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Symplectic integrators with adaptive time step applied to runaway electron dynamics

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Abstract

Studying the dynamics of runaway electrons has theoretical and practical significance. As the system is highly relativistic, multi-scale and nonlinear, accurate and efficient numerical methods with long-term stability are necessary. In this paper, we develop symplectic methods with adaptive time step and discuss the choice of step-size functions in accordance with the simulation problems for runaway electrons. In the implementation, in order to explore the practical impact of runaway electron dynamics, we use the electromagnetic field and some parameters often used in the study of plasma problems. Numerical results show that the new derived symplectic methods with adaptive time step exhibit good invariant-preserving property and superior stability over longtime integration. Moreover, with appropriate adaptive technique, the numerical efficiency in simulations is improved apparently. They are illustrated in the numerical experiments.

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Funding

This research was supported by the National Natural Science Foundation of China (11771436, 11261140328, 11305171), by the CAS Program for Interdisciplinary Collaboration Team, the Foundation for Innovative Research Groups of the NNSFC (11321061), and the ITER-China Program (2014GB124005, 2015GB111003), JSPS-NRF-NSFC A3 Foresight Program in the field of Plasma Physics (NSFC-11261140328).

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Authors and Affiliations

  1. LSEC, ICMSEC, Academy of Mathematics and Systems Science, CAS, Beijing, 100190, China

    Yanyan Shi & Yajuan Sun

  2. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China

    Yanyan Shi & Yajuan Sun

  3. School of Mathematics and Physics, University of Science and Technology, Beijing, 100083, China

    Yang He

  4. Plasma Physics Laboratory, Princeton University, Princeton, NJ, 08543, USA

    Hong Qin

  5. Department of Engineering and Applied Physics, USTC, Hefei, 230026, Anhui, China

    Hong Qin & Jian Liu

  6. Key Laboratory of Geospace Environment, CAS, Hefei, 230026, Anhui, People’s Republic of China

    Jian Liu

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  1. Yanyan Shi
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  2. Yajuan Sun
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  3. Yang He
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  4. Hong Qin
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  5. Jian Liu
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Correspondence to Yajuan Sun.

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Shi, Y., Sun, Y., He, Y. et al. Symplectic integrators with adaptive time step applied to runaway electron dynamics. Numer Algor 81, 1295–1309 (2019). https://doi.org/10.1007/s11075-018-0636-6

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  • DOI: https://doi.org/10.1007/s11075-018-0636-6

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