LONGITUDINAL SPACE-CHARGE IN FINAL-FOCUS SYSTEMS FOR LINEAR COLLIDERS

In the final-focus system of a linear collider, the effect of longitud inal 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 n eglected, causes an energy variation across the bunch which depends on the beam size, beam-pipe radius and bunch population and this may aff ect the chromatic correction of a beam line. Because of the inherent l arge chromaticity of a typical final-focus system, a very small energy variation, induced in the final focus, can lead to an intolerable inc rease of the spot size at the interaction point. The space-charge forc e, thus, gives rise to a limit on bunch intensity beyond which the res ulting spot-size increase will degrade the collider performance. In th is paper, we evaluate the effect of the longitudinal space charge and derive intensity limits for the three existing or proposed anal foci.