Geodesic
Model for investigation the physical properties of the system of charged particles taking into account the external magnetic field and friction force
Matematičeskoe modelirovanie, Tome 31 (2019) no. 11, pp. 132-144

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In the present work, a modified Verlet numerical scheme was 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 friction force. The particle dynamics are also affected by interparticle interaction and an external uniform magnetic field. To obtain the Verlet scheme, 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 were 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 with taking into account electromagnetic fields. The paper solved a test problem for which particle trajectories obtained based on the conventional and modified Verlet scheme for different values, both the friction parameter and the magnetic field parameter, were 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 Verlet scheme there is such dependence.
Keywords: molecular dynamics method, Verlet algorithm, external homogenous magnetic field, dusty plasma. 
@article{MM_2019_31_11_a9,
     author = {K. N. Dzhumagulova and T. S. Ramazanov and R. U. Masheyeva and M. N. Jumagulov},
     title = {Model for investigation the physical properties of the system of charged particles taking into account the external magnetic field and friction force},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {132--144},
     publisher = {mathdoc},
     volume = {31},
     number = {11},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2019_31_11_a9/}
}
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K. N. Dzhumagulova; T. S. Ramazanov; R. U. Masheyeva; M. N. Jumagulov. Model for investigation the physical properties of the system of charged particles taking into account the external magnetic field and friction force. Matematičeskoe modelirovanie, Tome 31 (2019) no. 11, pp. 132-144. http://geodesic.mathdoc.fr/item/MM_2019_31_11_a9/