Energy behaviour of the Boris method for charged-particle dynamics

Energy behaviour of the Boris method for charged-particle dynamics BIT Numer Math https://doi.org/10.1007/s10543-018-0713-1 Energy behaviour of the Boris method for charged-particle dynamics 1 2 Ernst Hairer · Christian Lubich Received: 13 July 2017 / Accepted: 18 May 2018 © Springer Science+Business Media B.V., part of Springer Nature 2018 Abstract The Boris algorithm is a widely used numerical integrator for the motion of particles in a magnetic field. This article proves near-conservation of energy over very long times in the special cases where the magnetic field is constant or the electric potential is quadratic. When none of these assumptions is satisfied, it is illustrated by numerical examples that the numerical energy can have a linear drift or its error can behave like a random walk. If the system has a rotational symmetry and the magnetic field is constant, then also the momentum is approximately preserved over very long times, but in a spatially varying magnetic field this is generally not satisfied. Keywords Boris algorithm · Charged particle · Magnetic field · Energy conservation · Backward error analysis · Modified differential equation Mathematics Subject Classification 65L06 · 65P10 · 78A35 · 78M25 1 Introduction For a particle with position x (t ) ∈ R moving in an electro-magnetic field, Newton’s http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png BIT Numerical Mathematics Springer Journals

Energy behaviour of the Boris method for charged-particle dynamics

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Publisher
Springer Netherlands
Copyright
Copyright © 2018 by Springer Science+Business Media B.V., part of Springer Nature
Subject
Mathematics; Computational Mathematics and Numerical Analysis; Numeric Computing; Mathematics, general
ISSN
0006-3835
eISSN
1572-9125
D.O.I.
10.1007/s10543-018-0713-1
Publisher site
See Article on Publisher Site

Abstract

BIT Numer Math https://doi.org/10.1007/s10543-018-0713-1 Energy behaviour of the Boris method for charged-particle dynamics 1 2 Ernst Hairer · Christian Lubich Received: 13 July 2017 / Accepted: 18 May 2018 © Springer Science+Business Media B.V., part of Springer Nature 2018 Abstract The Boris algorithm is a widely used numerical integrator for the motion of particles in a magnetic field. This article proves near-conservation of energy over very long times in the special cases where the magnetic field is constant or the electric potential is quadratic. When none of these assumptions is satisfied, it is illustrated by numerical examples that the numerical energy can have a linear drift or its error can behave like a random walk. If the system has a rotational symmetry and the magnetic field is constant, then also the momentum is approximately preserved over very long times, but in a spatially varying magnetic field this is generally not satisfied. Keywords Boris algorithm · Charged particle · Magnetic field · Energy conservation · Backward error analysis · Modified differential equation Mathematics Subject Classification 65L06 · 65P10 · 78A35 · 78M25 1 Introduction For a particle with position x (t ) ∈ R moving in an electro-magnetic field, Newton’s

Journal

BIT Numerical MathematicsSpringer Journals

Published: May 30, 2018

References

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