Longitudinal Space Charge in Nal-focus Systems for Linear Colliders

In the nal-focus system of a linear collider, the e ect of longitudinal space charge can be signi cant. 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 a ect the chromatic correction of a beam line. Because of the inherent large chromaticity of a typical nal-focus system, a very small energy variation, induced in the nal 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 e ect of the longitudinal space charge and derive intensity limits for three existing or proposed nal foci.