Effect of space charge on linear coupling and gradient errors in high-intensity rings

We study the response of coasting beams in the presence of space charge to linear coupling as well as gradient errors, based on linearizing the self-consistent Vlasov-Poisson equation. We determine the coherent shift of the resonance conditions as well as the response on lattice errors in smooth approximation, but allowing for arbitrary tune and/or emittance ratios. A characteristic feature is cancellation between the external forces due to the lattice errors and the beam induced space-charge forces, if the resonance condition is satisfied for the (space-charge shifted) single-particle tunes. For the linear coupling mode and small tune split we also identify a parameter region, where spontaneous instability exists in addition to the resonance.