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

JOURNAL OF COMPUTATIONAL PHYSICS

卷:403

Article

Albert, Christopher G.¹  Kasilov, Sergei, V^2,3  Kernbichler, Winfried² 

[1] Max Planck Inst Plasma Phys, Boltzmannstr 2, D-85748 Garching, Germany

[2] Graz Univ Technol, Inst Theoret & Computat Phys, Fus OAW, Petersgasse 16, A-8010 Graz, Austria

[3] Kharkov Inst Phys & Technol, Natl Sci Ctr, Inst Plasma Phys, Akad Skaya Str 1, UA-61108 Kharkov, Ukraine

关键词: Numerical integration;    Symplectic integration;    Hamiltonian systems;    Plasma;    Guiding-center dynamics;    Magnetic confinement;   

DOI  :  10.1016/j.jcp.2019.109065

来源: Elsevier

【 摘 要 】

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. (C) 2019 the Author(s). Published by Elsevier Inc. All rights reserved.

【 授权许可】

Free