  The realization and characterization of a high quality factor resonator
composed of two hollow-dielectric cylinders with its pseudo-TM$_{030}$ mode
resonating at 10.9 GHz frequency is discussed. The quality factor was measured
at the temperatures 300 K and 4 K obtaining $\mbox{Q}_{300\mbox{K}}=(150,000\pm
2,000)$ and $\mbox{Q}_{4\mbox{K}}=(720,000\pm 10,000)$respectively, the latter
corresponding to a gain of one order of magnitude with respect to a traditional
copper cylindrical-cavity with the corresponding TM$_{010}$ mode resonating at
the same frequency. The implications to dark-matter axion-searches with cavity
experiments are discussed showing that the gain in quality factor is not
spoiled by a reduced geometrical coupling $C_{030}$ of the cavity mode to the
axion field. This reduction effect is estimated to be at most 20%. Numerical
simulations show that frequency tuning of several hundreds MHz is feasible.
