Space charge effects on the third order coupled resonance

The effect of space charge on bunched beams has been the subject of numerous numerical and experimental studies in the first decade of 2000. Experimental campaigns performed at the CERN Proton Synchrotron in 2002 and at the GSI SIS18 in 2008 confirmed the existence of an underlying mechanism in the beam dynamics of periodic resonance crossing induced by the synchrotron motion and space charge. In this article we present an extension of the previous studies to describe the effect of space charge on a controlled coupled (2D) third order resonance. The experimental and simulation results of this latest campaign shed a new light on the difficulties of the 2D particle dynamics. We find striking experimental evidence that space charge and the coupled resonance create an unusual coupling in the phase space, leading to the formation of an asymmetric halo. Moreover, this study demonstrates a clear link between halo formation and fixed-lines.