A semianalytical aberration calculation method using polynomials and Lie algebra
Abstract
To investigate aberration coefficients up to order 11 or higher in rotationally symmetric magnetic fields, a semianalytical method is described. The field distribution and the trajectory of a charged particle are expressed by several polynomials to differentiate and integrate them analytically. The approximation error of the field can be reduced to less than 10 ^{13}. These polynomials are substituted in "interaction" Hamiltonian, and the aberration coefficients are obtained by Lie algebraic theory. An exponential model and Glaser's bellshaped model are used to compare the aberration coefficients above order 4.
 Publication:

Nuclear Instruments and Methods in Physics Research A
 Pub Date:
 August 1995
 DOI:
 10.1016/01689002(95)001581
 Bibcode:
 1995NIMPA.363..261M