Extended transfer matrix through aligned solenoidal fields using the traditional formalism

摘要

The traditional transfer matrix used in particle accelerators has been modified to easily take into account a non-zero angular canonical momentum, without the hard edge approximation of the field. To this end, we reformulate the transfer matrix based on an existing method, but by using both the explicit real transformation matrix in the Larmor frame of the 4D transverse phase space, and the real 4D transfer matrix of a solenoidal field in this frame and in the laboratory frame. This reformulation allows to clearly identify differences with the traditional matrix when performing analytic inter-comparisons. The implementation is also easier to perform. A comparison with computer simulation further illustrates its usefulness.