Eigenfunctions of the transfer matrix in the presence of linear coupling

This paper presents an approach to computing the change in the linear orbit parameters, due to a perturbing field that couples the x and y motions, by computing the change in the eigenfunctions of the transfer matrix and then using the relationship between the eigenfunctions and the orbit parameters. This can be compared with the approach that computes the change in the transfer matrix and uses the relationship between the elements of the transfer matrix and the orbit parameters. For the case of coupled motion, the eigenfunction approach appears to be easier to apply than the transfer matrix approach, partly because the relationship between the transfer matrix and the linear orbit parameters is considerably more complicated in this case. Results are found for the change in the four eigenfunctions of the transfer matrix in the presence of linear coupling, and for the relationship between the eigenfunctions and the orbit parameters.<>