The Case of Nonzero Initial Conditions in the Evolution of the Charge Density Distribution Function for a Spherically Symmetric System

Boris I. Sadovnikov, Alex A. Zhavoronkov

Faculty of Physics, Moscow State University, Moscow, Russian.
Moscow Institute of Physics and Technology, Dolgoprudny, Russian.

DOI: 10.4236/jamp.2014.27057                

Abstract

We explored the Cauchy problem for the evolution of the charge density distribution function for a spherically symmetric system with nonzero initial conditions. In our model, the evolution of the charge density distribution function is simulated for the case of a non-uniform charged sphere. The initial speed of the system is nonzero. The solution breaks down into two components: the first one describes the system’s motion as a whole and the second describes the process of the evolution of the charge density function under the influence of its own electric field in the center-of-mass system. In this paper we considered the characteristic features of the implementation of a difference scheme for numerical simulation. We also illustrate the process of “scattering” of a moving charged system under the influence of its own electric field on the basis of the solution of the Cauchy problem for vector functions of the electric field and vector velocity field of a charged medium.

Keywords

Cauchy Problem, Nonzero Initial Conditions, Charge Density Distribution

Conflicts of Interest

The authors declare no conflicts of interest.

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