本文用单粒子近似方法,讨论了在空间电荷自电磁场和理想“电子感应加速器”型外磁场的作用下,椭圆截面电子环(严格地说,应为电子-离子环)中一个电子的振荡方程。这里,圆筒形器壁效应的修正,用无限细线电子环在无限长圆筒形理想导体壁上的镜像场进行近似。线性化的电子振荡方程,给出了电子坏径向和轴向的聚焦条件。在相对论情况下,电子环内一定量的正离子可以起到自聚焦作用。电子环的自场产生一个扩张力,为了把电子环束缚在一定的轨道上,外磁场就必须增大。 In this paper, the single-particle approximation method is used to discuss the oscillation equation of an electron in the elliptical cross-section electron ring (strictly speaking, the electron-ion ring) under the effect of the space charge self-magnetic field and the ideal external electron field of the " . Here, the correction of the cylindrical wall effect is approximated by the mirror image field of an infinitely thin electron ring on an infinitely long cylindrical ideal conductor wall. The linearized electronic oscillation equation gives the electron radial and axial focusing conditions. In the case of relativity, a certain amount of positive ions in the electron ring can act as self-focusing. The electronic ring generates an expansion force from the field, in order to tie the electronic ring in a certain orbit, the external magnetic field must be increased.