扇形重叠场中三级离子轨迹理论(Ⅱ)——变换矩阵、刘维定理和转换矩阵

本文讨论了扇形重叠场的三级离子光学理论,给出了重叠场的三级变换矩阵,证明它们的行列式为1,从而刘维定理在三级近似计算中成立,引入了转换矩阵以实现变换矩阵在不同分散形式间的转化,对于径向三级离子轨迹及其斜率的展开式中的系数矩阵(S和H矩阵),推导了它们一些元素间的等式及对应关系,这些结果对于离子光学的理论研究和质谱仪器的实际设计有一定的意义。关键词：

ION OPTICAL THEORY FOR THE THIRD ORDER TRAJECTORY IN A CROSSED TOROIDAL ELECTRIC AND INHOMOGENEOUS MAGNETIC FIELD (II)——TRANSFER MATRIX, LIOUVILLE'S THEOREM AND TRANSFORM MATRIX

In this part, the ion optical theory for the third order trajectory in a crossed toroidal electric and inhomogeneous magnetic field is treated in detail. The transfer matrix are derived up to the third order. Consequently, for an ion optical system possessing the second and third order aberrations, the determinant of the transfer matrix is shown to be equal to 1. In order to transform the transfer matrix between different deviations the transform matrixes are derived. Some related equalities and corresponding relations for the elements of S and H matrixes are given. These results may be of use in designing mass spector meters.