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A high-order boris integrator. (English) Zbl 1349.78119

Summary: This work introduces the high-order Boris-SDC method for integrating the equations of motion for electrically charged particles in electric and magnetic fields. Boris-SDC relies on a combination of the Boris-integrator with spectral deferred corrections (SDC). SDC can be considered as preconditioned Picard iteration to compute the stages of a collocation method. In this interpretation, inverting the preconditioner corresponds to a sweep with a low-order method. In Boris-SDC, the Boris method, a second-order Lorentz force integrator based on velocity-Verlet, is used as a sweeper/preconditioner. The presented method provides a generic way to extend the classical Boris integrator, which is widely used in essentially all particle-based plasma physics simulations involving magnetic fields, to a high-order method. Stability, convergence order and conservation properties of the method are demonstrated for different simulation setups. Boris-SDC reproduces the expected high order of convergence for a single particle and for the center-of-mass of a particle cloud in a Penning trap and shows good long-term energy stability.

MSC:

78M25 Numerical methods in optics (MSC2010)
65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations
65L12 Finite difference and finite volume methods for ordinary differential equations
65L20 Stability and convergence of numerical methods for ordinary differential equations
78A35 Motion of charged particles
92C80 Plant biology
82D40 Statistical mechanics of magnetic materials

Software:

PFASST; RODAS; pySDC
PDFBibTeX XMLCite
Full Text: DOI arXiv Link

References:

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