Canonicalization And Symplectic Simulation Of The Gyrocenter Dynamics In Time-independent Magnetic Fields
Authors: Ruili Zhang, Jian Liu, Yifa Tang, Hong Qin, Jianyuan Xiao and Beibei Zhu
Abstract: The gyrocenter dynamics of charged particles in time-independent magnetic fields is a noncanonical
Hamiltonian system. The canonical description of the gyrocenter has both theoretical
and practical importance. We provide a general procedure of the gyrocenter canonicalization,
which is expressed by the series of a small variable ϵ depending only on the parallel velocity u and
can be expressed in a recursive manner. We prove that the truncation of the series to any given
order generates a set of exact canonical coordinates for a system, whose Lagrangian approximates
to that of the original gyrocenter system in the same order. If flux surfaces exist for the magnetic
field, the series stops simply at the second order and an exact canonical form of the gyrocenter
system is obtained. With the canonicalization schemes, the canonical symplectic simulation of
gyrocenter dynamics is realized for the first time. The canonical symplectic algorithm has the
advantage of good conservation properties and long-term numerical accuracy, while avoiding numerical
instability. It is worth mentioning that explicitly expressing the canonical Hamiltonian in
new coordinates is usually difficult and impractical. We give an iteration procedure that is easy
to implement in the original coordinates associated with the coordinate transformation. This is
crucial for modern large-scale simulation studies in plasma physics. The dynamics of gyrocenters
in the dipole magnetic field and in the toroidal geometry are simulated using the canonical
symplectic algorithm by comparison with the higher-order non symplectic Runge-Kutta scheme.
The overwhelming superiorities of the symplectic method for the gyrocenter system are evidently
exhibited.
__________________________________________________
Submitted to: Physics of Plasmas (December 2013)
__________________________________________________
Download PPPL-4997 (pdf 266 KB 24 pp)
__________________________________________________