Chaotic characteristics of electron motion in the static magnetic fields and self-fields of the electron beam

Abstract

In this paper We study the properties of electron motion when a nonneutral electron beam goes through a static magnetic field. The self-electronic and magnetic fields also affects on the test electron. The Hamiltonian equations of electron motion are deduced and the Poincare surface of section and the Lyapunov exponent are used to prove that the electron motion becomes chaotic when the fields are strong enough.