Paper Info
Title
An arbitrary order time-stepping algorithm for tracking particles in inhomogeneous magnetic fields.
Abstract
The Lorentz equations describe the motion of electrically charged particles in electric and magnetic fields and are used widely in plasma physics. The most popular numerical algorithm for solving them is the Boris method, a variant of the Störmer-Verlet algorithm. Boris method is phase space volume conserving and simulated particles typically remain near the correct trajectory. However, it is only second order accurate. Therefore, in scenarios where it is not enough to know that a particle stays on the right trajectory but one needs to know where on the trajectory the particle is at a given time, Boris method requires very small time steps to deliver accurate phase information, making it computationally expensive. We derive an improved version of the high-order Boris spectral deferred correction algorithm (Boris-SDC) by adopting a convergence acceleration strategy for second order problems based on the Generalised Minimum Residual (GMRES) method. Our new algorithm is easy to implement as it still relies on the standard Boris method. Like Boris-SDC it can deliver arbitrary order of accuracy through simple changes of runtime parameter but possesses better long-term energy stability. We demonstrate for two examples, a magnetic mirror trap and the Solev'ev equilibrium, that the new method can deliver better accuracy at lower computational cost compared to the standard Boris method. While our examples are motivated by tracking ions in the magnetic field of a nuclear fusion reactor, the introduced algorithm can potentially deliver similar improvements in efficiency for other applications.
Year
DOI
Venue
2019
10.1016/j.jcpx.2019.100036
Journal of Computational Physics: X
Keywords
Field
DocType
Boris integrator,Particle tracking,High-order time integration,Spectral deferred corrections,Fusion reactor
Residual,Order of accuracy,Magnetic field,Generalized minimal residual method,Magnetic mirror,Phase space,Algorithm,Lorentz transformation,Mathematics,Trajectory
Journal
Volume
ISSN
Citations 
4
2590-0552
0
PageRank 
References 
Authors
0.34
0
2
Name
Order
Citations
PageRank
Krasymyr Tretiak100.34
Daniel Ruprecht27110.02