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DOE OSTI2023

Hydrodynamic theory of scrambling in chaotic long-range interacting systems

The Fisher-Kolmogorov-Petrovsky-Piskunov (FKPP) equation provides a mean-field theory of out-of-time-ordered commutators in locally interacting quantum chaotic systems at high energy density. In systems with power-law interactions, the corresponding fractional-derivative FKPP equation provides an analogous mean-field theory. However, the fractional FKPP description is potentially subject to strong quantum fluctuation effects, so it is not clear a priori if it provides a suitable effective description for generic chaotic systems with power-law interactions. Here, in this work, we study this problem using a model of coupled quantum dots with interactions decaying as 1/r α , where each dot hosts N degrees of freedom. The large-N limit corresponds to the mean-field description, while quantum fluctuations contributing to the OTOC can be modeled by 1/N corrections consisting of a cutoff function and noise. Within this framework, we show that the parameters of the effective theory can be chosen to reproduce the butterfly light cone scalings previously found for N=1 and generic finite N. In order to reproduce these scalings, the fractional index μ in the FKPP equation needs to be shifted from the naïve value of μ=2⁢α–1 to a renormalized value μ=2⁢α–2. We provide supporting analytic evidence for the cutoff model and numerical confirmation for the full fractional FKPP equation with cutoff and noise.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2025

Search for nonvirialized axions with 3.3 − 4.2 μ ⁢eV mass at selected resolving powers

The Axion Dark Matter eXperiment is sensitive to narrow axion flows, given axions compose a fraction of the dark matter with a non-negligible local density. Detecting these low-velocity dispersion flows requires a high spectral resolution and careful attention to the expected signal modulation due to Earth’s motion. Here, we report an exclusion on the local axion dark matter density in narrow flows of ρ a ≳ 0.03 GeV/cm 3 and ρ a ≳ 0.004 GeV/cm 3 for Dine-Fischler-Srednicki-Zhitnitski and Kim-Shifman-Vainshtein-Zakharov axion-photon couplings, respectively, over the mass range 3.3−4.2 μeV. Measurements were made at selected resolving powers to allow for a range of possible velocity dispersions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2020

Design Principles to Govern Electrode Fabrication for the Lithium Trivanadate Cathode

A full depth of discharge mathematical model for the lithium trivanadate cathode, considering lithiation of the layered α-phase, phase change, and lithiation of the rock-salt like β-phase at lower potentials, is developed. The coupled electrode-scale and crystal-scale model is fit to electrochemical data, and additionally validated with operando EDXRD. There is good agreement between the simulated and measured spatial variation of the volume fraction of the β-phase. This mathematical model is used to guide electrode fabrication, accounting for both ionic and electronic transport effects. Values of three design parameters—electrode thickness, porosity, and volume fraction of conductor—are identified, and the sensitivity of the energy density to these design parameters is quantified. The model is also used to investigate electrode design to create electrodes that deliver the maximum achievable energy density under the constraint that the α to β-phase transition is avoided, since phase change has been demonstrated to reduce cycle life. The energy density sacrificed to avoid phase change decreases at higher discharge rates, but the target values for electrode fabrication remain the same as those when optimizing the electrode for the full depth of discharge.

25 ENERGY STORAGE↗

DOE OSTI2020

Sensitivity Analysis and Effective Parametrization of PEM Fuel Cell Models

The cost of proton-exchange-membrane fuel cells (PEMFCs) remains a major hurdle in large-scale commercialization of this technology. To improve their performance and reduce cost, novel materials and electrode designs are continuously envisioned, e.g., non-PGM catalyst layers, ultra-thin Pt/Pt-Ni based catalyst layers, structured ionomer arrays or NSTF catalyst layers.1 Understanding the impact of these improvement strategies can be extremely time and cost intensive due to complex physical phenomena and large design space. We have previously developed a PEMFC modeling framework2 which has been a time and cost effective tool for understanding and optimizing the complex multi-physics phenomena within PEMFCs; however, several of the cell parameters used in the modeling have large spread in measured data.3 Furthermore, several transport parameters such as water adsorption kinetics have not been accurately measured and the approximations are spread over several orders of magnitude. These uncertainties cause problems in ascertaining accuracy of the modeling approach and they reduce the predictive power of the numerical models. The aim of this work is to identify the sensitivity of PEFC numerical model outputs to various input parameters. The previously in-house developed MEA modeling framework2 is used for PEMFC modeling. The sensitivity of the model outputs with respect to inputs parameters is obtained by analyzing the condition numbers for different output-input pairs at varying operating conditions. An example of the sensitivity analysis is shown in Figure 1. The condition numbers are obtained for the entire possible range of input parameters at varying operating conditions to identify the most crucial parameters of the PEMFC model. Based on our preliminary analysis, parameters related to kinetics (exchange current density and ECSA) and heat/water management in electrodes and ionomer (ionomer fraction, thermal conductivity) are most crucial. One of the major goals of this work is to identify the most crucial set of parameters towards which the model shows maximum sensitivity. This will guide future experimentalists to measure these properties with higher accuracy. Furthermore, the sensitivity analysis will also enable us to optimize the PEMFC performance by selectively targeting the most sensitive parameters and thereby making the largest impact. Acknowledgements The work is funded under the Fuel Cell Performance and Durability Consortium (FC-PAD), by the Fuel Cell Technologies Office (FCTO), Office of Energy Efficiency and Renewable Energy (EERE), of the U.S. Department of Energy under contract number DE-AC02-05CH11231. The authors would like to thank Nathan Craig at Robert Bosch LLC for his valuable input in designing the sensitivity analysis. The authors would also like to thank Giovanna Bucci and Matthias Hanauer at Robert Bosch for their valuable inputs and discussion. References P. K. Sinha, W. Gu, A. Kongkanand and E. Thompson, J. Electrochem. Soc., 158, B831 (2011). L. M. Pant, M. R. Gerhardt, N. Macauley, R. Mukundan, R. L. Borup and A. Z. Weber, Electrochim. Acta, 326, 134963 (2019). R. Vetter and J. O. Schumacher, ArXiv181110091 Phys. (2018). Figure 1

Pant, Lalit↗

DOE OSTI2024

Development of Structure–Property Relationships for Ammonium Transport through Charged Organogels

Ammonia is a promising carbon-free fuel, but current methods to produce ammonia are energy intensive. New methods are thereby needed, with one promising method being electrochemical nitrogen reduction cells. Efficient cell operation requires robust catalysts but also efficient membrane separators that permit the selective transport of ions while minimizing the transport of the products across the cell. Commercial membranes have an unknown morphology which makes designing improved cells challenging. To address this problem, we synthesized a series of membranes with controlled crosslinking density and chemical composition to understand their impact on ammonium transport. Higher crosslinking density led to lower ammonium permeability. At the highest crosslinking density, similar ammonium permeability was observed independent of the water volume fraction and hydrophobicity of the monomers. These results suggest new directions to develop membranes with reduced ammonium crossover to improve the efficiency of these electrochemical cells.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Flux effects in precipitation under irradiation simulation of Fe-Cr alloys

Radiation-enhanced precipitation of Cr-rich α’ in irradiated Fe-Cr alloys, which results in hardening and embrittlement, depends on the irradiating particle and the displacement per atom (dpa) rate. Here, we utilize a Cahn-Hilliard phase-field based approach, that includes simple models for nucleation, irradiating particle and rate dependent radiation-enhanced diffusion and cascade mixing to simulate α’ evolution under neutrons, heavy ions, and electron irradiations. Different irradiating particles manifest very different cascade mixing efficiencies. The model was calibrated using neutron data. For cascade inducing neutron/heavy-ion dpa rates at 300 °C between 10-8 and 10-6 dpa/s the model predicts approximately constant number density, decreasing radius, decreasing α’ Cr composition, and lower α’ volume fraction. The model then predicts a dramatic transition to no α’ formation above approximately 10-5 dpa/s, while electron irradiation, with weak mixing, had little effect at dpa rates up to 10-3 dpa/s. These model predictions are consistent with experiments. We explain the results in terms of the flux dependence of the radiation enhanced diffusion, cascade mixing, and their ratio, which all vary significantly in relevant flux ranges for neutron and cascade inducing ion irradiations. These results show that both cascade mixing and radiation enhanced diffusion must be accounted for when attempting to emulate neutron-irradiation effects using accelerated ion irradiations.

Ke, Jia-Hong↗

DOE OSTI2024

Search for non-virialized axions with 3.3-4.2 $\mu$eV mass at selected resolving powers

The Axion Dark Matter eXperiment is sensitive to narrow axion flows, given axions compose a fraction of the dark matter with a non-negligible local density. Detecting these low-velocity dispersion flows requires a high spectral resolution and careful attention to the expected signal modulation due to Earth's motion. We report an exclusion on the local axion dark matter density in narrow flows of $\rho_a \gtrsim 0.03\,\mathrm{GeV/cm^3}$ and $\rho_a \gtrsim 0.004\,\mathrm{GeV/cm^3}$ for Dine-Fischler-Srednicki-Zhitnitski and Kim-Shifman-Vainshtein-Zakharov axion-photon couplings, respectively, over the mass range $3.3-4.2\,\mu\text{eV}$. Measurements were made at selected resolving powers to allow for a range of possible velocity dispersions.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

Relationships between the Stellar, Gaseous, and Star Formation Disks in LITTLE THINGS Dwarf Irregular Galaxies: Indirect Evidence for Substantial Fractions of Dark Molecular Gas

The stellar, gaseous and young stellar disks in the LITTLE THINGS sample of nearby dwarf irregular galaxies are fitted with functions to search for correlations between the parameters. We find that the H i radial profiles are generally flatter in the center and fall faster in the outer regions than the V-band profiles, while young stars are more centrally concentrated, especially if the H i is more centrally flat. This pattern suggests that the H i is turning into molecules in the center, and the molecular clouds are forming stars and FUV. A model that assumes the molecular surface density is proportional to the total gas surface density to a power of 1.5 or 2, in analogy with the Kennicutt–Schmidt relation, reproduces the relationship between the ratio of the visible to the H i scale length and the H i Sérsic index. The molecular fraction is estimated as a function of radius for each galaxy by converting the FUV to a molecular surface density using conventional calibrations. The average molecular fraction inside 3R {sub D} is 23% ± 17%. However, the break in the stellar surface brightness profile has no unified tracer related to star formation.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2020

Coupling computational thermodynamics with density-function-theory based calculations to design L12 precipitates in Fe Ni based alloys

Achieving a high-volume fraction of thermodynamically stable L12-type precipitates that are resistant to coarsening is of great importance for the development of low-cost FeNi based austenitic steels. With the aid of computational thermodynamics, this work designed two model alloys: Fe-37.4Ni-6.1Al-2.9Ti (FNAT) and Fe-45.2Ni-5.9Al-8.5Si (FNAS). Both alloys were designed to contain a similar amount of L1 2 precipitate in Fe-Ni matrix without forming other precipitates. Density-Function-Theory (DFT) calculation was coupled with computational thermodynamics to predict the critical radius at which the precipitates change shape from spherical to cuboidal. The calculation results suggest that critical radius for the FNAT alloy is about two orders of magnitude larger than that for the FeNiAlSi alloy. Phase stability and morphology of the L1 2 precipitates in these two alloys were experimentally investigated through X-ray diffraction, atom probe tomography, and scanning and transmission electron microscopy. The L1 2 precipitates in the FeNiAlSi system were found to be cuboidal and rod shaped, with much larger size than the spherical ones in the FeNiAlTi system, agreeing with the calculation results. This work suggested that coupling computational thermodynamics with DFT calculations can be reliably used to design L1 2 precipitates in FeNi based alloys.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Laser-plasma instabilities in long scale-length plasmas relevant to shock-ignition

We present 2D particle-in-cell simulations of laser-plasma instabilities (LPI) performed using conditions relevant to experiments on the OMEGA and NIF laser facilities. The laser intensity used is 2×10 15 W cm -2 , which allows comparison with previous experiments and simulations investigating shock ignition, though this is a relatively low intensity for the scheme. We find that the large convective gain of the instabilities leads to dynamics that are largely controlled by pump depletion and to scattering or absorption by LPIs predominantly occurring away from the quarter-critical density. The two-plasmon decay (TPD) instability is dominant for OMEGA-type conditions and remains important at the NIF-scale. In both cases, most absorption from TPD occurs near its Landau cutoff density, and we examine its nonlinear dynamics in this region, focusing on the ion-acoustic waves responsible for saturation. For NIF-type conditions, stimulated Raman scattering (SRS) and stimulated Brillouin scattering divert significant fractions of laser energy, and we find that SRS backscatter can occur with high gain at low densities due to kinetic effects. An in-depth analysis of hot-electron production is performed to identify the main sources and their characteristic electron temperature. For both simulations presented, the overall hot-electron temperature lies between 30 and 35 keV. This is relatively low and will likely increase shock pressure; however, the distributions also contain a significant number of high-energy (E k >100 keV) electrons that would likely cause unacceptable preheat. We, therefore, suggest some strategies that may be utilized to minimize this high-energy component. I. INTROD

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Cosmic Reionization on Computers: Statistics, Physical Properties, and Environments of Lyman Limit Systems at z ~ 6

Lyman limit systems (LLSs) are dense hydrogen clouds with high enough H i column densities to absorb Lyman continuum photons emitted from distant quasars. Their high column densities imply an origin in dense environments; however, the statistics and distribution of LLSs at high redshifts still remain uncertain. In this paper, we use self-consistent radiative transfer cosmological simulations from the Cosmic Reionization on Computers (CROC) project to study the physical properties of LLSs at the tail end of cosmic reionization at z ~ 6. We generate 3000 synthetic quasar sight lines to obtain a large number of LLS samples in the simulations. In addition, with the high physical fidelity and resolution of CROC, we are able to quantify the association between these LLS samples and nearby galaxies. Our results show that the fraction of LLSs spatially associated with nearby galaxies increases with H i column density. Moreover, we find that LLSs that are not near any galaxy typically reside in filamentary structures connecting neighboring galaxies in the intergalactic medium (IGM). This quantification of the distribution and association of LLSs to large-scale structure informs our understanding of the IGM–galaxy connection during the "Epoch of Reionization," and provides a theoretical basis for interpreting future observations.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

Investigation of the neoclassical ambipolar electric field in ion-root plasmas on W7-X

The role of the radial electric field in high-performance ion-root plasmas on Wendelstein 7-X (W7-X) is examined and compared with neoclassical predictions herein. The W7-X stellarator is the world’s first large-scale optimized stellarator. One of the important targets chosen for optimization during the W7-X design process was the reduction of core neoclassical heat transport. This optimization was targeted for reactor-relevant high-density plasmas with $T_e ≈ T_i$ in which the neoclassical ambipolar radial electric field is expected to be negative throughout the plasmas core. Measurements of the core radial electric field $(E_r)$ have confirmed that ion-root conditions (negative $(E_r)$ in the plasma core) have been achieved in W7-X with high-density plasmas and central ECRH. These measured $(E_r)$ profiles agree well with the neoclassical ambipolar $(E_r)$ predicted by the code SFINCS . This good agreement provides confidence in the validity of neoclassical calculations in high-density ion-root conditions, and enables initial studies on the role of neoclassical transport in the optimized high-density regime of W7-X. Profile measurements of electron temperature $(T_e)$, ion temperature $(T_i)$ and electron density $(n_e)$ along with approximations for the average value of $Z$ eff have been used as inputs to the sfincs code to calculate the ambipolar $E_r$ profile along with neoclassical ion and electron energy flux profiles $(Q$ NCi , $Q$ NCe $)$. Finally the total experimental energy input to the plasma from ECRH heating has been compared to the neoclassical energy fluxes to provide a first estimate for the fraction of transport that can be attributed to neoclassical processes in reactorrelevant high-density ion-root conditions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Higher Hall conductivity from a single wave function: Obstructions to symmetry-preserving gapped edge of (2+1)-dimensional topological order

A (2+1)D topologically ordered phase with U(1) symmetry may or may not have a symmetric gapped edge state, even if both thermal and electric Hall conductivity are vanishing. It has recently been discovered that there are “higher” versions of Hall conductivity valid for fermionic fractional quantum Hall (FQH) states that obstruct symmetry-preserving gapped edge states beyond thermal and electric Hall conductivity. In this paper, we show that one can extract higher Hall conductivity from a single wave function of an FQH state, by evaluating the expectation value of the “partial rotation” unitary, which is a combination of partial spatial rotation and a U(1) phase rotation. This result is verified numerically with the fermionic Laughlin state with 𝜈=1/3 and 1/5, as well as the non-Abelian Moore-Read state. Together with topological entanglement entropy, we prove that the expectation values of the partial rotation completely determine if a bosonic/fermionic Abelian topological order with U(1) symmetry has a symmetry-preserving gappable edge state or not. We also show that thermal and electric Hall conductivity of Abelian topological order can be extracted by partial rotations. Even in non-Abelian FQH states, partial rotation provides the Lieb-Schultz-Mattis type theorem constraining the low-energy spectrum of the bulk-boundary system. The generalization of higher Hall conductivity to the case with Lie group symmetry is also presented.

2-dimensional systems↗

DOE OSTI2022

Westinghouse advanced fuel management strategies leveraging high enrichment and high burnup fuel to optimize PWR economics

In the US, nuclear power plants have been focused on increasing electricity generation for over three decades via longer operating cycles, reduced number of outages and duration, and the implementation of power up-rates. The potential for zero-carbon emission credits and other carbon-reduction initiatives further makes nuclear power utilities to focus on increasing generation capability. Longer operating cycles provide increased energy generation and enable economic savings to nuclear utilities when the increase in fuel loading required to achieve the extended cycle energy target and resulting increase in total fuel cost is offset by the savings from outage avoidance and reduced replacement power costs. For the current licensed limits of 5 w/o {sup 235}U enrichment and 62 GWd/tU peak pin burnup, higher power density PWR plants, which are prevalent in the PWR fleet, require an excessively penalizing fraction of feed fuel assemblies to operate for the extended cycle duration, with inevitably poor fuel use and fuel cycle economics that cannot be counterbalanced by the savings on outage cost avoidance. To overcome this barrier, the nuclear industry is pursuing development of high enrichment/high burnup fuel technology ({sup 235}U enrichment up to 8 w/o and peak pin burnup up to 75 GWd/tU) which increases fuel energy generation capability and can enable high power density plants to achieve positive economics on 24-month cycle of operation. This paper presents advanced fuel management strategies developed by Westinghouse to enable transition of PWR reactors from 18-month to 24-month cycle of operation, with and without a core thermal power uprate, which are then used as basis to assess the economics of a direct transition from 18 to 24-month cycles with high enrichment/high burnup fuel. The results show that these fuel management strategies, especially if coupled with thermal power up-rates, present the opportunity for substantial economic benefits to utilities. The systematic review of fuel management strategies presented can provide an illustrative reference for decision makers as they consider how to maximize nuclear energy generation economically. (authors)

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2026

Impact of Cosmic Filaments on Galaxy Morphological Evolution and Predictions of Early Cosmic Web Structure for Roman

We leverage the IllustrisTNG cosmological simulations to test how the large-scale cosmic web shapes galaxy morphology and to forecast the early cosmic web structure that the Nancy Grace Roman Space Telescope will reveal. In the hydrodynamic TNG50 and N-body TNG50-Dark runs, we reconstruct the cosmic web at redshifts z = 0, 0.5, 1, 2, 3, and 4 with the Monte Carlo Physarum Machine density estimator and the DisPerSE structure identification framework. We confirm that dark matter halos start out predominantly prolate (elongated), and their shapes are aligned with their nearest filaments; prolate galaxies retain strong shape alignment with their outer halos to later times. At z ≥ 1, the fraction of prolate (spheroidal) halos increases (decreases) toward lower stellar mass, higher redshift, and lower filament density. At z < 1, more spheroidal (oblate) stellar structures preferentially reside in higher-density (lower-density) filaments. We also find that higher-density filaments favor extended rotationally supported disks, whereas lower-density filaments more often host smaller dispersion-supported systems. Then, generating mock galaxy samples from TNG100 and TNG50, we predict the early cosmic web accessible to Roman. We find that the spectroscopic emission-line depth planned for the High-Latitude Wide-Area Survey (HLWAS) yields a highly incomplete galaxy sample that does not accurately trace the z = 1 cosmic web. A survey ≥2.5× deeper over a few square degrees would enable a proper reconstruction and reveal qualitatively correct filament–galaxy morphology relationships. Nevertheless, the planned HLWAS Deep field should still identify most galaxy overdensities; targeted deeper spectroscopy of these regions would efficiently and adequately map the early filamentary structure.

Hasan, Farhanul [Space Telescope Science Institute↗

DOE OSTI2021

The Chemical Inventory of the Planet-hosting Disk PDS 70

As host to two accreting planets, PDS 70 provides a unique opportunity to probe the chemical complexity of atmosphere-forming material. We present ALMA Band 6 observations of the PDS 70 disk and report the first chemical inventory of the system. With a spatial resolution of 0."4–0."5 (~50 au), 12 species are detected, including CO isotopologs and formaldehyde, small hydrocarbons, HCN and HCO{sup +} isotopologs, and S-bearing molecules. SO and CH{sub 3}OH are not detected. All lines show a large cavity at the center of the disk, indicative of the deep gap carved by the massive planets. The radial profiles of the line emission are compared to the (sub)millimeter continuum and infrared scattered light intensity profiles. Different molecular transitions peak at different radii, revealing the complex interplay between density, temperature, and chemistry in setting molecular abundances. Column densities and optical depth profiles are derived for all detected molecules, and upper limits obtained for the nondetections. Excitation temperature is obtained for H{sub 2}CO. Deuteration and nitrogen fractionation profiles from the hydrocyanide lines show radially increasing fractionation levels. Comparison of the disk chemical inventory to grids of chemical models from the literature strongly suggests a disk molecular layer hosting a carbon-to-oxygen ratio C/O > 1, thus providing for the first time compelling evidence of planets actively accreting high C/O ratio gas at present time.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2023

Twin density and twin thickness evolution in sputtered Al–Mg alloys

Twinned Al–Mg alloys have been reported. However, the role of Mg solute in facilitating the formation of growth twins remains unclear. By using a precession-assisted crystal orientation mapping technique (PACOM) coupled with transmission electron microscopy (known as ASTAR), we examined the evolution of twin boundaries in Al, Al–1Mg, and Al–2.2Mg (at. %) films. The twinned grain fraction elevates with increasing film thickness until it reaches a peak when the film thickness is 120–160 nm. The Al–Mg alloys exhibited greater twinned grain fractions than pure Al. To investigate the fluctuation of twinned grain fraction, two types of twin boundaries were classified including intergranular and intragranular twins. The initial increase in twin density is attributed to the impingement of twinned grains during island coalescence and the twinned grains are more likely to survive during the grain growth process. Whereas the decrease in twinned grain fraction in thicker films is related to the removal of intragranular twins, and a lack of formation mechanisms of new twins.

Physics↗

DOE OSTI2021

Radially resolved active charge exchange measurements of the hydrogenic isotope fraction on DIII-D

Radially resolved hydrogenic isotope fraction measurement capabilities have been developed for DIII-D using the main-ion charge exchange recombination (MICER) spectroscopy system in preparation for mixed hydrogen and deuterium experiments. Constraints on the hydrogenic ion temperatures and velocities based on measurements of the impurity ion properties are required to accurately fit the spectrum. Corrections for cross sectional distortions, spatial smearing due to the halo, and a neoclassical offset between the impurity and hydrogenic toroidal rotation are applied to the constraints prior to fitting the MICER spectrum. Extensive atomic physics calculations have been performed using the FIDASIM code, which has recently been improved to allow simulations using mixtures of hydrogenic species. Overall, these results demonstrate that for the same plasma parameters, the Dα emission is 20%–30% brighter than Hα due to differences in rate coefficients associated with the different ion thermal velocities for the same temperature and therefore must be taken into consideration when calculating absolute densities. However, despite these differences, the absolute error when estimating the hydrogen isotope fraction [n H /(n H + n D )] by using the Hα radiance fraction [L Hα /(L Hα + L Dα )] is typically less than 5% due to the way the fraction is formed, making the radiance fraction a reasonably accurate estimate of the isotope fraction for most cases.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗