The purpose of this paper is to investigate the use of the finite element (FE) method in calculating accurate field gradients to achieve good estimates of aberration coefficients in accelerator tubes.
Gradient fields up to third order are calculated using FE calculations with higher order basis functions. A commercial code with the ability to use high order basis functions was embedded within the MathCad system which provides a convenient interface for evaluating the aberration coefficients. Analytic and realistic models are used to test the methodology.
It is shown that the ability to use higher order FEs achieves sufficient accuracy and smoothness to allow the third order aberration coefficients to be determined with confidence.
The results demonstrate the importance of using higher order basis FEs in determining optical properties of accelerator tubes and other particle optical devices.
