Symplectic integration with non-canonical quadrature for guiding-center orbits in magnetic confinement devices

Christopher G. Albert*, Sergei V. Kasilov, Winfried Kernbichler

*Corresponding author for this work

Research output: Contribution to journalArticle

Abstract

We study symplectic numerical integration of mechanical systems with a Hamiltonian specified in non-canonical coordinates and its application to guiding-center motion of charged plasma particles in magnetic confinement devices. The technique combines time-stepping in canonical coordinates with quadrature in non-canonical coordinates and is applicable in systems where a global transformation to canonical coordinates is known explicitly but its inverse is not. A fully implicit class of symplectic Runge-Kutta schemes has recently been introduced and applied to guiding-center motion by Zhang et al. (2014) [9]. Here a generalization of this approach with emphasis on semi-implicit partitioned schemes is described together with methods to enhance performance, in particular avoiding evaluation of non-canonical variables at full time steps. For application in toroidal plasma confinement configurations with nested magnetic flux surfaces a global canonicalization of coordinates for the guiding-center Lagrangian by a spatial transform is presented that allows for pre-computation of the required map in a parallel algorithm in the case of time-independent magnetic field geometry. Guiding-center orbits are studied in stationary magnetic equilibrium fields of an axisymmetric tokamak and a realistic three-dimensional stellarator configuration. Superior long-term properties of symplectic methods are demonstrated in comparison to a conventional adaptive Runge-Kutta scheme. Finally statistics of fast fusion alpha particle losses over their slowing-down time are computed in the stellarator field on a representative sample, reaching a speed-up of the symplectic Euler scheme by more than a factor three compared to usual Runge-Kutta schemes while keeping the same statistical accuracy and linear scaling with the number of computing threads.
Original languageEnglish
Article number109065
Number of pages23
JournalJournal of Computational Physics
Volume403
DOIs
Publication statusPublished - 15 Feb 2020

Keywords

  • Guiding-center dynamics
  • Hamiltonian systems
  • Magnetic confinement
  • Numerical integration
  • Plasma
  • Symplectic integration

ASJC Scopus subject areas

  • Computational Mathematics
  • Physics and Astronomy(all)
  • Applied Mathematics
  • Numerical Analysis
  • Computer Science Applications
  • Modelling and Simulation
  • Physics and Astronomy (miscellaneous)

Fields of Expertise

  • Information, Communication & Computing

Cooperations

  • NAWI Graz

Fingerprint Dive into the research topics of 'Symplectic integration with non-canonical quadrature for guiding-center orbits in magnetic confinement devices'. Together they form a unique fingerprint.

Cite this