ABSTRACT
Tracking codes using symplectic integration can be divided into two categories: those with the small angle approximations and those without. These codes are called "large machine" codes because it is traditionally for these machines that the small angle approximation has been working best. The code TEAPOT does not use the small angle approximation, but, unfortunately concocted for the defunct SSC, it misses several items needed in small machines. Another code called SAD, written in Japan, correctly includes large angle and fringe effects. These became necessary as the not so small "B-factories" started to display small machine diseases. The reason for deriving a Bend-Kick type integrator is grounded in the possibility that a straight magnet will be used to provide zeroth order bending to the beam—in other words, this magnet is located in a curved layout block. For both wigglers and solenoids the Hamiltonian can be written conveniently in Cartesian or cylindrical coordinates.
