Searches for dark matter axion involve the use of microwave resonant cavities operating in a strong magnetic field. Detector sensitivity is directly related to the cavity quality factor, which is limited, however, by the presence of the external magnetic field. In this paper we present a cavity of novel design whose quality factor is not affected by a magnetic field. It is based on a photonic structure by the use of sapphire rods. The quality factor at cryogenic temperature is in excess of $5 times 10^5$ for a selected mode.
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