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We report on the x-ray background rate measured with transition-edge sensors (TES) micro-calorimeters under frequency-domain multiplexing (FDM) readout as a possible technology for future experiments aiming at a direct detection of axion-like particles. Future axion helioscopes will make use of large magnets to convert axions into photons in the keV range and x-ray detectors to observe them. To achieve this, a detector array with high spectral performance and extremely low background is necessary. TES are single-photon, non-dispersive, high-resolution micro-calorimeters and represent a possible candidate for this application. We have been developing x-ray TES micro-calorimeters and an FDM readout technology in the framework of the space-borne x-ray astronomical observatories. We show that the current generation of our detectors is already a promising technology for a possible axion search experiment, having measured an x-ray background rate of 2.2(2) × 10−4 cm−2 s−1 keV−1 with a cryogenic demonstrator not optimized for this specific application. We then make a prospect to further improve the background rate down to the required value (< 1 0 − 7 cm−2 s−1 keV−1) for an axion-search experiment, identifying no fundamental limits to reach such a level. [ABSTRACT FROM AUTHOR]

The Transition-Edge Sensor (TES) is an extremely sensitive device, which is used to measure the energy of individual x-ray photons. For astronomical spectrometry applications, SRON develops a frequency domain multiplexing readout system for kilopixel arrays of such TESs. Each TES is voltage biased at a specific frequency in the range of 1-5 MHz. Isolation between the individual pixels is obtained through very narrow-band (high-Q) lithographic LC resonators. To prevent energy resolution degradation due to intermodulation line noise, the bias frequencies are distributed on a regular grid. The requirements on the accuracy of the LC resonance frequency are very high. The deviation of the resonance frequencies due to production tolerances is significant with respect to the bandwidth, and a controller is necessary to compensate for the LC series impedance. We present two such controllers: a simple orthogonal proportional-integral controller and a more complex impedance estimator. Both controllers operate in baseband and try to make the TES current in-phase with the bias voltage, effectively operating as phase-locked loops. They allow off-LC-resonance operation of the TES pixels while preserving the TES thermal response and energy resolution. Extensive experimental results-published in a companion paper recently-with the proposed methods show that these controllers allow the preservation of single pixel energy resolution in multiplexed operation.