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DOE OSTI2020

Diffraction and photon exchange processes at the LHC and parton saturation

We present a review of the recent theoretical and experimental developments related to the field of diffraction, parton saturation, and forward physics. We first discuss our present understanding of the proton structure in terms of quarks and gluons, the degrees of freedom of quantum chromodynamics. We then focus on some of the main results on diffraction at the HERA electron–proton collider in DESY, Germany, at the Tevatron proton–antiproton collider at Fermilab, Batavia, US, and at the CERN Large Hadron Collider (LHC) proton–proton and nucleus–nucleus collider, which is located in Geneva, Switzerland. We also present a selected amount of results on diffraction and photon exchanges that can be done at the LHC experiments and at a future Electron Ion Collider (EIC) to be built in the US at Brookhaven National Laboratory, New York.

Physics↗

DOE OSTI2021

X-ray computed tomography using partially coherent Fresnel diffraction with application to an optical fiber

A reconstruction algorithm for partially coherent x-ray computed tomography (XCT) including Fresnel diffraction is developed and applied to an optical fiber. The algorithm is applicable to a high-resolution tube-based laboratory-scale x-ray tomography instrument. The computing time is only a few times longer than the projective counterpart. The algorithm is used to reconstruct, with projections and diffraction, a tilt series acquired at the micrometer scale of a graded-index optical fiber using maximum likelihood and a Bayesian method based on the work of Bouman and Sauer. The inclusion of Fresnel diffraction removes some reconstruction artifacts and use of a Bayesian prior probability distribution removes others, resulting in a substantially more accurate reconstruction.

Levine, Zachary H. (ORCID:000000029928276X)↗

DOE OSTI2021

Evaluation of a fiber-coupled x-ray diffraction detector for dynamic compression experiments

The long-term x-ray diffraction (XRD) detector scheme compatible with Z-containment experiments will involve conversion of the diffracted x-rays to optical light, which will be transported away from the Z-Dynamic Materials Properties (DMP) load and detected on a fast-gated camera. In this so-called DIffraction SCintillator Optic (DISCO) scheme , the scintillator is coupled to a long, coherent imaging fiber bundle using a custom lens system with high numerical aperture. In addition, the DISCO diagnostic incorporates time-gating to allow measurement only during the short time window of the x-ray pulse in which XRD occurs, thereby significantly reducing unwanted background generated by the Z-DMP load. Dynamic compression experiments were performed at the Chama target chamber to evaluate the DISCO diagnostic . Specifically, a Zr sample was laser-shocked with the Chaco laser while the Z-Beamlet (ZBL) laser was used to generate x-rays, which enabled time-gated 6.7-keV XRD patterns from the compressed Zr sample to be obtained.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2024

Diffraction Measurement of Reaction Products in Shock Compressed TATB on the NIF

The shock-induced reaction of high explosives to gaseous and solid reaction products is a rapid, complex process. Understanding solid reaction product structure and formation kinetics is essential in determining the high-pressure equation of state of these multicomponent systems. We use the National Ignition Facility (NIF) to shock compress ~500-µm thick pressed powder high-explosive TATB samples to 70-135 GPa and collect in situ structural data on detonation byproducts using the TARDIS X-ray diffraction diagnostic. Velocimetry is used to record the transmitted compression wave profile, which is well described by Cheetah hydrocode simulations coupled with a reactive flow model, providing strong evidence of reaction in the TATB sample. While an unambiguous determination of the product phases was not possible owing to the low signal-to-noise quality of the diffraction signal, X-ray diffraction data of the product phases formed within the first 50 ns of the reaction is most consistent with a mixture of amorphous products and crystalline hexagonal diamond.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Extreme Longitudinal Compression of Optimized Beams for MEV Ultrafast Electron Diffraction (Final Technical Report)

We worked out the design of a high repetition rate MeV energy ultrafast electron diffraction instrument based on the existing Cornell photoinjector, which can readily be applied to the presented findings. This example is a blueprint of other similarly arranged UED setups. Using particle tracking simulations in conjunction with multiobjective genetic algorithm optimization, we explored the smallest bunch lengths, emittance, and probe spot sizes achievable. As two limits, we defined stroboscopic conditions (with single electrons per pulse) and operation with 10 5 electrons per bunch which may be suitable for single-shot diffraction images. In the stroboscopic case, the flexibility provided by the many cavity bunching and acceleration allows for longitudinal phase space linearization without a higher harmonic field, providing sub-fs bunch lengths at the sample. Given low emittance photoemission conditions, these small bunch lengths can be maintained with probe transverse sizes at the single micron (1 μm) scale and below. In the case of 10 5 electrons per pulse, we simulated state-of-the-art 5D brightness conditions: rms bunch lengths of 10 fs with 3-nm normalized emittances, while permitting repetition rates as high as 1.3 GHz. We showed that in conjunction with collimating apertures, a novel focusing scheme achieves very high-quality emittance compensation for the central core of the beam composing 40% of particles, for a resulting beam size of 5 μm (rms). Finally, to aid in the design of new SRF-based ultrafast electron diffraction machines, we simulated the trade-off between the number of cavities used and achievable bunch length and emittance. In the longitudinal dimension, we made use of the fact that MeV UED requires much lower energy than the 15-MeV maxi mum energy of Cornell’s CBETA injector, and we may therefore use several of the SRF cavities for bunch length compression. In practice, we used a genetic optimization algorithm to choose the phases and amplitudes of the cavities appropriately for optimal bunching. In the zero space charge case, we found that bunching and acceleration are distributed across the six cavities in a way that produces a linearizing effect. And we showed that the ultimate bunch length can be limited by time-of-flight differences arising from transverse size and transverse momentum spread. The space charge code developed and used for this development is now permanent part of the Bmad accelerator simulation code and has already contributed to other developments, e.g., for the EIC electron cooler design.

43 PARTICLE ACCELERATORS↗

DOE OSTI2020

Development of a Stress Sensor for In-Situ High-Pressure Deformation Experiments Using Radial X-Ray Diffraction

We developed a stress sensor for in-situ deformation experiments using synchrotron radial X-ray diffraction. This stress sensor provided nearly diffraction-plane-independent stress that, when used in series with a sample, reduced the uncertainty of the average stress estimation acting on a sample. Here, we present the results of a study where pyrope was used as a stress sensor. Using a Deformation-DIA (D-DIA) high-pressure deformation apparatus, pyrope, olivine and alumina were deformed in the same run/cell assembly placed in series along the compression direction. Deformation experiments were conducted at pressures between 4 and 5 GPa and temperatures between 730 and 1273 K with strain-rates between 10 –5 and 10 –6 s –1 . Stresses estimated from various (hkl) planes in pyrope were nearly the same; i.e., pyrope is plastically isotropic with ≤10 % variation with (hkl). However, stresses from various (hkl) planes in olivine and alumina varied by approximately a factor of 3. Comparisons between average stresses inferred from pyrope and those from different diffraction planes in olivine and alumina showed that the average stress in these materials evolved from low-end stress, estimated from various (hkl) planes at small strain, to high-end stress at a large strain. This suggests that the rate-controlling slip system in these materials changes from the soft to the hard slip system with strain.

58 GEOSCIENCES↗

DOE OSTI2026

In Situ High-Temperature Ultrafast Electron Diffraction through Integrated Furnace and MEMS Platforms

Temperature fundamentally governs phase stability, defect evolution, and transport behavior in materials. Despite its central role, direct measurements of structural evolution at elevated temperatures on ultrafast timescales have remained limited. Here, we report the design, integration, and validation of 2 complementary in situ heating platforms that substantially extend the thermal operating range of ultrafast electron diffraction (UED). A compact furnace-type heating stage enables stable diffraction measurements from room temperature to 800 K with ±0.1 K stability under ultrahigh vacuum, achieved through multi-sensor feedback control, dual air-cooling channels, and a thermally isolated motion stage. In parallel, a microelectromechanical system (MEMS)-based heating platform provides rapid thermal response and access to extreme temperatures ≥1,373 K with ±0.1 K stability over hundreds-micrometer regions while supporting simultaneous electrical biasing for electrothermal coupling studies. Absolute temperature calibration is established using diffraction-based thermometry via aluminum lattice expansion and independently validated through in situ melting of bismuth thin films. UED measurements further reveal pronounced temperature-dependent nonequilibrium lattice dynamics in bismuth, including modifications to electron–phonon coupling and Debye–Waller behavior, as well as enhanced ultrafast diffuse scattering in aluminum at elevated temperatures. Together, these developments establish a practical framework for quantitative, time-resolved studies of temperature-driven kinetics and nonequilibrium structural dynamics under extreme thermal environments.

Bai, Qianqian [Chinese Academy of Sciences (CAS), ↗

DOE OSTI2019

Quantitative Uncertainty Analysis for Diffraction

Current software uses a least squares statistical method. For each model parameter, current software yields a point estimate and estimated standard error for each point estimate. In contrast, we have employed a Bayesian approach with sampling algorithm to provide a full posterior probability density function on each model parameter. This yields a different type of solution (probabilistic) with better fidelity. The Quantitative Uncertainty Analysis for Diffraction (QUAD) package returns a matrix of affect model parameters as a function of iteration through the MCMC analysis. QUAD is a Python code that allows for analysis of X-ray and neutron diffraction data to infer the structure of materials with quantifiable certainty. The code uses Bayesian statistics and Markov chain sampling algorithms to create posterior probability distributions on all material structure parameters that are modeled by a researcher. The statistical packages use the open source GSASII project as a library to calculate model diffraction patterns.

Fancher, ChristopherM↗

NASA NTRS1974

Electromagnetic and scalar diffraction by a right-angled wedge with a uniform surface impedance

The diffraction of an electromagnetic wave by a perfectly-conducting right-angled wedge with one surface covered by a dielectric slab or absorber is considered. The effect of the coated surface is approximated by a uniform surface impedance. The solution of the normally incident electromagnetic problem is facilitated by introducing two scalar fields which satisfy a mixed boundary condition on one surface of the wedge and a Neumann of Dirichlet boundary condition on the other. A functional transformation is employed to simplify the boundary conditions so that eigenfunction expansions can be obtained for the resulting Green's functions. The eigenfunction expansions are transformed into the integral representations which then are evaluated asymptotically by the modified Pauli-Clemmow method of steepest descent. A far zone approximation is made to obtain the scattered field from which the diffraction coefficient is found for scalar plane, cylindrical or sperical wave incident on the edge. With the introduction of a ray-fixed coordinate system, the dyadic diffraction coefficient for plane or cylindrical EM waves normally indicent on the edge is reduced to the sum of two dyads which can be written alternatively as a 2 X 2 diagonal matrix.

Hwang, Y. M.↗

NASA NTRS1975

Calculation of arbitrary-order diffraction efficiencies of thick gratings with arbitrary grating shape

A method for calculating arbitrary-order diffraction efficiencies of thick, lossless transmission gratings with arbitrary periodic grating shapes has been developed. A Fourier-series representation of the grating is employed, along with a coupled-mode theory of diffraction. For illustration, numerical values of the diffraction efficiencies at the first three Bragg angles are calculated for sinusoidal, square-wave, triangular, and saw-tooth gratings. Numerical results for the same grating shapes with the same parameters are also calculated for comparison, by extending Burckhardt's numerical method for analyzing thick sinusoidal gratings. The comparison shows that the coupled-mode theory provides results with relative computational ease and results that are in agreement with calculations obtained by extending the more-rigorous Burckhardt theory to nonsinusoidal grating shapes and to higher-order Bragg angles.

Su, S. F.↗

NASA NTRS1976

Computer modeling of electromagnetic problems using the geometrical theory of diffraction

Some applications of the geometrical theory of diffraction (GTD), a high frequency ray optical solution to electromagnetic problems, are presented. GTD extends geometric optics, which does not take into account the diffractions occurring at edges, vertices, and various other discontinuities. Diffraction solutions, analysis of basic structures, construction of more complex structures, and coupling using GTD are discussed.

Burnside, W. D.↗

NASA NTRS1970

The far field diffraction pattern for corner reflectors with complex reflection coefficients

The far field diffraction pattern of a geometrically perfect corner reflector is examined analytically for normally incident monochromatic light. The states of polarization and the complex amplitudes of the emerging light are expressed through transformation matrices in terms of those of the original incident light for each sextant of the face in a single coordinate system. The analytic expression of the total diffraction pattern is obtained for a circular face. This expression consists of three component functions in addition to the basic Airy function. The coefficient of each function is expressed in terms of complex coefficients of reflectance of the reflecting surface. Some numerical results for different reflecting surfaces, including total internal reflection, are presented. The iso-intensity contours of the diffraction pattern evaluated from the analytical expressions for an uncoated solid corner reflector are also presented along with the photographs of the pattern.

Chang, R. F.↗

NASA NTRS1978

Effects of diffraction in multiple-grid telescopes for X-ray astronomy

Diffraction effects in modern designs for grid collimator telescopes (assumed to have roughly a 100-micron grid period) are apparent at wavelengths longer than 1 A and are dominant at wavelengths longer than 10 A. In collimators with many grids spaced far apart the effects of diffracation are to reduce strongly the peak transmission of the collimator at longer wavelengths and to broaden it by about the amount expected from Fraunhofer diffraction through a slit the size of the grid openings. Comparisons between two-collimator measurements and the present calculations show reasonable agreement; it is therefore concluded that the present single-collimator calculation gives a good representation of their diffraction-limited angular response.

Lindsey, C. A.↗

NASA NTRS1979

Diffraction by an arbitrary subreflector - GTD solution

The high-frequency asymptotic solution of diffraction by a conducting subreflector is investigated. The scattered field is determined up to and including terms of order k to the -1/2 relative to the incident field by using Keller's geometrical theory of diffraction and the newly developed uniform asymptotic theory of diffraction. The key feature of this approach is that the surface of the subreflector is completely arbitrary; in fact, it is only necessary to specify the surface at a set of discrete points over a random net.

Lee, S.-W.↗

NASA NTRS1980

Comparison of two leading uniform theories of edge diffraction with the exact uniform asymptotic solution

The diffraction of an arbitrary cylindrical wave by a half-plane has been treated by Rahmat-Samii and Mittra who used a spectral domain approach. In this paper, their exact solution for the total field is expressed in terms of a new integral representation. For large wave number k, two rigorous procedures are described for the exact uniform asymptotic expansion of the total field solution. The uniform expansions obtained are valid in the entire space, including transition regions around the shadow boundaries. The final results are compared with the formulations of two leading uniform theories of edge diffraction, namely, the uniform asymptotic theory and the uniform theory of diffraction. Some unique observations and conclusions are made in relating the two theories.

Boersma, J.↗

NASA NTRS1951

X-Ray Diffraction Study of the Internal Structure of Supercooled Water

A Bragg X-ray spectrometer equipped with a volume-sensitive Geiger counter and Soller slits and employing filtered molybdenum Ka radiation was used to obtain a set of diffracted intensity curves as a Punction of angle for supercooled water. Diffracted intensity curves in the temperature region of 21 to -16 C were obtained. The minimum between the two main diffraction peaks deepened continuously with lowering temperature, indicating a gradual change in the internal structure of the water. No discontinuity in this trend was noted at the melting point. The internal structure of supercooled water was concluded to become progressively more ice-like as the temperature is lowered.

Dorsch, Robert G.↗

NASA NTRS1985

Hadron cross sections at ultra high energies and unitarity bounds on diffraction dissociation

It was shown that if unitarity bounds on diffractive cross sections are valid at ultra high energies then diffractive dominance models which ascribe the increase in total hadron-hadron cross sections to diffractive processes only are ruled out. Calculations also show that cosmic ray cross sections derived from air shower experiments at ultra high energies clearly rule out models for hadron-hadron cross sections with nat.log ns energy dependence and favor those with nat.log n(2)s variation.

Yodh, G. B.↗

NASA NTRS1985

A method of rapidly obtaining concentration-depth profiles from X-ray diffraction

A broadened diffraction peak, or intensity band, is observed in the case diffraction from a nonhomogeneous phase in which the variations in compositions result in a range of lattice spacings. An intriguing aspect regarding the relationship between the X-ray diffraction band and the composition-depth profile is the hypersensitivity of the intensity band to the shape of the profile. A number of investigators have sought to use this sensitivity to construct high-precision profiles. Difficulties encountered are related to complications due to intensity broadening, and prohibitive computational requirements. Simulation techniques have provided the most accurate interpretation of the intensity band. However, the involved calculations have been prohibitively long. The present study discusses a technique which has simple computational requirements and is as accurate and flexible as the simulation techniques.

Wiedemann, K. E.↗