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DOE OSTI2026

Algorithm to extract direction in 2D discrete distributions and a continuous Frobenius norm

In this study, we present a novel algorithm for determining directionality in 2D distributions of discrete data. We compare a reference dataset with a known direction to a measured dataset with an unknown direction by the Frobenius norm of the difference (FND) to find the unknown direction. To generalize this concept, we develop a continuous Frobenius norm of the difference (CFND) as a continuous analog of the FND and derive its analytical expression. By relating fitted and normalized 2D Gaussian distributions, we show that the CFND approximates the FND, and we validate this relationship with computer simulations. We find that a first-order approximation of the CFND between two similar Gaussian distributions takes the form of an absolute sine function, offering a simple analytical form with potential applications in specialized areas such as segmented inverse beta decay neutrino detectors, astronomy, machine learning, and more. Our methodology consists of modeling a 2D Gaussian distribution, binning the data into a histogram, and encoding it as a square matrix. Rotating this matrix around its geometric center and comparing it to a measured dataset using the FND gives us rotational data that we fit with an absolute sine function. The location of the minimum of this fit is the angle closest to the true angle of the direction in the measured dataset. We present the derivation and discuss initial applications of the CFND in our novel algorithm, demonstrating its success in approximating directionality in 2D distributions.

Physics↗

DOE OSTI2017

Identification and positional distribution analysis of transcription factor binding sites for genes from the wheat fl-cDNA sequences

Abstract The binding sites of transcription factors (TFs) in upstream DNA regions are called transcription factor binding sites (TFBSs). TFBSs are important elements for regulating gene expression. To date, there have been few studies on the profiles of TFBSs in plants. In total, 4,873 sequences with 5ʹ upstream regions from 8530 wheat fl-cDNA sequences were used to predict TFBSs. We found 4572 TFBSs for the MADS TF family, which was twice as many as for bHLH (1951), B3 (1951), HB superfamily (1914), ERF (1820), and AP2/ERF (1725) TFs, and was approximately four times higher than the remaining TFBS types. The percentage of TFBSs and TF members showed a distinct distribution in different tissues. Overall, the distribution of TFBSs in the upstream regions of wheat fl-cDNA sequences had significant difference. Meanwhile, high frequencies of some types of TFBSs were found in specific regions in the upstream sequences. Both TFs and fl-cDNA with TFBSs predicted in the same tissues exhibited specific distribution preferences for regulating gene expression. The tissue-specific analysis of TFs and fl-cDNA with TFBSs provides useful information for functional research, and can be used to identify relationships between tissue-specific TFs and fl-cDNA with TFBSs. Moreover, the positional distribution of TFBSs indicates that some types of wheat TFBS have different positional distribution preferences in the upstream regions of genes.

Chen, Zhen-Yong↗

DOE OSTI2015

Genetic Identification of Chinook Salmon: Stock-Specific Distributions of Juveniles along the Washington and Oregon Coasts

Abstract We used microsatellite DNA data and genetic stock identification methods to delineate the temporal and spatial distributions of juvenile Chinook Salmon Oncorhynchus tshawytscha occupying coastal habitats extending from central Oregon to northern Washington. Juveniles were collected in trawl surveys conducted during spring, summer, and autumn over 15 years. Distributions (mean latitude and distance from shore) differed between yearling and subyearling life history types and between stocks; many of these differences were consistent across years. Yearlings were nearly all (98%) from Columbia River sources, and only 6% were naturally produced. In late May, yearlings from the lower Columbia and Willamette rivers were farther north than other yearlings, likely due to the early spring timing of their releases from hatcheries and subsequent out-migration from the Columbia River. However, yearling distributions in late June reflected known migration behaviors. Yearlings from interior Columbia and Snake River sources were farthest north by June, whereas yearlings from other stocks were more spread out in latitude. Subyearlings sampled in early summer were also largely from the Columbia River (98%), but greater percentages of subyearlings from coastal rivers were present during the fall (24%). In contrast to yearlings, natural production accounted for nearly one-third of subyearlings. Subyearlings of most stocks tended to remain relatively near their point of sea entry throughout the summer. Subyearlings from the Snake River fall-run stock and upper Columbia River summer–fall-run stock exhibited diverse distributions that included both southward and northward dispersal. Overall, distributions of Chinook Salmon stocks and life history types reflected differences in migration behavior but also reflected the influence of environmental factors and hatchery practices. Received November 13, 2014; accepted April 15, 2015

Teel, David J.↗

DOE OSTI2015

THE X-RAY FLUX DISTRIBUTION OF SAGITTARIUS A* AS SEEN BY CHANDRA

We present a statistical analysis of the X-ray flux distribution of Sgr A* from the Chandra X-Ray Observatory's 3 Ms Sgr A* X-ray Visionary Project in 2012. Our analysis indicates that the observed X-ray flux distribution can be decomposed into a steady quiescent component, represented by a Poisson process with rate Q = (5.24 ± 0.08) × 10{sup –3} counts s{sup –1}, and a variable component, represented by a power law process (dN/dF∝F {sup –ξ}, ξ=1.92{sub −0.02}{sup +0.03}). This slope matches our recently reported distribution of flare luminosities. The variability may also be described by a log-normal process with a median unabsorbed 2-8 keV flux of 1.8{sub −0.6}{sup +0.8}×10{sup −14} erg s{sup –1} cm{sup –2} and a shape parameter σ = 2.4 ± 0.2, but the power law provides a superior description of the data. In this decomposition of the flux distribution, all of the intrinsic X-ray variability of Sgr A* (spanning at least three orders of magnitude in flux) can be attributed to flaring activity, likely in the inner accretion flow. We confirm that at the faint end, the variable component contributes ∼10% of the apparent quiescent flux, as previously indicated by our statistical analysis of X-ray flares in these Chandra observations. Our flux distribution provides a new and important observational constraint on theoretical models of Sgr A*, and we use simple radiation models to explore the extent to which a statistical comparison of the X-ray and infrared can provide insights into the physics of the X-ray emission mechanism.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2015

SYNCHROTRON AND COMPTON SPECTRA FROM A STEADY-STATE ELECTRON DISTRIBUTION

Energy densities of relativistic electrons and protons in extended galactic and intracluster regions are commonly determined from spectral radio and (rarely) γ-ray measurements. The time-independent particle spectral density distributions are commonly assumed to have a power-law (PL) form over the relevant energy range. A theoretical relation between energy densities of electrons and protons is usually adopted, and energy equipartition is invoked to determine the mean magnetic field strength in the emitting region. We show that for typical conditions, in both star-forming and starburst (SB) galaxies, these estimates need to be scaled down substantially due to significant energy losses that (effectively) flatten the electron spectral density distribution, resulting in a much lower energy density than deduced when the distribution is assumed to have a PL form. The steady-state electron distribution in the nuclear regions of SB galaxies is calculated by accounting for Coulomb, bremsstrahlung, Compton, and synchrotron losses; the corresponding emission spectra of the latter two processes are calculated and compared to the respective PL spectra. We also determine the proton steady-state distribution by taking into account Coulomb and π production losses, and briefly discuss implications of our steady-state particle spectra for estimates of proton energy densities and magnetic fields.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2015

DISTRIBUTIONS OF LONG-LIVED RADIOACTIVE NUCLEI PROVIDED BY STAR-FORMING ENVIRONMENTS

Radioactive nuclei play an important role in planetary evolution by providing an internal heat source, which affects planetary structure and helps facilitate plate tectonics. A minimum level of nuclear activity is thought to be necessary—but not sufficient—for planets to be habitable. Extending previous work that focused on short-lived nuclei, this paper considers the delivery of long-lived radioactive nuclei to circumstellar disks in star forming regions. Although the long-lived nuclear species are always present, their abundances can be enhanced through multiple mechanisms. Most stars form in embedded cluster environments, so that disks can be enriched directly by intercepting ejecta from supernovae within the birth clusters. In addition, molecular clouds often provide multiple episodes of star formation, so that nuclear abundances can accumulate within the cloud; subsequent generations of stars can thus receive elevated levels of radioactive nuclei through this distributed enrichment scenario. This paper calculates the distribution of additional enrichment for {sup 40}K, the most abundant of the long-lived radioactive nuclei. We find that distributed enrichment is more effective than direct enrichment. For the latter mechanism, ideal conditions lead to about 1 in 200 solar systems being directly enriched in {sup 40}K at the level inferred for the early solar nebula (thereby doubling the abundance). For distributed enrichment from adjacent clusters, about 1 in 80 solar systems are enriched at the same level. Distributed enrichment over the entire molecular cloud is more uncertain, but can be even more effective.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2015

3D ELECTRON DENSITY DISTRIBUTIONS IN THE SOLAR CORONA DURING SOLAR MINIMA: ASSESSMENT FOR MORE REALISTIC SOLAR WIND MODELING

Knowledge of the electron density distribution in the solar corona put constraints on the magnetic field configurations for coronal modeling and on initial conditions for solar wind modeling. We work with polarized SOHO/LASCO-C2 images from the last two recent minima of solar activity (1996–1997 and 2008–2010), devoid of coronal mass ejections. The goals are to derive the 4D electron density distributions in the corona by applying a newly developed time-dependent tomographic reconstruction method and to compare the results between the two solar minima and with two magnetohydrodynamic models. First, we confirm that the values of the density distribution in thermodynamic models are more realistic than in polytropic ones. The tomography provides more accurate distributions in the polar regions, and we find that the density in tomographic and thermodynamic solutions varies with the solar cycle in both polar and equatorial regions. Second, we find that the highest-density structures do not always correspond to the predicted large-scale heliospheric current sheet or its helmet streamer but can follow the locations of pseudo-streamers. We deduce that tomography offers reliable density distributions in the corona, reproducing the slow time evolution of coronal structures, without prior knowledge of the coronal magnetic field over a full rotation. Finally, we suggest that the highest-density structures show a differential rotation well above the surface depending on how they are magnetically connected to the surface. Such valuable information on the rotation of large-scale structures could help to connect the sources of the solar wind to their in situ counterparts in future missions such as Solar Orbiter and Solar Probe Plus.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2015

MULTITHERMAL REPRESENTATION OF THE KAPPA-DISTRIBUTION OF SOLAR FLARE ELECTRONS AND APPLICATION TO SIMULTANEOUS X-RAY AND EUV OBSERVATIONS

Acceleration of particles and plasma heating is one of the fundamental problems in solar flare physics. An accurate determination of the spectrum of flare-energized electrons over a broad energy range is crucial for our understanding of aspects such as the acceleration mechanism and the total flare energy. Recent years have seen a growing interest in the kappa-distribution as a representation of the total spectrum of flare-accelerated electrons. In this work we present the kappa-distribution as a differential emission measure. This allows for inferring the electron distribution from X-ray observations and EUV observations by simultaneously fitting the proposed function to RHESSI and SDO/AIA data. This yields the spatially integrated electron spectra of a coronal source from less than 0.1 keV up to several tens of keV. The method is applied to a single-loop GOES C4.1 flare. The results show that the total energy can only be determined accurately by combining RHESSI and AIA observations. Simultaneously fitting the proposed representation of the kappa-distribution reduces the electron number density in the analyzed flare by a factor of ∼30 and the total flare energy by a factor of ∼5 compared with the commonly used fitting of RHESSI spectra. The spatially integrated electron spectrum of the investigated flare between 0.043 and 24 keV is consistent with the combination of a low-temperature (∼2 MK) component and a hot (∼11 MK) kappa-like component with spectral index 4, reminiscent of solar wind distributions.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2015

Engineering the CernVM-Filesystem as a High Bandwidth Distributed Filesystem for Auxiliary Physics Data

A common use pattern in the computing models of particle physics experiments is running many distributed applications that read from a shared set of data files. We refer to this data is auxiliary data, to distinguish it from (a) event data from the detector (which tends to be different for every job), and (b) conditions data about the detector (which tends to be the same for each job in a batch of jobs). Relatively speaking, conditions data also tends to be relatively small per job where both event data and auxiliary data are larger per job. Unlike event data, auxiliary data comes from a limited working set of shared files. Since there is spatial locality of the auxiliary data access, the use case appears to be identical to that of the CernVM- Filesystem (CVMFS). However, we show that distributing auxiliary data through CVMFS causes the existing CVMFS infrastructure to perform poorly. We utilize a CVMFS client feature called 'alien cache' to cache data on existing local high-bandwidth data servers that were engineered for storing event data. This cache is shared between the worker nodes at a site and replaces caching CVMFS files on both the worker node local disks and on the site's local squids. We have tested this alien cache with the dCache NFSv4.1 interface, Lustre, and the Hadoop Distributed File System (HDFS) FUSE interface, and measured performance. In addition, we use high-bandwidth data servers at central sites to perform the CVMFS Stratum 1 function instead of the low-bandwidth web servers deployed for the CVMFS software distribution function. We have tested this using the dCache HTTP interface. As a result, we have a design for an end-to-end high-bandwidth distributed caching read-only filesystem, using existing client software already widely deployed to grid worker nodes and existing file servers already widely installed at grid sites. Files are published in a central place and are soon available on demand throughout the grid and cached locally on the site with a convenient POSIX interface. This paper discusses the details of the architecture and reports performance measurements.

Dykstra, D.↗

DOE OSTI2022

The Milky Way tomography with APOGEE: intrinsic density distribution and structure of mono-abundance populations

ABSTRACT The spatial distribution of mono-abundance populations (MAPs, selected in [Fe/H] and [Mg/Fe]) reflect the chemical and structural evolution in a galaxy and impose strong constraints on galaxy formation models. In this paper, we use APOGEE data to derive the intrinsic density distribution of MAPs in the Milky Way, after carefully considering the survey selection function. We find that a single exponential profile is not a sufficient description of the Milky Way’s disc. Both the individual MAPs and the integrated disc exhibit a broken radial density distribution; densities are relatively constant with radius in the inner Galaxy and rapidly decrease beyond the break radius. We fit the intrinsic density distribution as a function of radius and vertical height with a 2D density model that considers both a broken radial profile and radial variation of scale height (i.e. flaring). There is a large variety of structural parameters between different MAPs, indicative of strong structure evolution of the Milky Way. One surprising result is that high-α MAPs show the strongest flaring. The young, solar-abundance MAPs present the shortest scale height and least flaring, suggesting recent and ongoing star formation confined to the disc plane. Finally we derive the intrinsic density distribution and corresponding structural parameters of the chemically defined thin and thick discs. The chemical thick and thin discs have local surface mass densities of 5.62 ± 0.08 and 15.69 ± 0.32 M⊙pc−2, respectively, suggesting a massive thick disc with a local surface mass density ratio between thick to thin disc of 36 per cent.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

Dark Energy Survey Year 3 results: marginalization over redshift distribution uncertainties using ranking of discrete realizations

ABSTRACT Cosmological information from weak lensing surveys is maximized by sorting source galaxies into tomographic redshift subsamples. Any uncertainties on these redshift distributions must be correctly propagated into the cosmological results. We present hyperrank, a new method for marginalizing over redshift distribution uncertainties, using discrete samples from the space of all possible redshift distributions, improving over simple parametrized models. In hyperrank, the set of proposed redshift distributions is ranked according to a small (between one and four) number of summary values, which are then sampled, along with other nuisance parameters and cosmological parameters in the Monte Carlo chain used for inference. This approach can be regarded as a general method for marginalizing over discrete realizations of data vector variation with nuisance parameters, which can consequently be sampled separately from the main parameters of interest, allowing for increased computational efficiency. We focus on the case of weak lensing cosmic shear analyses and demonstrate our method using simulations made for the Dark Energy Survey (DES). We show that the method can correctly and efficiently marginalize over a wide range of models for the redshift distribution uncertainty. Finally, we compare hyperrank to the common mean-shifting method of marginalizing over redshift uncertainty, validating that this simpler model is sufficient for use in the DES Year 3 cosmology results presented in companion papers.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

Magnetic braking saturates: evidence from the orbital period distribution of low-mass detached eclipsing binaries from ZTF

ABSTRACT We constrain the orbital period (Porb) distribution of low-mass detached main-sequence eclipsing binaries (EBs) with light-curves from the Zwicky Transient Facility (ZTF), which provides a well-understood selection function and sensitivity to faint stars. At short periods (Porb ≲ 2 d), binaries are predicted to evolve significantly due to magnetic braking (MB), which shrinks orbits and ultimately brings detached binaries into contact. The period distribution is thus a sensitive probe of MB. We find that the intrinsic period distribution of low-mass (0.1 ≲ M1/M⊙ < 0.9) binaries is basically flat (${\rm d}N/{\rm d}P_{\rm orb} \propto P_{\rm orb}^0$) from Porb = 10 d down to the contact limit. This is strongly inconsistent with predictions of classical MB models based on the Skumanich relation, which are widely used in binary evolution calculations and predict ${\rm d}N/{\rm d}P_{\rm orb} \propto P_{\rm orb}^{7/3}$ at short periods. The observed distributions are best reproduced by models in which the magnetic field saturates at short periods with a MB torque that scales roughly as $\dot{J}\propto P_{\rm orb}^{-1}$, as opposed to $\dot{J} \propto P_{\rm orb}^{-3}$ in the standard Skumanich law. We also find no significant difference between the period distributions of binaries containing fully and partially convective stars. Our results confirm that a saturated MB law, which was previously found to describe the spin-down of rapidly rotating isolated M dwarfs, also operates in tidally locked binaries. We advocate using saturated MB models in binary evolution calculations. Our work supports previous suggestions that MB in cataclysmic variables (CVs) is much weaker than assumed in the standard evolutionary model, unless mass transfer leads to significant additional angular momentum loss in CVs.

El-Badry, Kareem (ORCID:0000000268711752)↗

DOE OSTI2023

The intrinsic X-ray luminosity distribution of an optically selected SDSS quasar population

ABSTRACT In active galactic nuclei, the relationship between UV and X-ray luminosity is well studied (often characterised by αox) but often with heterogeneous samples. We have parametrized the intrinsic distribution of X-ray luminosity, LX, for the optically selected sample of SDSS quasars in the Stripe 82 and XXL fields across redshifts 0.5–3.5. We make use of the available XMM observations and a custom pipeline to produce Bayesian sensitivity curves that are used to derive the intrinsic X-ray distribution in a hierarchical Bayesian framework. We find that the X-ray luminosity distribution is well described by a Gaussian function in log10 LX space with a mean that is dependent on the monochromatic 2500 Å UV luminosity, L2500. We also observe some redshift dependence of the distribution. The mean of the LX distribution increases with redshift while the width decreases. This weak but significant redshift dependence leads to L2500–LX and L2500–αox relations that evolve with redshift, and we produce a redshift- and L2500-dependent αox equation. Neither black hole mass nor Eddington ratio appear to be potential drivers of the redshift evolution.

Rankine, Amy L. (ORCID:0000000220911966)↗

DOE OSTI2024

Spatially resolved microlensing time-scale distributions across the Galactic bulge with the VVV survey

ABSTRACT We analyse 1602 microlensing events found in the VISTA Variables in the Via Lactea (VVV) near-infrared (NIR) survey data. We obtain spatially resolved, efficiency-corrected time-scale distributions across the Galactic bulge (|ℓ| < 10°, |b| < 5°), using a Bayesian hierarchical model. Spatially resolved peaks and means of the time-scale distributions, along with their marginal distributions in strips of longitude and latitude, are in agreement at a 1σ level with predictions based on the Besançon model of the Galaxy. We find that the event time-scales in the central bulge fields (|ℓ| < 5°) are on average shorter than the non-central (|ℓ| > 5°) fields, with the average peak of the lognormal time-scale distribution at 23.6 ± 1.9 d for the central fields and 29.0 ± 3.0 d for the non-central fields. Our ability to probe the structure of the bulge with this sample of NIR microlensing events is limited by the VVV survey’s sparse cadence and relatively small number of detected microlensing events compared to dedicated optical surveys. Looking forward to future surveys, we investigate the capability of the Roman telescope to detect spatially resolved asymmetries in the time-scale distributions. We propose two pairs of Roman fields, centred on (ℓ = ±9, 5°, b = −0.125°) and (ℓ = −5°, b = ±1.375°) as good targets to measure the asymmetry in longitude and latitude, respectively.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2016

Testing the lognormality of the galaxy and weak lensing convergence distributions from Dark Energy Survey maps

It is well known that the probability distribution function (PDF) of galaxy density contrast is approximately lognormal; whether the PDF of mass fluctuations derived from weak lensing convergence (kappa_WL) is lognormal is less well established. We derive PDFs of the galaxy and projected matter density distributions via the Counts in Cells (CiC) method. We use maps of galaxies and weak lensing convergence produced from the Dark Energy Survey (DES) Science Verification data over 139 deg^2. We test whether the underlying density contrast is well described by a lognormal distribution for the galaxies, the convergence and their joint PDF. We confirm that the galaxy density contrast distribution is well modeled by a lognormal PDF convolved with Poisson noise at angular scales from 10-40 arcmin (corresponding to physical scales of 3-10 Mpc). We note that as kappa_WL is a weighted sum of the mass fluctuations along the line of sight, its PDF is expected to be only approximately lognormal. We find that the kappa_WL distribution is well modeled by a lognormal PDF convolved with Gaussian shape noise at scales between 10 and 20 arcmin, with a best-fit chi^2/DOF of 1.11 compared to 1.84 for a Gaussian model, corresponding to p-values 0.35 and 0.07 respectively, at a scale of 10 arcmin. Above 20 arcmin a simple Gaussian model is sufficient. The joint PDF is also reasonably fitted by a bivariate lognormal. As a consistency check we compare the variances derived from the lognormal modelling with those directly measured via CiC. Our methods are validated against maps from the MICE Grand Challenge N-body simulation.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2022

Determination of fluorine distribution in shark teeth by laser-induced breakdown spectroscopy

Quantifying the chemical composition of fast-growing hard tissues in the environment can shed valuable information in terms of understanding ecosystems both prehistoric and current. Changes in chemical composition can be correlated with environmental conditions and can provide information about the organism's life. Sharks can lose 0.1 to 1.1 teeth/day, depending on species, which offers a unique opportunity to record environmental changes over a short duration of time. Shark teeth contain a biomineral phase that is made up of fluorapatite [Ca 5 (PO 4 ) 3 F], and the F distribution within the tooth can be correlated to tooth hardness. Typically, this is determined by bulk acid digestion, energy-dispersive X-ray spectroscopy (EDS), or wavelength-dispersive spectroscopy. Here we present laser-induced breakdown spectroscopy (LIBS) as an alternative and faster approach for determining F distribution within shark teeth. Using a two-volume laser ablation chamber (TwoVol3) with innovative embedded collection optics for LIBS, shark teeth were investigated from sand tiger (Carcharias Taurus), tiger (Galeocerdo Cuvier), and hammerhead sharks (Sphyrnidae). Fluorine distribution was mapped using the CaF 603 nm band (CaF, Β 2 Σ + → X 2 Σ + ) and quantified using apatite reference materials. In addition, F measurements were cross referenced with EDS analyses to validate the findings. Distributions of F (603 nm), Na (589 nm), and H (656 nm) within the tooth correlate well with the expected biomineral composition and expected tooth hardness. This rapid methodology could transform the current means of determining F distribution, particularly when large sample specimens (350 mm 2 , presented here) and large quantities of specimens are of interest.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Impact of super-Gaussian electron distributions on plasma K-shell emission

Electron distributions in laser-produced plasmas will be driven toward a super-Gaussian distribution due to inverse bremsstrahlung absorption [Langdon, Phys. Rev. Lett. 44, 575 (1980)]. Both theoretical and experimental evidence suggest that fundamental plasma properties are altered by the super-Gaussian distribution. Here, this paper examines how the super-Gaussian distribution affects the ionization balance and K-shell emission of atomic plasmas, utilizing approximate formulas and detailed collisional-radiative simulations. While the impact on plasma ionization is small, K-shell spectra can be significantly modified. Based on these findings, we demonstrate that K-shell spectroscopy can be used to infer super-Gaussian or other similar nonequilibrium electron distributions.

Atomic spectra↗

DOE OSTI2023

Imaging electron angular distributions to assess a full-power petawatt-class laser focus

Here we present a technique to assess the focal volume of petawatt-class lasers at full power. Our approach exploits quantitative measurement of the angular distribution of electrons born in the focus via ionization of rarefied gas, which are accelerated forward and ejected ponderomotively by the field. We show that a bivariate (θ,Φ) angular distribution, which was obtained with image plates, not only enables the peak intensity to be extracted, but also reflects nonideality of the focal-spot intensity distribution. In our prototype demonstration at intensities of a few ×10 19 to a few ×10 20 W/cm 2 , an f/10 optic produced a focal spot in the paraxial regime. This allows a plane-wave parametrization of the peak intensity given by tanθ c =2/a 0 (a 0 being the normalized vector potential and θ c the minimum ejection angle) to be compared with our measurements. Qualitative agreement was found using an a 0 inferred from the pulse energy, pulse duration, and focal spot distribution with a modified parametrization, tanθ c =2η/a 0 ($η=2.02^{+0.26}_{–0.22}$). This highlights the need for (i) better understanding of intensity degradation due to focal-spot distortions and (ii) more robust modeling of the ejection dynamics. Using single-shot detection of electrons, we showed that while there is significant shot-to-shot variation in the number of electrons ejected at a given angular position, the average distribution scales with the pulse energy in a way that is consistent with that seen with the image plates. Finally, we note that the asymptotic behavior as θ→0° limits the usability of angular measurement. For 800 nm, this limit is at an intensity ~10 21 W/cm 2 .

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗