An Analytic Approach to the off-Momentum Closed Orbit in Storage Rings

The non-linear equation for the off-momentum closed orbit is solved analytically by using two independent approaches. Firstly expanding the solution with respect to the small parameter ¿=¿/p0 up to the first order in ¿ and secondly by using a new type of linearization procedure. The structure is made of LEP-type octants containing 32 regular cells (¿=900) with bending magnets, quadrupoles and four sextupole families, as well as two dispersion suppressors at both lattice ends and straight sections where the on-momentum ¿-function vanishes (see Fig.1). For the computations we replace the actual lattice elements of the structure by thin lenses with superimposed quadrupoles and sextupoles, which is a good approximation for LEP. All our results are compared with numerical computations, mainly with MAD [1]. While the first order theory works well up to ¿ = 1%, the linearization results are very accurate even at ¿ = 1.8%.