Analytical transfer matrix of a quadrupole fringe

Abstract：

The analytical linear transfer matrices for different quadrupole fringes including quadratic, high order power and exponential models are deduced in this paper. As an example, the transfer matrices of the quadrupole BEPCⅡ/ 105Q are computed for the above three models and compared with hard edge and slice-by-slice models in cases of near 60° and 90° FODO cells. These models' results are much better than the hard edge model's, and can meet the requirement of accurate calculation.