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X-ray diffraction gratings play an essential role in high-resolution spectroscopy of astrophysical phenomena. We present some scientific highlights from the X-ray grating spectrometers (XGS) on board of the Chandra and XMM/Newton missions, XGS optical design, and the basic physics of grating diffraction geometry and efficiency. We review design, fabrication, and performance of the currently orbiting transmission and reflection grating elements, followed by descriptions of the state-of-the art of more advanced grating technologies that promise orders-of-magnitude improvements in XGS performance, especially in combination with advanced X-ray telescope mirrors. A few key science questions that require new grating technology are posed, and powerful future mission concepts and recent and approved missions are presented., Comment: 40 pages, 12 figures. To be submitted to Springer for publication in the ISSI Scientific Reports series

High-resolution spectroscopy in soft X-rays ($<2$ keV) requires diffractive elements to resolve any astrophysically relevant diagnostics, such as closely spaced lines, weak absorption lines, or line profiles. The Rowland torus geometry describes how gratings and detectors need to be positioned to optimize the spectral resolving power. We describe how an on-axis Rowland geometry can be tilted to accommodate blazed gratings. In this geometry, two channels with separate optical axes can share the same detectors (double tilted Rowland spectrograph, DTRS). Small offsets between the channels can mitigate the effect of chip gaps and reduce the alignment requirements during the construction of the instrument. The DTRS concept is especially useful for sub-apertured mirrors, because it allows an effective use of space in the entrance aperture of a spacecraft. One mission that applies this concept is the Arcus Probe., Comment: Accepted by ApJ, 13 pages, 9 figures. Interactive figures are not available on arxiv, but will be hosted by ApJ

The Arcus Probe mission concept has been submitted as an Astrophysics Probe Explorer candidate. It features two co-aligned high-resolution grating spectrometers: one for the soft x-ray band and one for the far UV. Together, these instruments can provide unprecedented performance to address important key questions about the structure and dynamics of our universe across a large range of length scales. The X-ray Spectrometer (XRS) consists of four parallel optical channels, each featuring an x-ray telescope with a fixed array of 216 lightweight, high-efficiency blazed transmission gratings, and two CCD readout arrays. Average spectral resolving power $\lambda/\Delta \lambda > 2,500$ ($\sim 3500$ expected) across the 12-50 \AA \ band and combined effective area $> 350$ cm$^2$ ($> 470$ cm$^2$ expected) near OVII wavelengths are predicted, based on the measured x-ray performance of spectrometer prototypes and detailed ray trace modeling. We describe the optical and structural design of the grating arrays, from the macroscopic grating petals to the nanoscale gratings bars, grating fabrication, alignment, and x-ray testing. Recent x-ray diffraction efficiency results from chemically thinned grating bars are presented and show performance above mission assumptions., Comment: 30 pages, 11 figures, submitted to JATIS

Arcus is a concept for a probe class mission to deliver high-resolution FUV and X-ray spectroscopy. For X-rays, it combines cost-effective silicon pore optics (SPO) with high-throughput critical-angle transmission (CAT) gratings to achieve $R> 3000$ in a bandpass from 12-50 Angstroem. We show in detail how the X-ray and the UV spectrographs (XRS and UVS) on Arcus will be aligned to each other. For XRS we present ray-tracing studies to derive performance characteristics such as the spectral resolving power and effective area, study the effect of misalignments on the performance, and conclude that most tolerances can be achieved with mechanical means alone. We also present an estimate of the expected on-orbit background., Comment: submitted to SPIE UV, X-Ray, and Gamma-Ray Space Instrumentation for Astronomy XXIII (2023)

The Marshall Grazing Incidence X-ray Spectrometer (MaGIXS) sounding rocket experiment launched on July 30, 2021 from the White Sands Missile Range in New Mexico. MaGIXS is a unique solar observing telescope developed to capture X-ray spectral images, in the 6 - 24 Angstrom wavelength range, of coronal active regions. Its novel design takes advantage of recent technological advances related to fabricating and optimizing X-ray optical systems as well as breakthroughs in inversion methodologies necessary to create spectrally pure maps from overlapping spectral images. MaGIXS is the first instrument of its kind to provide spatially resolved soft X-ray spectra across a wide field of view. The plasma diagnostics available in this spectral regime make this instrument a powerful tool for probing solar coronal heating. This paper presents details from the first MaGIXS flight, the captured observations, the data processing and inversion techniques, and the first science results., Comment: 20 pages, 18 figures

Arcus is a proposed soft x-ray grating spectrometer Explorer. It aims to explore cosmic feedback by mapping hot gases within and between galaxies and galaxy clusters and characterizing jets and winds from supermassive black holes, and to investigate the dynamics of protoplanetary discs and stellar accretion. Arcus features 12 m-focal-length grazing-incidence silicon pore optics (SPO) developed for the Athena mission. Critical-angle transmission (CAT) gratings efficiently disperse high diffraction orders onto CCDs. We report new and improved x-ray performance results for Arcus-like CAT gratings, including record resolving power for two co-aligned CAT gratings. Multiple Arcus prototype grating facets were illuminated by an SPO at the PANTER facility. The facets consist of $32\times32.5$ mm$^2$ patterned silicon membranes, bonded to metal frames. The bonding angle is adjusted according to the measured average tilt angle of the grating bars in the membrane. Two simultaneously illuminated facets show minor broadening of the Al-K$_{\alpha}$ doublet in 18$^{\rm th}$ and 21$^{\rm st}$ orders with a best fit record effective resolving power of $R_G \approx 1.3^{+\infty}_{-0.5}\times10^4$ ($3\sigma$), about 3-4 times the Arcus requirement. We measured the diffraction efficiency of quasi-fully illuminated gratings at O-K wavelengths in orders 4-7 in an Arcus-like configuration and compare results with synchrotron spot measurements. After corrections for geometrical effects and bremsstrahlung continuum we find agreement between full and spot illumination at the two different facilities, as well as with the models used for Arcus effective area predictions. We find that these flight-like gratings meet diffraction efficiency and greatly exceed resolving power Arcus requirements., Comment: 19 pages, 16 figures

The Marshall Grazing Incidence X-ray Spectrometer (MaGIXS) is a sounding rocket experiment that observes the soft X-ray spectrum of the Sun from 6.0 - 24 Angstrom (0.5 - 2.0 keV), successfully launched on 30 July 2021. End-to-end alignment of the flight instrument and calibration experiments are carried out using the X-ray and Cryogenic Facility (XRCF) at NASA Marshall Space Flight Center. In this paper, we present the calibration experiments of MaGIXS, which include wavelength calibration, measurement of line spread function, and determination of effective area. Finally, we use the measured instrument response function to predict the expected count rates for MaGIXS flight observation looking at a typical solar active region, Comment: 20 pages, 16 figures, Accepted for publication in the Astrophysical Journal

High-resolution ($R = \lambda /\Delta \lambda > 2000$) x-ray absorption and emission line spectroscopy in the soft x-ray band is a crucial diagnostic for the exploration of the properties of ubiquitous warm and hot plasmas and their dynamics in the cosmic web, galaxy clusters, galaxy halos, intragalactic space, and star atmospheres. Soft x-ray grating spectroscopy with $R > 10{,}000$ has been demonstrated with critical-angle transmission (CAT) gratings. CAT gratings combine the relaxed alignment and temperature tolerances and low mass of transmission gratings with high diffraction efficiency blazed in high orders. They are an enabling technology for the proposed Arcus grating explorer and were selected for the Lynx design reference mission grating spectrometer instrument. Both Arcus and Lynx require the manufacture of hundreds to perhaps $\approx 2000$ large-area CAT gratings. We are developing new patterning and fabrication process sequences that are conducive to large-format volume processing on state-of-the-art 200 mm wafer tools. Recent x-ray tests on 200 nm-period gratings patterned using e-beam-written masks and 4x projection lithography in conjunction with silicon pore focusing optics demonstrated $R \approx 10^4$ at 1.49 keV. Extending the grating depth from 4 $\mu$m to 6 $\mu$m is predicted to lead to significant improvements in diffraction efficiency and is part of our current efforts using a combination of deep reactive-ion etching and wet etching in KOH solution. We describe our recent progress in grating fabrication and report our latest diffraction efficiency and modeling results., Comment: 11 pages, 8 figures, submitted to Proc. SPIE 11444

We describe a new implementation of a broad-band soft X-ray polarimeter, substantially based on a previous design. This implementation, the Pioneer Soft X-ray Polarimeter (PiSoX) is a SmallSat, designed for NASA's call for Astrophysics Pioneers, small missions that could be CubeSats, balloon experiments, or SmallSats. As in the REDSoX Polarimeter, the grating arrangement is designed optimally for the purpose of polarimetry with broad-band focussing optics by matching the dispersion of the spectrometer channels to laterally graded multilayers (LGMLs). The system can achieve polarization modulation factors over 90%. For PiSoX, the optics are lightweight Si mirrors in a one-bounce parabolic configuration. High efficiency, blazed gratings from opposite sectors are oriented to disperse to a LGML forming a channel covering the wavelength range from 35 to 75 Angstroms (165 - 350 eV). Upon satellite rotation, the intensities of the dispersed spectra, after reflection and polarizing by the LGMLs, give the three Stokes parameters needed to determine a source's linear polarization fraction and orientation. The design can be extended to higher energies as LGMLs are developed further. We describe examples of the potential scientific return from instruments based on this design., Comment: 20 pages, 8 figures, to appear in Proceedings SPIE, volume 11444

Lynx is one of four large-mission concept studies for NASA's 2020 Decadal survey. The design reference mission includes an X-ray grating spectrometer (XGS) based on critical-angle transmission (CAT) gratings. In the past we studied different grating sizes and arrangements using traditional flat CAT gratings with constant bar spacing. However, new technology development brings chirped gratings in reach. Using chirped gratings where the grating bar spacing varies over a grating allows us to fill the aperture with larger gratings because the chirp can compensate for some aberrations caused by the deviation of large flat gratings from the Rowland torus. This reduces the area blocked by grating support structures. Using larger gratings also carries potential cost savings. We use ray-tracing to study an XGS design with chirped grating and find that using chirped gratings of $80 * 160$ mm size allows us to reduce the number of gratings from a few thousand to a few hundred, while simultaneously increasing the effective area by 25% and keeping the resolving power constant. Bending those gratings to maintain a constant blaze angle over the entire grating increases the effective area by another 5-10%., Comment: will be published in SPIE proceedings

Astronomical imaging with micro-arcsecond ($\mu$as) angular resolution could enable breakthrough scientific discoveries. Previously-proposed $\mu$as X-ray imager designs have been interferometers with limited effective collecting area. Here we describe X-ray telescopes achieving diffraction-limited performance over a wide energy band with large effective area, employing a nested-shell architecture with grazing-incidence mirrors, while matching the optical path lengths between all shells. We present two compact nested-shell Wolter Type 2 grazing-incidence telescope designs for diffraction-limited X-ray imaging: a micro-arcsecond telescope design with 14 $\mu$as angular resolution and 2.9 m$^2$ of effective area at 5 keV photon energy ($\lambda$=0.25 nm), and a smaller milli-arcsecond telescope design with 525 $\mu$as resolution and 645 cm$^2$ effective area at 1 keV ($\lambda$=1.24 nm). We describe how to match the optical path lengths between all shells in a compact mirror assembly, and investigate chromatic and off-axis aberrations. Chromatic aberration results from total external reflection off of mirror surfaces, and we greatly mitigate its effects by slightly adjusting the path lengths in each mirror shell. The mirror surface height error and alignment requirements for diffraction-limited performance are challenging but arguably achieveable in the coming decades. Since the focal ratio for a diffraction-limited X-ray telescope is extremely large ($f/D$~10$^5$), the only important off-axis aberration is curvature of field, so a 1 arcsecond field of view is feasible with a flat detector. The detector must fly in formation with the mirror assembly, but relative positioning tolerances are on the order of 1 m over a distance of some tens to hundreds of kilometers. While there are many challenges to achieving diffraction-limited X-ray imaging, we did not find any fundamental barriers., Comment: 20 pages, 11 figures, accepted for publication in Applied Optics

We present measurements of the resolving power of a soft x-ray spectrometer consisting of 200 nm-period lightweight, alignment-insensitive critical-angle transmission (CAT) gratings and a lightweight slumped-glass Wolter-I focusing mirror pair. We measure and model contributions from source, mirrors, detector pixel size, and grating period variation to the natural line width spectrum of the Al and Mg K$_{\alpha_1 \alpha_2}$ doublets. Measuring up to 18$^{\rm th}$ diffraction order at characteristic Al-K wavelengths we consistently obtain small broadening due to gratings corresponding to a minimum effective grating resolving power $R_g > 10,000$ with 90\% confidence. Upper limits are often compatible with $R_g = \infty$. Independent fitting of different diffraction orders, as well as ensemble fitting of multiple orders at multiple wavelengths, gives compatible results. Our data leads to uncertainties for the Al-K$_{\alpha}$ doublet line width and line separation parameters 2-3 times smaller than values found in the literature. Data from three different gratings are mutually compatible. This demonstrates that CAT gratings perform in excess of the requirements for the Arcus Explorer mission and are suitable for next-generation space-based x-ray spectrometer designs with resolving power 5-10 times higher than the transmission grating spectrometer on the Chandra X-ray Observatory.

Several high priority subjects in astrophysics can be addressed by a state-of-the-art soft x-ray grating spectrometer (XGS). An Explorer-scale, large-area (> 1,000 cm2), high resolving power (R > 3,000) XGS is highly feasible based on Critical-Angle Transmission (CAT) gratings, even for telescopes with angular resolution of 5-10 arcsec. Significantly higher performance can be provided by a CAT XGS on an X-ray-Surveyor-type mission. CAT gratings combine the advantages of blazed reflection gratings (high efficiency, use of higher diffraction orders) with those of transmission gratings (low mass, relaxed alignment and temperature requirements, transparent at high energies) with minimal mission resource demands. They are high-efficiency blazed transmission gratings that consist of freestanding, ultra-high aspect-ratio grating bars made from SOI wafers using anisotropic dry and wet etch techniques. Blazing is achieved through reflection off grating bar sidewalls. Silicon is well matched to the soft x-ray band, and existing silicon CAT gratings exceed 30% absolute diffraction efficiency, with clear paths for improvement. CAT gratings coated with heavier elements allow extension of the CAT grating principle to higher energies and larger angles, enabling higher resolving power at shorter wavelengths. We show x-ray data from CAT gratings coated with platinum using atomic layer deposition, and demonstrate blazing to higher energies and much larger blaze angles than possible with silicon. We measure resolving power of a CAT XGS consisting of a Wolter-I focusing mirror pair from GSFC and CAT gratings, performed at the MSFC SLF. Measurement of the Al Ka doublet in 18th order shows resolving power > 10,000, based on preliminary analysis. This demonstrates that currently fabricated CAT gratings are compatible with the most advanced XGS designs for future soft x-ray spectroscopy missions., Comment: submitted to Proc. SPIE 9905

We investigate the three-state antiferromagnetic Potts model on a simple cubic lattice with a cluster flipping Monte Carlo simulation algorithm in the temperature region below the transition into disorder at T_{c1}. We find both the well established broken-sublattice-symmetry (BSS) phase at low temperature and a new, rotationally symmetric phase at higher temperature, but below T_{c1}. The properties of the second phase and the transition temperature to the BSS phase are in disagreement with recent cluster-variation and Monte Carlo simulation results, but in agreement with simulations by Kolesik and Suzuki., Comment: 8 pages, RevTeX + 3 figures in a PostScript file

Lynx, one of the four strategic mission concepts under study for the 2020 Astrophysics Decadal Survey, provides leaps in capability over previous and planned x-ray missions and provides synergistic observations in the 2030s to a multitude of space- and ground-based observatories across all wavelengths. Lynx provides orders of magnitude improvement in sensitivity, on-axis subarcsecond imaging with arcsecond angular resolution over a large field of view, and high-resolution spectroscopy for point-like and extended sources in the 0.2- to 10-keV range. The Lynx architecture enables a broad range of unique and compelling science to be carried out mainly through a General Observer Program. This program is envisioned to include detecting the very first seed black holes, revealing the high-energy drivers of galaxy formation and evolution, and characterizing the mechanisms that govern stellar evolution and stellar ecosystems. The Lynx optics and science instruments are carefully designed to optimize the science capability and, when combined, form an exciting architecture that utilizes relatively mature technologies for a cost that is compatible with the projected NASA Astrophysics budget.

Lynx is a concept under study for prioritization in the 2020 Astrophysics Decadal Survey. Providing orders of magnitude increase in sensitivity over Chandra, Lynx will examine the first black holes and their galaxies, map the large-scale structure and galactic halos, and shed new light on the environments of young stars and their planetary systems. In order to meet the Lynx science goals, the telescope consists of a high-angular resolution optical assembly complemented by an instrument suite that may include a High Definition X-ray Imager, X-ray Microcalorimeter and an X-ray Grating Spectrometer. The telescope is integrated onto the spacecraft to form a comprehensive observatory concept. Progress on the formulation of the Lynx telescope and observatory configuration is reported in this paper.

NASA's Chandra X-ray Observatory continues to provide an unparalleled means for exploring the high-energy universe. With its half-arcsecond angular resolution, Chandra studies have deepened our understanding of galaxy clusters, active galactic nuclei, galaxies, supernova remnants, neutron stars, black holes, and solar system objects. As we look beyond Chandra, it is clear that comparable or even better angular resolution with greatly increased photon throughput is essential to address ever more demanding science questions-such as the formation and growth of black hole seeds at very high redshifts; the emergence of the first galaxy groups; and details of feedback over a large range of scales from galaxies to galaxy clusters. Recently, we initiated a concept study for such a mission, dubbed X-ray Surveyor. The X-ray Surveyor strawman payload is comprised of a high-resolution mirror assembly and an instrument set, which may include an X-ray microcalorimeter, a high-definition imager, and a dispersive grating spectrometer and its readout. The mirror assembly will consist of highly nested, thin, grazing-incidence mirrors, for which a number of technical approaches are currently under development-including adjustable X-ray optics, differential deposition, and new polishing techniques applied to a variety of substrates. This study benefits from previous studies of large missions carried out over the past two decades and, in most areas, points to mission requirements no more stringent than those of Chandra.

The future of x-ray astronomy depends upon development of x-ray telescopes with larger aperture areas (approx. = 3 square meters) and fine angular resolution (approx. = 1 inch). Combined with the special requirements of nested grazing-incidence optics, the mass and envelope constraints of space-borne telescopes render such advances technologically and programmatically challenging. Achieving this goal will require precision fabrication, alignment, mounting, and assembly of large areas (approx. = 600 square meters) of lightweight (approx. = 1 kilogram/square meter areal density) high-quality mirrors at an acceptable cost (approx. = 1 million dollars/square meter of mirror surface area). This paper reviews relevant technological and programmatic issues, as well as possible approaches for addressing these issues-including active (in-space adjustable) alignment and figure correction.