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
BIT Numerical Mathematics – Springer Journals
Published: May 30, 2018
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