  This paper is devoted to the numerical symplectic approximation of the
charged-particle dynamics (CPD) with arbitrary electromagnetic fields. By
utilizing continuous-stage methods and exponential integrators, a general class
of symplectic methods is formulated for CPD under a homogeneous magnetic field.
Based on the derived symplectic conditions, two practical symplectic methods up
to order four are constructed where the error estimates show that the proposed
second order scheme has a uniform accuracy in the position w.r.t. the strength
of the magnetic field. Moreover, the symplectic methods are extended to CPD
under non-homogeneous magnetic fields and three algorithms are formulated.
Rigorous error estimates are investigated for the proposed methods and one
method is proved to have a uniform accuracy in the position w.r.t. the strength
of the magnetic field. Numerical experiments are provided for CPD under
homogeneous and non-homogeneous magnetic fields, and the numerical results
support the theoretical analysis and demonstrate the remarkable numerical
behavior of our methods.
