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Advanced technical solution for the design of a low perveance electron gunwith a high quality beam dedicated to high power Ka-band klystrons is presentedin this paper. The proposed electron gun can be used to feed linearaccelerating structures at 36 GHz with an estimated input power of 20 MW, thusachieving an effective accelerating electric field in the (100-150) MV/m range.additionally, in the framework of the Compact Light XLS project, a shortKa-band accelerating structure providing an integrated voltage of at least 15MV, has been proposed for bunch-phase linearization. For the klystron, a verysmall beam dimension is needed and the presented electron gun responds to thisrequirement. An estimate of the rotational velocity at beam edge indicates thatthe diamagnetic field due to rotational currents are small compared to thelongitudinal volume. A detailed analysis of how this is arrived at, bycompression of the beam, rotation in the magnetic field, and analysis of thesubsequently generated diamagnetic field has been discussed.

Relativistic approach to a low perveance high quality matched beam for a high efficiency Ka-Band klystron