  Notably innovative technologies will permit compact and affordable advanced
accelerators as the linear collider and X-ray free-electron lasers (XFELs) with
accelerating gradients over twice the value achieved with current technologies.
In particular XFEL is able to produce coherent X-ray pulses with peak
brightness 10 orders of magnitude greater than preceding approaches, which has
revolutionized numerous fields through imaging of the nanoscopic world at the
time and length scale of atom-based systems, that is of femtosecond and
Angstrom. There is a strong interest for combining these two fields, to form a
proper tool with the goal of producing a very compact XFEL in order to
investigate multi-disciplinary researches in chemistry, biology, materials
science, medicine and physics.
  In the framework of the Ultra -Compact XFEL project (UC-XFEL) under study at
the UCLA, an ultra high gradient higher harmonic RF accelerating structure for
the longitudinal space phase linearization is foreseen. To this aim, a Ka-Band
linearizer (34.2 GHz) with an integrated voltage of at least 15 MV working on
6th harmonic with respect to the main Linac frequency (5.712 GHz) is required.
We here present the electromagnetic design of a cold ultra compact Ka-band SW
linearizer, 8 cm long, working on pi mode with an ultra high accelerating
gradient (beyond 100 MV/m) and minimum surface electric field for minimizing
the probability of RF breakdown. Moreover, we discuss a TW option and compare
it with the initial SW structure, by means of main RF parameters as well as
beam-dynamics considerations. The numerical electromagnetic studies have been
performed by using the well known SuperFish, HFSS and CST.
