Numerical-analytical algorithms for integrating the equations of motion of charged particles in electric fields are proposed and experimentally investigated. The need to develop such algorithms arose in the simulation of intense beams of charged particles in extended systems. A characteristic task is to determine, as far as possible, the beam expansion and its angular divergence at a considerable distance from the start (emitter) surface. The use of classical numerical algorithms did not give adequate results. Therefore, a proposal arose at each step of numerical integration to use an analytical solution of the equations of motion, making simplifying assumptions about electric fields. Simplifying assumptions within the numerical integration step, which provide sufficient accuracy and, at the same time, a simple solution, were as follows: in the longitudinal direction the field is assumed to be constant, and in the transverse direction - linear in the coordinate, which is characteristic of intense beams. An experimental comparison of numerical-analytical algorithms with numerical algorithms is given, which showed the advantage of the developed approach.
|Состояние||Опубликовано - 1 янв 2019|