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Title: 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 long-term numerical fidelity [1] and [5]. Excellent long-term 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 long-term behavior; energy-preserving, symplectic, and volume-preserving methods each have particular implications for the qualitative numerical behavior [6], [7], [8], [9], [10] and [11].
 [1] ;  [1] ;  [2]
  1. Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
  2. Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Univ Sci & Technol China, Dept Modern Phys, Hefei 230026, Anhui, Peoples R China.
Publication Date:
OSTI Identifier:
Report Number(s):
Journal ID: ISSN 0021-9991; PII: S0021999115005884
Grant/Contract Number:
Accepted Manuscript
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 301; Journal Issue: C; Journal ID: ISSN 0021-9991
Research Org:
Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
Sponsoring Org:
Country of Publication:
United States
97 MATHEMATICS AND COMPUTING; Symplectic integration; Boris algorithm; Variational integrators; volume-preserving integrators; Computer Science; Physics