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 Φ 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 $50\mathrm{\%}$.

研究了椭圆截面电子气柱和电子束中轴向磁场和自场的影响。进一步研究了横截面降级和电子束速度对电子旋转频率的影响。结果表明，电子旋转频率有快和慢两种解。获得的结果以图形方式呈现。除了轴向磁场的影响外，还研究了自场、平面摆动磁场（PWMF）和螺旋摆动磁场（HWMF）对椭圆截面相对论电子束轨迹的影响。通过求解所考虑场中电子的运动方程，计算了平均轴向速度和函数 Φ 的两个方程。研究了椭圆截面降级和椭圆电子束密度的影响。以图形方式研究了横截面降级和椭圆电子束密度的影响，因此对椭圆和圆形电子束的结果进行了比较。结果表明，随着电子束密度值的减小，电子的横向速度增加约$50\mathrm{\%}$.