Effect of local linear coupling on linear and nonlinear observables in circular accelerators

Operation of particle accelerators and correction of unavoidable magnet or alignment errors critically depend on the assessment of both global and local observables such as tune or resonance driving terms. With most of the observables being a sum of different error sources, careful disentangling is necessary in order to establish an optimal correction and allow for smooth operation. In the LHC, linear coupling has been proven to have a major impact on the beam dynamics and is taken to be one of the main sources of uncertainty when establishing corrections. In this paper an approach to evaluate the change of the Hamiltonian terms with linear coupling is presented. The validity of derived equations is demonstrated on a number of observables and benchmarked against simulations.