Open AccessAPPLICATION OF LIOUVILLE'S THEOREM TO ELECTRON AND ION OPTICAL SYSTEMS POSSESSING THE PRIMARY ABERRATIONS
Author(s) -
Jiye Ximen
Publication year - 1981
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.30.1318
Subject(s) - ion , physics , electron , matrix (chemical analysis) , toroid , electron optics , electron transfer , atomic physics , optics , quantum mechanics , materials science , plasma , chemistry , organic chemistry , composite material
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.