The Evolution of the Charge Density Distribution Function for Spherically Symmetric System with Zero Initial Conditions

The evolution of the charge density distribution function is simulated for both the case of a uniformly charged sphere with zero initial conditions and for the case of a non-uniform charged sphere. For the case of a uniformly charged sphere, the comparison of a numerical result and an exact analytical solution, demonstrated the agreement between the results. The process of “scattering” of a charged system under the influence of its own electric field has been illustrated on the basis of both the particle-in-cell method and the solution of the Cauchy problem for vector functions of the electric field and vector velocity field of a charged medium.