On the consideration of interactions in the structures forming the axially symmetric beams of charged particles

The problem of calculating the Coulomb field of charged particle beam in the injection systems is considered. To calculate the internal field of the beam we use both numerical and analytical methods of solving boundary value problem for the Poisson equation. The first, numerical, method consists in solving the Poisson equation by the finite difference method for the beam field potential with the boundary conditions on the electrodes of the accelerating structure, which depend on the actual configuration of the structure. For the analytical method the axially symmetrical beam of charged particles is represented by a set of annular cylinders. At each cylinder, the transverse beam charge density is assumed to be constant, and the longitudinal density is modeled by a trigonometric polynomial. For each cylinder, the Poisson equation is solved analytically with boundary conditions for the potential in the metal tube of a constant radius. An effective algorithm with parallel computing is proposed for the analytical method of calculation of the internal field. Bibliogr. 11. Il. 4. Table 1.