A filtered two-step variational integrator for charged-particle dynamics in a moderate or strong magnetic field

Abstract This article is concerned with a new filtered two-step variational integrator for solving the charged-particle dynamics in a mildly nonuniform moderate or strong magnetic field with a dimensionless parameter $\varepsilon$ inversely proportional to the strength of the magnetic field. In the case of a moderate magnetic field ($\varepsilon =1$) second-order error bounds and long-time near-conservation of energy and momentum are obtained. Moreover, the proof of the long-term analysis is accomplished by the backward error analysis. For $0