The purpose of this paper is to derive the on and off-axes magnetic field of a solenoid with the use of a novel method. We have found a solution for the Biot-Savart law by considering the solenoid with a stationary electric current. The results have
been compared to numerical simulations showing a good agreement.
Advanced technical solution for the design of a low perveance electron gun with a high quality beam dedicated to high power Ka-band klystrons is presented in this paper. The proposed electron gun can be used to feed linear accelerating structures at
36 GHz with an estimated input power of 20 MW, thus achieving an effective accelerating electric field in the (100-150) MV/m range. additionally, in the framework of the Compact Light XLS project, a short Ka-band accelerating structure providing an integrated voltage of at least 15 MV, has been proposed for bunch-phase linearization. For the klystron, a very small beam dimension is needed and the presented electron gun responds to this requirement. An estimate of the rotational velocity at beam edge indicates that the diamagnetic field due to rotational currents are small compared to the longitudinal volume. A detailed analysis of how this is arrived at, by compression of the beam, rotation in the magnetic field, and analysis of the subsequently generated diamagnetic field has been discussed.
