  There is a strong demand for accelerating structures able to achieve higher
gradients and more compact dimensions for the next generation of linear
accelerators for research, industrial and medical applications. In the
framework of the Compact Light XLS project, an ultra high gradient higher
harmonic RF accelerating structure is needed for the linearization of the
longitudinal space phase. In order to determine the maximum sustainable
gradients in normal conducting RF powered particle beam accelerators with
extremely low probability of RF breakdown, investigations are in progress for
using shorts accelerating structures in the Ka-band regime. We here report an
electromagnetic design of a compact linearizer standing wave (SW) accelerating
structure 8 cm long operating on $\pi$ mode, third harmonic with respect to the
Linac frequency (11.994 GHz) with a 100 MV/m accelerating gradient and minimum
surface electric field. Numerical electromagnetic studies have been performed
by using the well known SuperFish, HFSS and CST computing software.
