Symplectic integrators with adaptive time step applied to runaway electron dynamics

  • Yanyan Shi
  • Yajuan SunEmail author
  • Yang He
  • Hong Qin
  • Jian Liu
Original Paper


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.


Runaway electrons Symplectic methods Adaptive time step 


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Funding information

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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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Yanyan Shi
    • 1
    • 2
  • Yajuan Sun
    • 1
    • 2
    Email author
  • Yang He
    • 3
  • Hong Qin
    • 4
    • 5
  • Jian Liu
    • 5
    • 6
  1. 1.LSEC, ICMSEC, Academy of Mathematics and Systems ScienceCASBeijingChina
  2. 2.School of Mathematical SciencesUniversity of Chinese Academy of SciencesBeijingChina
  3. 3.School of Mathematics and PhysicsUniversity of Science and TechnologyBeijingChina
  4. 4.Plasma Physics LaboratoryPrinceton UniversityPrincetonUSA
  5. 5.Department of Engineering and Applied PhysicsUSTCHefeiChina
  6. 6.Key Laboratory of Geospace EnvironmentCASHefeiPeople’s Republic of China

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