Emittance growth rates for displaced beams

Abstract

We analyze emittance growth rates for beams initially displaced in focusing channels. If the focusing force is slightly nonlinear, there is a gradual transfer of the potential energy of beam displacement into kinetic energy associated with emittance growth. We present explicit results for the emittance growthdistance as a function of the nonlinearity of the channel. These results will have practical importance for designers of accelerators and transport systems when setting realistic tolerances for initial beam alignment. These tolerances will depend on the nonlinearity and the length of the system.