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Publisher DOI: 10.1016/j.jcpx.2019.100036
arXiv ID: 1812.08117v2
Title: An arbitrary order time-stepping algorithm for tracking particles in inhomogeneous magnetic fields
Language: English
Authors: Tretiak, Krasymyr 
Ruprecht, Daniel  
Keywords: Boris integrator;Fusion reactor;High-order time integration;Particle tracking;Spectral deferred corrections;Mathematics - Numerical Analysis;Mathematics - Numerical Analysis;Computer Science - Computational Engineering; Finance; and Science;Computer Science - Numerical Analysis
Issue Date: 23-Aug-2019
Publisher: Elsevier
Source: Journal of Computational Physcs: X 4 (): 100036 (2018)
Journal: Journal of computational physics: X 
Abstract (english): 
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 St\"ormer-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.
DOI: 10.15480/882.3818
ISSN: 2590-0552
Document Type: Article
Funded by: Engineering and Physical Sciences Research Council EPSRC
More Funding information: This work was support by the Engineering and Physical Sciences Research Council EPSRC under grant EP/P02372X/1 “A new algorithm to track fast ions in fusion reactors”.
Peer Reviewed: Yes
License: CC BY 4.0 (Attribution) CC BY 4.0 (Attribution)
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