Model for Investigating the Physical Properties of a System of Charged Particles Taking into Account the External Magnetic Field and Friction Force

Abstract

In the present work, a numerical modified Verlet scheme (MVS) is obtained. This scheme is intended to solve the equations of motion of charged particles immersed in an external stationary environment and a uniform magnetic field, for example, charged particles of a condensed substance in a buffer plasma (dusty plasma). The influence of the environment on the particle dynamics is described by the friction force. The particle dynamics are also affected by interparticle interaction and an external uniform magnetic field. To obtain the Verlet scheme (VS), the coordinates and velocities of the particles are decomposed into a Taylor series, taking into account the Lorentz force and the friction force. All Taylor series expansion terms that give the same order of accuracy are taken into account. In the obtained numerical scheme, the time step of modeling does not depend on the magnitude of the magnetic field but is determined only by the internal physical properties of the system under consideration, which is important when modeling an ensemble of charged particles taking electromagnetic fields into account. The paper solves a test problem for which particle trajectories obtained based on the conventional and modified VS for different values, both the friction parameter and the magnetic field parameter, are compared. Based on the analysis of the dependence of the maximum relative deviation of the coordinate on the time step, the time step is independent of the magnetic field in the Taylor expansion scheme, while in the inverse VS it is dependent.