  In this paper, we rigorously analyze the energy, momentum and magnetic moment
behaviours of two splitting methods for solving charged-particle dynamics. The
near-conservations of these invariants are given for the system under constant
magnetic field or quadratic electric potential. By the approach named as
backward error analysis, we derive the modified equations and modified
invariants of the splitting methods and based on which, the near-conservations
over long times are proved. Some numerical experiments are presented to
demonstrate these long time behaviours.
