Brownian Dynamics of charged particles in a constant magnetic field

Numerical algorithms are proposed for simulating the Brownian dynamics of charged particles in an external magnetic field, taking into account the Brownian motion of charged particles, damping effect and the effect of magnetic field self-consistently. Performance of these algorithms is tested in terms of their accuracy and long-time stability by using a three-dimensional Brownian oscillator model with constant magnetic field. Step-by-step recipes for implementing these algorithms are given in detail. It is expected that these algorithms can be directly used to study particle dynamics in various dispersed systems in the presence of a magnetic field, including polymer solutions, colloidal suspensions and, particularly complex (dusty) plasmas. The proposed algorithms can also be used as thermostat in the usual molecular dynamics simulation in the presence of magnetic field.