Accelerator physics challenges in future linear colliders

At the present time, there are a number of future linear collider designs with a center-of-mass energy of 500 GeV or more that have luminosities in excess of 10/sup 34/ cm/sup -2/ s/sup -1/. Many of these designs are very advanced, however, to attain the high luminosity, the colliders require very small beam emittances, strong focusing, and very good stability. In this paper, some of the outstanding issues related to the small spot sizes are discussed. Although the different designs are based very different RF technologies, many of these problems are common to all designs.