  Self consistent analytic and numeric design for a set of electron guns with a
high beams quality to be used in high power Ka-band klystrons are presented in
this paper. The set of electron guns can be used in the high power Ka-band
klystrons in order to feed linear accelerating structures at 36 GHz with an
estimated 20 MW input power by achieving an effective accelerating electric
field in the (100-150) MV/m range. In the framework of the Compact Light XLS
project, a short Ka-band linearizer by working at 36 GHz able for providing an
integrated voltage of at least 15 MV is proposed for bunch-phase linearization.
In order to optimize the Ka-band klystrons efficiency for achieving 20 MW RF
output power, different electron guns and beam focusing channel designs are
examined and discussed in this paper.
