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 ch arged particle whose trajectory is parallel to the axis receives no ne t focusing from the periodic transverse forces arising from the axisym metric rf wave. However, if the lowest-order periodic transverse motio n of the particles is included, a net ponderomotive focusing force is obtained when the momentum transfer is averaged over a period of the m otion. Since this force is second order in the electric-field amplitud e, the resultant focusing can be non-negligible in high gradient struc tures. In order to produce and preserve high-brightness beams in rf li nacs it is necessary to obtain a better understanding of all the force s acting on the beam and the subsequent beam dynamics. To this end we examine the lowest-order ponderomotive rf focusing of electrons in axi symmetric standing- and traveling-wave linac structures. We obtain a g eneralized paraxial envelope equation which includes the effects of th e ponderomotive focusing and longitudinal acceleration to describe the transverse beam envelope evolution. The implications of our results o n beam dynamics in electron linacs are examined, and extensions of the results to positron and proton linacs are discussed.