A filtered Boris algorithm for charged-particle dynamics in a
strong magnetic field
Ernst Hairer, Christian Lubich, and Bin Wang,
Abstract. A modification of the standard Boris algorithm, called filtered
Boris algorithm, is proposed for the numerical integration of the equations of motion
of charged particles in a strong non-uniform magnetic field in the asymptotic scaling
known as maximal ordering. With an appropriate choice of filters, second-order error
bounds in the position and in the parallel velocity, and first-order error bounds in
the normal velocity are obtained with respect to the scaling parameter.
The proof compares the modulated Fourier expansions of the exact and the numerical
solutions. Numerical experiments illustrate the error behaviour of the filtered Boris
algorithm.
Key Words. Charged particle, magnetic field, guiding center, Boris algorithm,
filter functions, exponential integrator, modulated Fourier expansion.