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The TROPOMI-SWIR HgCdTe detector on the Sentinel-5 Precursor mission has been performing in-orbit measurements of molecular absorption in Earth's atmosphere since its launch in October 2017. In its polar orbit the detector is continuously exposed to potentially harmful energetic particles. Calibration measurements taken during the eclipse are used to inspect the performance of this detector. This paper explores the in-orbit degradation of the HgCdTe detector. After five years, the detector is still performing within specifications, even though pixels are continuously hit by cosmic radiation. The bulk of the impacts have no lasting effects, and most of the damaged pixels (95%) appear to recover on the order of a few days to several months, attributed to a slow spontaneous recovery of defects in the HgCdTe detector material. This is observed at the operational temperature of 140 K. The distribution of the observed recovery times has a mean around nine days with a significant tail towards several months. Pixels that have degraded have a significant probability to degrade again. The location of faulty pixels follows a Poissonian distribution across the detector. No new clusters have appeared, revealing that impacts are dominated by relatively low energetic protons and electrons. Due to the observed spontaneous recovery of pixels, the fraction of pixels meeting all quality requirements in the nominal operations phase has always been over 98.7%. The observed performance of the TROPOMI-SWIR detector in-flight impacts selection criteria of HgCdTe detectors for future space instrumentation., Comment: 18 pages, accepted for publication in MST

We present a hybrid optimization framework for a class of problems, formalized as a generalization of the Continuous Energy-Con\-strained Scheduling Problem (CECSP), introduced by Nattaf et al. (2014). This class is obtained from challenges concerning demand response in energy networks. Our framework extends a previously developed approach. A set of jobs has to be processed on a continuous, shared resource. Consequently, a schedule for a job does not only contain a start and completion time, but also a resource consumption profile, where we have to respect lower and upper bounds on resource consumption during processing. In this work, we develop a hybrid approach for the case where the objective is a step-wise increasing function of completion time, using local search, linear programming and O(n) lower bounds. We exploit that the costs are known in the local search and use bounds to assess feasibility more efficiently than by LP. We compare its performance to a mixed-integer linear program. After that, we extend this to a hybrid optimization framework for the General CECSP. This uses an event-based model, and applies a decomposition in two parts: 1) determining the order of events and 2) finding the event times, and hence the start and completion times of jobs, together with the resource consumption profiles. We argue the broad applicability of this framework., Comment: 33 pages, 7 figures, submitted to annals of operations research

Using recently developed techniques, we consider weak-field test-particle scattering angle calculations in two distinct settings: Charged test-particles in spacetimes of charged sources and Effective One-Body theory with spin. We present scattering angle calculations up to $\mathcal O(G^4)$ of charged particles in the Kerr-Newman metric, including electromagnetic interactions up to second order in charge. Coulomb scattering is also discussed, and the well-known Darwin scattering formula is rederived by resummation. An Effective One-Body metric for a Kerr-Schwarzschild binary is constructed in a post-Minkowskian framework up to $\mathcal O(G^2)$ and first order in spin. Facilitated by explicit scattering calculations, our approach is equivalent with existing literature through gauge-like transformations. Finally, we investigate if the Newman Janis Algorithm applied to an Effective One-Body metric of non-spinning binaries represents a binary system with spin., Comment: 24 pages, 3 tables

The Athena X-ray Integral Unit (X-IFU) is the high resolution X-ray spectrometer, studied since 2015 for flying in the mid-30s on the Athena space X-ray Observatory, a versatile observatory designed to address the Hot and Energetic Universe science theme, selected in November 2013 by the Survey Science Committee. Based on a large format array of Transition Edge Sensors (TES), it aims to provide spatially resolved X-ray spectroscopy, with a spectral resolution of 2.5 eV (up to 7 keV) over an hexagonal field of view of 5 arc minutes (equivalent diameter). The X-IFU entered its System Requirement Review (SRR) in June 2022, at about the same time when ESA called for an overall X-IFU redesign (including the X-IFU cryostat and the cooling chain), due to an unanticipated cost overrun of Athena. In this paper, after illustrating the breakthrough capabilities of the X-IFU, we describe the instrument as presented at its SRR, browsing through all the subsystems and associated requirements. We then show the instrument budgets, with a particular emphasis on the anticipated budgets of some of its key performance parameters. Finally we briefly discuss on the ongoing key technology demonstration activities, the calibration and the activities foreseen in the X-IFU Instrument Science Center, and touch on communication and outreach activities, the consortium organisation, and finally on the life cycle assessment of X-IFU aiming at minimising the environmental footprint, associated with the development of the instrument. Thanks to the studies conducted so far on X-IFU, it is expected that along the design-to-cost exercise requested by ESA, the X-IFU will maintain flagship capabilities in spatially resolved high resolution X-ray spectroscopy, enabling most of the original X-IFU related scientific objectives of the Athena mission to be retained. (abridged)., Comment: 48 pages, 29 figures, Accepted for publication in Experimental Astronomy with minor editing

Scattering angles for probes in Kerr metrics are derived for scattering in the equatorial plane of the black hole. We use a method that naturally resums all orders in the spin of the Kerr black hole, thus facilitating comparisons with scattering-angle computations based on the Post-Minkowskian expansion from scattering amplitudes or worldline calculations. We extend these results to spinning black-hole probes up to and including second order in the probe spin and any order in the Post- Minkowskian expansion, for probe spins aligned with the Kerr spin. When truncating to third Post-Minkowskian order, our results agree with those obtained by amplitude and worldline methods., Comment: 18 pages, 3 tables

We present a characterization of the sensitivity of TES X-ray micro-calorimeters to environmental conditions under frequency-domain multiplexing (FDM) readout. In the FDM scheme, each TES in a readout chain is in series with a LC band-pass filter and AC biased with an independent carrier at MHz range. Using TES arrays, cold readout circuitry and warm electronics fabricated at SRON and SQUIDs produced at VTT Finland, we characterize the sensitivity of the detectors to bias voltage, bath temperature and magnetic field. We compare our results with the requirements for the Athena X-IFU instrument, showing the compliance of the measured sensitivities. We find in particular that FDM is intrinsically insensitive to the magnetic field because of TES design and AC readout., Comment: This paper has been accepted for publication in Journal of Low Temperature Physics

The X-IFU is the cryogenic spectrometer onboard the future ATHENA X-ray observatory. It is based on a large array of TES microcalorimeters, which works in combination with a Cryogenic AntiCoincidence detector (CryoAC). This is necessary to reduce the particle background level thus enabling part of the mission science goals. Here we present the first joint test of X-IFU TES array and CryoAC Demonstration Models, performed in a FDM setup. We show that it is possible to operate properly both detectors, and we provide a preliminary demonstration of the anti-coincidence capability of the system achieved by the simultaneous detection of cosmic muons., Comment: Accepted for publication in the Journal of Low Temperature Physics for LTD-19 special issue

We have measured and characterized the thermal crosstalk in two different arrays of transition-edge sensor (TES) X-ray micro-calorimeters with frequency-domain multiplexing (FDM) readout. The TES arrays are fabricated at SRON and are a 8$\times$8 and a 32$\times$32 "kilo-pixel" uniform array. The amount of crosstalk is evaluated as the ratio between the averaged crosstalk signal and the X-ray pulse amplitudes. The crosstalk ratios (CR) for our detectors are compliant with the requirements for future X-ray space missions, such as Athena X-IFU (CR$< 10^{-3}$ for first-neighbour pixels): we measured a nearest-neighbour thermal crosstalk ratio at a level of $10^{-4}$, with a highest crosstalk ratio of $4\times 10^{-4}$ for the kilo-pixel array (worst case, center of array) and $1\times 10^{-4}$ for the 8$\times$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 crosstalk ratios, we have estimated the impact on the spectral resolution by means of noise equivalent power (NEP) 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.

We report on the development and demonstration of a MHz frequency domain multiplexing (FDM) technology to read out arrays of cryogenic transition edge sensor (TES) X-ray microcalorimeters. In our FDM scheme, TESs are AC-biased at different resonant frequencies in the low MHz range through an array of high-$Q$ LC resonators. The current signals of all TESs are summed at superconducting quantum interference devices (SQUIDs). We have demonstrated multiplexing for a readout of 31 pixels using room temperature electronics, high-$Q$ LC filters and TES arrays developed at SRON, and SQUID arrays from VTT. We repeated this on a second setup with 37 pixels. The summed X-ray spectral resolutions $@$ 5.9 keV are $\Delta E_{\rm 31 pix ~MUX}=2.14\pm0.03$ eV and $\Delta E_{\rm 37 pix ~MUX}=2.23\pm0.03$ eV. The demonstrated results are comparable with other multiplexing approaches. There is potential to further improve the spectral resolution and to increase the number of multiplexed TESs, and to open up applications for TES X-ray microcalorimeters., Comment: 6 pages, 3 figures, accepted for publication on Applied physics letters

Transition Edge Sensors (TESs) are the selected technology for future spaceborne X-ray observatories, such as Athena, Lynx, and HUBS. These missions demand thousands of pixels to be operated simultaneously with high energy-resolving power. To reach these demanding requirements, every aspect of the TES design has to be optimized. Here we present the experimental results of tests on different devices where the coupling between the x-ray absorber and the TES sensor is varied. In particular, we look at the effects of the diameter of the coupling stems and the distance between the stems and the TES bilayer. Based on measurements of the AC complex impedance and noise, we observe a reduction in the excess noise as the spacing between the absorber stem and the bilayer is decreased. We identify the origin of this excess noise to be internal thermal fluctuation noise between the absorber stem and the bilayer. Additionally, we see an impact of the coupling on the superconducting transition in the appearance of kinks. Our observations show that these unwanted structures in the transition shape can be avoided with careful design of the coupling geometry. Also the stem diameter appears to have a significant impact on the smoothness of the TES transition. This observation is still poorly understood, but is of great importance for both AC and DC biased TESs., Comment: 9 pages, 8 figures

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 $\mathrm{\Delta}E<$3 eV full-width-half-maximum (FWHM) in the soft X-ray energy range. We are currently developing X-ray microcalorimeter arrays as a backup option for the X-IFU instrument on board of ATHENA space telescope, led by ESA and foreseen to be launched in 2031. In this contribution, we report on the development and the characterization of a uniform 32$\times$32 pixel array with (length$\times $width) 140$\times$30 $\mu$m$^2$ TiAu TESs, which have \textcolor{black}{a 2.3 $\mu$m} thick Au absorber for X-ray photons. The pixels have a typical normal resistance $R_\mathrm{n}$ = 121 m$\Omega$ and a critical temperature $T_\mathrm{c}\sim$ 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$\times$10$^{-3}$ when considering the ratio between the amplitude of the crosstalk signal to an X-ray pulse (for example at 5.9 keV)

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$\times$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 $^{55}$Fe radioactive source (emitting Mn-K$\alpha$ at 5.9 keV) and a Modulated X-ray Source (MXS, providing Cr-K$\alpha$ at 5.4 keV and Cu-K$\alpha$ at 8.0 keV). First, we report the procedure used to perform the detector energy scale calibration, usually achieving a calibration accuracy better than $\sim$ 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: $\Delta$E$_{FWHM}$ = 2.40 $\pm$ 0.09 eV @ 5.4 keV; 2.53 $\pm$ 0.10 eV @ 5.9 keV; 2.78 $\pm$ 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 ($\sim$ 1 day), we finally detected also the Al-K$\alpha$ 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 ($\Delta$E$_{FWHM}$ = 1.91 eV $\pm$ 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)., Comment: Accepted for publication in IEEE Transactions on Applied Superconductivity for ASC2020 special issue

In the frequency-domain multiplexing (FDM) scheme, transition-edge sensors (TES) are individually coupled to superconducting LC filters and AC biased at MHz frequencies through a common readout line. To make efficient use of the available readout bandwidth and to minimize the effect of non-linearities, the LC resonators are usually designed to be on a regular grid. The lithographic processes however pose a limit on the accuracy of the effective filter resonance frequencies. Off-resonance bias carriers could be used to suppress the impact of intermodulation distortions, which nonetheless would significantly affect the effective bias circuit and the detector spectral performance. In this paper we present a frequency shift algorithm (FSA) to allow off-resonance readout of TES's while preserving the on-resonance bias circuit and spectral performance, demonstrating its application to the FDM readout of a X-ray TES microcalorimeter array. We discuss the benefits in terms of mitigation of the impact of intermodulation distortions at the cost of increased bias voltage and the scalability of the algorithm to multi-pixel FDM readout. We show that with FSA, in multi-pixel and frequencies shifted on-grid, the line noises due to intermodulation distortion are placed away from the sensitive region in the TES response and the X-ray performance is consistent with the single-pixel, on-resonance level., Comment: Accepted for publication on Review of Scientific Instruments