Explicit symplectic algorithms based on generating functions for relativistic charged particle dynamics in time-dependent electromagnetic field

摘要

Relativistic dynamics of a charged particle in time-dependent electromagneticfields has theoretical significance and a wide range of applications. It isoften multi-scale and requires accurate long-term numerical simulations usingsymplectic integrators. For modern large-scale particle simulations in complex,time-dependent electromagnetic field, explicit symplectic algorithms are muchmore preferable. In this paper, we treat the relativistic dynamics of aparticle as a Hamiltonian system on the cotangent space of the space-time, andconstruct for the first time explicit symplectic algorithms for relativisticcharged particles of order 2 and 3 using the sum-split technique and generatingfunctions.