(untitled) (Communications in Computational Physics, 2010)
Test-particle simulations provide a useful complement to the kinetic simulations of many-body systems and their approximate treatment with multiple moments. In a kinetic approach, systems are described at a microscopic level in terms of a large number of degrees of freedom. Fluid or multiple moment approaches, however, provide a description at the macroscopic level, in terms of relatively few physical parameters involving averages or moments of particle distribution functions. Ideally, fully kinetic descriptions should be done whenever possible. Due to their complexity, the use of these approaches is often not practical in many cases of interest. In comparison, the fluid approximation is much simpler to implement and solve. It can be used to describe complex phenomena in multi-dimensional geometry with realistic boundary conditions. Its main drawback is its inability to account for many phenomena taking place on fine space or time scales, or phenomena involving nonlocal transport. Macroscopic approaches are also not adapted to describe large deviations from local equilibrium, such as the occurrence of particle beams or otherwise strong anisotropy. With the test-particle method, particle trajectories are calculated using approximated fields obtained from a low level approach, such as multiple moments. Approximate fields can also be obtained from experiments or observations. Assuming that these fields are representative of actual systems, various kinetic and statistical properties of the system can then be calculated, such as particle distribution functions and moments thereof. In this paper, the test-particle method is discussed in the context of classical statistical physics of many-body interacting point particles. Four different formulations of the method are presented, which correspond to four broad categories of the application encountered in the field of plasma physics and astronomy.