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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Quantitative phase retrieval and characterization of magnetic nanostructures via Lorentz (scanning) transmission electron microscopy

Magnetic materials phase reconstruction using Lorentz transmission electron microscopy (LTEM) measurements have traditionally been achieved using longstanding methods such as off-axis holography (OAH) fast-Fourier transform technique and the transport-of-intensity equation (TIE). The increase in access to processing power alongside the development of advanced algorithms have allowed for phase retrieval of nanoscale magnetic materials with greater efficacy and resolution. Specifically, reverse-mode automatic differentiation (RMAD) and the extended electron ptychography iterative engine (ePIE) are two recent developments of phase retrieval that can be applied to analyzing micro-to-nano- scale magnetic materials. This work evaluates phase retrieval using TIE, RMAD, and ePIE in simulations of Permalloy (Ni 80 Fe 20 ) nanoscale islands, or nanomagnets. Extending beyond simulations, we demonstrate total phase retrieval and image reconstructions of a NiFe nanowire using OAH and RMAD in LTEM and ePIE in Lorentz-mode-4D scanning transmission electron microscopy experiments and determine the saturation magnetization through corroborations with micromagnetic modeling. Finally, we demonstrate the efficacy of these methods in retrieving the total phase and highlight its use in characterizing and analyzing the proximity effect of the magnetic nanostructures.

Lorentz transmission electron microscopy↗
DOE OSTI2020

White-light interferometry for early-stage metal oxide growth characterization

Oxidation of metals can provide a functional oxide film or an oxide layer that can lead to material degradation causing performance limiting concerns. Because of the technological and economic impacts of oxidation, understanding early-stage oxidation growth and its mechanisms is of high importance. Unfortunately, poor empirical data during early-stage oxidation has left our current understanding of oxidation incomplete and woefully inadequate. Measurement techniques previously used for oxidation kinetics characterization include microbalance, x-ray diffraction, Fourier-transform infrared spectroscopy, and spectroscopic ellipsometry. However, these techniques lack the necessary time-resolution or vertical resolution in addition to not providing any spatial data, which is essential to early-stage oxidation studies to understand both oxidation kinetics and mechanisms. Here, a novel rapid and surface-sensitive data collection technique that provides three-dimensional spatial data of a growing oxide layer with sub-nanometer thickness resolution using white-light interferometry has been developed. This technique will be the first technique capable of providing real-time spatial results of early-stage oxidation growth. The effectiveness of this characterization tool is shown by observing the early-stage oxidation kinetics and film cracking of uranium heated to 90 °C under 500 torr of pure O 2 . Initially a parabolic oxidation growth is observed. Once the oxide layer reaches ≈ 30 nm, the epitaxial stresses between the uranium substrate and oxide film layer causes localized cracking in addition to the observed transition of the parabolic growth rate to a linear growth rate. The results of the white-light interferometry are verified by glancing incidence x-ray diffraction.

47 OTHER INSTRUMENTATION↗
DOE OSTI2022

Computational approaches to model X-ray photon correlation spectroscopy from molecular dynamics

X-ray photon correlation spectroscopy (XPCS) allows for the resolution of dynamic processes within a material across a wide range of length and time scales. X-ray speckle visibility spectroscopy (XSVS) is a related method that uses a single diffraction pattern to probe ultrafast dynamics. Interpretation of the XPCS and XSVS data in terms of underlying physical processes is necessary to establish the connection between the macroscopic responses and the microstructural dynamics. To aid the interpretation of the XPCS and XSVS data, we present a computational framework to model these experiments by computing the X-ray scattering intensity directly from the atomic positions obtained from molecular dynamics simulations. We compare the efficiency and accuracy of two alternative computational methods: the direct method computing the intensity at each diffraction vector separately, and a method based on fast Fourier transform that computes the intensities at all diffraction vectors at once. Furthermore, the computed X-ray speckle patterns capture the density fluctuations over a range of length and time scales and are shown to reproduce the known properties and relations of experimental XPCS and XSVS for liquids.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Resolving crystallographic geometrically necessary dislocations in three dimensions in a hexagonal close packed titanium alloy

Abstract Geometrically necessary dislocation (GND) content is measured from mm 3 -scaled Ti7Al three-dimensional (3D) microstructural data using a theory extended for hexagonal close packed crystals, which accounts for basal, prismatic and pyramidal ⟨ c + a ⟩ type dislocation content. The Ti7Al samples have been mechanically pre-strained to two different strain levels, and will then be strained along the same axis in uniaxial tension during simulation. Both inter- and intragranular GNDs across the microstructures have been characterized, with a large contribution of pyramidal ⟨ c + a ⟩ GNDs, consistent with the relative slip activity involved in pre-straining. The spatially resolved crystallographic GND distributions within the 3D microstructures are used to instantiate a microstructure model for forward modeling deformation simulations by a dislocation density hardening elasto-viscoplastic fast Fourier transform framework. Coarsening the voxel resolution during the initial microstructure construction procedure is shown to strongly impact both the magnitude and spatial distribution of the GNDs and in turn the forward deformation response of the pre-strained material. This study indicates that the voxel resolution desired when transferring from measured to model microstructures need not only be proportionally scaled with the microstructure but also sufficiently fine to capture the subgranular orientation gradients that may already be present in the material.

Materials Science↗
DOE OSTI2023

Modeling the co-assembly of binary nanoparticles

Abstract In this work, we present a binary assembly model that can predict the co-assembly structure and spatial frequency spectra of monodispersed nanoparticles with two different particle sizes. The approach relies on an iterative algorithm based on geometric constraints, which can simulate the assembly patterns of particles with two distinct diameters, size distributions, and at various mixture ratios on a planar surface. The two-dimensional spatial-frequency spectra of the modeled assembles can be analyzed using fast Fourier transform analysis to examine their frequency content. The simulated co-assembly structures and spectra are compared with assembled nanoparticles fabricated using transfer coating method are in qualitative agreement with the experimental results. The co-assembly model can also be used to predict the peak spatial frequency and the full-width at half-maximum bandwidth, which can lead to the design of the structure spectra by selection of different monodispersed particles. This work can find applications in fabrication of non-periodic nanostructures for functional surfaces, light extraction structures, and broadband nanophotonics.

Mohanty, Saurav (ORCID:0009000302592855)↗
DOE OSTI2022

Kinetic theory of particle-in-cell simulation plasma and the ensemble averaging technique

Abstract We derive the kinetic theory of fluctuations in physically and numerically stable particle-in-cell (PIC) simulations of electrostatic plasmas. The starting point is the single-time correlation at the start of the simulation between the statistical fluctuations of the weighted densities of macroparticle centers in the plasma particle phase-space. The fluctuations are associated with different initial conditions, typically due to the random initial conditions (in velocity space) of the macroparticles/simulation plasma, assigned according to their initial distribution of probability. The single-time correlations at all time steps and in each spatial grid cell are then determined from the Laplace–Fourier transforms of the discretized Klimontovich-like equation for the macroparticles and Maxwell’s equations for the fields, as computed by modern PIC codes. We recover the expressions for the electrostatic field and the plasma particle density fluctuation autocorrelation spectra as well as the kinetic equations describing the average evolution of PIC-simulated plasma particles, first derived by Langdon (1970b Proc. 4th Conf. Numerical Simulation of Plasmas ) using a test macroparticle approach perturbing a discretized Vlasovian plasma and then averaging the obtained physical quantity over the initial macroparticle velocity distribution. We generalize and extend these results to the modern algorithms in PIC codes using arbitrary macroparticle weights. Analytical estimates of statistical fluctuation amplitudes are derived as a function of the plasma simulation parameters, using the central limit theorem in the limit of a large number of macroparticles per cell. The theory is then used to analyze the ensemble averaging technique of PIC simulations where statistical averages are performed over ensembles of PIC simulations, modeling the same plasma physics problem but using different statistical realizations of the initial distribution functions of the macroparticles. This method is illustrated by linear Landau damping uncovering (from noise, which is usually considered numerical) the physical fluctuations driven by a single small amplitude electrostatic wave perturbing a PIC simulation plasma in equilibrium.

fluctuations correlations↗
DOE OSTI2025

Numerical investigation of two-dimensional buoyancy-driven eddies in liquid metal magnetohydrodynamic flows in breeding blankets *

Abstract Lead–lithium flows are key features in the design of tokamak breeding blanket concepts such as the dual-coolant lead–lithium (DCLL). Since they flow under magnetic fields, they are affected by magnetohydrodynamic (MHD) effects. The neutron flux originating in the tokamak plasma heats the breeding blanket channels in a non-uniform manner, inducing buoyancy forces in the liquid metal. Buoyancy may become a source of quasi-two-dimensional (Q2D) turbulence, and the appearance of eddies may affect the transport of heat and tritium across the blanket. Blankets characterized by high-speed liquid metal flows (such as DCLL) will need ceramic insulating walls to reduce the MHD-related pressure drop in the channels. In our simulations, we have used the Q2D model proposed by Sommeria and Moreau (SM82) which is especially suitable for modeling electrically insulating channel flows. On top of that, we have modelled buoyancy forces in the momentum equation using the Oberbeck–Boussinesq approximation. In this work, we include a validation of the implemented Q2D model in buoyancy-driven cases and identify a thermohydraulic configuration that promotes the generation of eddies and the accumulation of tritium. We also show the results provided by our post-processing tool based on the bi-dimensional fast Fourier transform for eddy detection and characterization. We complete our investigation by performing an initial assessment of how eddies can accumulate tritium in the breeding blanket. We conclude by discussing the relevance of preventing accumulation of tritium within the blanket and suggest a possible solution.

Suarez, Daniel (ORCID:0000000251740100)↗
DOE OSTI2023

Foundations of machine learning for low-temperature plasmas: methods and case studies

Abstract Machine learning (ML) and artificial intelligence have proven to be an invaluable tool in tackling a vast array of scientific, engineering, and societal problems. The main drivers behind the recent proliferation of ML in practically all aspects of science and technology can be attributed to: (a) improved data acquisition and inexpensive data storage; (b) exponential growth in computing power; and (c) availability of open-source software and resources that have made the use of state-of-the-art ML algorithms widely accessible. The impact of ML on the field of low-temperature plasmas (LTPs) could be particularly significant in the emerging applications that involve plasma treatment of complex interfaces in areas ranging from the manufacture of microelectronics and processing of quantum materials, to the LTP-driven electrification of the chemical industry, and to medicine and biotechnology. This is primarily due to the complex and poorly-understood nature of the plasma-surface interactions in these applications that pose unique challenges to the modeling, diagnostics, and predictive control of LTPs. As the use of ML is becoming more prevalent, it is increasingly paramount for the LTP community to be able to critically analyze and assess the concepts and techniques behind data-driven approaches. To this end, the goal of this paper is to provide a tutorial overview of some of the widely-used ML methods that can be useful, amongst others, for discovering and correlating patterns in the data that may be otherwise impractical to decipher by human intuition alone, for learning multivariable nonlinear data-driven prediction models that are capable of describing the complex behavior of plasma interacting with interfaces, and for guiding the design of experiments to explore the parameter space of plasma-assisted processes in a systematic and resource-efficient manner. We illustrate the utility of various supervised, unsupervised and active learning methods using LTP datasets consisting of commonly-available, information-rich measurements (e.g. optical emission spectra, current–voltage characteristics, scanning electron microscope images, infrared surface temperature measurements, Fourier transform infrared spectra). All the ML demonstrations presented in this paper are carried out using open-source software; the datasets and codes are made publicly available. The FAIR guiding principles for scientific data management and stewardship can accelerate the adoption and development of ML in the LTP community.

Physics↗
DOE OSTI2023

Ammonia generation in Ns pulse and Ns pulse/RF discharges over a catalytic surface

Plasma-catalytic ammonia synthesis in a ns pulse discharge and a 'hybrid' ns pulse/RF discharge in plane-to-plane geometry is studied by Fourier Transform infrared absorption spectroscopy. The data are taken in a preheated H 2 –N 2 mixture, with and without Ni/γ-Al 2 O 3 or Co/γ-Al 2 O 3 catalyst placed in the discharge section. The measurement results are taken using two different approaches. The first is a 'single-stage' process, where a ns pulse discharge in the H 2 –N 2 mixture is sustained continuously. In this case, the ammonia yield increases slowly, over a period of tens of minutes. The second is a 'two-stage' process, where the catalyst is first activated by the ns pulse discharge sustained in pure nitrogen, and then the activated catalyst is exposed to the H 2 –N 2 flow, with or without the discharge. In this case, a strong overshoot of the NH 3 number density at the reactor exit is detected, by over a factor of two compared to the single-stage process. After the initial overshoot, the ammonia yield gradually decreases to the 'single stage' value (with the discharge on), or to near zero (with the discharge off). The results demonstrate that the ammonia yield in the plasma-catalytic reactor is controlled by the N atom accumulation on the catalyst surface, which reacts with H atoms thermally dissociated on the catalyst or generated in the plasma. The results also show that the plasma-catalytic ammonia yield is significantly higher compared to that in the ns pulse discharge without the catalyst. The accumulation of H atoms on the catalyst, with their subsequent reactions with N atoms generated in the plasma, is of relatively minor importance at the present conditions. An additional series of measurements was made with a sub-breakdown RF waveform overlapped with the ns pulse discharge train, to enhance the vibrational excitation of nitrogen. The ammonia yield measured with the RF waveform added is approximately 20% higher compared to that at the baseline ns pulse discharge conditions, both with and without the catalyst. This effect is weaker compared to that of the catalyst activation by N atoms. Additional data are necessary to isolate the possible effect of the vibrationally excited N 2 molecules on the ammonia synthesis in the plasma catalytic reactions.

surface reactions↗
DOE OSTI2024

Enhancing nitrogen fixation efficiency in glow-like discharge by reducing cathode-fall voltage

In plasma nitrogen fixation devices, discharge electrodes are crucial yet susceptible to oxidation and corrosion due to plasma’s high temperatures and oxygen content, which could alter discharge modes. This research evaluates the impact of different electrode materials, including iron, chromium, nickel, copper, and 304 stainless steel, on nitrogen fixation efficiency in glow-like discharges driven by high-voltage DC power. Notably, iron and 304 stainless steel cathodes undergo a mode transition at increased currents, evident from plasma color shifts and significant voltage reductions. Fourier transform infrared spectroscopy analyses reveal that such mode changes minimally affect nitrogen oxide production rates, leading to a notable decrease in energy consumption for nitrogen fixation by up to 40%. OES and SEM-EDS measurements suggest that iron oxide, with its higher secondary electron emission, replaces metal as the cathode material, facilitating mode transitions and maintaining discharge current at lower voltages. Further, this voltage change is largely attributed to the cathode voltage drop, highlighting the minimal role of the cathode fall region in NO x synthesis. These findings underscore the potential for improving plasma nitrogen fixation energy efficiency by choosing suitable cathode materials to lower the cathode-fall voltage.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Noise resilience of variational quantum compiling

Variational hybrid quantum-classical algorithms (VHQCAs) are near-term algorithms that leverage classical optimization to minimize a cost function, which is efficiently evaluated on a quantum computer. Recently VHQCAs have been proposed for quantum compiling, where a target unitary U is compiled into a short-depth gate sequence V. In this work, we report on a surprising form of noise resilience for these algorithms. Namely, we find one often learns the correct gate sequence V (i.e. the correct variational parameters) despite various sources of incoherent noise acting during the cost-evaluation circuit. Our main results are rigorous theorems stating that the optimal variational parameters are unaffected by a broad class of noise models, such as measurement noise, gate noise, and Pauli channel noise. Furthermore, our numerical implementations on IBM's noisy simulator demonstrate resilience when compiling the quantum Fourier transform, Toffoli gate, and W-state preparation. Hence, variational quantum compiling, due to its robustness, could be practically useful for noisy intermediate-scale quantum devices. Finally, we speculate that this noise resilience may be a general phenomenon that applies to other VHQCAs such as the variational quantum eigensolver.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Decoherence factor as a convolution: an interplay between a Gaussian and an exponential coherence loss

Abstract We identify and investigate the origin and nature of the transition between Gaussian and exponential forms of decoherence: the decoherence factor (that controls the time dependence of the off-diagonal terms of the density matrix expressed in the pointer basis representation) is the convolution of the Fourier transforms of the spectral density and of the overlap (between the eigenstates the environment with and without couplings to the system). Spectral density alone tends to lead to the (approximately) Gaussian decay of coherence while the overlap alone results in a (largely) exponential decay. We show that these two contributions combine as a convolution, their relative importance controlled by the strength of the system-environment coupling. The resulting decoherence factor in the strong and weak coupling limits leads to predominantly Gaussian or exponential decay, respectively, as is demonstrated with two paradigmatic examples of decoherence—a spin-bath model and the quantum Brownian motion.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Mock data sets for the Eboss and DESI Lyman-α forest surveys

We present a publicly-available code to generate sets of mock Lyman-α (Lyα) forest data that have realistic large-scale correlations including those due to the Baryonic Acoustic Oscillations (BAO). The primary purpose of these mocks is to test the analysis procedures of the Extended Baryon Oscillation Survey (eBOSS) and the Dark Energy Spectroscopy Instrument (DESI) surveys. The transmitted flux fraction, F(λ), of background quasars due to Lyα absorption in the intergalactic medium (IGM) is simulated using the Fluctuating Gunn-Petterson Approximation (FGPA) applied to Gaussian random fields produced through the use of fast Fourier transforms (FFT). The output includes the IGM-Lyα transmitted flux fraction along quasar lines of sight and a catalog of high-column-density systems appropriately placed at high-density regions of the IGM. This output serves as input to additional code that superimposes the IGM tranmission on realistic quasar spectra, adds absorption by high-column-density systems and metals, and simulates instrumental transmission and noise. Redshift space distortions (RSD) of the flux correlations are implemented by including the large-scale velocity-gradient field in the FGPA resulting in a correlation function of F(λ) that can be accurately predicted. One hundred realizations have been produced over the 14,000 deg 2 DESI survey footprint with 100 quasars per deg 2 . The analysis of these realizations shows that the correlations of F(λ) follows the prediction within the accuracy of eBOSS survey. Here, the most time-consuming part of the mock production occurs before application of the FGPA, and the existing pre-FGPA forests can be used to easily produce new mock sets with modified redshift-dependent bias parameters or observational conditions.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Measurement of the small-scale 3D Lyman- α forest power spectrum

Small-scale correlations measured in the Lyman-α (Lyα) forest encode information about the intergalactic medium and the primordial matter power spectrum. In this article, we present and implement a simple method to measure the 3-dimensional power spectrum, P 3D , of the Lyα forest at wavenumbers k corresponding to small, ~ Mpc scales. In order to estimate P 3D from sparsely and unevenly distributed data samples, we rely on averaging 1-dimensional Fourier Transforms, as previously carried out to estimate the 1-dimensional power spectrum of the Lyα forest, P 1D . Further, this methodology exhibits a very low computational cost. We confirm the validity of this approach through its application to Nyx cosmological hydrodynamical simulations. Subsequently, we apply our method to the eBOSS DR16 Lyα forest sample, providing as a proof of principle, a first P 3D measurement averaged over two redshift bins z = 2.2 and z = 2.4. This work highlights the potential for forthcoming P 3D measurements, from upcoming large spectroscopic surveys, to untangle degeneracies in the cosmological interpretation of P 1D .

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

DESI DR1 Lyα 1D power spectrum: the optimal estimator measurement

The one-dimensional power spectrum P 1D of Lyα forest offers rich insights into cosmological and astrophysical parameters, including constraints on the sum of neutrino masses, warm dark matter models, and the thermal state of the intergalactic medium. We present the measurement of P 1D using the optimal quadratic maximum likelihood estimator applied to over 300,000 Lyα quasars from Data Release 1 (DR1) of the Dark Energy Spectroscopic Instrument (DESI) survey. This sample represents the largest to date for P 1D measurements and is larger than the Extended Baryon Oscillation Spectroscopic Survey (eBOSS) by a factor of 1.7. We conduct a meticulous investigation of instrumental and analysis systematics and quantify their impact on P 1D . This includes the development of a cross-exposure estimator that eliminates the need to model the pipeline noise and has strong potential for future P 1D measurements. We also present new insights into metal contamination through the 1D correlation function. Using a fitting function we measure the evolution of the Lyα forest bias with high precision: b F (z) = (-0.218 ± 0.002) × ((1 + z)/4) 2.96±0.06 . In a companion validation paper, we substantially extend our previous suite of CCD image simulations to quantify the pipeline's exquisite performance accurately. In another companion paper, we present DR1 P 1D measurements using the Fast Fourier Transform (FFT) approach to power spectrum estimation. These two measurements produce a forest bias parameter that differs by 2.2 sigma. However, our model is simplistic, so this disagreement will be investigated in future work.

Lyman alpha forest↗
DOE OSTI2025

SPECTER: an instrument concept for CMB spectral distortion measurements with enhanced sensitivity

Deviations of the cosmic microwave background (CMB) energy spectrum from a perfect blackbody uniquely probe a wide range of physics, ranging from fundamental physics in the primordial Universe (μ-distortion) to late-time baryonic feedback processes (y-distortion). While the y-distortion can be detected with a moderate increase in sensitivity over that of COBE/FIRAS, the ΛCDM-predicted μ-distortion is roughly two orders of magnitude smaller and requires substantial improvements, with foregrounds presenting a serious obstacle. Within the standard model, the dominant contribution to μ arises from energy injected via Silk damping, yielding sensitivity to the primordial power spectrum at wavenumbers k ≈ 1-10 4 Mpc -1 . Here, we present a new instrument concept, SPECTER, with the goal of robustly detecting μ. The instrument technology is similar to that of LiteBIRD, but with an absolute temperature calibration system. Using a Fisher approach, we optimize the instrument's configuration to target μ while marginalizing over foreground contaminants. Unlike Fourier-transform-spectrometer-based designs, the specific bands and their individual sensitivities can be independently set in this instrument, allowing significant flexibility. We forecast SPECTER to observe the ΛCDM-predicted μ-distortion at ≈ 5σ (10σ) assuming an observation time of 1 (4) year(s) (corresponding to mission duration of 2 (8) years), after foreground marginalization. Our optimized configuration includes 16 bands spanning 1–2000 GHz with ∼degree-scale angular resolution at ∼ 150 GHz and 1100 total detectors. SPECTER will additionally measure the y-distortion at sub-percent precision and its relativistic correction at percent-level precision, yielding tight constraints on the total thermal energy and mean temperature of ionized gas.

CMBR experiments↗
DOE OSTI2025

Modeling of the high column density systems in the Lyman-Alpha forest

The Lyman-α forests observed in the spectra of high-redshift quasars can be used as a tracer of the cosmological matter density to study baryon acoustic oscillations (BAO) and the Alcock-Paczynski effect. Extraction of cosmological information from these studies requires modeling of the forest correlations. While the models depend most importantly on the bias parameters of the intergalactic medium (IGM), they also depend on the numbers and characteristics of high-column-density systems (HCDs) ranging from Lyman-limit systems with column densities log N HI /1cm -2 > 17 to damped Lyman-α systems (DLAs) with log N HI /1cm -2 > 20.2. These HCDs introduce broad damped absorption characteristic of a Voigt profile. Consequently they imprint a component on the power spectrum whose modes in the radial direction are suppressed, leading to a scale-dependent bias. Using mock data sets of known HCD content, we test a model that describes this effect in terms of the distribution of column densities of HCDs, the Fourier transforms of their Voigt profiles and the bias of the halos containing the HCDs. Our results show that this physically well-motivated model describes the effects of HCDs with an accuracy comparable to that of the ad-hoc models used in published forest analyses. We also discuss the problems of applying the model to real data, where the HCD content and their bias is uncertain.

Lyman alpha forest↗
DOE OSTI2026

DESI DR1 Ly α 1D power spectrum: Validation of estimators

The Data Release 1 (DR1) of the Dark Energy Spectroscopic Instrument (DESI) is the largest sample to date for small-scale Lyα forest cosmology, accessed through its one-dimensional power spectrum (P 1D ). The Lyα forest P 1D is extracted from quasar spectra that are highly inhomogeneous (both in wavelength and between quasars) in noise properties due to intrinsic properties of the quasar, atmospheric and astrophysical contamination, and also sensitive to low-level details of the spectral extraction pipeline. We employ two estimators in DR1 analysis to measure P 1D : the optimal estimator and the fast Fourier transform (FFT) estimator. To ensure robustness of our DR1 measurements, we validate these two power spectrum and covariance matrix estimation methodologies against the challenging aspects of the data. First, using a set of 20 synthetic 1D realizations of DR1, we derive the masking bias corrections needed for the FFT estimator and the continuum fitting bias needed for both estimators. We demonstrate that both estimators, including their covariances, are unbiased with these corrections using the Kolmogorov-Smirnov test. Second, we substantially extend our previous suite of CCD image simulations to include 675,000 quasars, allowing us to accurately quantify the pipeline's performance. This set of simulations reveals biases at the highest k values, corresponding to a resolution error of a few percent. We base the resolution systematics error budget of DR1 P 1D on these values, but do not derive corrections from them since the simulation fidelity is insufficient for precise corrections.

Lyman alpha forest↗