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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 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Understanding and controlling capsule symmetry in near vacuum hohlraums at the National Ignition Facility

The near vacuum hohlraum platform is an inertial confinement fusion design at the National Ignition Facility (NIF) that uses the lowest practical density of helium gas of 30 μg/cc to fill the hohlraum, which is ten times lower than now used routinely. This has several advantages, such as high laser coupling; however, the inability to understand and simulate the symmetry of the imploded capsule has limited the use of this platform. This work presents the first simulations that are able to accurately capture the highly prolate implosion seen experimentally without unphysical, ad hoc model changes. While previous investigations attributed this asymmetry to multi-species interpenetration in the hohlraum, we find that this alone has little effect on symmetry. Instead, it is the presence of crossed-beam energy transfer (CBET), occurring with no applied wavelength shift between the laser beams, that increases the laser power to the inner cones and causes a more prolate implosion. The effect of CBET is increased in the simulation model when the hohlraum laser entrance hole hardware is included. Using this understanding, CBET is exploited by shifting the inner-beam wavelength by –0.75 Å (at 1ω) with respect to the outer-beams. This transfers laser power to the outer-beams in contrast to positive wavelength shifts as done routinely on NIF and produces a round capsule implosion in our simulations. Furthermore, this work shows the possibility of the near vacuum hohlraum as a viable experimental platform.

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

Pitfalls in the n -mode representation of vibrational potentials

Simulations of anharmonic vibrational motion rely on computationally expedient representations of the governing potential energy surface. The n-mode representation (n-MR)—effectively a many-body expansion in the space of molecular vibrations—is a general and efficient approach that is often used for this purpose in vibrational self-consistent field (VSCF) calculations and correlated analogues thereof. In the present analysis, a lack of convergence in many VSCF calculations is shown to originate from negative and unbound potentials at truncated orders of the n-MR expansion. For cases of strong anharmonic coupling between modes, the n-MR can both dip below the true global minimum of the potential surface and lead to effective single-mode potentials in VSCF that do not correspond to bound vibrational problems, even for bound total potentials. The present analysis serves mainly as a pathology report of this issue. Furthermore, this insight into the origin of VSCF non-convergence provides a simple, albeit ad hoc, route to correct the problem by “painting in” the full representation of groups of modes that exhibit these negative potentials at little additional computational cost. Somewhat surprisingly, this approach also reasonably approximates the results of the next-higher n-MR order and identifies groups of modes with particularly strong coupling. The method is shown to identify and correct problematic triples of modes—and restore SCF convergence—in two-mode representations of challenging test systems, including the water dimer and trimer, as well as protonated tropine.

Chemistry↗
DOE OSTI2024

Staged Z-pinch radiation-hydrodynamic simulations on a 20-MA driver

We report on one-dimensional simulations of a staged Z-pinch (SZP) fusion scheme using the radiation-hydrodynamics code HYDRA [Marinak et al., Phys. Plasmas 8, 2275 (2001)]. A pulsed-power driver, based on the Z-machine at Sandia National Laboratories, with a peak current around 20 MA, is used to implode a high-Z gas liner surrounding a cylindrical DT fuel target. For the best conditions used in this work, excluding some physical processes, such as mix, we find a “clean” fusion yield of 7.05 MJ (2.5 ×1018 neutrons), thus showing the potential for high yields using this scheme. The design achieving this yield was determined through a study of different liner materials, liner masses, and fuel masses. We also address previous simulations of the SZP setup that used ad hoc limits of the total internal energy of the liner that can artificially increase fusion yields.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

EFIT-Prime: Probabilistic and physics-constrained reduced-order neural network model for equilibrium reconstruction in DIII-D

We introduce EFIT-Prime, a novel machine learning surrogate model for EFIT (Equilibrium FIT) that integrates probabilistic and physics-informed methodologies to overcome typical limitations associated with deterministic and ad hoc neural network architectures. EFIT-Prime utilizes a neural architecture search-based deep ensemble for robust uncertainty quantification, providing scalable and efficient neural architectures that comprehensively quantify both data and model uncertainties. Physically informed by the Grad–Shafranov equation, EFIT-Prime applies a constraint on the current density J tor and a smoothness constraint on the first derivative of the poloidal flux, ensuring physically plausible solutions. Furthermore, the spatial location of the diagnostics is explicitly incorporated in the inputs to account for their spatial correlation. Extensive evaluations demonstrate EFIT-Prime's accuracy and robustness across diverse scenarios, most notably showing good generalization on negative-triangularity discharges that were excluded from training. Timing studies indicate an ensemble inference time of 15 ms for predicting a new equilibrium, offering the possibility of plasma control in real-time, if the model is optimized for speed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Direct comparison of gyrokinetic and fluid scrape-off layer simulations

Typically, fluid simulations are used for tokamak divertor design. However, fluid models are only valid if the scrape-off layer (SOL) is highly collisional. This assumption is valid in many present-day experiments but is questionable in the upstream SOL of some high-power scenarios envisioned for burning plasmas and fusion pilot plants. This paper reports on comparisons between fluid and kinetic simulations of the SOL for upstream parameters and geometry representative of the Spherical Tokamak for Energy Production fusion pilot plant. The SOLPS-ITER (fluid) and Gkeyll (gyrokinetic) codes are operated in a two-dimensional axisymmetric mode, which replaces turbulence with ad-hoc diffusivities. In kinetic simulations, we observe that the ions in the upstream SOL experience significant mirror trapping. This substantially increases the upstream temperature and has important implications for impurity dynamics. We show that the mirror force, which is excluded in SOLPS’s fluid equations, enhances the electrostatic potential drop along the field line in the SOL. We also show that the assumption of equal main ion and impurity temperatures, which is made in commonly used fluid codes, is invalid for the regimes explored here. The combination of these effects results in superior confinement of impurities to the divertor region in kinetic simulations, consistent with our earlier predictions [Kotschenreuther et al., in 29th IAEA 29 Fusion Energy Conference (IAEA, London, UK, 2023)]. This effect can be dramatic, reducing the midplane impurity density by orders of magnitude. These results indicate that in lower collisionality SOL’s the tolerable downstream impurity densities may be higher than would be predicted by fluid simulations, allowing for higher radiated power while avoiding unacceptable core contamination. Our results highlight the importance of kinetic simulations for divertor design and optimization for fusion pilot plants.

Computational fluid dynamics↗
DOE OSTI2023

Two-Phase Turbulent Kinetic Energy Budget Computation in Co-Current Taylor Bubble Flow

Simulation of two-phase flows is relevant for reactor design and safety at normal operation or during accident scenarios. Often, the two-phase flow is in a regime in which slugs are formed or where the flow stratifies. Modeling such situations using standard single-phase Reynolds-averaged Navier-Stokes (RANS) turbulence models fails due to an overestimation of the eddy viscosity at the resolved two-phase interface. To solve this, an ad hoc turbulence damping term has been proposed in the literature that reduces the turbulence production locally at a two-phase interface, analogously to turbulence wall functions. However, this approach must be tailored to the specific setting and does not consider physical contributions such as surface tension or flow topology. Therefore, the problem of two-phase interfacial turbulence must be studied more in-depth. In this work, we consider co-current turbulent Taylor bubble flow using high-fidelity numerical simulation. The Basilisk code is used to simulate a Taylor bubble rising in a vertical pipe. By simulating the bubble in a moving frame of reference, we may study the turbulent kinetic energy (TKE) budgets ahead of the bubble, in its wake, and across the interface. The implementation of the TKE budget computation and the underlying averaging techniques are validated for the single-phase region ahead of the Taylor bubble using reference direct numerical simulation data. The analysis of the TKE budgets in the setting of Taylor bubble flow allows for the study of how turbulence behaves due to the presence of a two-phase interface and, in turn, supports the improvement of two-phase RANS models.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

Implementation of the D1S Methodology for Shutdown Dose Rate Calculations in the OpenMC Monte Carlo Particle Transport Code

We present an implementation of the direct one-step (D1S) methodology for shutdown dose rate (SDR) calculations in the OpenMC Monte Carlo particle transport code. In addition to being the first fully open-source D1S implementation, it is also the first to require no ad hoc source code or nuclear data library modifications. The code can seamlessly switch between production of prompt and decay photons based on a user input parameter, and the decay data needed for decay photon generation are made available through a depletion chain file, which is already used for OpenMC’s built-in depletion/activation solver. A set of Python functions significantly eases the burden of computing and applying time correction factors needed to properly account for the time dependence of radionuclide activity. To assess the accuracy of the D1S implementation, SDR calculations have been carried out for three problems: a prism of iron irradiated by 14-MeV neutrons, the ITER port plug computational benchmark, and the Frascati Neutron Generator (FNG) ITER dose rate benchmark problem from the Shielding INtegral Benchmark Archive and Database (SINBAD). For each of these problems, comparisons were made to calculations using the rigorous two-step (R2S) method. The results on the iron prism problem illustrate how the D1S method achieves superior spatial resolution compared to the R2S method without the need for spatial discretization of the activation regions. The D1S and R2S results for the ITER port plug benchmark agree well with previously reported results in the literature. While the D1S results are 10% to 15% lower than the R2S results, this may be due to stochastic uncertainty and/or spatial discretization in the R2S calculations. On the FNG dose rate benchmark problem, the D1S method produces dose rate estimates that are within 4% of the dose rates predicted using a cell-based R2S workflow. The D1S estimates of the SDR are also in reasonable agreement with the experimental measurements and show the same basic trends that have been observed in previous works. A qualitative analysis of the execution time and uncertainty for the R2S and D1S workflows suggests that the D1S method would attain a higher figure of merit.

D1S method↗
DOE OSTI2021

Occupant-Centric key performance indicators to inform building design and operations

Building performance indicators are widely used to guide building design and track and benchmark operational performance. Traditional building performance indicators mostly focus on the energy efficiency perspective. As occupants are the primary building service recipients in residential and most commercial buildings, their comfort and wellbeing are crucial. As such, this study first identified significant attributes of occupant-centric key performance indicators (KPIs) and analyzed the diverse factors that should be considered in formulating an occupant-centric KPI. Then a suite of occupant-centric KPIs were synthesized from the review and enhancement of existing occupant-related performance metrics. The proposed occupant KPIs represent the occupant lens on three integrative aspects of building performance: resource use (including energy and water), indoor environmental quality, and human–building interactions. A simulation-based case study was conducted to demonstrate how occupant-centric KPIs can be used to quantify the impacts of building operation changes from the occupants’ point of view. Highlights: Occupant-centric metrics are currently ad hoc and limited, yet crucial to inform building design and operations. Literature was reviewed to reveal the state-of-the-art and gaps of occupant-centric metrics. A suite of occupant-centric key performance indicators (KPIs) covering five groups of building services were synthesized. Proposed occupant KPIs represent three aspects of performance: resource use and demand, occupant comfort and health, and human–building interactions. A case study using whole building simulation was conducted to demonstrate the use of occupant-centric KPIs in evaluating building operations during a power outage.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2021

Optimizing Vehicle Fleet and Assignment for Concentrating Solar Power Plant Heliostat Washing

Concentrating solar power central-receiver plants use thousands of sun-tracking mirrors, i.e., heliostats, to reflect sunlight to a central receiver, which collects and uses the heat to generate electricity. Over time, soiling reduces the reflectivity of the heliostats and, therefore, the efficiency of the system. Current industry practice sends vehicles to wash heliostats in an ad hoc fashion. We present a mixed-integer nonlinear program that determines wash vehicle fleet size, mix, and assignment of wash crews to heliostats to minimize the sum of (i) the revenues lost due to heliostat soiling, (ii) the costs of hiring wash crews and operating the vehicles, and (iii) the costs of purchasing wash vehicles. We establish conditions for convexity of the objective function, and then propose a decomposition method that enables near-optimal solutions to the wash vehicle fleet sizing and assignment problem on the order of a couple of minutes. Furthermore, these solutions yield hundreds of thousands of dollars in savings per year over current industry practices.

14 SOLAR ENERGY↗
DOE OSTI2026

Active learning of a crystal plasticity flow rule from discrete dislocation dynamics simulations

Continuum-scale material deformation models, such as crystal plasticity (CP), can significantly enhance their predictive accuracy by incorporating input from lower-scale (i.e. mesoscale) models. The procedure to generate and extract the relevant information is however typically complex and ad hoc, involving decision and intervention by domain experts, leading to long development times. In this study, we develop a principled approach for calibration of continuum-scale models using lower scale information by representing a CP flow rule as a Gaussian process model. This representation allows for efficient parameter space exploration, guided by the uncertainty embedded in the model through a process known as Bayesian optimization (BO). We demonstrate a semi-autonomous BO loop which instantiates discrete dislocation dynamics simulations whose initial conditions are automatically chosen to optimize the uncertainty of a model CP flow rule. Our self-guided computational pipeline efficiently generated a dataset and corresponding model whose error, uncertainty, and physical feature sensitivities were validated with comparison to an independent dataset four times larger, demonstrating a valuable and efficient active learning implementation readily transferable to similar material systems.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Interpretation of Lyman opacity measurements in JET with the ITER-like wall using a particle balance approach

Recent measurements of the Ly β /D α ratio in the JET ITER-like wall (ILW) divertor show comparatively more pronounced Ly β reabsorption relative to previous results in JET with the carbon wall (JET-C). At the outer horizontal target ion current rollover point a Ly β reabsorption rate of 60% is measured, increasing to 80% in more pronounced detachment, implying a Ly α reabsorption rate of 90%–98%. The radially resolved Ly β /D α measurements are used to constrain Lyman opacity corrections to atomic rate coefficients using the population escape factor technique in order to capture the local changes to the excited state population structure in the high Lyman opacity regions at and outboard of the outer strike point. To check the self-consistency of the Lyman opacity measurements, a detailed spectroscopic interpretation of the outer divertor particle balance is presented, in which the impact of opacity corrections to the Ly α inverse photon efficiency coefficients is assessed. A five-fold deficit in the estimated D + source rate obtained with optically thin plasma assumptions is reconciled once the opacity corrections are factored into the Ly α photon rate to ionization rate conversion. The experiment results are reproduced in EDGE2D-EIRENE density scan simulations in which an imposed ad hoc Lyman reabsorption rate is recovered spectroscopically using synthetic measurements, and a similar shortfall in the D + source rate estimates is reconciled using Lyman opacity corrected atomic data. The model limitations prevent a more detailed self-consistent analysis of the Lyman opacity impact on divertor parameters and detachment evolution, and hence motivate renewed efforts to re-establish routine exploitation of the photon transport modelling capabilities in the EIRENE code package. Lyman opacity corrections to atomic data coefficients are necessary for spectroscopic interpretation of the JET-ILW divertor plasma, with significant influence on the divertor plasma also a likely consequence of the presence of strong Ly α reabsorption. Finally, a scan of auxiliary heating powers spanning L-mode and H-mode conditions reveals a strong correlation of the measured Ly β opacity with the outer target temperature, suggesting new possibilities for using Lyman opacity measurements in establishing detachment scalings.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Near real-time streaming analysis of big fusion data

Experiments on fusion plasmas produce high-dimensional data time series with ever-increasing magnitude and velocity, but turn-around times for analysis of this data have not kept up. For example, many data analysis tasks are often performed in a manual, ad-hoc manner some time after an experiment. In this article, we introduce the Delta framework that facilitates near real-time streaming analysis of big and fast fusion data. By streaming measurement data from fusion experiments to a high-performance compute center, Delta allows computationally expensive data analysis tasks to be performed in between plasma pulses. This article describes the modular and expandable software architecture of Delta and presents performance benchmarks of individual components as well as of an example workflow. Focusing on a streaming analysis workflow where electron cyclotron emission imaging (ECEi) data is measured at KSTAR on the National Energy Research Scientific Computing Center's (NERSC's) supercomputer we routinely observe data transfer rates of about 4 Gigabit per second. In NERSC, a demanding turbulence analysis workflow effectively utilizes multiple nodes and graphical processing units and executes them in under 5 min. We further discuss how Delta uses modern database systems and container orchestration services to provide web-based real-time data visualization. For the case of ECEi data we demonstrate how data visualizations can be augmented with outputs from machine learning models. Here, by providing session leaders and physics operators, results of higher-order data analysis using live visualizations may make more informed decisions on how to configure the machine for the next shot.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

3D simulations of inertial confinement fusion implosions part 2: systematic flow anomalies and impact of low modes on performances in OMEGA experiments

We present the first 3D radiation-hydrodynamic simulations of directly driven inertial confinement fusion implosions with an inline package for polarized crossed-beam energy transfer, which were used to assess the impact of the current distributed polarization rotators (DPRs) on OMEGA as well as other known sources of asymmetry. Applied to OMEGA implosions, the simulations predict bang times with no need for ad hoc multipliers, as well as yields—if you separately account for the impacts of imprint and fuel age. The magnitude of the flow is well reproduced when the low mode sources are large, whereas the modeling of the stalk is thought to be required to match the flow magnitude in the remaining cases. For the cases explored in more detail, polarized cross-beam energy transfer (CBET)—the only known systematic drive asymmetry, brought the results closest to the measured flow vectors. The remaining discrepancies are shown to be stemming from the limited knowledge of the laser pointing modes. For typical current levels of beam mispointing, power imbalance, target offset, and asymmetry caused by polarized CBET, low modes degrade the yield by more than 40%. The current strategy of attempting to compensate the mode-1 asymmetry with a preimposed target offset recovers only about one-third of the losses caused by the low modes due to the dynamic nature of the multiple asymmetries and the presence of low modes other than l = 1. Furthermore, addressing the root causes of the drive asymmetries is apt to be more beneficial. To that end, one possible solution to the specific issue of polarized CBET (10 µm DPRs) is shown to work well.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Modeling of convective cells, turbulence, and transport induced by a radio-frequency antenna in the tokamak boundary plasma

The edge turbulence model Hermes (Dudson et al 2017 Plasma Phys. Control. Fusion 59 05401) is set up for plasma boundary simulations with an radiofrequency (RF) antenna, using parameters characteristic of a tokamak edge. Cartesian slab geometry is used with thin plate limiters representing the ion cyclotron range of frequency (ICRF) antenna side-wall limiters. Ad-hoc DC electric biasing of the limiters, motivated by calculations with VSim (Nieter et al 2004 J. Comput. Phys. 196 448), represents an induced RF sheath rectified potential in the plasma turbulence model. Flux-driven turbulence simulations demonstrate a realistic distribution of plasma profiles and fluctuations. There is a clear effect of the antenna sheath voltage leading to formation of convective cells; bias-induced convective transport flattens the scrape-off layer density profile and fluctuations penetrate into the shadow region of the limiters as the bias voltage increases. Turbulent transport for impurity ions is inferred by following ion trajectories in the simulated plasma turbulence fields, showing Bohm-like effective diffusion rates. All in all, the model elucidates the key physical phenomena governing the effects of ICRF-induced antenna biasing on the tokamak boundary plasma.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

The principle of minimal power

This article is devoted to the memory of Yuri P Raizer, who passed away in 2021. He left a noticeable trace in gas discharge physics. The principle of minimal power (the state that requires minimal power is most probable) is thoroughly used in his books. Although the fundamental laws of physics do not imply this ad hoc principle, a detailed analysis of underlying phenomena can often reveal why nature prefers this path. Raizer illustrated this principle for plasma stratification, formation of electrode spots, discharge constriction, the shape of an arc channel, etc. We argue that the nonlinearity of equations describing gas discharges can often justify the realization of a plasma state maintained at minimal electric power. This nonlinearity appears because small groups of energetic electrons often control the ionization processes. The number of these electrons depends strongly on the ratio of the electric field to gas density, E/N. Under certain conditions, the ionization rate can also depend nonlinearly on electron density due to stepwise ionization and Coulomb collisions. Here, we use the principle of minimal power to illustrate some of Raizer's contributions to gas discharge physics from a single point of view. We demonstrate that nonlinearity of ionization processes in gas discharges can substantiate this principle for plasma stratification. However, striations of s, p, and r types in neon could exist with minimal or no ionization enhancement. This reminds us of Raizer's warning that applying the minimal power principle could lead to erroneous predictions, and a proper theory is required in each case to justify its use. 'The phenomenon of striations satisfies the principle of minimal power' – Yuri Raizer

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Simple and statistically sound recommendations for analysing physical theories

Physical theories that depend on many parameters or are tested against data from many different experiments pose unique challenges to statistical inference. Many models in particle physics, astrophysics and cosmology fall into one or both of these categories. These issues are often sidestepped with statistically unsound ad hoc methods, involving intersection of parameter intervals estimated by multiple experiments, and random or grid sampling of model parameters. Whilst these methods are easy to apply, they exhibit pathologies even in low-dimensional parameter spaces, and quickly become problematic to use and interpret in higher dimensions. In this article we give clear guidance for going beyond these procedures, suggesting where possible simple methods for performing statistically sound inference, and recommendations of readily-available software tools and standards that can assist in doing so. Our aim is to provide any physicists lacking comprehensive statistical training with recommendations for reaching correct scientific conclusions, with only a modest increase in analysis burden. Furthermore, our examples can be reproduced with the code publicly available at Zenodo.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
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↗