Test-Particle Simulation of Space Plasmas (Communications in Computational Physics, 2010)
Test-particle simulations provide a useful complement to the kinetic simulationsof 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 largenumber of degrees of freedom. Fluid or multiple moment approaches, however, providea description at the macroscopic level, in terms of relatively few physical parametersinvolving averages or moments of particle distribution functions. Ideally, fullykinetic descriptions should be done whenever possible. Due to their complexity, theuse 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 todescribe complex phenomena in multi-dimensional geometry with realistic boundaryconditions. Its main drawback is its inability to account for many phenomena takingplace on fine space or time scales, or phenomena involving nonlocal transport.Macroscopic approaches are also not adapted to describe large deviations from localequilibrium, such as the occurrence of particle beams or otherwise strong anisotropy.With the test-particle method, particle trajectories are calculated using approximatedfields obtained from a low level approach, such as multiple moments. Approximatefields can also be obtained from experiments or observations. Assuming that thesefields are representative of actual systems, various kinetic and statistical properties ofthe system can then be calculated, such as particle distribution functions and momentsthereof. In this paper, the test-particle method is discussed in the context of classicalstatistical physics of many-body interacting point particles. Four different formulationsof the method are presented, which correspond to four broad categories of theapplication encountered in the field of plasma physics and astronomy.