Abstract:
A mathematical model of an axially symmetric inhomogeneous beam of charged particles is considered. It is proposed to represent a beam as a set of charged hollow cylinders being in the circular metal tube of a constant radius. It is proposed to simulate the function of the beam charge density by an analytical function. By solving a boundary value problem for the Poisson equation the analytical formulas for intensity of the electrostatic field of a charged particle beam are obtained.
Keywords:mathematical modeling, accelerators of the charged particles, bunches of the charged particles, Kulon field of the charged bunches, calculation of an internal field of bunches.