Explicit relativistic energy-conserving PIC scheme and conservative particle down-sampling

The absence of exact preservation of energy and other physically conserved quantities in PIC simulations is known to enable numerical heating, instabilities and other artefacts that must be restrained, sometimes at the cost of excessive computational demands. For example, the conservation of energy can be enforced in implicit relativistic or semi-implicit non-relativistic schemes. Highly scalable explicit relativistic PIC simulations commonly require high-order weighting, current smoothing and a large number of particles per cell, as well as small time and space steps that can be much smaller than the spatiotemporal scales of interest. Another example concerns the problem of down-sampling particle ensembles in case of growing number of particles due to ionization, pair production or other processes. Particle merging may smoothen particle distributions, while thinning may cause a local violation of conservation laws with difficult-to-assess consequences. We propose methods for solving the outlined problems. The first method provides a way to enforce an exact energy conservation in explicit relativistic PIC method and thereby eliminates the related excessive computational demands [Gonoskov arXiv:2302.01893 (2023)]. The second method provides a way to reduce the number of macroparticles without any systematic influence on distribution functions, while locally preserving any number of conserved quantities and central moments [Gonoskov Comput. Phys. Commun. 271, 108200 (2022)].