Confinement and stability of a crystal beams

The following is an analysis of the confinement and stability issues of a crystal beam. A method is described to determine the equilibrium configuration of a beam of highly charged particles. It is required that the beam has a uniform distribution in the direction of motion, which is stable and does not need therefore confinement with external means. It is shown that this can be obtained only for a relatively longitudinally compact beam. Confinement in the plane transverse to the direction of motion is obtained with external means, which also provide stability. It is important that particles are distributed so that the resulting space charge forces are linear with respect to the particle transverse coordinates