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An arbitrary order time-stepping algorithm for tracking particles in inhomogeneous magnetic fields
Citation Link: https://doi.org/10.15480/882.3818
Publikationstyp
Journal Article
Date Issued
2019-08-23
Sprache
English
Author(s)
TORE-DOI
Volume
4
Article Number
100036
Citation
Journal of Computational Physcs: X 4 (): 100036 (2018)
Publisher DOI
Scopus ID
ArXiv ID
Publisher
Elsevier
Peer Reviewed
true
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.
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.
Subjects
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
DDC Class
004: Informatik
510: Mathematik
Funding Organisations
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”.
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