Particle distributions for beam in electric field

In the present report an approach for determination of particle distribution density in analytical form for beam in electric field is presented. It was applied previously for beams in magnetic fields. The purpose of the report is to extend this approach on beams in electric field. For low current beam, the expressions for particle density are obtained in various cases. For intense beam, the integral equation for particle density in the space of first integrals of motion equations is proposed. The well known KV distribution is one of its solutions