Space charge effects with periodic focusing

The dielectric response of a charged particle beam to a periodic focusing field enhances the effective focusing strength of the channel, reducing the matched beam radius and affecting the motion of halo particles. The dielectric response depends on the shape of the beam, the type of focusing and the ratio of the plasma frequency of the beam to the frequency of the focusing. TRACE 3-D is used to find the change in the effective focusing strength for a uniform-density beam in a quadrupole channel, showing agreement with theory for enhancements in the effective focusing strength of up to about 10%.