Longitudinal space charge in final-focus systems for linear colliders

In the final-focus system of a linear collider, the effect of longitudinal space charge can be significant. A diverging or converging ultra-relativistic beam experiences a longitudinal space-charge force which is independent of the beam energy. This force, though weak and often neglected, causes an energy variation across the bunch which depends on the beam size, beam-pipe radius and bunch population and this may affect the chromatic correction of a beam line. Because of the inherent large chromaticity of a typical final-focus system, a very small energy variation, induced in the final focus, can lead to an intolerable increase of the spot size at the interaction point. The space-charge force, thus, gives rise to a limit on bunch intensity beyond which the resulting spot-size increase will degrade the collider performance. In this paper, we evaluate the effect of the longitudinal space charge and derive intensity limits for the three existing or proposed final foci.