Exact charge conservation scheme for Particle-in-Cell simulations for a big class of form-factors

As an alternative to solving of Poisson equation in Particle-in-Cell methods, a new construction of current density exactly satisfying continuity equation in finite differences is developed. This procedure called density decomposition is proved to be the only possible linear procedure for defining the current density associated with the motion of a particle. Density decomposition is valid at least for any n-dimensional form-factor which is the product of one-dimensional form-factors. The algorithm is demonstrated for parabolic spline form-factor.