Parameter study of the invisible long straight section for synchrotrons

A symmetric inseretion containing an unusually long unobstructed drift space is described. A consequence of its identity transfer properties in the radial plane (2π betatron phase advance) and its transverse reflection properties in the vertical plane (π betatron phase advance) is its invisibility, neither disturbing the betatron oscillation in either plane for particles of synchronous energy nor disturbing the closed (equilibrium) orbit properties for particles of different energy. Because of the different phase advances in the two planes, the insertion can be designed so that all of its six quadrupole magnets lie at the extreme ends of the insertion. This leaves all of the drift space, excepting only that portion required for coil terminations, etc., in a single unobstructed drift space. A thorough parameter study with linear and aberration properties through third order is reported.