存在初级象差下电子和离子光学系统中刘维定理的应用

在电子和离子光学理论(特别是象差理论)中,广泛地应用了矩阵的运算方法。本文讨论了旋转对称电子光学系统与重叠场(环形电场与非均匀磁场的叠加)离子光学系统中存在初级象差下的变换矩阵,证明了这些变换矩阵的行列式数值恒为1.这个普遍结论是刘维定理的具体应用。这对于电子和离子光学象差理论及计算机辅助设计具有一定意义。 关键词：

APPLICATION OF LIOUVILLE'S THEOREM TO ELECTRON AND ION OPTICAL SYSTEMS POSSESSING THE PRIMARY ABERRATIONS

The method of matrix calculations is widely applied in the theory of electron- and ion-optics, especially in the aberration theory. In the present paper, a rotationally symmetrical electron-optical system and an ion-optical system with crossed toroidal electric and inhomogeneous magnetic fields are treated respestively. The general transfer matrices for the above mentioned electron- and ion-optical systems possessing the primary aberrations are derived. As a direct consequence of Liouville's theorem, we prove that the determinant of the transfer matrix has the value 1 in the approximation up to the primary aberrations. This general conclusion is useful for the electron-and ion-optical a berration theory and the computer-aided design.