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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 325 records · Page 18
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

In-Operando Study of Shape Retention and Microstructure Development in a Hydrolyzing Sol–Gel Ink during 3D-Printing

3D printing of amorphous and crystalline ceramics is of paramount importance for the fabrication of a wide range of devices with applications across different technology fields. Printed ceramics are remarkably enabled by the sol-gel synthesis method in conjunction with continuous filament direct ink writing. During printing, multiple processes contribute to the evolution of inks including shape retention, chemical conversion, solidification, and microstructure formation. Traditionally, depending on the ink composition and printing environment, several mechanisms have been associated with the shape retention and solidification of 3D printed structures: gelation, rapid solvent evaporation, energy-driven phase transformation, and chemical-driven phase transformation. Understanding the fundamental differences between these mechanisms becomes key since they strongly influence the spatiotemporal evolution of the materials, as the out-of-equilibrium processes inherent to the extrusion, relaxation, and solidification of printed materials have significant effects on the materials properties. Herein, we investigate the shape retention mechanism and the hydrolysis-induced material conversion and microstructure formation during the 3D printing of a water reactive sol-gel ink that transforms into titanium dioxide-based ceramic. This study aims at identifying characteristic mechanisms associated with the material transformation, establishing connections between the microstructure development and the timescales associated with solidification under operando 3D-printing conditions. The investigation of this material's out-of-equilibrium pathways under processing conditions is enabled by time-resolved coherent X-ray scattering, providing simultaneous access to temporospatially resolved microstructural and dynamics information. Furthermore, we explore X-ray speckle tracking as a tool to resolve deformations of the microstructure in a printed filament associated with the deposition of consecutive filaments. Through this work, we aim at providing a fundamental understanding of the relationships behind these transformative processes in 3D printing and their timescales as the basis for achieving unprecedented control over printed materials microstructure.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Split-pulse X-ray photon correlation spectroscopy with seeded X-rays from X-ray laser to study atomic-level dynamics

Abstract With their brilliance and temporal structure, X-ray free-electron laser can unveil atomic-scale details of ultrafast phenomena. Recent progress in split-and-delay optics (SDO), which produces two X-ray pulses with time-delays, offers bright prospects for observing dynamics at the atomic-scale. However, their insufficient pulse energy has limited its application either to phenomena with longer correlation length or to measurement with a fixed delay-time. Here we show that the combination of the SDO and self-seeding of X-rays increases the pulse energy and makes it possible to observe the atomic-scale dynamics in a timescale of picoseconds. We show that the speckle contrast in scattering from water depends on the delay-time as expected. Our results demonstrate the capability of measurement using the SDO with seeded X-rays for resolving the dynamics in temporal and spatial scales that are not accessible by other techniques, opening opportunities for studying the atomic-level dynamics.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Method for conducting in situ high-temperature digital image correlation with simultaneous synchrotron measurements under thermomechanical conditions

This work presents a novel method of obtaining in situ strain measurements at high temperature by simultaneous digital image correlation (DIC), which provides the total strain on the specimen surface, and synchrotron x-ray diffraction (XRD), which provides lattice strains of crystalline materials. DIC at high temperature requires specialized techniques to overcome the effects of increased blackbody radiation that would otherwise overexpose the images. The technique presented herein is unique in that it can be used with a sample enclosed in an infrared heater, remotely and simultaneously with synchrotron XRD measurements. The heater included a window for camera access, and the light of the heater lamps is used as illumination. High-temperature paint is used to apply a random speckle pattern to the sample to allow the tracking of displacements and the calculation of the DIC strains. An inexpensive blue theatrical gel filter is used to block interfering visible and infrared light at high temperatures. This technique successfully produces properly exposed images at 870 °C and is expected to perform similarly at higher temperatures. The average strains measured by DIC were validated by an analytical calculation of the theoretical strain. Simultaneous DIC and XRD strain measurements of Inconel 718 (IN718) tensile test specimens were performed under thermal and mechanical loads and evaluated. Finally, this approach uses the fact that with DIC, the total strain is measured, including plastic strain, while with XRD, only elastic strain is captured. The observed differences were discussed with respect to the effective deformation mechanisms.

47 OTHER INSTRUMENTATION↗
DOE OSTI2022

A machine learning photon detection algorithm for coherent x-ray ultrafast fluctuation analysis

X-ray free electron laser experiments have brought unique capabilities and opened new directions in research, such as creating new states of matter or directly measuring atomic motion. One such area is the ability to use finely spaced sets of coherent x-ray pulses to be compared after scattering from a dynamic system at different times. This enables the study of fluctuations in many-body quantum systems at the level of the ultrafast pulse durations, but this method has been limited to a select number of examples and required complex and advanced analytical tools. By applying a new methodology to this problem, we have made qualitative advances in three separate areas that will likely also find application to new fields. As compared to the “droplet-type” models, which typically are used to estimate the photon distributions on pixelated detectors to obtain the coherent x-ray speckle patterns, our algorithm achieves an order of magnitude speedup on CPU hardware and two orders of magnitude improvement on GPU hardware. We also find that it retains accuracy in low-contrast conditions, which is the typical regime for many experiments in structural dynamics. Finally, it can predict photon distributions in high average-intensity applications, a regime which up until now has not been accessible. Our artificial intelligence-assisted algorithm will enable a wider adoption of x-ray coherence spectroscopies, by both automating previously challenging analyses and enabling new experiments that were not otherwise feasible without the developments described in this work.

47 OTHER INSTRUMENTATION↗
DOE OSTI2020

Super-resolution surface slope metrology of x-ray mirrors

We present experimental, analytical, and numerical methods developed for reconstruction (deconvolution) of one-dimensional (1D) surface slope profiles over the spatial frequency range where the raw data are significantly perturbed due to the limited resolution of the measurement instrument. We characterize the spatial resolution properties of a profiler with the instrument's transfer function (ITF). To precisely measure the ITF, we apply a recently developed method utilizing test surfaces with 1D linear chirped height profiles of constant slope amplitude. Based on the results of the ITF calibration, we determine parameters of an analytical model for the ITF that is used in the original reconstruction software. Here, we treat surface slope metrology data obtained with the Optical Surface Measuring System (OSMS), using as a sensor an electronic autocollimator (AC) ELCOMAT-3000. The spatial resolution of the OSMS is limited by the size of the AC light-beam-collimating aperture. For the purposes of this investigation, the OSMS is equipped with a circular aperture with a diameter of 2.5 mm. This is a typical arrangement of most AC-based slope profilers developed for surface slope metrology of state-of-the-art x-ray mirrors. Using the example of surface slope metrology of two state-of-the-art elliptically shaped x-ray focusing mirrors, we demonstrate that the developed data reconstruction procedure allows us to significantly improve the accuracy of surface slope metrology with the OSMS over the spatial wavelength range from ~1.6 mm to 7 mm. Thus, the amplitude of the quasi-periodic error characteristic of the deterministic polishing process used appears to be higher by a factor of~2 than is apparent from the rough metrology data. Underestimation of the surface slope errors in this spatial wavelength range can lead to serious errors in the expected performance of x-ray mirrors in synchrotron beamlines, especially at modern light sources utilizing coherent x rays, where the perturbations can lead to increased speckle-like intensity variation.

47 OTHER INSTRUMENTATION↗
DOE OSTI2020

Laser propagation in a subcritical foam: Subgrid model

Here, we present a subgrid model for laser propagation in a subcritical foam. Our model describes the expansion of laser-irradiated foam elements that are below the resolution of the simulation grid and predicts the plasma conditions that result from burning down the foam. Our model can be included as a module within a larger multiphysics code, and we have implemented it within the code pF3D, which is used for simulating a laser-plasma interaction. The model predicts a reduced propagation velocity for a laser through a subcritical foam compared to simulating that foam as a homogeneous gas. This is attributed to the laser energy that goes into burning down the foam microstructure. We compare our model against experimental data by simulating a 2 mg/cc SiO 2 foam shot performed at the Janus laser facility at the Lawrence Livermore National Laboratory. pF3D simulations with the foam model predict hot ion temperatures. This leads to a reduction in the level of stimulated Brillouin scattering (SBS), bringing the simulated level of SBS into agreement with the data. Intensity fluctuations at the foam front due to laser speckles and refraction result in ion temperature fluctuations when the foam burns down. These drive long-lived electron density fluctuations on scales that are large compared to the pore size.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Order-of-magnitude laser imprint reduction using pre-expanded high-Z coatings on targets driven by a third harmonic Nd:glass laser

A hybrid early time x-ray drive followed by conventional laser direct drive obtained by utilizing a thin high-Z overcoat on plastic ablator targets has proven to be very effective at reducing laser imprint in experiments driven by the Nike krypton-fluoride laser. An inherent low level laser prepulse from that laser system heated and expanded the coating prior to the main pulse. Here, we report on results using a frequency tripled Nd:glass laser system (Omega EP) where the inherent prepulse was several orders of magnitude smaller. By applying a separate prepulse, these experiments allowed us to test if the prepulse is important for mitigating imprint with the high-Z layer. The results show that the high-Z coating is much more effective at reducing laser imprint when it is pre-expanded, in this case, by an externally generated low level soft x-ray prepulse of ∼10 J/cm2. With the x-ray prepulse, laser imprint at spatial wavelengths below 100 μm was reduced by an order of magnitude, similar to that observed with the laser prepulse on Nike. Furthermore, the experiments here establish that high-Z coating is effective in reducing imprint even in the case of a fixed speckle pattern. Rayleigh–Taylor-amplified laser imprint and high-Z layer dynamics were measured using through-foil and side-on x-ray radiography. Pre-expansion times from 30 down to 6 ns were effective, potentially compatible with laser prepulse generation using existing NIF and OMEGA front ends; however, temporal beam smoothing appears to be necessary for the laser prepulse that directly illuminates the high-Z coating. The highest imprint reduction is observed for Pd and Au coatings of at least 400 Å thickness; thicknesses down to 200 Å show a reduction in imprint with an adjusted prepulse.

Karasik, Max (ORCID:0000000162354670)↗
DOE OSTI2022

Cross-beam energy transfer in direct-drive ICF. I. Nonlinear and kinetic effects

Results are presented from a series of simulations examining the susceptibility of the cross-beam energy transfer (CBET) instability to nonlinear processes in the context of direct-drive inertial confinement fusion experiments on the OMEGA laser facility. These form the basis for the second paper of this series [A. G. Seaton, L. Yin, R. Follett, B. J. Albright, and A. Le, “Cross-beam energy transfer in direct-drive ICF. II. Theory and simulation of mitigation through increased laser bandwidth,” Phys. Plasmas 29, 042707 (2022)], where we examine the efficacy of increases in laser bandwidth at suppressing CBET. We choose laser and plasma conditions for the simulations that are favorable to CBET and promote nonlinearity. Through a comparison of outputs from the particle-in-cell code vector particle in cell (VPIC) and the linearized fluid code laser-plasma simulation environment (LPSE), a series of nonlinear effects have been identified in the kinetic simulations that include particle trapping, the two-ion wave decay, and ion-acoustic wave self-focusing. These effects produce time-dependent energy transfer, in contrast to the linearized fluid simulations in which a steady state is reached after an initial transient. Ion trapping is shown to allow for increased energy transfer relative to fluid simulations, with the remaining nonlinear processes acting to reduce the energy transfer. Nonlinear dynamics is contrasted for low- and high-intensity beams as well as between speckled and planar beams. For the parameters under consideration, beam profile has a significant effect on nonlinear dynamics, though the greatest sensitivity is to beam intensity.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Time-dependent saturation and physics-based nonlinear model of cross-beam energy transfer

The nonlinear physics of cross-beam energy transfer (CBET) for multi-speckled laser beams is examined using large-scale particle-in-cell simulations for a range of laser and plasma conditions relevant to indirect-drive inertial confinement fusion (ICF) experiments. The time-dependent growth and saturation of CBET involve complex, nonlinear ion and electron dynamics, including ion trapping-induced enhancement and detuning, ion acoustic wave (IAW) nonlinearity, oblique forward stimulated Raman scattering (FSRS), and backward stimulated Brillouin scattering (BSBS) in a CBET-amplified seed beam. Ion-trapping-induced detuning of CBET is captured in the kinetic linear response by a new δf-Gaussian-mixture algorithm, enabling an accurate characterization of trapping-induced non-Maxwellian distributions. Ion trapping induces nonlinear processes, such as changes to the IAW dispersion and nonlinearities (e.g., bowing and self-focusing), which, together with pump depletion, FSRS, and BSBS, determine the time-dependent nature and level of CBET gain as the system approaches a steady state. Using VPIC simulations at intensities at and above the onset threshold for ion trapping and the insight from the time-dependent saturation analyses, we construct a nonlinear CBET model from local laser and plasma conditions that predicts the CBET gain and the energy deposition into the plasma. This model is intended to provide a more accurate, physics-based description of CBET saturation over a wide range of conditions encountered in ICF hohlraums compared with linear CBET gain models with ad hoc saturation clamps often used in laser ray-based methods in multi-physics codes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Nonlinear models for coupling the effects of stimulated Raman scattering to inertial confinement fusion codes

Laser plasma instabilities (LPI) reduce driver-target coupling, alter implosion symmetry, and therefore can fundamentally limit fusion performance in inertial confinement fusion (ICF). Developing a predictive modeling capability for LPI effects can critically advance the success of the field. We perform vector particle-in-cell simulations of multi-speckled laser beams undergoing stimulated Raman scattering (SRS) at various densities and intensities relevant to mainly indirectly driven and a subset of parameter space for directly driven ICF systems, focusing on the regimes with intensities above the onset of electron trapping. Based on the wavenumber of the SRS daughter electron plasma wave, we identify several regions with underpinning SRS saturation physics: the electron-trapping dominated region with intermediate kλD values, the strong Landau damping region at larger kλD values, and the region where the Langmuir decay instability arises at lower kλD values. We develop a nonlinear SRS reflectivity model that features the base trapping-dominated scaling of (kλD)−4 and its modifications. Electron trapping deforms the initialized electron distribution functions, and we have developed a new δf-Gaussian-mixture algorithm for an accurate characterization of the trapped hot electron population. With this SRS hot electron description, we construct a nonlinear energy deposition model and a hot electron source model—based on a modified Manley–Rowe relation—suitable for including SRS effects as a sub-grid module in a high-fidelity ICF design code.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Modeling stimulated Brillouin backscatter from outer-cone quads across multiple inertial confinement fusion hohlraum designs

Stimulated Brillouin scattering (SBS) is a potential risk for laser damage in the experiments carried out at the National Ignition Facility (NIF), and by altering the energy deposition pattern in hohlraums, it affects the symmetry of indirect-drive inertial confinement fusion implosions. We have surveyed backward SBS on outer-cone quads across NIF integrated hohlraums of various platforms numerically, using three-dimensional (3D) simulations with the backscatter code pF3D [Berger et al. Phys. Plasmas 5, 4337 (1998)] and ray-based gain calculations. Simulated reflected powers and energies, as well as the spectrum of reflected light all compare favorably with measurements. Ray-based calculations of exponential SBS amplification (“gain”), which assume a strongly damped plasma wave and steady-state response, are performed using a novel method that includes the 3D speckled field of the laser that drives SBS. This approach is useful for understanding qualitative differences between hohlraum designs and identifying regions susceptible to SBS within hohlraums. Quantitatively, gains are not found to correlate with SBS reflectivities in 3D, necessitating fully wave-based calculations that naturally include diffraction and various temporal dependencies.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Exact wave solver for nonparaxial laser beam propagation

Simulations of inertial confinement fusion (ICF) experiments require high-fidelity models for laser beam propagation in a nonuniform plasma with varying index of refraction. We describe a new numerical wave solver that is applicable to centimeter-scale length plasmas encountered in indirect drive ICF applications. The one-way Helmholtz equation (OHE) generalizes the time-harmonic paraxial wave equation to large angles. Here, we present a methodology to numerically evaluate the exact solution to the OHE. This solution is computed by analytically advancing eigenfunctions of the one-way Helmholtz operator along a propagation direction and is applicable to any given index of a refraction profile. We compare our exact method with a commonly used approximate split-step technique for solving the OHE. As a test problem, we consider nonparaxial propagation of Gaussian and speckled beams in a plasma density channel with internal reflection. We find that the split-step approach incurs significant errors compared to the exact solution computed using the novel algorithm.

Belyaev, Mikhail A. (ORCID:0000000224908887)↗
DOE OSTI2025

Low-mode nonuniformity in direct-drive ICF implosions due to laser smoothing techniques employed on OMEGA

For successful laser-direct-drive inertial confinement fusion implosions, the laser irradiation must be highly uniform over the target surface. On OMEGA, multiple laser beams are used to illuminate targets quasi-uniformly. High-mode-number nonuniformities due to laser speckle on each individual beam are reduced by splitting each beam into two orthogonal polarizations (i.e., polarization smoothing, or PS) and a range of wavelengths (i.e., smoothing by spectral dispersion) that are dispersed at the target plane. However, cross-beam energy transfer (CBET) is sensitive to both the polarizations and wavelengths of the interacting beams, so the interplay between CBET and the laser-smoothing schemes results in unique intensity variation across each beam profile, which is a systematic source of low-mode drive nonuniformity on OMEGA. Here, we model these effects and find that the predicted ℓ = 1 mode in the laser-absorption distribution is consistent with the systematic core-flow direction that has been determined from the OMEGA implosion database. We also observe good agreement with the measured core-flow directions for two specific sets of implosions (one with PS, the other without PS) when we also account for the measured beam mispointing and the beam power imbalance.

Crossed beam scattering↗
DOE OSTI2024

The SparkPix-S ASIC for the sparsified readout of 1 MHz frame-rate X-ray cameras at LCLS-II: pixel design and simulation results

Exploiting the “sparse” nature of the information in XPCS (X-ray Photon Correlation Spectroscopy) and XSVS (Speckle Visibility Spectroscopy) experiments, we present the SparkPix-S, a 3-sides buttable Application Specific Integrated Circuit (ASIC) based on a sparsified readout strategy for large-format hybrid detectors. The SparkPix-S architecture, based on the successful ePix family, will be composed as follows: a front-end 2-D matrix of 384×352 square pixels with 50 µm pitch is arranged to match the dimensions of a PIN Si-sensor matrix; charge readout, signal shaping and amplitude discrimination is performed at pixel-level, by means of a low-power (<18 µW) analog processor, which, in case of an event, negotiates access to an analog bus placed every other column; on the chip periphery (balcony), the information on each bus is digitized by an array of successive approximation analog-to-digital converters (SAR-ADCs) running at 10 Msps; on the digital back-end the global logic will generate the output data stream using low-voltage differential signalling (LVDS). A first prototype of the SparkPix-S, with a reduced matrix size of 96×96 pixels, is currently under production on a 130 nm CMOS technology. Simulated performance results show an equivalent noise charge <60 el. r.m.s. at 1 MHz repetition rate, with a maximum input energy of 60 keV and capability to discriminate charge signals with equivalent energy as low as 900 eV.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2021

Nanoscale dynamics during self-organized ion beam patterning of Si. II. Kr + bombardment

Understanding the self-organized ion beam nanopatterning of elemental semiconductors, particularly silicon, is of intrinsic scientific and technological interest. This is the second component of a two-part coherent x-ray scattering and x-ray photon correlation spectroscopy (XPCS) investigation of the kinetics and fluctuation dynamics of nanoscale ripple development on silicon during 1 keV Ar + (part I) and Kr + bombardment at 65° polar angle. Here it is found that the ion-enhanced viscous flow relaxation is essentially equal for Kr + -induced patterning as previously found for Ar + patterning despite the difference in ion masses. However, the magnitude of the surface curvature-dependent roughening rate in the early-stage kinetics is larger for Kr + than for Ar + , consistent with expectations that the heavier ion gives an increased mass redistributive contribution to the initial surface instability. As with the Ar + case, fluctuation dynamics in the late stage show a peak in correlation times at the length scale corresponding to the dominant structural feature on the surface—the ripples. Finally, it is shown that speckle motion during the surface evolution can be analyzed to determine spatial inhomogeneities in erosion rate and ripple velocity. This allows the direction and speed of ripple motion to be measured in a real time experiment. In the present case, ripple motion is found to be into the projected direction of the ion source, in contrast to expectations from an existing sputter erosion driven model with parameters derived from binary collision approximation simulations.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Dynamics of a fractal set of first-order magnetic phase transitions in frustrated Lu 2 CoMnO 6

The axial next-nearest-neighbor Ising model predicts a fractal (infinite) set of phases with incommensurate wave vectors that are separated by first-order phase boundaries. This complexity results from a simple frustration condition between nearest- and next-nearest-neighbor interactions along a chain of Ising spins. Using x-ray photon correlation spectroscopy (XPCS), we investigate the surprising antiferromagnetic dynamics that emerge from such a complex phase diagram over a wide range of temperatures. In this work, we present XPCS measurements of the frustrated magnetic chain compound Lu 2 CoMnO 6 and Monte Carlo simulations. Incommensurate magnetic Bragg peaks slide towards commensurate “up-up-down-down” spin order with decreasing temperature and increasing time. Both simulation and experiment support a counterintuitive “upside-down” temperature dependence of the magnetic dynamics: at higher temperatures in the region of first-order phase boundaries, slower dynamics are observed where the speckle maintains its coherence. At the lowest temperatures, where part of the sample adopts commensurate order, the dynamics speed up and result in fast decoherence.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Implementing a microphysics model in hydrodynamic simulations to study the initial plasma formation in dielectric ablator materials for direct-drive implosions

A microphysics model to describe the photoionization and impact ionization processes in dielectric ablator materials like plastic has been implemented into the 1-D hydrodynamic code LILAC for planar and spherical targets. Currently, the initial plasma formation during the early stages of a laser drive are modeled in an ad hoc manner, until the formation of a critical surface. Implementation of the physics-based models predict higher values of electron density, electron temperature, and pressure than the ad hoc model. Moreover, the numerical predictions are consistent with previous experimental observations of the shinethrough mechanism in plastic ablators. For planar targets, a decompression of the rear end of the target was observed, that is similar to recent experiments. An application of this model is to understand the laser-imprint mechanism that is caused by nonuniform laser irradiation due to single beam speckle.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Electron acceleration at oblique angles via stimulated Raman scattering at laser irradiance >10 16 W cm –2 μm 2

The generation of hot, directional electrons via laser-driven stimulated Raman scattering (SRS) is a topic of great importance in inertial confinement fusion (ICF) schemes. Little recent research has been dedicated to this process at high laser intensity, in which back, side, and forward scatter simultaneously occur in high energy density plasmas, of relevance to, for example, shock ignition ICF. In this paper, we present an experimental and particle-in-cell (PIC) investigation of hot electron production from SRS in the forward and near-forward directions from a single speckle laser of wavelength λ 0 = 1.053μm, peak laser intensities in the range I 0 = 0.2–1.0×10 17 Wcm –2 and target electron densities between ne = 0.3–1.6% n c , where n c is the plasma critical density. As the intensity and density are increased, the hot electron spectrum changes from a sharp cutoff to an extended spectrum with a slope temperature T = 34 ± 1 keV and maximum measured energy of 350 keV experimentally. Multidimensional PIC simulations indicate that the high energy electrons are primarily generated from SRS-driven electron plasma wave phase fronts with k vectors angled ~50° with respect to the laser axis. These results are consistent with analytical arguments that the spatial gain is maximized at an angle which balances the tendency for the growth rate to be larger for larger scattered light wave angles until the kinetic damping of the plasma wave becomes important. The efficiency of generated high energy electrons drops significantly with a reduction in either laser intensity or target electron density, which is a result of the rapid drop in growth rate of Raman scattering at angles in the forward direction.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗