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 $mbox{Q}_{300mbox{K}}=(150,000pm 2,000)$ and $mbox{Q}_{4mbox{K}}=(720,000pm 10,000)$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.
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