Geometric Algorithms for Relativistic Dynamics

Dynamics of relativistic charged particles in external or self-consistent electromagnetic fields serves as the fundamental model underlying many subfields of physics. A series of geometric algorithms for relativistic and nonrelativistic systems have been systematically constructed, such as volume-preserving algorithms and explicit symplectic algorithms $^{\mathrm{1-3}}$. Taking advantage of the long-term conservativeness and accuracy of relativistic geometric algorithms, long-term simulations of runaway electrons in tokamak configurations have been carried out. And a new collisionless pitch-angle scattering process and better confinement of runaway electrons are discovered $^{\mathrm{4,5}}$. The Lorentz covariance of geometric algorithms are strictly defined and investigated for the first time. These geometric algorithms are building blocks for the recently developed structure-preserving geometric algorithms for the Vlasov-Maxwell system, e.g., the canonical and non-canonical PIC methods $^{\mathrm{6-8}}$. [1] R. Zhang et al., PoP 22, 044501 (2015). [2] Y. He et al., JCP 305, 172 (2016). [3] R. Zhang et al., CiCP 19, 1397. (2016) [4] J. Liu et al., NF 56, 064002 (2016). [5] Y. Wang et al., PoP 23, 062505 (2016). [6] J. Xiao et al., PoP 22, 112504 (2015). [7] H. Qin et al. NF 56, 014001 (2016). [8] He et al, PoP 22, 124503 (2015).