Applied mathematics

On quasiperiodic beam of interacting particles dynamics modeling

I. D. Rubtsova

St. Petersburg State University, 199034, St. Petersburg, Russia Federation

Abstract: In this paper, the problems of modeling of intense charged particle beam dynamics in accelerating and focusing systems are considered. Longitudinal dynamics of quasiperiodic beam is described on a basis of integrodifferential model, suggested by D. A. Ovsyannikov. Smoothed particle interaction model is used under the assumption of beam spatial periodicity. Integral representation of Coulomb field is obtained. The system of integrodifferential equations describing beam evolution satisfies the conditions of solution existence and uniqueness. The assumptions are fulfilled to formulate trajectory ensemble optimal control problem. The simple method is proposed for testing of particle interaction simulation code. The method is based on Coulomb field approximation by trigonometric polynomial. The results obtained may be effectively used in solving problems of modeling and optimization of charged beam dynamics. Bibliogr. 20.

Keywords: mathematical modeling, intense charged particle beams, integrodifferential equations, quasiperiodic beam, trigonometric polynomial, code testing.

UDC: 621.384.6

Received: October 31, 2013