  Dielectric Assist Accelerating (DAA) structures based on ultralow-loss
ceramic are being studied as an alternative to conventional disk-loaded copper
cavities. This accelerating structure consists of dielectric disks with irises
arranged periodically in metallic structures working under the TM$_{02}$-$\pi$
mode. In this paper, the numerical design of an S-band DAA structure for low
beta particles, such as protons or carbon ions used for Hadrontherapy
treatments, is shown. Four dielectric materials with different permittivity and
loss tangent are studied as well as different particle velocities. Through
optimization, a design that concentrates most of the RF power in the vacuum
space near the beam axis is obtained, leading to a significant reduction of
power loss on the metallic walls. This allows to fabricate cavities with an
extremely high quality factor, over 100 000, and shunt impedance over 300
M$\Omega$/m at room temperature. During the numerical study, the design
optimization has been improved by adjusting some of the cell parameters in
order to both increase the shunt impedance and reduce the peak electric field
in certain locations of the cavity, which can lead to instabilities in its
normal functioning.
