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Title: Comment on “Symplectic integration of magnetic systems”: A proof that the Boris algorithm is not variational

Journal Article · · Journal of Computational Physics
 [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.

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].

Research Organization:
Princeton Plasma Physics Laboratory (PPPL), Princeton, NJ (United States)
Sponsoring Organization:
USDOE
Grant/Contract Number:
AC02-09CH11466
OSTI ID:
1256706
Alternate ID(s):
OSTI ID: 1247040
Report Number(s):
PPPL-5109; PII: S0021999115005884
Journal Information:
Journal of Computational Physics, Vol. 301, Issue C; ISSN 0021-9991
Publisher:
ElsevierCopyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 17 works
Citation information provided by
Web of Science

References (12)

Why is Boris algorithm so good? journal August 2013
Efficiency of a Boris-like integration scheme with spatial stepping journal September 2002
Boris push with spatial stepping journal July 2003
Volume-preserving integrators have linear error growth journal May 1998
Solution of the inverse problem of the calculus of variations journal January 1941
Symplectic integration of magnetic systems journal August 2014
Comment on “Symplectic integration of magnetic systems” by Stephen D. Webb [J. Comput. Phys. 270 (2014) 570–576] journal February 2015
Helmholtz's inverse problem of the discrete calculus of variations journal September 2013
Volume-preserving integrators journal October 1995
Volume-preserving algorithms for charged particle dynamics journal January 2015
Existence of invariant tori in volume-preserving diffeomorphisms journal September 1992
Ueber die physikalische Bedeutung des Prinicips der kleinsten Wirkung. journal January 1887

Cited By (8)

Long-term analysis of a variational integrator for charged-particle dynamics in a strong magnetic field journal January 2020
A Comprehensive Comparison of Relativistic Particle Integrators journal March 2018
Exponential energy-preserving methods for charged-particle dynamics in a strong and constant magnetic field preprint January 2018
High-order energy-conserving Line Integral Methods for charged particle dynamics text January 2019
Large-stepsize integrators for charged-particle dynamics over multiple time scales preprint January 2021
Energy behaviour of the Boris method for charged-particle dynamics journal May 2018
Efficient energy-preserving methods for charged-particle dynamics preprint January 2018
Explicit symplectic algorithms based on generating functions for charged particle dynamics journal July 2016

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