Phase stability analysis of Boris-like volume-preserving algorithms for charged particle orbit in tokamak plasmas

A class of Boris-like second-order volume-preserving algorithms (VPAs) for simulating charged particle motion in electromagnetic fields have been generalized to a rotating angle formulation by matrix notation. The phase stability of this class of VPAs has been analyzed by utilizing discrete Fourier transformations (DFT) technique. It is found that two prominent VPAs, namely the G_\texth^2 and the well-known Boris algorithm, exhibit optimal phase precision for high-frequency (gyro motion) and low-frequency dynamics (transit/bounce motion), respectively. These findings have been empirically verified through numerical experiments. The insights gained from this study enable the selection of an appropriate VPA for practical simulations based on the characteristic frequencies of specific physics problems, which can substantially enhance numerical accuracy and improve computational efficiency for long-term calculations.