[Table of Contents]

Plasma and Fusion Research

Volume 6, 2401028 (2011)

Regular Articles

A Numerical Method for Parallel Particle Motions in Gyrokinetic Vlasov Simulations
Shinya MAEYAMA, Akihiro ISHIZAWA1), Tomo-Hiko WATANABE1), Noriyoshi NAKAJIMA1), Shunji TSUJI-IIO and Hiroaki TSUTSUI
Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku 152-8550, Japan
1)
National Institute for Fusion Science, 322-6 Oroshi-cho, Toki 509-5292, Japan
(Received 15 December 2010 / Accepted 21 February 2011 / Published 1 July 2011)

Abstract

A semi-Lagrangian scheme is applied for the first time to computations of charged particle motions along magnetic field lines, to numerically solve the δf gyrokinetic equations in a flux tube geometry. This new solver adopted in the gyrokinetic Vlasov simulations has an advantage over the conventional Eulerian codes in calculating the parallel dynamics, because semi-Lagrangian schemes are free of the Courant-Friedrichs-Lewy (CFL) condition that restricts the time step size. A study of the accuracy of the parallel motion simulations reveals that numerical errors mainly stem from spatial (not temporal) discretization for realistic values of the grid spacing and time step, and it demonstrates the advantage of the semi-Lagrangian scheme. This novel numerical method is successfully applied to linear gyrokinetic simulations of the ion temperature gradient instability, where time steps larger than those restricted by the CFL condition can be employed.

Keywords

gyrokinetic simulation, semi-Lagrangian scheme, symplectic integrator

DOI: 10.1585/pfr.6.2401028

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References

  • [1] M. J. Pueschel, T. Dannert and F. Jenko, Comput. Phys. Commun. 181, 1428 (2010).
  • [2] V. Grandgirard et al., Plasma Phys. Control. Fusion 49, B173 (2007).
  • [3] T.-H. Watanabe and H. Sugama, Nucl. Fusion 46, 24 (2006).
  • [4] M. A. Beer, S. C. Cowley and G. W. Hammett, Phys. Plasmas 2, 2687 (1995).
  • [5] H. Yoshida, Phys. Lett. A 150, 262 (1990).
  • [6] T.-H. Watanabe and H. Sugama, Trans. Theory Stat. Phys. 34, 287 (2005).
  • [7] G. Farin, Curves and Surfaces for CAGD: A Practical Guide (Morgan Kaufmann, San Francisco, 2002) p. 106.
  • [8] Y. Imai and T. Aoki, J. Comp. Phys. 217, 453 (2006).
  • [9] F. Filbet and E. Sonnendrücker, Comput. Phys. Commun. 150, 247 (2003).
  • [10] C. C. Ober and J. N. Shadid, J. Comput. Phys. 195, 743 (2004).
  • [11] A. M. Dimits et al., Phys. Plasmas 7, 969 (2000).

This paper may be cited as follows:

Shinya MAEYAMA, Akihiro ISHIZAWA, Tomo-Hiko WATANABE, Noriyoshi NAKAJIMA, Shunji TSUJI-IIO and Hiroaki TSUTSUI, Plasma Fusion Res. 6, 2401028 (2011).