Scaling laws for crossing nonlinear space charge resonances

Intrinsic fourth order space charge resonances may occur in linear as well as in circular accelerators. The fourth order difference resonance ("emittance exchange" or "Montague" coupling-resonance) and the fourth order structure resonance lead to emittance degradation depending on the strength of space charge, the crossing rate through the resonance and the lattice. Based on fully self-consistent simulation with a 2D code in the coasting beam limit, we present scaling laws for the "Montague" resonance and for the fourth order structure resonance in terms of simple power law expressions.