In the framework of the Compact Light XLS project, we have designed a higher harmonic RF accelerating structure in order to linearize the longitudinal space phase. The design of this compact Traveling Wave (TW) accelerating structure operating on the third harmonic with respect to the linac frequency (11.994 GHz) with a (100-125) MV/m accelerating gradient is presented, together with numerical electromagnetic simulations were carried out by using the numerical codes High Frequency Structure Simulator (HFSS) and CST Particle Studio.
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