cn (Y. Wang)
*Corresponding author. Email addresses:rlzhang@ustc.edu.cn (R. Zhang), jliuphy@ustc.edu.cn (J. Liu), hongqin@ustc.edu.cn (H. Qin), tyf@lsec.cc.ac.cn (Y. Tang), heyang14@ustc.edu.cn (Y. He), wyulei@mail.ustc.edu.cn (Y. Wang)
*Corresponding author. Email addresses:rlzhang@ustc.edu.cn (R. Zhang), jliuphy@ustc.edu.cn (J. Liu), hongqin@ustc.edu.cn (H. Qin), tyf@lsec.cc.ac.cn (Y. Tang), heyang14@ustc.edu.cn (Y. He), wyulei@mail.ustc.edu.cn (Y. Wang)
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Abstract

Volume-preserving algorithms (VPAs) for the charged particles dynamics is preferred because of their long-term accuracy and conservativeness for phase space volume. Lie algebra and the Baker-Campbell-Hausdorff (BCH) formula can be used as a fundamental theoretical tool to construct VPAs. Using the Lie algebra structure of vector fields, we split the volume-preserving vector field for charged particle dynamics into three volume-preserving parts (sub-algebras), and find the corresponding Lie subgroups. Proper combinations of these subgroups generate volume preserving, second order approximations of the original solution group, and thus second order VPAs. The developed VPAs also show their significant effectiveness in conserving phase-space volume exactly and bounding energy error over long-term simulations.

Keywords

Lie algebraLie groupvolume-preserving algorithmcharged particles dynamics

MSC classification

Secondary: 17B81: Applications to physics 22E70: Applications of Lie groups to physics; explicit representations 70H33: Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction 70H40: Relativistic dynamics
Type
Research Article
Information
Communications in Computational Physics , Volume 19 , Issue 5 , May 2016 , pp. 1397 - 1408
Copyright
Copyright © Global-Science Press 2016 

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