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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]

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]

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 

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]

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]

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]

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]