| PHYSICS OF GASES, PLASMAS, AND ELECTRIC DISCHARGES |
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Energy behavior of Boris algorithm |
| Abdullah Zafar1,? and Majid Khan2 |
1 Department of Engineering and Applied Physics, University of Science and Technology of China, Hefei 230026, China;
2 Department of Physics, Quaid-i-Azam University, Islamabad 45320, Pakistan |
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Abstract Boris numerical scheme due to its long-time stability, accuracy and conservative properties has been widely applied in many studies of magnetized plasmas. Such algorithms conserve the phase space volume and hence provide accurate charge particle orbits. However, this algorithm does not conserve the energy in some special electromagnetic configurations, particularly for long simulation times. Here, we empirically analyze the energy behavior of Boris algorithm by applying it to a 2D autonomous Hamiltonian. The energy behavior of the Boris method is found to be strongly related to the integrability of our Hamiltonian system. We find that if the invariant tori is preserved under Boris discretization, the energy error can be bounded for an exponentially long time, otherwise the said error will show a linear growth. On the contrary, for a non-integrable Hamiltonian system, a random walk pattern has been observed in the energy error.
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Received: 17 August 2020
Revised: 27 November 2020
Accepted manuscript online: 08 December 2020
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PACS:
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52.25.Xz
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(Magnetized plasmas)
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52.20.Dq
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(Particle orbits)
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05.45.Pq
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(Numerical simulations of chaotic systems)
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Corresponding Authors:
Abdullah Zafar
E-mail: zafar@mail.ustc.edu.cn
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Cite this article:
Abdullah Zafar and Majid Khan Energy behavior of Boris algorithm 2021 Chin. Phys. B 30 055203
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