Plasma Transport Coefficients Research Articles

ETHOS: An automated framework to generate multi-fidelity constitutive data tables and propagate uncertainties to hydrodynamic simulations

Accurate constitutive data, such as equations of state and plasma transport coefficients, are necessary for reliable hydrodynamic simulations of plasma systems such as fusion targets, planets, and stars. Here, we develop a framework for automatically generating transport-coefficient tables using a parameterized model that incorporates data from both high-fidelity sources (e.g., density functional theory calculations and reference experiments) and lower-fidelity sources (e.g., average-atom and analytic models). The framework incorporates uncertainties from these multi-fidelity sources, generating ensembles of optimally diverse tables that are suitable for uncertainty quantification of hydrodynamic simulations. We illustrate the utility of the framework with magnetohydrodynamic simulations of magnetically launched flyer plates, which are used to measure material properties in pulsed-power experiments. We explore how changes in the uncertainties assigned to the multi-fidelity data sources propagate to changes in simulation outputs and find that our simulations are most sensitive to uncertainties near the melting transition. The presented framework enables computationally efficient uncertainty quantification that readily incorporates new high-fidelity measurements or calculations and identifies plasma regimes where additional data will have high impact.

MONKES: a fast neoclassical code for the evaluation of monoenergetic transport coefficients in stellarator plasmas

MONKES is a new neoclassical code for the evaluation of monoenergetic transport coefficients in stellarators. By means of a convergence study and benchmarks with other codes, it is shown that MONKES is accurate and efficient. The combination of spectral discretization in spatial and velocity coordinates with block sparsity allows MONKES to compute monoenergetic coefficients at low collisionality, in a single core, in approximately one minute. MONKES is sufficiently fast to be integrated into stellarator optimization codes for direct optimization of the bootstrap current and to be included in predictive transport suites. The code and data from this paper are available at https://github.com/JavierEscoto/MONKES/.

Quantum effects on dynamic structure factors in dense magnetized plasmas

We extend the classical magnetohydrodynamics formalism to include nonlocal quantum behavior via the phenomenological Bohm potential. We then solve the quantum magnetohydrodynamics equations to obtain a new analytical form of the dynamic structure factor (DSF), a fundamental quantity linking theory and experiments. Our results show that the three-peak structure—one central Rayleigh peak and two Brillouin peaks—of the DSF arising from quantum hydrodynamic fluctuations becomes (in general) a five-peak structure—one central Rayleigh peak and two pairs of peaks associated with fast and slow magnetosonic waves. The Bohm contribution influences the positions and characteristics (height, width, and intensity) of the peaks by introducing three significant modifications: (i) an increase in effective thermal pressure, (ii) a reduction in the adiabatic index, and (iii) an enhancement of effective thermal diffusivity. The multiple DSF peaks enable concurrent measurements of diverse plasma properties, transport coefficients, and thermodynamic parameters in magnetized dense plasmas. The potential for experimental validation of our theory looms large, particularly through future experiments conducted at state-of-the-art laser facilities. Published by the American Physical Society 2024

Numerical studies of plasma edge in W7-X with 3D FINDIF code

Abstract Modelling of the plasma transport for inherently three-dimensional (3D) problems as in stellarators requires dedicated complex codes. FINDIF is a 3D multifluid plasma edge transport code that has been previously successfully used for the analysis of energy transport in the TEXTOR-DED tokamak [1], where 3D perturbations led to an ergodic structure of field lines in the plasma edge. The ongoing efforts to apply it meaningfully to Wendelstein 7-X (W7-X) plasma problems resulted in advancements in the main model and accompanying tools for mesh generation and post-processing. In order to verify the applicability of the code and to compare with the reported simulation (EMC3-EIRENE) and experimental (OP1.1) results, a series of simulations for varying plasma density, temperature and anomalous transport coefficients as well as for fixed input power were performed. The connection length pattern of FINDIF traced magnetic field lines on the limiter was reproduced and its impact on heat loads was confirmed. An increase in the peak heat load on the limiter with a rise in plasma density, temperature and anomalous plasma transport coefficients was observed. The decay lengths of density, electron temperature and heat flux did not change with density, and were decreasing with temperature and increasing with anomalous plasma transport coefficient, which was compared to the simple scrape-off layer (SOL) model.

Bottom Hadrochemistry in High-Energy Hadronic Collisions.

The hadrochemistry of bottom quarks (b) produced in hadronic collisions encodes valuable information on the mechanism of color neutralization in these reactions. Since the b-quark mass is much larger than the typical hadronic scale of ∼1 GeV, bb[over ¯] pair production is expected to be well separated from subsequent hadronization processes. A significantly larger fraction of b baryons has been observed in proton-proton (pp) and proton-antiproton (pp[over ¯]) reactions relative to e^{+}e^{-} collisions, challenging theoretical descriptions. We address this problem by employing a statistical hadronization approach with an augmented set of b-hadron states beyond currently measured ones, guided by the relativistic quark model and lattice-QCD computations. Assuming relative chemical equilibrium between different b-hadron yields, thermal densities are used as fragmentation weights of b quarks into various hadron species. With quark model estimates of the decay patterns of excited states, the fragmentation fractions of weakly decaying b hadrons are computed and found to agree with measurements in pp[over ¯] collisions at the Tevatron. By combining transverse-momentum (p_{T}) distributions of b quarks from perturbative QCD with thermal weights and independent fragmentation toward high p_{T}, a fair description of the p_{T}-dependent B[over ¯]_{s}^{0}/B^{-} and Λ_{b}^{0}/B^{-} ratios measured in pp collisions at the LHC is obtained. The observed enhancement of Λ_{b}^{0} production is attributed to the feeddown from thus far unobserved excited b baryons. Finally, we implement the hadrochemistry into a strongly coupled transport approach for b quarks in heavy-ion collisions, utilizing previously determined b-quark transport coefficients in the quark-gluon plasma, to highlight the modifications of hadrochemistry and collective behavior of b hadrons in Pb-Pb collisions at the LHC.

Inference of main ion particle transport coefficients with experimentally constrained neutral ionization during edge localized mode recovery on DIII-D

The plasma and neutral density dynamics after an edge localized mode are investigated and utilized to infer the plasma transport coefficients for the density pedestal. The Lyman-Alpha Measurement Apparatus (LLAMA) diagnostic provides sub-millisecond profile measurements of the ionization and neutral density and shows significant poloidal asymmetries in both. Exploiting the absolute calibration of the LLAMA diagnostic allows quantitative comparison to the electron and main ion density profiles determined by charge-exchange recombination, Thomson scattering and interferometry. Separation of diffusion and convection contributions to the density pedestal transport are investigated through flux gradient methods and time-dependent forward modeling with Bayesian inference by adaptation of the Aurora transport code and IMPRAD framework to main ion particle transport. Both methods suggest time-dependent transport coefficients and are consistent with an inward particle pinch on the order of 1 m s−1 and diffusion coefficient of 0.05 m2 s−1 in the steep density gradient region of the pedestal. While it is possible to recreate the experimentally observed phenomena with no pinch in the pedestal, low diffusion in the core and high outward convection in the near scrape-off layer are required without an inward pedestal pinch.

Transport Coefficients of H2–Cu/Al2O3 Plasma Mixtures Considering Solid and Liquid Status

Obtaining the plasma transport coefficients of the mixed system of arc-extinguishing medium and erosion product is the precondition of numerical simulation of erosion–diffusion in an arc chamber. In this article, the minimum Gibbs free energy method was used to calculate the composition of the H2–Cu/Al2O3 system, including solid and liquid copper (aluminum oxide), because copper and aluminum oxide are commonly used as electrode and ceramic materials in hydrogen dc contactors, respectively. The transport coefficients of H2–Cu/Al2O3 system and the phase transition of erosion products provide the basis for the subsequent simulation of erosion–diffusion of electrode and arc chamber in the H2 plasma. Results revealed that: 1) in the low-temperature range, copper (aluminum oxide) mainly exists in the form of a solid or a liquid state, resulting in the transport coefficients of the H2–Cu/Al2O3 system consistent with that of the H2 system; 2) as temperature increases, the copper (aluminum oxide) undergoes gasification (sublimation–decomposition) reaction that exists in a gaseous state and begins to affect the transport properties of the H2–Cu/Al2O3 system; in particular, the proportion of copper (aluminum oxide) has the most significant effect on viscosity; and 3) as the temperature continues to rise, atoms and molecules in the H2–Cu/Al2O3 system are completely ionized and the proportion of copper (aluminum oxide) has little effect on the transport properties (except electrical conductivity) of the H2–Cu/Al2O3 system. Finally, the transport coefficients of H2–Cu/Al2O3 plasma mixtures are reliable enough, in engineering application aspect, to be applied for simulation of erosion–diffusion in hydrogen dc contactors.

Toward a Realistic Evaluation of Transport Coefficients in Non-equilibrium Space Plasmas

Abstract Recent studies have outlined the interest for the evaluation of transport coefficients in space plasmas, where the observed velocity distributions of plasma particles are conditioned not only by the binary collisions, e.g., at low energies, but also by the energization of particles from their interaction with wave turbulence and fluctuations, generating the suprathermal kappa-distributed populations. This paper provides a first estimate of the main transport coefficients based on regularized kappa distributions, which, unlike standard kappa distributions (SKDs), enable macroscopic parameterization without mathematical divergences or physical inconsistencies. All transport coefficients derived here, i.e., the diffusion and mobility coefficients, electric conductivity, thermoelectric coefficient, and thermal conductivity, are finite and well defined for all values of κ > 0. Moreover, for low values of κ (i.e., below the SKD poles), the transport coefficients can be orders of magnitudes higher than the corresponding Maxwellian limits, meaning that significant underestimations can be made if suprathermal electrons are ignored.

Experimental inference of neutral and impurity transport in Alcator C-Mod using high-resolution x-ray and ultra-violet spectra

We present experimental inferences of cross-field impurity transport coefficients for AlcatorC-Mod plasmas without edge-localized modes, leveraging a novel forward model for the entire Ca K α spectrum, including satellite lines within the spectral range, to compare to high-resolution x-ray imaging crystal spectroscopy (XICS). These measurements are complemented by extreme ultra-violet (EUV) spectroscopy that constrains transport closer to the edge. Using new atomic data sets for both XICS and EUV analysis has enabled consideration of line ratios across both spectral ranges and has increased the accuracy of inferred transport coefficients. Inclusion of charge exchange between edge thermal neutrals and impurities is shown to be extremely important in C-Mod pedestals. Atomic D neutral densities from experimental D Ly α measurements at the midplane are compared to SOLPS-ITER simulations, finding good agreement. Bayesian inferences of impurity transport coefficients are presented for L-, EDA H-, and I-mode discharges, making use of the Aurora package for forward modeling and combining our spectroscopic constraints. Experimentally inferred diffusion profiles are found to match turbulent transport models at midradius within uncertainties, using both quasilinear gyro-fluid TGLF SAT-1 and nonlinear ion-scale gyrokinetic CGYRO simulations. Significant discrepancies in convection are observed in some cases, suggesting difficulties in predictions of flat or hollow impurity profiles.

Transport coefficients enhanced by suprathermal particles in nonequilibrium heliospheric plasmas

Context.In heliospheric plasmas, such as the solar wind and planetary magnetospheres, the transport of energy and particles is governed by various fluxes (e.g., heat flux, particle flux, current flow) triggered by different forces, electromagnetic fields, and gradients in density or temperature. In the outer corona and at relatively low heliocentric distances in the solar wind (i.e., < 1 AU), particle-particle collisions play an important role in the transport of energy, momentum, and matter, described within classical transport theory by the transport coefficients, which relate the fluxes to their sources.Aims.The aim of the present paper is to improve the evaluation of the main transport coefficients in such nonequilibrium plasmas, on the basis of an implicit realistic characterization of their particle velocity distributions, in accord with the in situ observations. Of particular interest is the presence of suprathermal populations and their influence on these transport coefficients.Methods.Using the Boltzmann transport equation and macroscopic laws for the energy and particle fluxes, we derived transport coefficients, namely, electric conductivity, thermoelectric coefficient, thermal conductivity, diffusion, and mobility coefficients. These are conditioned by the electrons, which are empirically well described by the Kappa distribution, with a nearly Maxwellian (quasi-thermal) core and power-law tails enhanced by the suprathermal population. Here we have adopted the original Kappa approach that has the ability to outline and quantify the contribution of suprathermal populations.Results.Without exception, the transport coefficients are found to be systematically and markedly enhanced in the presence of suprathermal electrons (i.e., for finite values of theκparameter), due to the additional kinetic energy with which these populations contribute to the dynamics of space plasma systems. The present results also show how important an adequate Kappa modeling of suprathermal populations is, which is in contrast to other modified interpretations that underestimate the effects of these populations.

Exploring theoretical uncertainties in the hydrodynamic description of relativistic heavy-ion collisions

We explore theoretical uncertainties in the hydrodynamic description of relativistic heavy-ion collisions by examining the full non-linear causality conditions and quantifying the second-order transport coefficients' role on flow observables. The causality conditions impose physical constraints on the maximum allowed values of inverse Reynolds numbers during the hydrodynamic evolution. Including additional second-order gradient terms in the Denicol-Niemi-Moln\'{a}r-Rischke (DNMR) theory significantly shrinks the casual regions compared to those in the Israel-Stewart hydrodynamics. For Au+Au collisions, we find the variations of flow observables are small with and without imposing the necessary causality conditions, suggesting a robust extraction of the Quark-Gluon Plasma's transport coefficients in previous model-to-data comparisons. However, sizable sensitivity is present in small p+Au collisions, which poses challenges to study the small systems' collectivity.

Equations and improved coefficients for parallel transport in multicomponent collisional plasmas: Method and application for tokamak modeling

New analytical expressions for parallel transport coefficients in multicomponent collisional plasmas are presented in this paper. They are improved versions of the expressions written in Zhdanov [Transport Processes in Multicomponent Plasma, English ed. (Taylor and Francis, London, New York, 2002)], based on Grad's 21N-moment method. Both explicit and approximate approaches for the calculation of transport coefficients are considered. Accurate application of this closure for the Braginskii transport equations is discussed. Viscosity dependence on the heat flux is taken into account. Improved expressions are implemented into the SOLPS-ITER code and tested for deuterium and neon ITER cases. Some typos found in Zhdanov [Transport Processes in Multicomponent Plasma, English ed. (Taylor and Francis, London, New York, 2002)] are corrected.

Transport properties of Heavy Quarks: anisotropic flows υn and their correlations to the bulk dynamics and initial Electromagnetic field

We study the correlations between light flavor and heavy quarks (HQs) flow harmonics at LHC energy within a transport approach. We have investigated the role of transport coefficient in developing these anisotropic flows correlations. We suggest correlation and the relative fluctuations of anisotropic flows συη /〈υn 〉 as novel observables to constrain the HQ transport coefficients in quark gluon plasma. Finally, very strong electro-magnetic (E.M.) fields are created in Ultra-relativistic Heavy-Ion Collision (HIC). We show within relativistic Boltzmann transport approach coupled with E.M. field that the strong e.m. field is responsible for a splitting of directed flow υ 1 of D and anti-D mesons of few percent, i.e. much larger compared to the observed charged particles. Moreover, we discuss the role played by the initial large bulk vorticity on the build up of rapidity odd HQs directed flow υ 1.

Transport Coefficients of Air - PMMA Mixtures Thermal Plasmas

The transport coefficients of Air - PMMA mixtures thermal plasmas is important to estimate the performances of cutting of the electrical arc in this gas by a circuit breaker. In this paper, Air - PMMA mixtures thermal plasmas dynamical viscosity, thermal and electrical conductivities coefficients are calculated in a temperature range from 5000K to 30000K. The calculations are made by supposing thermodynamic equilibrium at pressure of 1 bar to 10 bar. The results of the calculations show the influence of the initial proportion of PMMA but also that of the pressure on the mixture plasma transport coefficients. As the efficiency of the breaking of the electric current by the circuit breaker depends closely on the thermal and electrical characteristics of the extinguishing medium, this extinguishing medium should have a high thermal conductivity and an electrical conductivity varying rapidly with temperature. The plasma of the mixture constituted by 80% of air and 20% of PMMA presents at first sight best characteristics for the breaking of electric current. It has the highest thermal conductivity peak among the plasmas of the mixtures studied.

Theoretical research on the transport and ionization rate coefficients in glow discharge dusty plasma

The electron kinetic model for investigating the transport and ionization rate coefficients of argon glow discharge dusty plasma is developed from the Boltzmann equation. Both of the electron–neutral and electron–dust collisions are considered as collision terms in the kinetic equation. The kinetic equation is simplified by employing the local approximation and nonlocal approach under the same discharge conditions, and the corresponding simplified kinetic equations are known as local and nonlocal kinetic equations respectively. Then the electron energy distribution function (EEDF) is obtained by numerically solving the local and nonlocal kinetic equations and the dust charging equations simultaneously. Based on the obtained EEDFs, the effective electron temperature, electron mobility, electron diffusion coefficient and ionization rate coefficient are calculated for different discharge conditions. It is shown that the EEDFs calculated from the local kinetic model clearly differ from the nonlocal EEDFs and both the local and nonlocal EEDFs are also clearly different with Maxwellian distributions. The appearance of dust particles results in an obvious decrease of high energy electrons and increase of low energy electrons when axial electric field is low. With the increase of axial electric field, the influence of dust particles on the EEDFs becomes smaller. The electron mobility and diffusion coefficients calculated on the basis of local and nonlocal EEDFs do not differ greatly to the dust-free ones. While, when dust density nd = 106 cm−3, the electron mobility increases obviously compared with the dust-free results at low axial electric field and decreases with the increasing axial electric field until they are close to the dust-free ones. Meanwhile, electron diffusion coefficients for dusty case become smaller and decrease with the increasing axial electric field. The ionization rate coefficients decrease when dust particles are introduced and they approach the dust-free results gradually with the increasing axial electric field.

Simple scaling laws for the transport coefficients calculated by density-functional theory molecular dynamics

Density-functional theory molecular dynamics (DFT-MD) is a first-principles approach suited for and widely applied to the calculation of warm dense plasmas properties at equilibrium. It is shown that under the very general hypotheses underlying this approach, the transport coefficients of pure fluids obey simple scaling laws. The extension of these scaling laws to mixtures is possible under specific conditions. Apart from the practical interest of deducing the DFT-MD transport coefficients of an isotope of a given element from those already calculated for another isotope of the same element, these laws are fundamental constraints to be imposed to the construction of fits or of mixing rules for transport coefficients of warm dense plasmas.

Toward the determination of heavy-quark transport coefficients in quark-gluon plasma

Several transport models have been employed in recent years to analyze heavy-flavor meson spectra in high-energy heavy-ion collisions. Heavy-quark transport coefficients extracted from these models with their default parameters vary, however, by up to a factor of 5 at high momenta. To investigate the origin of this large theoretical uncertainty, a systematic comparison of heavy-quark transport coefficients is carried out between various transport models. Within a common scheme devised for the nuclear modification factor of charm quarks in a brick medium of a quark-gluon plasma, the systematic uncertainty of the extracted drag coefficient among these models is shown to be reduced to a factor of 2, which can be viewed as the smallest intrinsic systematical error band achievable at present time. This indicates the importance of a realistic hydrodynamic evolution constrained by bulk hadron spectra and of heavy-quark hadronization for understanding the final heavy-flavor hadron spectra and extracting heavy-quark drag coefficient. The transverse transport coefficient is less constrained due to the influence of the underlying mechanism for heavy-quark medium interaction. Additional constraints on transport models such as energy loss fluctuation and transverse-momentum broadening can further reduce theoretical uncertainties in the extracted transport coefficients.

Boltzmann equation studies on electron swarm parameters in Townsend breakdown of copper vapor plasma using independently assessed electron-collision cross sections

Electron transport coefficients in copper vapor plasma are calculated both by two-term expansion of electron Boltzmann equation Bolsig+ and tracking the random motion of electrons using Monte Carlo collision code METHES based upon recently evaluated cross section sets. The copper atoms are evaporated from hot electrode during the post-arc phase of vacuum circuit breakers, in which Townsend breakdown between electrode gaps is probable. The electron energy probability function, electron mean energy, flux/transport mobility and diffusion coefficients, as well as Townsend ionization coefficients are shown in reduced fields 10∼1000 Td at a typical vapor temperature 2000 K. The validity of two-term approximation is checked by comparison to well benchmarked METHES code. If the electrode temperature varies between 1500∼2500 K, the influence of vapor temperature on ionization coefficients is about 5% at 200.4 Td, and drops to 0.5% at 493 Td according to Bolsig+ results. Similar to classic gas discharge theory, the Paschen curve is proposed for Townsend breakdown of metal vapor. Using the calculated ionization coefficient and a constant secondary electron yield, the Paschen minimum is determined to be 106∼122 V at a critical value of the product of vapor density and gap length (4.7∼5.7)×1019 m-2. A satisfactory agreement was found with the previously measured ignition voltage between vacuum interrupter contacts after the arcing.

Influence of metastable atoms on the formation of nonlocal EDF, electron reaction rates, and transport coefficients in argon plasma

The influence of metastable atoms on formation of the nonlocal electron distribution function (EDF) and other characteristics of gas-discharge plasma in argon is investigated in this paper. Superelastic collisions of electrons with metastable atoms strongly affect the shape of the EDF, the behavior of reaction rate constants, and other plasma characteristics. An interesting phenomenon of EDF replication emerges with a period of excitation threshold; this effect can increase the rate constants of excitation and ionization processes by several orders of magnitude, especially at the periphery of the plasma volume. Thus, collisions between electrons and metastable atoms are important in the formation of a nonlocal EDF, and neglecting them can lead to large errors in calculations of plasma characteristics.

Coulomb log for conductivity of dense plasmas

The Coulomb log (log Λ) approximation is widely used to approximate electron transport coefficients in dense plasmas. It is a classical approximation to the momentum transport cross section. The accuracy of this approximation for electrical conductivity in dense plasmas is assessed by comparing to fully quantum mechanical calculations for realistic scattering potentials. It is found that the classical approximation is accurate to ±10% when log Λ > 3, irrespective of the plasma species. The thermodynamic regime (density and temperature) for which log Λ > 3 corresponds to does, however, strongly depend on the material. For increasing Z, log Λ is greater than 3 for increasingly high temperatures and lower densities.