  The development of high gradient accelerating structures is one of the
leading activities of the accelerator community. In the technological research
of new construction methods for these devices, high-power testing is a critical
step for the verification of their viability. Recent experiments showed that
accelerating cavities made from hard copper alloys, can achieve better
performance as compared with soft copper ones. The results of experiments
showed that welded, hard copper cavities have shown breakdown rate of
$10^{-3}$/pulse/meter at a gradient of about 150 MV/m, in the X-band, a using a
shaped pulse with a 150 ns flat part. We continue the design, construction, and
higher power experimental tests of three cells standing wave (SW) 11.424 GHz
accelerating cavities fabricated with hard CuAg alloy to study the RF breakdown
physics. Our aim is to fabricate the accelerating structures with innovative
technologies easier to handle and cheaper; easier for surfaces inspection;
easier for data elaboration and validation of joining techniques. The choice of
these new technological approaches and design methods provides also the
possibility of allocating the parasitic Higher Order Mode dampers. This paper
describes the design of an optimized cavity made with sectors which provides a
high longitudinal shunt impedance $R_{sh}$ of the operating mode. The cavity
will be fabricated by using the Tungsten Inert Gas process to realize a hard
CuAg structure. Two three-cells SW X-band accelerating cavities, to be operated
in the $\pi$-mode and made out of hard CuAg alloy, were already fabricated at
INFN-LNF by means of clamping and welding by using the TIG approach. Finally,
we also report the RF characterization and low-power RF tests of a two-halves
split hard CuAg structure that will be consequently TIG welded and employed for
high-gradient tests and for the study of the RF breakdown physics.
