PONDEROMOTIVE FOCUSING IN AXISYMMETRICAL RF LINACS

In many present and planned compact electron sources and linacs, very large rf accelerating fields are present in the linac structures. A charged particle whose trajectory is parallel to the axis receives no net focusing from the periodic transverse forces arising from the axisymmetric rf wave. However, if the lowest-order periodic transverse motion of the particles is included, a net ponderomotive focusing force is obtained when the momentum transfer is averaged over a period of the motion. Since this force is second order in the electric-field amplitude, the resultant focusing can be non-negligible in high gradient structures. In order to produce and preserve high-brightness beams in rf linacs it is necessary to obtain a better understanding of all the forces acting on the beam and the subsequent beam dynamics. To this end we examine the lowest-order ponderomotive rf focusing of electrons in axisymmetric standing- and traveling-wave linac structures. We obtain a generalized paraxial envelope equation which includes the effects of the ponderomotive focusing and longitudinal acceleration to describe the transverse beam envelope evolution. The implications of our results on beam dynamics in electron linacs are examined, and extensions of the results to positron and proton linacs are discussed.