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Numerical treatment of charged particle dynamics in a magnetic field

Presented by: 
Ernst Hairer
Monday 28th October 2019 - 12:00 to 12:45
INI Seminar Room 2

Combining the Lorentz force equations with Newton's law gives a second
order dierential equation in space for the motion of a charged particle in a magnetic
eld. The most natural and widely used numerical discretization is the Boris algorithm,
which is explicit, symmetric, volume-preserving, and of order 2.
In a rst part we discuss geometric properties (long-time behaviour, and in particular
near energy conservation) of the Boris algorithm. This is achieved by applying standard
backward error analysis. Near energy conservation can be obtained also in situations,
where the method is not symplectic.
In a second part we consider the motion of a charged particle in a strong magnetic eld.
Backward error analysis can no longer be applied, and the accuracy (order 2) breaks
down. To improve accuracy we modify the Boris algorithm in the spirit of exponential
integrators. Theoretical estimates are obtained with the help of modulated Fourier
expansions of the exact and numerical solutions.
This talk is based on joint work with Christian Lubich, and Bin Wang.
Related publications (2017{2019) can be downloaded from

Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons