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Present models of the superconducting-to-normal transition in transition-edge sensors (TESs) do not describe the current distribution within a biased TES. This distribution is complicated by normal-metal features that are integral to TES design. We present a model with one free parameter that describes the evolution of the current distribution with bias. To probe the current distribution experimentally, we fabricated TES devices with different current return geometries. Devices where the current return geometry mirrors current flow within the device have sharper transitions, thus allowing for a direct test of the current-flow model. Measurements from these devices show that current meanders through a TES low in the resistive transition but flows across the normal-metal features by 40% of the normal-state resistance. Comparison of transition sharpness between device designs reveals that self-induced magnetic fields play an important role in determining the width of the superconducting transition. [ABSTRACT FROM AUTHOR]

Superconducting transition-edge sensors (TESs) used in X-ray and γ -ray microcalorimeters suffer degraded performance if cooled in a magnetic field B sufficient to trap flux in the sensors. We report measurements of γ -ray TESs before and after implementing measures to reduce stray B fields from sources inside and outside the cryostat. These measurements showed a correlation between anomalous features in TES current–voltage (IV) curves and degraded energy resolution. After reducing internal sources of stray B field and improving shielding against external sources, both IV curves and energy resolution improved. Finally, we placed magnetized screws with remnant fields ∼ 10 μ T near similar γ -ray TESs in a different type of detector package and observed the same effects. [ABSTRACT FROM AUTHOR]

The nonlinear energy response of cryogenic microcalorimeters is usually corrected through an empirical calibration. X-ray or gamma-ray emission lines of known shape and energy anchor a smooth function that generalizes the calibration data and converts detector measurements to energies. We argue that this function should be an approximating spline. The theory of Gaussian process regression makes a case for this functional form. It also provides an important benefit previously absent from our calibration method: a quantitative uncertainty estimate for the calibrated energies, with lower uncertainty near the best-constrained calibration points. [ABSTRACT FROM AUTHOR]

Exotic atom experiments place transition-edge sensor (TES) microcalorimeter arrays in a high-energy charged particle-rich environment. When a high-energy charged particle passes through the silicon substrate of a TES array, a large amount of energy is deposited and small pulses are generated across multiple pixels in the TES array due to thermal crosstalk. We have developed analysis techniques to assess and reduce the effects of charged particle events on exotic atom X-ray measurements. Using this technique, the high-energy and low-energy components of the X-ray peaks due to pileup are eliminated, improving the energy resolution from 6.6 to 5.7 eV at 6.9 keV. [ABSTRACT FROM AUTHOR]

A novel triggering function developed for 240-pixel Transition-Edge Sensors is demonstrated under the high rate of particle background. The function is integrated into the standard data acquisition system in the NIST TES framework. It enables any type of combination of trigger pattern when a pixel is triggered, which is called "group trigger." As a practical implementation, the primary trigger is distributed to the four physically nearest pixels. The group trigger function was utilized throughout the entire one-month J-PARC experiment for the measurement of the Kaonic-atom X-rays. This trigger allowed us to confirm that the increased background and degraded energy resolution we observed when operating the TES array in the presence of an ion beam are the result of thermal crosstalk from charged particles. We show that the maximum of the average of the signals among the neighboring four pixels is useful for event selection. We use cuts based on this parameter to improve the peak-to-background level in a measured x-ray energy spectrum by a factor of ∼ 2, while keeping 95% of measured events. This flexible group triggering technique allows us to improve the signal to noise on the very faint Kaonic Helium x-ray lines we are measuring, better understand our experiment environment, and we believe this technique may prove useful in other ground and space-based TES applications. [ABSTRACT FROM AUTHOR]

A useful function, called group trigger, is implemented in a data acquisition system of a 240-pixel X-ray transition-edge sensor array to store simultaneous waveforms from any desired set of pixels. It works as a diagnostic tool which can record both primary pulses and associated crosstalk events with enough freedom to optimize the data output. Under a high rate of charged particle background, such as in an accelerator, investigating signals from any combination of trigger patterns for a particular event is of high importance. We utilized this function throughout an entire experiment at J-PARC, measuring kaonic atom X-rays in 2018. This was the first time a group trigger was applied to exotic-atom spectroscopy. In this experiment, the primary trigger was distributed to the four physical nearest neighbor pixels for practical purposes. The function clarified the effect of thermal and electrical cross talk from X-rays and charged particles, resulting in a better understanding of the behavior of the TES array in such a high-background environment. [ABSTRACT FROM AUTHOR]

We integrated a TES X-ray spectrometer with a charged kaon beam line at J-PARC to perform X-ray spectroscopy of kaonic helium atoms. Limited beam intensity and a broad beam spot size made it crucial to increase the detector acceptance angle as much as possible, requiring significant development. To this end, our TES system shared the same vacuum with a cryogenic system of the liquid helium experimental target. We also specially developed a target cell for liquid helium and a thinned aperture array on top of the TES detector. Additionally, thermal and magnetic shields and infrared filters were optimized in terms of a larger acceptance angle and energy resolution of the detector. The scientific campaign was performed in June, 2018, where the whole system was stably operated for almost one month. [ABSTRACT FROM AUTHOR]

Transition-edge sensor microcalorimeters have found success as X-ray detectors at synchrotron light-sources, due to a unique combination of high collecting area and good energy resolution. However, the upcoming generation of free-electron lasers (FELs), such as the Linac Coherent Light Source II, is designed to deliver more than 10 10 photons in a 100 fs pulse at a 100 kHz rate, potentially leading to severe pulse-pileup issues. We will demonstrate that, for most relevant science cases, it is possible to mitigate pulse pile-up using simple X-ray filters in a way that takes advantage of the substantial increase in X-ray flux at modern FELs. [ABSTRACT FROM AUTHOR]

A principal component analysis (PCA) of clean microcalorimeter pulse records can be a first step beyond statistically optimal linear filtering of pulses toward a fully nonlinear analysis. For PCA to be practical on spectrometers with hundreds of sensors, an automated identification of clean pulses is required. Robust forms of PCA are the subject of active research in machine learning. We examine a version known as coherence pursuit that is simple and fast and well matched to the automatic identification of outlier records, as needed for microcalorimeter pulse analysis. [ABSTRACT FROM AUTHOR]

Time division multiplexing (TDM) uses a digital flux-locked loop (DFLL) to linearize each first-stage SQUID amplifier. Presently, the dynamic range of our TDM systems is limited by the use of a proportional-integral controller to maintain the DFLL. In this paper, we use simulations to assess the improvements possible with a predictive control algorithm that anticipates rapid changes in transition-edge sensor current during the rising edge of an X-ray pulse. We calculate that the predictive control algorithm can improve our TDM architecture's dynamic range by 35%. This significant increase in multiplexing capabilities could be used to read out higher-energy X-rays, reduce readout noise, increase multiplexing factors, or reduce SQUID power output. [ABSTRACT FROM AUTHOR]

Microwave SQUID multiplexing has become a key technology for reading out large arrays of X-ray and gamma-ray microcalorimeters with mux factors of 100 or more. The desire for fast X-ray pulses that accommodate photon counting rates of hundreds or thousands of counts per second per sensor drives system design toward high sensor current slew rate. Typically, readout of high current slew rate events is accomplished by increasing the sampling rate, such that rates of order 1 MHz may be necessary for some experiments. In our microwave multiplexed readout scheme, the effective sampling rate is set by the frequency of the flux-ramp modulation ( f r ) used to linearize the SQUID response. The maximum current slew rate between samples is then nominally Φ 0 f r / 2 M in (where M in is the input coupling) because it is generally not possible to distinguish phase shifts of > π from negative phase shifts of < - π . However, during a pulse, we know which direction the current ought to be slewing, and this makes it possible to reconstruct a pulse where the magnitude of the phase shift between samples is > π . We describe a practical algorithm to identify and reconstruct pulses that exceed this nominal slew rate limit on the rising edge. Using pulses produced by X-ray transition-edge sensors, we find that the pulse reconstruction has a negligible impact on energy resolution compared to arrival time effects induced by under-sampling the rising edge. This technique can increase the effective slew rate limit by more than a factor of two, thereby either reducing the resonator bandwidth required or extending the energy range of measurable photons. The extra margin could also be used to improve crosstalk or to decrease readout noise. [ABSTRACT FROM AUTHOR]

We report on the design, commissioning, and initial measurements of a Transition-Edge Sensor (TES) x-ray spectrometer for the Electron Beam Ion Trap (EBIT) at the National Institute of Standards and Technology (NIST). Over the past few decades, the NIST EBIT has produced numerous studies of highly charged ions in diverse fields such as atomic physics, plasma spectroscopy, and laboratory astrophysics. The newly commissioned NIST EBIT TES Spectrometer (NETS) improves the measurement capabilities of the EBIT through a combination of high x-ray collection efficiency and resolving power. NETS utilizes 192 individual TES x-ray microcalorimeters (166/192 yield) to improve upon the collection area by a factor of ∼30 over the 4-pixel neutron transmutation doped germanium-based microcalorimeter spectrometer previously used at the NIST EBIT. The NETS microcalorimeters are optimized for the x-ray energies from roughly 500 eV to 8000 eV and achieve an energy resolution of 3.7 eV–5.0 eV over this range, a more modest (<2×) improvement over the previous microcalorimeters. Beyond this energy range, NETS can operate with various trade-offs, the most significant of which are reduced efficiency at lower energies and being limited to a subset of the pixels at higher energies. As an initial demonstration of the capabilities of NETS, we measured transitions in He-like and H-like O, Ne, and Ar as well as Ni-like W. We detail the energy calibration and data analysis techniques used to transform detector counts into x-ray spectra, a process that will be the basis for analyzing future data. [ABSTRACT FROM AUTHOR]

Low-temperature detector technologies provide extraordinary sensitivity for applications ranging from precision measurements of the cosmic microwave background to high-resolution, high-rate x-ray, and γ-ray spectroscopy. To utilize this sensitivity, new instruments are being built, and new instruments are imagined, with ever greater pixel counts, but the scale of these instruments is limited by the capability of the readout electronics. Microwave SQUID multiplexing addresses the needs of these future instruments, exploiting gigahertz of bandwidths of coaxial cables and broadband components to combine hundreds to thousands of signals on a single readout line. A key feature of any multiplexer is the level of crosstalk between input channels. This crosstalk can degrade the sensitivity of the instrument, introduce systematic error, or simply confound data analysis. In this letter, we explain the primary mechanisms of crosstalk in a microwave SQUID multiplexer, calculate and measure their magnitude, and consider their effect and methods of mitigation. [ABSTRACT FROM AUTHOR]

The readout requirements for instruments based on transition-edge sensors (TESs) have dramatically increased over the last decade as demand for systems with larger arrays and faster sensors has grown. Emerging systems are expected to contain many thousands of sensors and/or sensors with time constants as short as 100 ms. These requirements must be satisfied while maintaining low noise, high dynamic range, and low crosstalk. A promising readout candidate for future TES arrays is the microwave SQUID multiplexer, which offers several gigahertz of readout bandwidth per pair of coaxial cables. In microwave SQUID multiplexing, sensor signals are coupled to RF-SQUIDs embedded in superconducting microwave resonators, which are probed via a common microwave feedline and read out using gigahertz signals. This form of SQUID multiplexing moves complexity from the cryogenic stages to room temperature hardware and digital signal processing firmware which must synthesize the microwave tones and process the information contained within them. To demultiplex signals from the microwave SQUID multiplexer, we have implemented an FPGA-based firmware architecture that is flexible enough to read out a variety of differently optimized TESs. A gamma-ray spectrometer targeted at nuclear materials accounting applications, known as SLEDGEHAMMER, is an early adopter of microwave SQUID multiplexing and is driving our current firmware development effort. This instrument utilizes 300 kHz full-width half-maximum resonators with 256 channels in a one gigahertz wide band. We have recently demonstrated undegraded readout of 128 channels using two ROACH2s on a single pair of coaxial cables. This manuscript describes the firmware implementation for the readout electronics of these early array-scale demonstrations. [ABSTRACT FROM AUTHOR]

Transition-edge sensor X-ray microcalorimeters are usually calibrated empirically, as the most widely used calibration metric, optimal filtered pulse height (OFPH), in general has an unknown dependence on photon energy, Eγ. Because the calibration function can only be measured at specific points where photons of a known energy can be produced, this unknown dependence of OFPH on Eγ leads to calibration errors and the need for time-intensive calibration measurements and analysis. A calibration metric that is nearly linear as a function of Eγ could help alleviate these problems. In this work, we assess the linearity of a physically motivated calibration metric, EJoule. We measure calibration pulses in the range 4.5 keV 

Transition edge sensors (TESs) have proven to be highly sensitive and versatile X-ray spectrometers. Upcoming missions, including Athena X-IFU, will rely on highly multiplexed focal planes where more than 32 TES pixels are read out using a single SQUID amplifier channel. We have implemented an error correction algorithm for code-division multiplexed TES signals that can compensate for potential failures of individual SQUID readout channels and that is both scalable and easily implemented in hardware. We present this algorithm for error correction and show results of laboratory tests to assess algorithm performance at recovering TES channels after a SQUID failure. [ABSTRACT FROM AUTHOR]

We consider how to analyze microcalorimeter pulses for quantities that are nonlinear in the data, while preserving the signal-to-noise advantages of linear optimal filtering. We successfully apply our chosen approach to compute the electrothermal feedback energy deficit (the “Joule energy”) of a pulse, which has been proposed as a linear estimator of the deposited photon energy. [ABSTRACT FROM AUTHOR]

The number of elements in most cryogenic sensor arrays is limited by the technology available to multiplex signals from the arrays into a smaller number of wires and readout amplifiers. The largest demonstrated arrays of transition-edge sensor (TES) microcalorimeters contain roughly 250 detectors and use time-division multiplexing with Superconducting Quantum Interference Devices (SQUIDs). The bandwidth limits of this technology constrain the number of sensors per amplifier chain, a quantity known as the multiplexing factor, to several 10s. With microwave SQUID multiplexing, we can expand the readout bandwidth and enable much larger multiplexing factors. While microwave SQUID multiplexing of TES microcalorimeters has been previously demonstrated with small numbers of detectors, we now present a fully scalable demonstration in which 128 TES detectors are read out on a single pair of coaxial cables. [ABSTRACT FROM AUTHOR]

In order to improve pixel count and collecting area, future transition edge sensor X-ray focal planes require pixels with both a higher coverage of the active area and compatibility with in-focal-plane multiplexing. To achieve these improvements, we have developed a pixel with an “overhanging” geometry that allows us room for multiplexing elements underneath the absorber simultaneously with the possibility of near full coverage of the focal plane. We have fabricated and tested such a pixel. We have demonstrated a spectroscopic resolution of 3.2 eV full-width at half-maximum at 5.9 keV, thereby showing that it is suitable for applications in the near future. [ABSTRACT FROM PUBLISHER]

The so-called “optimal filter” analysis of a microcalorimeter's x-ray pulses is statistically optimal only if all pulses have the same shape, regardless of energy. However, the shapes of pulses from a nonlinear detector can and do depend on the pulse energy. A pulse-fitting procedure that we call “tangent filtering” accounts for the energy dependence of the shape and should, therefore, achieve superior energy resolution. We take a geometric view of the pulse-fitting problem and give expressions to predict how much the energy resolution stands to benefit from such a procedure. We also demonstrate the method with a case study of K-line fluorescence from several 3d transition metals. The method improves the resolution from 4.9 to 4.2 eV at the Cu K $\alpha$ line (8.0 keV). [ABSTRACT FROM PUBLISHER]

In superconducting transition-edge sensor X-ray detectors, we observe that as the thermal conductance (G) to the heat bath increases, the resistive transition broadens. Consequently, the sensitivity of films to deposited energy worsens. Using a two-fluid model for the superconducting-to-normal transition in a thin film, we show that this broadening can be attributed to the larger current (I0) necessary for biasing the film at a given point in the transition for higher-G devices, resulting in a higher Ic0/I0 ratio (Ic0 is the film's critical current at zero temperature). To recover a sharper transition, we fabricated rectangular films with varying numbers of internal normal-metal structures while keeping G constant, allowing the independent variation of both I0 and Ic0. We show that it is possible to manipulate the transition width and G independently, thus enabling fast thermal sensors with an excellent energy resolution. [ABSTRACT FROM AUTHOR]

Code-division multiplexing (CDM) offers a path to reading out large arrays of transition edge sensor (TES) X-ray microcalorimeters with excellent energy and timing resolution. We demonstrate the readout of X-ray TESs with a 32-channel flux-summed code-division multiplexing circuit based on superconducting quantum interference device (SQUID) amplifiers. The best detector has energy resolution of 2.28 ± 0.12 eV FWHM at 5.9 keV and the array has mean energy resolution of 2.77 ± 0.02 eV over 30 working sensors. The readout channels are sampled sequentially at 160 ns/row, for an effective sampling rate of 5.12 μ/channel. The SQUID amplifiers have a measured flux noise of 0:17 μΦ0/√Hz (non-multiplexed, referred to the first stage SQUID). The multiplexed noise level and signal slew rate are sufficient to allow readout of more than 40 pixels per column, making CDM compatible with requirements outlined for future space missions. Additionally, because the modulated data from the 32 SQUID readout channels provide information on each X-ray event at the row rate, our CDM architecture allows determination of the arrival time of an X-ray event to within 275 ns FWHM with potential benefits in experiments that require detection of near-coincident events. [ABSTRACT FROM AUTHOR]

X-ray emission spectroscopy (XES) is a powerful element-selective tool to analyze the oxidation states of atoms in complex compounds, determine their electronic configuration, and identify unknown compounds in challenging environments. Until now the low efficiency of wavelength-dispersive X-ray spectrometer technology has limited the use of XES, especially in combination with weaker laboratory X-ray sources. More efficient energy-dispersive detectors have either insufficient energy resolution because of the statistical limits described by Fano or too low counting rates to be of practical use. This paper updates an approach to high-resolution X-ray emission spectroscopy that uses a microcalorimeter detector array of superconducting transition-edge sensors (TESs). TES arrays are discussed and compared with conventional methods, and shown under which circumstances they are superior. It is also shown that a TES array can be integrated into a table-top time-resolved X-ray source and a soft X-ray synchrotron beamline to perform emission spectroscopy with good chemical sensitivity over a very wide range of energies. [ABSTRACT FROM AUTHOR]

This work presents an x-ray absorption measurement by use of ionizing radiation generated by a femtosecond pulsed laser source. The spectrometer was a microcalorimetric array whose pixels are capable of accurately measuring energies of individual radiation quanta. An isotropic continuum x-ray spectrum in the few-keV range was generated from a laser plasma source with a water-jet target. X rays were transmitted through a ferrocene powder sample to the detector, whose pixels have average photon energy resolution ΔE=3.14 eV full-width-at-half-maximum at 5.9 keV. The bond distance of ferrocene was retrieved from this first hard-x-ray absorption fine-structure spectrum collected with an energy-dispersive detector. This technique will be broadly enabling for time-resolved observations of structural dynamics in photoactive systems. [ABSTRACT FROM AUTHOR]

We demonstrate the code-division multiplexing (CDM) readout of eight transition-edge sensor microcalorimeters. The energy resolution is 3.0 eV (full width at half-maximum) or better at 5.9 keV, with a best resolution of 2.3 eV and a mean of 2.6 eV over the seven modulated detectors. The flux-summing CDM system is described and compared with similar time-division multiplexing (TDM) readout. We show that the [formula] multiplexing disadvantage associated with TDM is not present in CDM. This demonstration establishes CDM as both a simple route to higher performance in existing TDM microcalorimetric experiments and a long-term approach to reaching higher multiplexing factors. [ABSTRACT FROM AUTHOR]

High-resolution superconducting gamma-ray sensors show potential for the more accurate analysis of nuclear material. These devices are part of a larger class of microcalorimeters and bolometers based on transition edge sensors (TESs) that have two distinct thermal bodies. We derive the time domain behavior of the current and temperature for compound TES devices in the small signal limit and demonstrate the utility of these equations for device design and characterization. In particular, we use the model to fit pulses from our gamma-ray microcalorimeters and demonstrate how critical damping and electrothermal stability can be predicted. [ABSTRACT FROM AUTHOR]

Improvements in superconductor device fabrication, detector hybridization techniques, and superconducting quantum interference device readout have made square-centimeter-sized arrays of gamma-ray microcalorimeters, based on transition-edge sensors (TESs), possible. At these collecting areas, gamma microcalorimeters can utilize their unprecedented energy resolution to perform spectroscopy in a number of applications that are limited by closely-spaced spectral peaks, for example, the nondestructive analysis of nuclear materials. We have built a 256 pixel spectrometer with an average full-width-at-half-maximum energy resolution of 53 eV at 97 keV, a useable dynamic range above 400 keV, and a collecting area of 5 cm2. We have demonstrated multiplexed readout of the full 256 pixel array with 236 of the pixels (91%) giving spectroscopic data. This is the largest multiplexed array of TES microcalorimeters to date. This paper will review the spectrometer, highlighting the instrument design, detector fabrication, readout, operation of the instrument, and data processing. Further, we describe the characterization and performance of the newest 256 pixel array. [ABSTRACT FROM AUTHOR]