Gauge Properties Of The Guiding Center Variational Symplectic Integrator

J. Squire, H. Qin and W. Tang

关键词: Guiding-center Approximations;    Hamiltonian;    Computer Simulation;   

DOI  :  10.2172/1063125
RP-ID  :  PPPL-4741
PID  :  OSTI ID: 1063125

学科分类：物理（综合）

美国|英语

来源: SciTech Connect

【 摘 要 】

Recently, variational symplectic algorithms have been developed for the long-time simulation of charged particles in magnetic fields1-3. As a direct consequence of their derivation from a discrete variational principle, these algorithms have very good long-time energy conservation, as well as exactly preserving discrete momenta. We present stability results for these algorithms, focusing on understanding how explicit variational integrators can be designed for this type of system. It is found that for explicit algorithms an instability arises because the discrete symplectic structure does not become the continuous structure in the t ??? 0 limit. We examine how a generalized gauge transformation can be used to put the Lagrangian in the "antisymmetric discretization gauge," in which the discrete symplectic structure has the correct form, thus eliminating the numerical instability. Finally, it is noted that the variational guiding center algorithms are not electromagnetically gauge invariant. By designing a model discrete Lagrangian, we show that the algorithms are approximately gauge invariant as long as A and are relatively smooth. A gauge invariant discrete Lagrangian is very important in a variational particle-in-cell algorithm where it ensures current continuity and preservation of Gauss's law4.