Effects of magnetic focusing on longitudinal emittance and energy dispersion of an intense short accelerating electron pulse

Magnetic focusing by coils appropriately disposed and fed has been widely proposed and used as a transverse emittance recovering technique, in particular for the accelerating electron beam of FEL RF-photoinjectors. After a new investigation of the effect on radial emittance, we address the question of the consequences of magnetic focusing on longitudinal emittance and energy dispersion. With the theoretical method described in a previous article, the radial, transverse, longitudinal, and 3D-rms emittances of the whole beam pulse are computed from the cathode onwards, for sample beam parameters, and various magnetic field intensities. Obviously beneficial in terms of beam radius, magnetic focusing seems to induce only a moderate anti transitory radial emittance reduction and, on the other hand, a strong degradation of longitudinal emittance and energy dispersion