New Methods for Multiturn Injection into Synchrotrons

In Part I we derive equations for the matched betatron phase space acceptance polygon for the nth turn and for the phase area swept out by the septum. A variable rate of shifting of the equilibrium orbit past the septum is considered with the object being to maximize the accelerated charge subject to a constraint on the permissible beam cross section at full energy. In Part II we describe spiral stacking¿a method of systematic laying of successiveturn phase space ellipses along a logarithmic spiral in matched radial phase space; this results in uniformly dense packing of the beam with losses. The beam is injected above the median plane and placed along the spiral through a programmed tune shift and a programmed displacement of the equilibrium orbit.