Nonlinear phenomena in space–charge dominated beams

We discuss the effect of space charge on nonlinear dynamics issues of high-intensity beams in the approximation of 2D coasting beams. Space charge induces a coherent shift of the resonance conditions as well as nonlinear saturation of the emittance transfer, which is demonstrated by an octupolar nonlinear resonance. We find that the coherent effects and the collective “feedback” depend strongly on the distribution function. The problem of self-consistent resonance crossing is studied with the example of self-skewing. We demonstrate that space charge enforces a pronounced directionality in its effects on emittance exchange. This leads to “collective nonlinearity”, while the single-particle motion remains fully linear.