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At least 469 records · Page 26

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DOE OSTI2026

Linear simulations of a wide pedestal quiescent H-mode plasma with the extended-MHD code NIMROD

We present linear simulations of a Wide Pedestal QH (WPQH)-mode DIII-D plasma with the NIMROD code to address the role of ion multispecies collisionality on WPQH-modes. We use a full extended-MHD model that captures Alfvénic and magnetoacoustic waves, including two-fluid, ion gyroviscosity and cross heat flux. We show that two-fluid and ion gyroviscous effects destabilize electron-directed peeling–ballooning modes in the pedestal. The linear growth rates of the modes decrease when carbon (C) is added to a deuterium plasma because the multispecies collisional effects increase the plasma resistivity. When replacing C with tungsten (W), the multispecies collisional effects increase the resistivity further, as well as the stabilizing effect on the instabilities. The resistivity impact on mode stability is reversed when both two-fluid and ion gyroviscous effects are ignored, which is consistent with previous works, proving that multispecies collisional effects, together with two-fluid and ion gyroviscosity, should be considered to address the stability of plasmas with significant impurity content.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Thermodynamic Phase Transition in Magnetic Reconnection

By examining the entropy production in fully kinetic simulations of collisional plasmas, it is shown that the transition from collisional Sweet-Parker reconnection to collisionless Hall reconnection may be viewed as a thermodynamic phase transition. The phase transition occurs when the reconnection electric field satisfies E = $E_{D}\sqrt{m{e}/{m}_i}$ , where ${m{e}/{m}_i}$ is the electron-to-ion mass ratio and E D is the Dreicer electric field. This condition applies for all ${m{e}/{m}_i}$, including ${m{e}/{m}_i}$ = 1 , where the Hall regime vanishes and a direct phase transition from the collisional to the kinetic regime occurs. In the limit ${m{e}/{m}_i}$ → 0, this condition is equivalent to there being a critical electron temperature $Te ≈ m_iΩ^{2}_{i}δ^{2}$, where $Ω_i$ is the ion cyclotron frequency and δ is the current sheet half-thickness. The heat capacity of the current sheet changes discontinuously across the phase transition, and a critical power law is identified in an effective heat capacity. A model for the time-dependent evolution of an isolated current sheet in the collisional regime is derived.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Gaussian Mixture Model Solvers for the Boltzmann Equation

This report documents our experience constructing a numerical method for the collisional Boltzmann equation that is capable of accurately capturing the collisionless through strongly collisional limits. We explore three different functional representations and present a detailed account of a numerical method based on a spatially dependent Gaussian mixture model (GMM). The Kullback-Leibler divergence is used as a closeness measure and various expectation maximization (EM) solution algorithms are implemented to find a compact representation in velocity space for distribution functions that exhibit significant non-Maxwellian character. We discuss issues that appear with this representation over a range of Knudsen numbers for a prototypical test problem and demonstrate that the strongly collisional limit recovers a solution to Euler's equations. Looking forward, this approach is broadly applicable to the non-relativistic and relativistic collisional Vlasov equations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Reimagining full wave rf quasilinear theory in a tokamak

The velocity dependent resonant interaction of particles with applied radio frequency (rf) waves during heating and current drive in the presence of pitch angle scattering collisions gives rise to narrow collisional velocity space boundary layers that dramatically enhance the role of collisions as recently shown by Catto (J. Plasma Phys., vol. 86, 815860302, 2020). The behavior is a generalization of the narrow collisional boundary layer that forms during Landau damping as found by Johnston (Phys. Fluids, vol. 14, 1971, pp. 2719-2726) and Auerbach (Phys. Fluids, vol. 20, 1977, pp. 1836-1844). For a wave of parallel wave number k|| interacting with weakly collisional plasma species of collision frequency ν and thermal speed vth , the effective collision frequency becomes of order ν(k_||v_th /ν)^2/3>> ν . The narrow boundary layers that arise because of the diffusive nature of the collisions allows a physically meaningful wave-particle interaction time to be defined that is the inverse of this effective collision frequency. The collisionality implied by the narrow boundary layer results in changes in the standard quasilinear treatment of applied rf fields in tokamaks while remaining consistent with causality. These changes occur because successive poloidal interactions with the rf are correlated in tokamak geometry and because the resonant velocity space dependent interactions are controlled by the spatial and temporal behavior of the perturbed full wave fields rather than just the spatially local Landau and Doppler shifted cyclotron wave-particle resonance condition associated with unperturbed motion of the particles. The correlation of successive poloidal circuits of the tokamak leads to the appearance in the quasilinear operator of transit averaged resonance conditions localized in velocity space boundary layers that maintain negative definite entropy production.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1980

Effects of angular-momentum-changing collisions on dielectronic satellite spectra

A generalization of the low-density corona-model theory of the intensities of satellite lines of the resonance lines emitted by multiply charged helium-like ions in the X-ray spectra of high-temperature plasmas is developed in order to take account of electron collisional transitions between close autoionizing levels. A formalism for determining the population densities of the autoionizing levels and the satellite line intensities is presented, and the quantum mechanical calculation of autoionization, radiative decay and electron-induced collisional transitions is discussed. Generalized emission rate coefficients corresponding to dielectronic recombination and inner-shell-electron collisional excitation are tabulated as functions of electron density and temperature. The procedure is then used to illustrate the effects of angular-momentum-changing electron collisions on the intensities of the satellites of the 1s2p 1P to 1s2 1S resonance line of the ions Al XII and Si XIII. It is concluded that the collisional transitions have their most significant effect on the intensities of satellite transitions from metastable autoionizing states, which may be useful in determining plasma densities.

Jacobs, V. L.↗

NASA NTRS1985

Theory of the current-driven ion cyclotron instability in the bottomside ionosphere

A comprehensive treatment of the theory of electrostatic ion cyclotron instability in the collisional bottomside ionosphere is given. The linear dispersion relations for the ion cyclotron instability (electron and ion collisions) are derived. Analytical solutions to the dispersion relation are obtained in three limits: collisionless; weakly collisional; and collisional. In addition, the linear dispersion relation is solved numerically, using parameters typical of the high-latitude bottomside ionosphere. It is pointed out that the linear growth rates in the bottomside collisional regime can be of the same order as the corresponding topside collisionless growth rates. A nonlinear saturation mechanism for the electrostatic ion cyclotron instability is proposed on the basis of Dupree's (1966) resonance broadening theory.

Satyanarayana, P.↗

NASA NTRS2001

Measuring Rocket Engine Temperatures with Hydrogen Raman Spectroscopy

Optically accessible, high pressure, hot fire test articles are available at NASA Marshall for use in development of advanced rocket engine propellant injectors. Single laser-pulse ultraviolet (UV) Raman spectroscopy has been used in the past in these devices for analysis of high pressure H2- and CH4-fueled combustion, but relies on an independent pressure measurement in order to provide temperature information. A variation of UV Raman (High Resolution Hydrogen Raman Spectroscopy) is under development and will allow temperature measurement without the need for an independent pressure measurement, useful for flows where local pressure may not be accurately known. The technique involves the use of a spectrometer with good spectral resolution, requiring a small entrance slit for the spectrometer. The H2 Raman spectrum, when created by a narrow linewidth laser source and obtained from a good spectral resolution spectrograph, has a spectral shape related to temperature. By best-fit matching an experimental spectrum to theoretical spectra at various temperatures, a temperature measurement is obtained. The spectral model accounts for collisional narrowing, collisional broadening, Doppler broadening, and collisional line shifting of each Raman line making up the H2 Stokes vibrational Q-branch spectrum. At pressures from atmospheric up to those associated with advanced preburner components (5500 psia), collisional broadening though present does not cause significant overlap of the Raman lines, allowing high resolution H2 Raman to be used for temperature measurements in plumes and in high pressure test articles. Experimental demonstrations of the technique are performed for rich H2-air flames at atmospheric pressure and for high pressure, 300 K H2-He mixtures. Spectrometer imaging quality is identified as being critical for successful implementation of technique.

Wehrmeyer, Joseph A.↗

NASA NTRS2002

Measurements of [C I] 9850 A Emission from Comet Hale-Bopp

We present quantitative measurements of cometary [C I] 9850 A, emission obtained during observations of comet Hale-Bopp (C/1995 O1) in 1997 March and April. The observations were carried out using a high-resolution (lambda/Delta lambda approx. 40,000) Fabry-Perot/CCD spectrometer at the McMath-Pierce solar telescope on Kitt Peak. This forbidden line, the carbon analog of [O I] 6300 A, is emitted in the radiative decay of C(1D) atoms. In the absence of other sources and sinks, [C I] 9850 A emission may be used as a direct tracer of CO photodissociation in comets. However, in Hale-Bopp's large, dense coma, other processes, such as collisional excitation of ground-state C(3P), dissociative recombination of CO+, and collisional dissociation of CO and CO2 may produce significant amounts of C(1D). The long C(1D) radiative lifetime (approx. 4000 s) makes collisional de-excitation (quenching) the primary loss mechanism in the inner coma. Thus, a detailed, self-consistent global model of collisional and photochemical interactions is necessary to fully account for [C I] 9850 A emission in comet Hale-Bopp.

Oliversen, R. J.↗

NASA NTRS2003

Sheet Flows, Avalanches, and Dune Evolution on Earth and Mars

This investigation is a collaboration between researchers at Cornell University, the University of Florida, and the University of Rennes 1, France. Flow modeling at Cornell University focused on mechanisms for the suspension and transport of wind-blown sand that are important in both terrestrial and Martian environments. These mechanisms include the saltation (or jumping) of grains, collisions between grains, and the interaction of grains with the velocity fluctuations of the turbulent wind. Of particular interest are sheet flows; these are relatively thin, highly concentrated regions of grains flowing near the ground under the influence of a strong turbulent wind. In them, the grains are suspended by interparticle collisions. Sheet flows may be relatively rare events, but they have the capacity to move great amounts of sand. In order to describe sheet flows, a turbulent mixture theory was formulated for particles in a fluid in which fluctuations in the volume fiaction of the particles take place on the scale of the turbulent eddies. Ensemble averaged equations for particle and fluid mass, momentum, and energy and fluid rate of dissipation were expressed in terms of Farve (concentration) averaged velocities and the associated velocity fluctuations. Correlations that describe the turbulent suspension of particles and dissipation of turbulent energy of both phases due to fluid particle interactions were modeled and boundary conditions at the bed and at the upper surface of the collisional flow were formulated. The boundary conditions at the upper surface were tested in a numerical simulation developed at the University of Florida. Steady and unsteady solutions for steady and unsteady fully-developed flows were obtained over a range of wind speeds fiom the lowest for which collisional between particles occurred to at which turbulent suspension is found to dominate collisional suspension. Below the value of the wind speed at which collisions between particles were unimportant, numerical solutions were obtained for the velocity distribution function and the resulting fields of concentration, particle and gas mean velocity, and particle shear stress for the steady two-dimensional saltation of spherical sand particles driven by a turbulent wind over a bed characterized by a simple relationship (the splash function) between the properties of incoming particles and those of the rebounding particles and other particles ejected fiom the bed. At the University of Rennes 1, experiments devoted to the characterization of the splash function for beds consisting of either random or ordered arrays of spheres in two- dimensions were completed. These indicated the role played by the packing geometry in the rebound and ejection of grains. Preliminary experiments on response of a three- dimensional collision bed to a collision with a single particle were performed. Data was taken with a single camera focused on the plane of collision. Here, for example, the decrease of the effective coefficient of restitution of the bed with an increase of the angle of incidence of the incoming particle has been measured. Other experiments on avalanches at Rennes studied the properties of the flows of particles that are responsible for the motion of the leeward side of a dune. In these, the dependence of the initiation of avalanches on the packing and depth of the particles was measured. Particle migration was studied in inclined flows of a binary mixture of disks and the mechanisms of diffision and segregation were isolated and characterized. The influence of side wall on dense, rapid inclined flows was measured and shown to be the reason why the angle of the free surface in such flows can exceed the static angle of repose. Future research will be devoted to a better understanding the transition between saltating (collisionless) and collisional flows as the wind speed the increases. This will involve the understanding of the evolution of the splash function as clisions with the bed become more numerous, more frequent, and more violent.

Source record↗

DOE OSTI2025

Ionization dynamics of intense laser-produced argon plasmas revealed by NLTE modeling

The ionization dynamics and transient behavior of under-dense plasma irradiated by an intense laser are investigated. We report two significant effects in the ionization behavior: (1) a surprisingly large delay in ionization response and (2) a stepwise ionization process which involves collisional and laser-driven photoionization (LDP) processes. Ionization induced by intense lasers can exhibit delayed responses due to rapid changes in conditions, particularly when atomic transition processes occur more slowly than the relevant time scales. Furthermore, modeling reveals that the two-step ionization process—collisional excitation followed by LDP—plays an important role in this ionization delay, with collisional excitation acting as the bottleneck. Even low-energy photons (∼3.5 eV) can predominantly ionize plasmas, challenging the conventional belief that such energies are insufficient to overcome the binding energy of bound electrons. These findings underscore the necessity of including such processes into plasma simulations for various laser-plasma experiments.

Collisional excitation↗

DOE OSTI2025

Coupling to rotational manifolds to improve gas-phase pump–probe spectroscopic models

The physical picture of gas-phase optical transitions is normally presented as an isolated two-level system balanced by upward and downward processes. Isolated models assume a phenomenological treatment of collisional dephasing but do not strictly account for collisional population exchange with the rotational baths. While this assumption is valid under low-intensity conditions, where excitation is rate-limiting, isolated models can deviate from Beer’s Law at sufficient pressures and monochromatic intensities when both collisional broadening and power broadening are comparable to (or greater than) lifetime broadening, which are not uncommon conditions for cavity enhanced spectroscopies in the mid-IR spectral range. Although this problem has been addressed by rate-equation models for linear absorption measurements, a general treatment for multi-level quantum mechanical models suitable for non-linear absorption measurements (two-photon/two-color/pump–probe) is lacking. Isolated models require physical parameter inputs that disagree with expected values by at least an order of magnitude. These non-physical models undermine the ability to predict non-linear signal strengths under untested conditions and thereby limit the potential to optimize the sensitivity of non-linear spectroscopies and to expand their analytical applications (e.g., new analytes and/or buffer gases, changes in cavity free-spectral-range, changes in intracavity powers or wavelengths, and accurate investigation of physical phenomena). In this study, we derive bath-coupled models for gaseous pump–probe spectroscopy by application of the quantum Lindblad equation and detailed balance. Bath-coupled models are shown to fit data consistently across variations in intensity and agree with all physically expected values.

Cavity ring-down spectroscopy↗

DOE OSTI2025

Comparative studies of cross-phase dynamics in turbulent momentum flux and particle flux at the tokamak edge

Turbulent transport events, including turbulent transport flux of momentum (i.e., turbulent momentum flux or Reynolds stress) and turbulent transport flux of particle (i.e., turbulent particle flux), have important effects on the confinement performance of magnetic confinement fusion devices. Poloidal Reynolds stress is the ensemble average of the product of radial velocity fluctuations and poloidal velocity fluctuations, i.e., $\langle {\widetilde{v}}_{r}{\widetilde{v}}_{\theta }\rangle$. Turbulent particle flux is the ensemble average of the product of radial velocity fluctuations and density fluctuations, i.e., $\langle \widetilde{n}{\widetilde{v}}_{r}\rangle$. Changes in either amplitude of fluctuations or cross phase between fluctuations can cause changes in turbulent transport. In this paper, cross-phase dynamics in the Reynolds stress and turbulent particle flux at the tokamak edge are studied in detail. Reynolds stress and turbulent particle flux are, respectively, written as the product of fluctuation amplitudes and an average cross-phase factor. The mathematical expressions of the average cross-phase factors are derived. The average cross-phase factors and the power spectra of cross phase are obtained using experimental measurement data. It is found that the cross-phase dynamics in Reynolds stress and particle flux are very different. Reynolds stress is found to be more sensitive to cross phase than particle flux is. In the strong $E\times B$ shear layer, spatial slips of cross phase lead to the obvious radial gradient of Reynolds stress. In the no/weak $E\times B$ shear region, the cross phase in Reynolds stress tends to lock. Here, phase locking refers to that the power spectra of phase tend to distribute around a fixed phase which does not change with radial position, while phase slip means that the power spectra of cross phase tend to distribute around a phase that varies with radial position. Phase slip or locking mainly describes the central phase weighted by the power spectra, while the phase scattering mainly describes the dispersion of the power spectrum distribution of the phase. The increased scattering of cross phase, which indicates the power spectra distribution of the phase is more dispersed, contributes to the decreased Reynolds stress for higher collisionality. The cross phase in particle flux tends to lock in both strong and no/weak shear regions. The degree of scattering of cross phase in the particle flux does not change obviously as collisionality increases. For higher collisionality, it is the increased density fluctuation amplitude rather than cross-phase dynamics that leads to the increased particle flux. The underlying physical mechanism that causes Reynolds stress and particle flux to exhibit different phase dynamics is discussed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

An asymptotic-preserving 2D-2P relativistic Drift-Kinetic-Equation solver for runaway electron simulations in axisymmetric tokamaks

We propose an asymptotic-preserving (AP), uniformly convergent numerical scheme for the relativistic collisional Drift-Kinetic Equation (rDKE) to simulate runaway electrons in axisymmetric toroidal magnetic field geometries typical of tokamak devices. The approach is derived from an exact Green's function solution with numerical approximations of quantifiable impact, and results in a simple, two-step operator-split algorithm, consisting of a collisional Eulerian step, and a Lagrangian orbit-integration step with analytically prescribed kernels. The AP character of the approach is demonstrated by analysis of the dominant numerical errors, as well as by numerical experiments. We demonstrate the ability of the algorithm to provide accurate answers regardless of plasma collisionality on a circular axisymmetric tokamak geometry.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Kinetic stability of Chapman–Enskog plasmas

In this paper, we investigate the kinetic stability of classical, collisional plasma – that is, plasma in which the mean-free-path $\lambda$ of constituent particles is short compared with the length scale $L$ over which fields and bulk motions in the plasma vary macroscopically, and the collision time is short compared with the evolution time. Fluid equations are typically used to describe such plasmas, since their distribution functions are close to being Maxwellian. The small deviations from the Maxwellian distribution are calculated via the Chapman–Enskog (CE) expansion in $\lambda /L \ll 1$ , and determine macroscopic momentum and heat fluxes in the plasma. Such a calculation is only valid if the underlying CE distribution function is stable at collisionless length scales and/or time scales. We find that at sufficiently high plasma $\beta$ , the CE distribution function can be subject to numerous microinstabilities across a wide range of scales. For a particular form of the CE distribution function arising in strongly magnetised plasma ( viz. plasma in which the Larmor periods of particles are much smaller than collision times), we provide a detailed analytic characterisation of all significant microinstabilities, including peak growth rates and their associated wavenumbers. Of specific note is the discovery of several new microinstabilities, including one at sub-electron-Larmor scales (the ‘whisper instability’) whose growth rate in certain parameter regimes is large compared with other instabilities. Our approach enables us to construct the kinetic stability maps of classical, two-species collisional plasma in terms of $\lambda$ , the electron inertial scale $d_e$ and the plasma $\beta$ . This work is of general consequence in emphasising the fact that high- $\beta$ collisional plasmas can be kinetically unstable; for strongly magnetised CE plasmas, the condition for instability is $\beta \gtrsim L/\lambda$ . In this situation, the determination of transport coefficients via the standard CE approach is not valid.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Ion thermal transport in the H-mode edge transport barrier on DIII-D

The power balance ion heat flux in the pedestal region on DIII-D increases and becomes increasingly anomalous (above conventional neoclassical) in experiments with higher temperature and lower density pedestals where the ion collisionality ($v^*_i$) is lowered toward values expected on ITER. Direct measurements of the main-ion temperature are shown to be essential on DIII-D when calculating the ion heat flux due to differences between the temperature of $D^+$ and the more commonly measured $C^{6+}$ impurity ions approaching the separatrix. Neoclassical transport calculations from NEO and non-linear gyrokinetic calculations using CGYRO are consistent with these observations and show that while neoclassical transport plays an important role, the turbulent ion heat flux due to ion scale electrostatic turbulence is significant and can contribute similar or larger ion heat fluxes at lower collisionality. Beam emission spectroscopy and Doppler backscattering measurements in the steep gradient region of the H-mode pedestal reveal increased broadband, long-wavelength ion scale fluctuations for the low $v^*_i$ discharges at the radius where the non-linear CGYRO simulations were run. Taken together, increased fluctuations, power balance calculations, and gyrokinetic simulations show that the above neoclassical ion heat fluxes, including the increases at lower $v^*_i$, are likely due to weakly suppressed ion scale electrostatic turbulence. These new results are based on world first inferred ion and electron heat fluxes in the pedestal region of deuterium plasmas using direct measurements of the deuterium temperature for power balance across ion collisionalities covering an order of magnitude from high $v^*_i$ values of 1.3 down to ITER relevant $v^*_i$ ~0.1.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Resolving the mystery of electron perpendicular temperature spike in the plasma sheath

A large family of plasmas has collisional mean-free-path much longer than the non-neutral sheath width, which scales with the plasma Debye length. The plasmas, particularly the electrons, assume strong temperature anisotropy in the sheath. The temperature in the sheath flow direction (Te∥) is lower and drops toward the wall as a result of the decompressional cooling by the accelerating sheath flow. The electron temperature in the transverse direction of the flow field (Te⊥) not only is higher but also spikes up in the sheath. This abnormal behavior of Te⊥ spike is found to be the result of a negative gradient of the parallel heat flux of transverse degrees of freedom (qes) in the sheath. The non-zero heat flux qes is induced by pitch-angle scattering of electrons via either their interaction with self-excited electromagnetic waves in a nearly collisionless plasma or Coulomb collision in a collisional plasma, or both in the intermediate regime of plasma collisionality.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Three-dimensional plasmoid-mediated reconnection and turbulence in Hall magnetohydrodynamics

Plasmoid instability accelerates reconnection in collisional plasmas by transforming a laminar reconnection layer into numerous plasmoids connected by secondary current sheets in two dimensions (2D) and by fostering self-generated turbulent reconnection in three dimensions (3D). In large-scale astrophysical and space systems, plasmoid instability likely initiates in the collisional regime but may transition into the collisionless regime as the fragmentation of the current sheet progresses toward kinetic scales. Hall magnetohydrodynamics (MHD) models are widely regarded as a simplified yet effective representation of the transition from collisional to collisionless reconnection. However, plasmoid instability in 2D Hall MHD simulations often leads to a single-X-line reconnection configuration, which significantly differs from fully kinetic particle-in-cell simulation results. This study shows that single-X-line reconnection is less likely to occur in 3D compared to 2D. Moreover, depending on the Lundquist number and the ratio between the system size and the kinetic scale, Hall MHD can also realize 3D self-generated turbulent reconnection. We analyze the features of the self-generated turbulent state, including the energy power spectra and the scale dependence of turbulent eddy anisotropy.

Physics↗

DOE OSTI2025

Toward an improved nonlocal thermodynamic equilibrium model for more predictive simulations of ignition scale hohlraums

Recently, nonlocal thermodynamic equilibrium (NLTE) modeling has been identified as the primary reason for discrepant predictions of the peak neutron production time in indirectly driven inertial confinement fusion (ICF) platforms. It has also been observed that predictions of collisional excitation rates differ by as much as 50% from measurements. Theoretical uncertainties in dielectronic recombination rates have also been posited as possibly contributing to errors in NLTE predictions. This work examines the impact of multipliers on collisional excitation and dielectronic recombination rates on simulations of a directly driven gold sphere and an indirect drive ICF implosion. It is found that multipliers on the collisional excitation rates have a strong impact on radiant intensity and electron temperature and a weaker impact on ionization state, whereas multipliers on dielectronic recombinations rates strongly impact ionization state with a smaller impact on radiant intensity and electron temperature. A self-consistent NLTE model which places multipliers on differing transitions, as motivated by experimental measurements and more detailed atomic physics predictions, improves agreement but does not completely eliminate discrepancies with measurements of the radiant intensity within the 2–4 keV spectral range.

Farmer, W. A. [Lawrence Livermore National Laborat↗