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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 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

Analysis of Water Coupling in Inelastic Neutron Spectra of Uranyl Fluoride

Inelastic neutron scattering (INS) is uniquely sensitive to hydrogen due to its comparatively large thermal neutron scattering cross-section (82 b). Consequently, the inclusion of water in real samples presents significant challenges to INS data analysis due directly to the scattering strength of hydrogen. Here, we investigate uranyl fluoride (UO 2 F 2 ) with inelastic neutron scattering. UO 2 F 2 is the hydrolysis product of uranium hexafluoride (UF 6 ), and is a hygroscopic, uranyl-ion containing particulate. Raman spectral signatures are commonly used for inferential understanding of the chemical environment for the uranyl ion in UO 2 F 2 , but no direct measurement of the influence of absorbed water molecules on the overall lattice dynamics has been performed until now. To deconvolute the influence of waters on the observed INS spectra, we use density functional theory with full spectral modeling to separate lattice motion from water coupling. In particular, we present a careful and novel analysis of the Q-dependent Debye–Waller factor, allowing us to separate spectral contributions by mass, which reveals preferential water coupling to the uranyl stretching vibrations. Coupled with the detailed partial phonon densities of states calculated via DFT, we infer the probable adsorption locations of interlayer waters. We explain that a common spectral feature in Raman spectra of uranyl fluoride originates from the interaction of water molecules with the uranyl ion based on this analysis. In conclusion, the Debye–Waller analysis is applicable to all INS spectra and could be used to identify light element contributions in other systems.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
NASA NTRS1972

RF sheath and admittance characteristics of a spherical plasma probe.

Development of a radio-frequency sheath model for a spherical probe in a collisionless plasma. The method of solution is based on the quasi-static approximation and the electrostatic probe theory of Bernstein and Rabinowitz (1959). The resistive part of the admittance is ascribed to the sheath transit-time collisionless dissipation mechanism suggested by Mayer (1963) and developed by Gould (1964). Expressions are obtained for the effective sheath thickness and the equivalent resistance of the transit-time dissipation. The sheath model and, hence, the admittance are completely determined in terms of the bias potential, the probe radius, the plasma frequency, and the Debye length - i.e., there are no adjustable parameters in the proposed theory which are to be determined by experiment. The results obtained agree favorably with Cohen and Bekefi's (1971) experimental data on the conductance resonant frequency and the width of the conductance peak.

Kan, J. R.↗
DOE OSTI2026

IRMA

IRMA (In)elastic Representation of Materials As S(α,β) evaluations IRMA turns one phonon model into three outputs that usually require three separate tool chains: an evaluated nuclear-data file, predicted neutron-scattering spectra, and scattering kernels for Monte Carlo transport. The three outputs draw on a single, consistent description of the material, so the evaluation, the spectroscopy that can validate it, and the transport that uses it always agree about the physics. Nuclear data. IRMA writes ENDF-6 File 7 thermal scattering evaluations on automatically constructed (α, β) grids. This part reimplements and generalizes NJOY's LEAPR: the classic kernels reproduce freshly generated NJOY2016 tapes digit for digit and published reference tapes to about 1e-4, and the generalized paths add the exact coherent one-phonon term, anisotropic Debye-Waller tensors, coherent elastic for arbitrary crystals, and a per-species partition for polyatomic materials. The tapes feed NJOY, AMPX, FUDGE, and every transport code downstream of them. Neutron spectroscopy. The irma.spectra forward model projects the same physics onto an instrument's kinematics and resolution: INS spectra for VISION and generic indirect geometries, and 2-D S(Q,E) powder maps for direct-geometry spectrometers, from a phonopy model or straight from a phonon DOS. It can be used to predict a proposed measurement before beam time; in analysis, it supplies the calculated single-scattering counterpart of a measured spectrum, from the same material description the evaluation was built from. Monte Carlo transport. The irma.ncrystal exporter writes per-temperature scattering kernels for the companion NCrystal plugin, so McStas, OpenMC, and other NCrystal-aware codes sample the same physics. The exported kernels carry the per-site anisotropic Debye-Waller tensors, keeping directional coherent-elastic physics that NCrystal's standard scalar treatment does not represent. With the same physics inside a transport code, an entire beamline becomes a virtual experiment: IRMA's end-to-end validation ran a custom McStas implementation of the ARCS spectrometer, assembled from the existing McVine and McStas models, against measured data. From a bare crystal structure. The irma mlip front end builds the phonon model itself: a structure file and a choice of potential are enough. Nine pretrained machine-learned interatomic potentials are supported, on a laptop CPU, with no first-principles calculation; an approximate phonon model for a new material costs minutes, not a DFT campaign, and the build emits prefilled inputs for all three outputs. The result is a good starting point rather than a finished evaluation: survey-quality physics with every parameter exposed for review. A converged atomistic calculation enters the same way, as a phonopy model, when higher fidelity is needed.

Ramic, Kemal [Oak Ridge National Laboratory (ORNL)↗
NASA NTRS2013

Athermal Energy Loss from X-rays Deposited in Thin Superconducting Films on Solid Substrates

When energy is deposited in a thin-film cryogenic detector, such as from the absorption of an X-ray, an important feature that determines the energy resolution is the amount of athermal energy that can be lost to the heat bath prior to the elementary excitation systems coming into thermal equilibrium. This form of energy loss will be position-dependent and therefore can limit the detector energy resolution. An understanding of the physical processes that occur when elementary excitations are generated in metal films on dielectric substrates is important for the design and optimization of a number of different types of low temperature detector. We have measured the total energy loss in one relatively simple geometry that allows us to study these processes and compare measurements with calculation based upon a model for the various di.erent processes. We have modeled the athermal phonon energy loss in this device by finding an evolving phonon distribution function that solves the system of kinetic equations for the interacting system of electrons and phonons. Using measurements of device parameters such as the Debye energy and the thermal di.usivity we have calculated the expected energy loss from this detector geometry, and also the position-dependent variation of this loss. We have also calculated the predicted impact on measured spectral line-shapes, and shown that they agree well with measurements. In addition, we have tested this model by using it to predict the performance of a number of other types of detector with di.erent geometries, where good agreement is also found.

Kozorezov, Alexander G.↗
DOE OSTI2024

Accuracy of the explicit energy-conserving particle-in-cell method for under-resolved simulations of capacitively coupled plasma discharges

The traditional explicit electrostatic momentum-conserving particle-in-cell algorithm requires strict resolution of the electron Debye length to deliver numerical stability and accuracy. The explicit electrostatic energy-conserving particle-in-cell algorithm alleviates this constraint with minimal modification to the traditional algorithm, retaining its simplicity, ease of parallelization, and acceleration on modern supercomputing architectures. In this article, we apply the algorithm to model a one-dimensional radio frequency capacitively coupled plasma discharge relevant to industrial applications. The energy-conserving approach closely matches the results from the momentum-conserving algorithm and retains accuracy even for cell sizes up to 8 times the electron Debye length. For even larger cells, the algorithm loses accuracy due to poor resolution of steep gradients within the radio frequency sheath. Accuracy can be recovered by adopting a non-uniform grid, which resolves the sheath and allows for cell sizes up to 32 times the electron Debye length in the quasi-neutral bulk of the discharge. The effect is an up to 8 times reduction in the number of required simulation cells, an improvement that can compound in higher-dimensional simulations. We therefore consider the explicit energy-conserving algorithm as a promising approach to significantly reduce the computational cost of full-scale device simulations and a pathway to delivering kinetic simulation capabilities of use to industry.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1978

Differential photoelectric charging of nonconducting surfaces in space

The photoelectric charging caused by an infinitely long strip of sunlight across a nonconducting plane is studied by use of a model which contains an electrical cutoff radius, and the results of numerical calculations are presented. The model simulates charging of a sunlit area with dimensions equal to the strip's width, exposed to a plasma with a comparatively large Debye length. Uniform potential is quickly established on a uniformly sunlit strip as a result of charge redistribution by low-energy photoelectrons. The results are in accord with a theoretical surface conductivity derived for photoelectron sheaths above highly charged sunlit areas. The surface potential, which drops sharply across the sunlight-shadow boundary, is discussed.

Pelizzari, M. A.↗
DOE OSTI2020

A generalized Boltzmann kinetic theory for strongly magnetized plasmas with application to friction

Coulomb collisions in plasmas are typically modeled using the Boltzmann collision operator, or its variants, which apply to weakly magnetized plasmas in which the typical gyroradius of particles significantly exceeds the Debye length. Conversely, O’Neil has developed a kinetic theory to treat plasmas that are so strongly magnetized that the typical gyroradius of particles is much smaller than the distance of the closest approach in a binary collision. Here, we develop a generalized collision operator that applies across the full range of magnetization strength. Since there is no closed-form solution for the scattering cross section when plasma is strongly magnetized, the input to the collision operator is obtained by numerically calculating particle trajectories. To demonstrate novel physics associated with strong magnetization, it is used to compute the friction force on a massive test charge. In addition to the traditional stopping power component, this is found to exhibit a transverse component that is perpendicular to both the velocity and Lorentz force vectors in the strongly magnetized regime, as was predicted recently using linear response theory. As a result, good agreement is found between the collision theory and linear response theory in the regime in which both apply, but the new collision theory also applies to stronger magnetization strength regimes than the linear response theory is expected to apply in.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Collaborative Research: Unravelling the Physics Associated with the Production of Extremely Dense Plasma States of Microscale (Final Report) Nanosecond-pulsed Discharges

The aim of this project is to study and establish the physical mechanisms that contribute to the formation of anomalously dense plasmas in high-pressure nanosecond-pulsed discharges. These discharges have a broad range of applications such as plasma-assisted combustion, plasma flow actuators, biomedical sterilization and exotic materials synthesis. The structure and formation of these discharges, producing high plasma densities of ~10 14 -10 15 cm -3 , are well-studied and understood. Fast-pulsed microscale high-pressure discharges can be driven to even higher densities of > 10 19 cm -3 , approaching warm dense matter conditions. The mechanisms that generate these plasmas have not been understood. Analysis of the warm dense matter state under laboratory conditions is an expensive and non-trivial endeavor. For instance, dense plasmas can be generated by electrical explosions of metal foils and wires. Plasmas generated after the explosion have a short lifetime and often present difficult conditions for diagnostics. Generation of dense plasmas was also achieved during high-voltage nanosecond pulsed discharges when the so-called explosive electron emission is obtained. Unfortunately, this process is very difficult to control for the studies of warm dense matter. In our recent study, we have shown that additional heating of plasma by lasers can further increase the density of plasma and even lead to the fully ionized state. This method, potentially, allows better control of the plasma parameters. In this work, we studied a second stage laser-heated micro-discharge using a self-consistent one-dimensional particle-in-cell Monte Carlo-collision (1D PIC-MCC) model coupled with Maxwell’s equations. We predicted the generation of a fully ionized plasma on the picosecond time scale. However, this model considered the plasma as an ideal gas despite the high pressure and the nearly fully ionized state. The ideal plasma model assumes that the dilute gas approximation is valid, where the inter-particle interactions are negligible. For charged particles this assumption holds as long as the shielded Coulomb potential assumption is valid. For very high plasma densities, this concept breaks down since the Debye sphere surrounding each charged particle no longer contains enough electrons to statistically provide the shielding of the single particle Coulomb interaction potential. At such densities, the plasma can no longer be described as ideal and non-ideal coupling effects need to be considered. In this report, we elucidate our recent work of developing a PIC-MCC model with improvements for non-ideal plasma conditions due to Coulomb coupling at high densities. In particular, we study the interaction of green light radiation and a dense microplasma, and explore the non-ideal plasma effects in this interaction. In this computational model, we implement the two most important non-ideal effects: ionization potential depression (IPD) and enhanced collision cross sections. Our primary goal is to study the physics associated with electromagnetic (EM) wave heating, also called the second-stage wave-heating, and establish the role of plasma non-ideality in this phenomenon. Our secondary goal is to improve the chemistry mechanism of the 1D PIC-MCC model by including a more detailed excited species collision treatment. At high pressures, stepwise ionization from excited species might play an important role in the ionization process. Previously, this ionization mechanism was neglected due to the excitation collision cross section of xenon being smaller than that of ionization. However, a preliminary study showed that the excited species density in the initial microplasma was an order of magnitude higher than the electron density. Therefore, my aim is to determine the significance of this additional ionization pathway to the plasma generation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1982

Simple phenomenological modeling of transition-region capacitance of forward-biased p-n junction diodes and transistor diodes

The derivation of a simple expression for the capacitance C(V) associated with the transition region of a p-n junction under a forward bias is derived by phenomenological reasoning. The treatment of C(V) is based on the conventional Shockley equations, and simpler expressions for C(V) result that are in general accord with the previous analytical and numerical results. C(V) consists of two components resulting from changes in majority carrier concentration and from free hole and electron accumulation in the space-charge region. The space-charge region is conceived as the intrinsic region of an n-i-p structure for a space-charge region markedly wider than the extrinsic Debye lengths at its edges. This region is excited in the sense that the forward bias creates hole and electron densities orders of magnitude larger than those in equilibrium. The recent Shirts-Gordon (1979) modeling of the space-charge region using a dielectric response function is contrasted with the more conventional Schottky-Shockley modeling.

Lindholm, F. A.↗
DOE OSTI2018

Microstructural analysis of undoped and moderately Sc-doped TiO2 anatase nanoparticles using Scherrer equation and Debye function analysis

Highlights: • UV light sensitive undoped and moderate Sc-doped anatase nanocrystallites were prepared without post-synthesis annealing. • Elongated nanocrystallites were found by Scherrer equation and Debye Function Analysis applied to XRD data and also HRTEM. • 4 at.% Sc doping reduced the amount of Ti vacancies by half. • Doping showed ~0.3% growth of lattice parameters. - Abstract: UV light sensitive undoped and moderate (4 at.%) Sc-doped anatase nanocrystallites were prepared by an efficient and environmentally benign method based on homogeneous hydrolysis of TiOSO{sub 4} and Sc{sub 2}(C{sub 2}O{sub 4}){sub 3.5}H{sub 2}O aqueous solutions using urea as a precipitation agent, without post-synthesis calcination or annealing. X-ray diffraction study of the obtained powders revealed single phase anatase in both samples. Two different methods were applied to estimate the anatase crystallite size and shape from the X-ray diffraction data. The first one is based on the more conventional Scherrer equation (as implanted in GSAS-II program) while the second one is based on Debye function analysis (as implanted in DUBUSSY suite version 2.2), which is considered to be more adequate for nanocrystallites. Although each program has its own shape models, both methods indicated similar results of elongated nanocrystallite geometry for Sc-doped TiO{sub 2}: (i) GSAS-II confirmed ellipsoid shape with equatorial size of 5.1(0) nm and axial size of 6.8(0), (ii) DEBUSSY suite 2.2 showed cylinder shape with diameter of equivalent circle in the ab-plane, D{sub ab} = 4.9(1.0) nm and crystallite length along the c-axis, L{sub c} = 5.4(3.2) nm. For the undoped TiO{sub 2} sample, equatorial size of 5.5(0) nm and axial size of 7.3(0) nm for the ellipsoid shape was determined according to GSAS-II, while D{sub ab} = 5.5(1.3) nm and L{sub c} = 6.0(2.2) nm for the cylinder shape was determined by DEBUSSY suite 2.2. These outcomes were found to corroborate with HRTEM analysis. Doping with 4 at.% Sc caused ~0.3% growth of lattice parameters from a = 3.7979 [4] Å, c = 9.4995 [9] Å for the undoped sample to a = 3.8110 [7] Å, c = 9.5274 [16] Å for the moderately Sc doped sample, while reduction in the Ti vacancies by half was confirmed by both methods. The introducing of Sc as electronically active secondary species into the crystal lattice of TiO{sub 2} can greatly alter its optical absorption. The incorporation of Sc into the crystal lattice of TiO{sub 2} favors the substitution of Ti, as both have approximately the same ionic size, and generates surface oxygen vacancies which can act as trapping center for the photogenerated electrons and reduce the recombination of electron–hole pairs. We can expect Sc doped TiO{sub 2} nanomaterials to have applications as effective photocatalysts for selective photocatalytic oxidation of various environmental organic pollutants.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2020

First-principles study on structural mechanical and thermodynamic properties of HfMoTaTiZr

This study calculates the phase diagram of HfMoTaTiZr using the TCHEA1 database in Thermo-Calc software. Furthermore, it also investigates the structural and mechanical properties of HfMoTaTiZr by applying first-principles calculations. The elastic and other mechanical properties such as Young’s modulus, pugh ratio, hardness, bulk modulus was derived and discussed. These parameters were found to be in good harmony with previously available experimental reports. Vickers hardness of HfMoTaTiZr predicted from the Tians model agrees with the available experimental result. This study also investigates the thermal coefficient of linear expansion and vibrational heat capacity of the HfMoTaTiZr using the Debye–Grüneisen theory.

36 MATERIALS SCIENCE↗
DOE OSTI2025

X-ray diffraction strains in laser-ablated aluminum, nickel, sodium, and invar: Pressures to 475 GPa

Dynamically compressed materials in longitudinal waves are described by two physical models: hydrostatic pressure, with equal, normal, principal stresses or material uniaxially strained in the wave propagation direction. These models are disparate, so experimental comparisons and evaluations are important. Polycrystalline material in a state of hydrostatic pressure will have no eccentricity of x-ray-diffracted Debye–Scherrer rings. A general three-dimensional solution of Bragg diffracted x rays based on principal crystallographic strains in the compression wave was found. The distortion of x-ray diffraction beams has been used for strain measurements; the analysis developed incorporates a strained reciprocal lattice and the incident x-ray beam. Strain-distorted Polanyi surfaces form an annulus of compression with an ellipsoid of revolution in reciprocal space, which is intersected by Ewald's sphere for Bragg diffraction. The in situ measurements for strain describe nanosecond diffraction evaluated using two planes, (hkl) and (h′k′l′), both in the same crystallographic phase. Diffraction from Al, Ni, Na, and Invar quantifies the compression axial strains in these materials: The compression axial ratios are 0.65, 1.05, 0.88, and 1.58 at pressures of 291, 402, 409, and 367 GPa for the respective materials. Crystal structure transformations with homogeneous pressurized stresses, mandating equal normal strains, should not be anticipated to agree with heterogeneous, uniaxially strained, and sheared crystalline phases. Measurements support in-plane strains increasing with pressure, p , in fcc and hcp aluminum as ε 22 = −0.21 p /TPa.

Alloys↗
NASA NTRS1977

Thermodynamics of Thomas-Fermi screened Coulomb systems

We obtain in closed analytic form, estimates for the thermodynamic properties of classical fluids with pair potentials of Yukawa type, with special reference to dense fully ionized plasmas with Thomas-Fermi or Debye-Hueckel screening. We further generalize the hard-sphere perturbative approach used for similarly screened two-component mixtures, and demonstrate phase separation in this simple model of a liquid mixture of metallic helium and hydrogen.

Firey, B.↗
NASA NTRS1973

Magnetic sheath adjacent to absorbing surfaces.

Major attention is given to the existence and structure of a 'magnetic sheath' adjacent to perfectly absorbing solid surfaces. The basic equations for a two-field continuum model are presented, and the quasi-neutral approximation and Bohm's criterion are briefly reviewed. The infinite conductivity MHD equations are recovered by invoking the small magnetic Debye length approximation. This approximation is relaxed, and the appropriate 'boundary layer' equation for the magnetic sheath is presented. The first magnetic sheath criterion is derived, which states that the conditions at the edge of the sheath, as characterized by a point in the Friedrichs diagram, must be located in certain restricted regions in order for a magnetic sheath to exist. The second magnetic sheath criterion is discussed.

Lam, S. H.↗
DOE OSTI2025

Giant Dipole Moments: Remarkable Effects Mono‐, Di‐, and Tri‐ Hydrated 5,6‐Diaminobenzene‐1,2,3,4‐Tetracarbonnitrile

The molecule 5,6-diaminobenzene-1,2,3,4-tetracarbonnitrile (MOI) was first synthesized by Müllen and coworkers in 2016 and boasts an ultrastrong dipole moment of $14.1\pm 0.7$ Debye in THF. Gas phase DFT computations do not fully reflect this ultrastrong dipole moment, demonstrating the role of solvent in increasing this dipole moment. Here, we investigate the effect of solvent molecule position on the dipole moment of this species, computationally examining systems with giant dipole moments. These systems are optimized in the gas phase with the B3LYP functional, employing the aug-cc-pVTZ and def2-TZVP basis sets, as well as the B3LYP-D3BJ/aug-cc-pVTZ functional in Orca. Single point DLPNO-CCSD/aug-cc-pVDZ results were obtained from Orca and Psi4, as well as DLPNO-CCSD(T)/CBS information from Psi4. Additionally, these are compared to the dipole moments of di- and tri-hydrated systems, and the SMD models for THF and water at the B3LYP/aug-cc-pVTZ level of theory. The dissociation energies, HOMO-LUMO energy gaps, and dipole moments are presented. These metrics show the nh1nh1′ THF system boasts the largest dissociation energy and dipole moment of the singly solvated systems, due to its strong hydrogen bonding. The importance of solvent placement is highlighted and may guide the synthesis of macromolecules or organic frameworks incorporating the MOI or MOI-like subunits. Remarkably, a single solvent molecule provides a good model for the difference between the gas phase and solvated species. The predicted gas phase dipole moments computed with B3LYP/aug-cc-pVTZ for the MOI, its monohydrated complex, dihydrated complex, and its trihydrated complex are 9.6, 14.2, 16.0, and 16.8 Debye, respectively.

dipole↗
DOE OSTI2018

Dynamical Theory of X-Ray Diffraction for Restricted Beams: II. Diffuse Scattering by a Porous Crystal

A theory of X-ray diffuse scattering of restricted beams by a porous crystal is developed. Models of cylindrical and ellipsoidal pores, as well as the pores in the form of rectangular and triangular prisms, are considered. For these pores, the expressions for correlation eigenfunctions, static Debye—Weller factors, and correlation volumes are derived. The effect of the inclination and spatial correlation of pores on the equal-intensity diffuse-scattering contours is analyzed. The influence of the pore size fluctuation on the scattered intensity distribution is demonstrated.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Lattice dynamics and thermodynamics for δ -plutonium from density functional theory

Here, we present results from density functional theory (DFT) calculations of the lattice dynamics (phonons) and thermodynamics for δ-phase plutonium. The fully relativistic electronic structure is calculated assuming a three-dimensional noncollinear magnetic structure in conjunction with DFT and the general gradient approximation for the electron exchange and correlation interactions. The electronic-structure model is further enhanced by addressing strong orbital-orbital coupling via the conventional orbital-polarization (OP) scheme as has been successfully done for plutonium. The temperature dependence of the phonons is calculated within the self-consistent ab initio lattice dynamics approach. The obtained phonons compare very well with measurements although a modest overestimation of the transverse L-point [ξξξ] phonon is acknowledged. Calculated thermal vibration amplitudes and the associated Debye-Waller temperatures are close to experiments. Lattice, electronic, and magnetic contributions to the heat capacity are predicted and consistent to a few percent with that deduced from experimental data. Good agreement is only achieved when a magnetic contribution to the specific heat is recognized. The parameter-free DFT+OP electronic model is thus capable of predicting phonon properties and thermodynamic behavior of δ-phase plutonium rather accurately.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Bohm Criterion of Plasma Sheaths away from Asymptotic Limits

The plasma exit flow speed at the sheath entrance is constrained by the Bohm criterion. The so-called Bohm speed regulates the plasma particle and power exhaust fluxes to the wall, and it is commonly deployed as a boundary condition to exclude the sheath region in quasineutral plasma modeling. In this work, the Bohm criterion analysis is performed in the intermediate plasma regime away from the previously known limiting cases of adiabatic laws and the asymptotic limit of infinitesimal Debye length in a finite-size system, using the transport equations of an anisotropic plasma. The resulting Bohm speed has explicit dependence on local plasma heat flux, temperature isotropization, and thermal force. Comparison with kinetic simulations demonstrates its accuracy over the plasma-sheath transition region in which quasineutrality is weakly perturbed and the Bohm criterion applies.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗