The influence of axial magnetic field and self-fields in the electron gas column and electron beam with elliptical cross section is investigated. Further effects of cross section demotions and beam velocity on the electron rotating frequency are studied. It is shown that there are two solutions of fast and slow for electron rotating frequency. The obtained results are graphically presented. Besides the effects of axial magnetic field, self-fields, both planar wiggler magnetic field (PWMF) and helical wiggler magnetic field (HWMF) on trajectories of relativistic electron beam with elliptical cross section are investigated. By solving the motion equation for an electron in the considered fields, two equations for the average axial velocity and the function are calculated. The effects of elliptical cross section demotions and elliptical electron beam density are studied. The effects of cross-section demotions and elliptical electron beam density are graphically investigated and so the results are compared for elliptical and circular electron beams. It is shown that with decreasing of value of electron beam density transverse velocity of electron increases about 50%.
