Comment on “Symplectic integration of magnetic systems”: A proof that the Boris algorithm is not variational
One popular technique for the numerical time advance of charged particles interacting with electric and magnetic fields according to the Lorentz force law [1], [2], [3] and [4] is the Boris algorithm. Its popularity stems from simple implementation, rapid iteration, and excellent longterm numerical fidelity [1] and [5]. Excellent longterm behavior strongly suggests the numerical dynamics exhibit conservation laws analogous to those governing the continuous Lorentz force system [6]. Moreover, without conserved quantities to constrain the numerical dynamics, algorithms typically dissipate or accumulate important observables such as energy and momentum over long periods of simulated time [6]. Identification of the conservative properties of an algorithm is important for establishing rigorous expectations on the longterm behavior; energypreserving, symplectic, and volumepreserving methods each have particular implications for the qualitative numerical behavior [6], [7], [8], [9], [10] and [11].
 Authors:

^{[1]};
^{[1]};
^{[2]}
 Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
 Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Univ Sci & Technol China, Dept Modern Phys, Hefei 230026, Anhui, Peoples R China.
 Publication Date:
 Report Number(s):
 PPPL5109
Journal ID: ISSN 00219991; PII: S0021999115005884
 Grant/Contract Number:
 AC0209CH11466
 Type:
 Accepted Manuscript
 Journal Name:
 Journal of Computational Physics
 Additional Journal Information:
 Journal Volume: 301; Journal Issue: C; Journal ID: ISSN 00219991
 Publisher:
 Elsevier
 Research Org:
 Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
 Sponsoring Org:
 USDOE
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; Symplectic integration; Boris algorithm; Variational integrators; volumepreserving integrators; Computer Science; Physics
 OSTI Identifier:
 1256706
 Alternate Identifier(s):
 OSTI ID: 1247040
Ellison, C. L., Burby, J. W., and Qin, H.. Comment on “Symplectic integration of magnetic systems”: A proof that the Boris algorithm is not variational. United States: N. p.,
Web. doi:10.1016/j.jcp.2015.09.007.
Ellison, C. L., Burby, J. W., & Qin, H.. Comment on “Symplectic integration of magnetic systems”: A proof that the Boris algorithm is not variational. United States. doi:10.1016/j.jcp.2015.09.007.
Ellison, C. L., Burby, J. W., and Qin, H.. 2015.
"Comment on “Symplectic integration of magnetic systems”: A proof that the Boris algorithm is not variational". United States.
doi:10.1016/j.jcp.2015.09.007. https://www.osti.gov/servlets/purl/1256706.
@article{osti_1256706,
title = {Comment on “Symplectic integration of magnetic systems”: A proof that the Boris algorithm is not variational},
author = {Ellison, C. L. and Burby, J. W. and Qin, H.},
abstractNote = {One popular technique for the numerical time advance of charged particles interacting with electric and magnetic fields according to the Lorentz force law [1], [2], [3] and [4] is the Boris algorithm. Its popularity stems from simple implementation, rapid iteration, and excellent longterm numerical fidelity [1] and [5]. Excellent longterm behavior strongly suggests the numerical dynamics exhibit conservation laws analogous to those governing the continuous Lorentz force system [6]. Moreover, without conserved quantities to constrain the numerical dynamics, algorithms typically dissipate or accumulate important observables such as energy and momentum over long periods of simulated time [6]. Identification of the conservative properties of an algorithm is important for establishing rigorous expectations on the longterm behavior; energypreserving, symplectic, and volumepreserving methods each have particular implications for the qualitative numerical behavior [6], [7], [8], [9], [10] and [11].},
doi = {10.1016/j.jcp.2015.09.007},
journal = {Journal of Computational Physics},
number = C,
volume = 301,
place = {United States},
year = {2015},
month = {11}
}