Collective emittance exchange with linear space charge forces and linear coupling.

We show that pronounced collective nonlinear behavior is present in a beam with linear coupling and space charge as described by the complete second order moment equations. The collective effects result in a shifted and broadened resonance condition as well as saturation effects in the emittance transfer. For slow stop-band crossing either the beam evolves along a skewed matched solution with full emittance exchange or the exchange is hindered by collective space charge effects, depending on the emittance ratio and direction of crossing.