We theoretically predict and experimentally observe the onset of weak-link physics in the dynamical response of transition-edge sensors (TESs). We develop a theoretical framework based on a Fokker-Planck description that incorporates both the TESs electrical response, stemming from Josephson phenomena, and the electrothermal effects due to coupling to a thermal bath. Our measurements of a varying dynamic resistance are in excellent agreement with our theory, thereby establishing weak-link phenomena as the main mechanism underlying the operation of TESs. Furthermore, our description enables the calculation of power spectral densities, paving the way for a more thorough investigation of the unexplained "excess noise"in long diffusive junctions and TESs reported in recent experiments.

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We have measured and characterized the thermal crosstalk in two different arrays of transition-edge sensor (TES) X-ray microcalorimeters with frequency-domain multiplexing (FDM) readout. The TES arrays are fabricated at SRON and are a 8 × 8 and a 32 × 32 'kilo-pixel' uniform array. The amount of crosstalk is evaluated as the ratio between the averaged crosstalk signal and the X-ray pulse amplitudes. The crosstalk ratios (CRs) for our detectors are compliant with the requirements for future X-ray space missions, such as Athena X-IFU (CR < 10^{-3 for first-neighbor pixels): We measured a nearest neighbor thermal CR at a level of 10^{-4, with a highest CR of 4× 10^{-4 for the kilo-pixel array (worst case, center of array) and 1× 10^{-4 for the 8 × 8 array, with a margin of improvement achievable by optimizing the Cu metallization and the width of the Si supporting structures (muntins) in the backside of the TES array chip. Based on the measured CRs, we have estimated the impact on the spectral resolution by means of noise equivalent power considerations and a Monte Carlo simulation, finding an average degradation in quadrature of less than 40 meV, compliant with the <0.2 eV requirement for Athena X-IFU.

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In the early 2030s, ESAs new X-ray observatory, Athena, is scheduled to be launched. It will carry two main
instruments, one of which is the X-ray Integral Field Unit (X-IFU), an X-ray imaging spectrometer, which will consist of an array of several thousand transition-edge sensors (TESs) with a proposed energy resolution of 2.5 eV for photon energies up to 7 keV. At SRON we develop the backup TES
array based on Ti/Au bilayers with a transition temperature just below 100 mK. In this contribution we will give a broad overview of the properties and capabilities of these state-of-the-art detectors. Over the years we have fabricated and studied a large number of detectors with various
geometries, providing us with a good understanding of how to precisely control the properties of our detectors. We are able to accurately vary the most important detector properties, such as the normal resistance, thermal conductance and critical temperature. This allows us to finely tune our
detectors to meet the demands of various applications. The detectors have demonstrated excellent energy resolutions of below 1.8 eV for 5.9 keV X-rays. By tuning the properties of the devices, they can be optimally matched to various read-out schemes using both AC and DC biasing. The next step is to increase the size of our TES arrays from our current kilo-pixel arrays towards the
full-sized array for X-IFU.
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Large format arrays of transition edge sensor (TES) are crucial for the next generation of X-ray space observatories. Such arrays are required to achieve an energy resolution of Δ E < 3 eV full-width-half-maximum (FWHM) in the soft X-ray energy range. We are currently developing X-ray microcalorimeter arrays as a backup option for the X-IFU instrument on board of ATHENA space telescope, led by ESA and foreseen to be launched in 2031. In this contribution, we report on the development and the characterization of a uniform 32 × 32 pixel array with (length × width) 140 × 30 μ m2 TiAu TESs, which have a 2.3 μ m thick Au absorber for X-ray photons. The pixels have a typical normal resistance Rn = 121 m Ω and a critical temperature Tc ∼ 90 mK. We performed extensive measurements on 60 pixels out of the array in order to show the uniformity of the array. We obtained an energy resolutions between 2.4 and 2.6 eV (FWHM) at 5.9 keV, measured in a single-pixel mode at AC bias frequencies ranging from 1 to 5 MHz, with a frequency domain multiplexing (FDM) readout system, which is developed at SRON/VTT. We also present the detector energy resolution at X-ray with different photon energies generated by a modulated external X-ray source from 1.45 keV up to 8.9 keV. Multiplexing readout across several pixels has also been performed to evaluate the impact of the thermal crosstalk to the instrument's energy resolution budget requirement. This value results in a derived requirement, for the first neighbour, that is less than 1;× 10-3 when considering the ratio between the amplitude of the crosstalk signal to an X-ray pulse (for example at 5.9 keV).

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We are developing a kilo-pixels Ti/Au TES array as a backup option for Athena X-IFU. Here we report on single-pixel performance of a 32 × 32 array operated in a Frequency Division Multiplexing (FDM) readout system, with bias frequencies in the range 1-5 MHz. We have tested the pixels response at several photon energies, by means of a 55Fe radioactive source (emitting Mn-Kα at 5.9 keV) and a Modulated X-ray Source (MXS, providing Cr-Kα at 5.4 keV and Cu-Kα at 8.0 keV). First, we report the procedure used to perform the detector energy scale calibration, usually achieving a calibration accuracy better than ∼0.5 eV in the 5.4-8.9 keV energy range. Then, we present the measured energy resolution at the different energies (best single pixel performance: ΔEFWHM = 2.40 ± 0.09 eV @ 5.4 keV; 2.53 ± 0.10 eV @ 5.9 keV; 2.78 ± 0.16 eV @ 8.0 keV), investigating also the performance dependency from the pixel bias frequency and the count rate. Thanks to long background measurements (∼1 d), we finally detected also the Al-Kα line at 1.5 keV, generated by fluorescence inside the experimental setup. We analyzed this line to obtain a first assessment of the single-pixel performance also at low energy (ΔEFWHM = 1.91 eV ± 0.21 eV @ 1.5 keV), and to evaluate the linearity of the detector response in a large energy band (1.5-8.9 keV).

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Pneumatic conveying of particles is generally applied in large ducts. However, new applications are emerging which benefit from millimeter-sized ducts; for example, triboelectric separators where intensive wall-particle contact is desirable. An optical method is proposed to measure the distribution of the position and velocity of 100-1000 μm particles in such narrow ducts. Images of the system are captured using a digital camera on which a Hough transform is applied to detect the particles and their positions. The velocities are acquired by applying a hybrid particle tracking and particle image velocimetry approach. This made it is possible to overcome challenges caused by suboptimal lighting, nonsmooth background, and a large ratio between particle and duct diameter (>O(0.1)). It is shown that the algorithm is subpixel accurate when sufficient particles can be sampled. Finally, typical results are shown to illustrate the method's capabilities.@en