Emittance compensation for magnetized beams

Emittance compensation is a well established technique [1] for minimizing the emittance of an electron beam from a RF photo-cathode gun. Longitudinal slices of a bunch have a small emittance, but due to the longitudinal charge distribution of the bunch and time dependent RF fields they are not focused in the same way, so that the direction of their phase ellipses diverges in phase space and the projected emittance is much larger. Emittance compensation reverses the divergence. At the location where the slopes of the phase ellipses coincide the beam is accelerated, so that the space charge forces are reduced. A recipe for emittance compensation is given in [2]. For magnetized beams (where the angular momentum is non-zero) such emittance compensation is not sufficient because variations in the slice radius lead to variations in the angular speed and therefore to an increase of emittance in the rotating frame. We describe a method and tools for a compensation that includes the beam magnetization.