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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[1] Boris J P 1970 Proceedings of the Fourth Conference on Numerical Simulation Plasmas (U.S. Government Printing Office, Washington D.C.) pp. 3-67 [2] Hairer E and Lubich C 2018 BIT Numer. Math. 58 969 [3] Qin H, Zhang S, Xiao J, Liu J, Sun Y and Tang W M 2013 Phys. Plasmas 20 084503 [4] Stoltz P H, Cary J R, Penn G and Wurtele J 2002 Phys. Rev. ST Accel. Beams 5 094001 [5] Qiang J 2017 Nucl. Instrum. Methods Phys. Res. 867 15 [6] Webb S D 2014 J. Comput. Phys. 270 570 [7] Khan M, Zafar A and Kamran M 2015 J. Fusion Energy 34 298 [8] Khan M, Schoepf K, Goloborod'Ko V and Sheng Z M 2017 J. Fusion Energy 36 40 [9] Ellison C L, Burby J W and Qin H 2015 J. Comput. Phys. 301 489 [10] Khan M, Khalid M, Kamran M and Khan R 2020 J. Fusion Energy 39 77 [11] Zhang S, Jia Y and Sun Q 2015 J. Comput. Phys. 282 43 [12] Hairer E, McLachlan R I and Skeel R D 2009 ESAIM: M2AN 43 631 [13] He Y, Zhou Z, Sun Y, Liu J and Qin H 2017 Phys. Lett. A 381 568 [14] Gómez A and Meiss J D 2002 Chaos 12 289 [15] Cheng C Q and Sun Y S 1989 Celest. Mech. Dyn. Astron 47 275 [16] Xia Z 1992 Ergod. Theory Dyn. Syst. 12 621 [17] Goldstein H, Poole C and Safko J 2002 Classical Mechanics 3rd edn (San Francisco: Addison-Wesley) [18] Henon M and Heiles C 1964 Astron. J. 69 73 [19] Teschl G 2012 Ordinary Differential Equations and Dynamical Systems, Graduate Studies in Mathematics (American Mathematical Society) Vol. 140 p. 295 [20] Zotos E E 2015 Nonlinear Dyn. 79 1665 [21] Hunter C 2000 Spectral Analysis of Orbits via Discrete Fourier Transforms in Observational Manifestation of Chaos in Astro-physical Objects, invited talks for a workshop held in Moscow, Sternberg Astronomical Institute, 28-29 August 2000, ed Fridman A M, Marov M Y and Miller R H (Dordrecht: Springer, 2002) pp. 83-99 [22] Voyatzis G and Ichtiaroglou S 1992 J. Phys. A: Math. Gen. 25 5931 |
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