The production of high spectral brilliance radiation from electron beam sources depends critically on the electron beam qualities. One must obtain very high electron beam brightness, implying simultaneous high peak current and low emittance. These attributes are enabled through the use of very high field acceleration in a radio-frequency (rf) photoinjector source. Despite the high fields currently utilized, there is a limit on the achievable peak current in high brightness operation, in the range of tens of Ampere. This limitation can be overcome by the use of a hybrid standing wave/traveling wave structure; the standing wave portion provides acceleration at a high field from the photocathode, while the traveling wave part yields strong velocity bunching. This approach is explored here in a C-band scenario, at field strengths ($>100\mathrm{MV}/\mathrm{m}$) at the current state-of-the-art. It is found that one may arrive at an electron beam with many hundreds of Amperes with well-sub-micron normalized emittance. This extremely compact injector system also possesses attractive simplification of the rf distribution system by eliminating the need for an rf circulator. We explore the use of this device in a compact 400 MeV-class source, driving both inverse Compton scattering and free-electron laser radiation sources with unique, attractive properties.

In this paper we present the analytical calculations to derive the magnetic field of a solenoid by solving exactly a fractional integral with the use of a novel method. Starting from the Biot-Savart law, we consider a coil of negligible thickness with a stationary electric current. We derive the expressions of the on- and off-axes magnetic field components. The results have been compared to some simplified and known analytical formulae as well as to a commercial numerical code 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 has been achieved, including compression of the beam, rotation in the magnetic field, and analysis of the subsequently generated diamagnetic field has been discussed.