Analytical study of the conjecture rule for the combination of multipole effects in LHC

This paper summarizes the analytical investigation done on the conjecture law found by tracking for the effect on the dynamic aperture of the combination of two multipoles of various order. A one-dimensional model leading to an integrable system has been used to find closed formulae for the dynamic aperture associated with a fully distributed multipole. The combination has then been studied and the resulting expression compared with the assumed conjecture law. For integrated multipoles small with respect to the focusing strength, the conjecture appears to hold, though with an exponent different from the one expected by crude reasoning.