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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Nonlinear models for coupling the effects of stimulated Raman scattering to inertial confinement fusion codes

Laser plasma instabilities (LPI) reduce driver-target coupling, alter implosion symmetry, and therefore can fundamentally limit fusion performance in inertial confinement fusion (ICF). Developing a predictive modeling capability for LPI effects can critically advance the success of the field. We perform vector particle-in-cell simulations of multi-speckled laser beams undergoing stimulated Raman scattering (SRS) at various densities and intensities relevant to mainly indirectly driven and a subset of parameter space for directly driven ICF systems, focusing on the regimes with intensities above the onset of electron trapping. Based on the wavenumber of the SRS daughter electron plasma wave, we identify several regions with underpinning SRS saturation physics: the electron-trapping dominated region with intermediate kλD values, the strong Landau damping region at larger kλD values, and the region where the Langmuir decay instability arises at lower kλD values. We develop a nonlinear SRS reflectivity model that features the base trapping-dominated scaling of (kλD)−4 and its modifications. Electron trapping deforms the initialized electron distribution functions, and we have developed a new δf-Gaussian-mixture algorithm for an accurate characterization of the trapped hot electron population. With this SRS hot electron description, we construct a nonlinear energy deposition model and a hot electron source model—based on a modified Manley–Rowe relation—suitable for including SRS effects as a sub-grid module in a high-fidelity ICF design code.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Experimental observation of a field-aligned ion beam produced by magnetic reconnection of two flux ropes

An ion beam field-aligned to the background guide field ($B$ 0 = $330$ G) was observed in a reconnection experiment on the Large Plasma Device and, to the authors' knowledge, is the first experimental observation of its kind. Two kink-unstable flux ropes ( L = 11 m, d = 7.6 cm) were made to collide, which allows magnetic reconnection to occur. Sub-Alfvénic ion beams with energies of up to 15 eV were then observed from measurements of the local ion energy distribution function. The beam ions do not appear to be heated. Further, they were correlated with the collision of the ropes and appear to be energized by magnetic reconnection. The results and interpretation of the measurements are supported by three-dimensional gyrokinetic particle simulations of the merging flux ropes and electric field measurements from previous experiments [W. Gekelman et al. , Astrophys. J. 853, 33 (2018)]. The mechanism behind the acceleration appears to be non-local.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Local cation ordering in compositionally complex Ruddlesden–Popper n = 1 oxides

The Ruddlesden–Popper (RP) layered perovskite structure is of great interest due to its inherent tunability, and the emergence and growth of the compositionally complex oxide (CCO) concept endows the RP family with further possibilities. Here, a comprehensive assessment of thermodynamic stabilization, local order/disorder, and lattice distortion was performed in the first two reported examples of lanthanum-deficient La n+1 B n O 3n+1 (n = 1, B = Mg, Co, Ni, Cu, Zn) obtained via various processing conditions. Chemical short-range order (CSRO) at the B-site and the controllable excess interstitial oxygen (δ) in RP-CCOs are uncovered by neutron pair distribution function analysis. Reverse Monte Carlo analysis of the data, Metropolis Monte Carlo simulations, and extended x-ray absorption fine structure analysis implies a modest degree of magnetic element segregation on the local scale. Further, ab initio molecular dynamics simulations results obtained from special quasirandom structure disagree with experimentally observed CSRO but confirm Jahn–Teller distortion of CuO 6 octahedra. These findings highlight potential opportunities to control local order/disorder and excess interstitial oxygen in layered RP-CCOs and demonstrate a high degree of freedom for tailoring application-specific properties. They also suggest a need for expansion of theoretical and data modeling approaches in order to meet the innate challenges of CCO and related high-entropy phases.

36 MATERIALS SCIENCE↗
DOE OSTI2023

A confocal laser-induced fluorescence diagnostic with an annular laser beam

Here, in this work, we report an annular beam confocal laser-induced fluorescence (LIF) configuration, which allows for high spatial resolution measurements of plasma properties in plasma setups and sources with limited optical access. The proposed LIF configuration utilizes the annular laser beam generated by a pair of diffractive axicons. The LIF signal is collected along the main optical axis within the ring region. It is shown experimentally that at a focal distance of 300 mm, a spatial resolution of ~5.3 mm can be achieved. Using geometric optics estimations, we showed that ~1 mm resolution at the same focal distance could potentially be achieved by modifying laser beam parameters. This approaches the localization accuracy of conventional LIF collection methods (with crossing laser beam injection and fluorescence collection optical paths). Measurements of the ion velocity distribution function in an argon plasma using both the confocal LIF with an annular laser beam and conventional LIF demonstrate a satisfactory agreement. The proposed LIF setup has potential applications for diagnostics in various plasma processing equipment and plasma sources, such as hollow cathodes, microplasmas, electric propulsion, etc.

47 OTHER INSTRUMENTATION↗
DOE OSTI2023

Overview of the Langmuir probe system on the Mega Ampere Spherical Tokamak (MAST) Upgrade

A detailed description of the Langmuir probe system on Mega Ampere Spherical Tokamak Upgrade is presented. The system features 850 tile-embedded probes and 40 bespoke electronic modules that each have the capability to drive and acquire data from up to 16 probes in a time-multiplexed manner. The system provides spatiotemporal-resolved measurements (1 cm and ~1 ms, respectively) in the divertor region of ion saturation current, electron temperature, and floating potential. The standard interpretation of current-voltage (IV) characteristics is to apply a four-parameter fit, based on unmagnetized probe theory, which includes a linear model for the ion saturation region. In conclusion, to mitigate the effect of the magnetic field, analysis is restricted to the region of the IV characteristic, which is sensitive to only the tail of the electron energy distribution function.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Origin of medium-range atomic correlation in simple liquids: Density wave theory

The atomic pair-distribution function of simple liquid and glass shows exponentially decaying oscillations beyond the first peak, representing the medium-range order (MRO). The structural coherence length that characterizes the exponential decay increases with decreasing temperature and freezes at the glass transition. Conventionally, the structure of liquid and glass is elucidated by focusing on a center atom and its neighboring atom shell characterized by the short-range order (SRO) and describing the global structure in terms of overlapping local clusters of atoms as building units. However, this local bottom-up approach fails to explain the strong drive to form the MRO, which is different in nature from the SRO. We propose to add an alternative top-down approach based upon the density wave theory. In this approach, one starts with a high-density gas state and seeks to minimize the global potential energy in reciprocal space through density waves using the pseudopotential. The local bottom-up and global top-down driving forces are not mutually compatible, and the competition and compromise between them result in a final structure with the MRO. This even-handed approach provides a more intuitive explanation of the structure of simple liquid and glass.

42 ENGINEERING↗
DOE OSTI2023

Implementation of a drive cylinder for low collisional experiments on magnetic reconnection

For most laboratory plasma experiments, Coulomb collisions between the particle species are sufficiently frequent that the particle distribution functions are relaxed to a near-Maxwellian form. This hampers the applicability of such experiments to phenomena observed in tenuous and near-collisionless space plasma. The Terrestrial Reconnection EXperiment (TREX) at the Wisconsin Plasma Physics Laboratory aims to study collisionless reconnection for parameters relevant to the Earth’s magnetosphere. To reduce the role of collisional effects, a reconnection Drive Cylinder has been developed, which increases both the effective system size of the TREX configuration and the rate at which reconnection can be driven. These two effects now permit TREX to reach a kinetic reconnection regime where collisional effects are minimized. The Drive Cylinder is comprised of 12 single loop drive-coils connected in parallel to a 10 kV capacitor bank. Insulated sheets of aluminum are applied to smooth the magnetic fields and enhance the drive efficiency. Following is a description of the technical details and performance of the Drive Cylinder.

Instruments & Instrumentation↗
DOE OSTI2023

The theory of kinetic effects on resistive wall mode stability in tokamaks

Tokamak fusion plasmas benefit from high pressures but are then susceptible to modes of instability. These magnetohydrodynamic (MHD) modes are macroscopic distortions of the plasma, but certain collective motions of individual particles can provide stabilizing effects opposing them. The presence of a resistive wall slows the mode growth, converting a kink to a resistive wall mode (RWM). A kinetic MHD model includes Maxwell's equations, ideal MHD constraints, and kinetic effects included through the pressure tensor, calculated with the perturbed drift-kinetic distribution function of the particles. The kinetic stabilizing effects on the RWM arise through resonances between the plasma rotation and particle drift motions: precession, bounce, and transit. A match between particle motions and the mode allows efficient transfer of energy that would otherwise drive the growth of the mode, thus damping the growth. The first approach to calculating RWM stability is to write a set of equations for the complex mode frequency in terms of known quantities and then to solve the system. The “energy principle” approach, which has the advantage of clarity in distinguishing the various stabilizing and destabilizing effects, is to change the force balance equation into an equation in terms of changes of kinetic and potential energies, and then to write a dispersion relation for the mode frequency in terms of those quantities. These methods have been used in various benchmarked codes to calculate kinetic effects on RWM stability. Importantly, the theory has illuminated the important roles of plasma rotation, energetic particles, and collisions in RWM stability.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Nonlinear dynamics of multiple Alfvén modes driven by trapped energetic ions in tokamaks: A triplet paradigm

Non-linear dynamics of multiple infernal Alfvén eigenmodes—a subset of global Alfvén eigenmodes in tokamak plasmas with extended low-shear central core [Marchenko et al., Phys. Plasmas 16, 092502 (2009)]—is studied. The analysis is carried out for a mode triplet with toroidal mode-numbers n=1, 2, 3. It was assumed that the n = 1 mode was linearly unstable due to precession resonance with trapped fast ions, whereas the other modes were linearly damped. The modes were coupled due to a non-linearity in a bounce-averaged drift kinetic equation for the distribution function of fast ions. Nonlinear equations for the mode amplitudes and phases are derived and solved numerically. It is found that the temporal evolution of the amplitudes and the phase (responsible for the frequency chirping) of the modes exhibit Hopf bifurcations to stable limit cycles. This can explain a synchronous cyclic destabilization of multiple modes in Alfvén avalanches (sudden growth of amplitudes of the mode cluster with different n and approximately equal frequency spacing) in NSTX and bursting modes in MAST—events, which resulted in enhanced loss of fast ions.

Marchenko, V. S. (ORCID:0000000261480533)↗
DOE OSTI2024

Loss cone effects and monotonic sheath conditions of a partially magnetized plasma sheath

In this Letter, we propose the conditions for monotonic plasma sheaths adjacent to a floating wall in the presence of an applied, oblique magnetic field. The electron velocity distribution function (VDF) at the sheath edge obtained from a kinetic model exhibits a loss cone shaped truncation. Using an approximation of the truncated VDF, we derive an analytical framework of the sheath edge condition (i.e., Bohm condition), namely, the relation of ion injection velocity and sheath potential drop as a function of the magnetic field angle. The results show that the sheath edge velocity and total potential drop decrease for a steady-state sheath, which eventually collapses when the magnetic field lines become parallel to the wall.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Production of warm ions in electron beam generated E × B plasma

Several recent experiments have demonstrated low-damage processing of 2D materials, such as graphene and single crystal diamond, using electron beam (e-beam) generated plasmas with applied crossed electric and magnetic (E × B) fields. Here, the low damage of these sensitive materials is commonly attributed to the low energy of ions incident to the substrate surface and the ion confinement in E x B fields. In this work, measurements of atom and ion velocity distribution functions in an e-beam E × B plasma at sub-mTorr argon pressures using a laser-induced fluorescence diagnostic revealed the presence of a warm population of ions with temperatures of ~ 1 eV that are sufficient to destroy the ion confinement in E × B fields and drive the ion flux by cross field diffusion in the direction opposite to the applied electric field, toward the plasma-bounded walls or substrate. Thus, it is this nearly ambipolar diffusion process that is responsible for the flux of charged particles impinging on the wall/substrate surface.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2024

Structure and phase transitions in niobium and tantalum derived nanoscale transition metal perovskites, Ba(Ti,MV)O3, M=Nb,Ta

The prospect of creating ferroelectric or high permittivity nanomaterials provides motivation for investigating complex transition metal oxides of the form Ba(Ti, MV)O3, where M = Nb or Ta. Solid state processing typically produces mixtures of crystalline phases, rarely beyond minimally doped Nb/Ta. Using a modified sol-gel method, we prepared single phase nanocrystals of Ba(Ti, M)O3. Compositional and elemental analysis puts the empirical formulas close to BaTi0.5Nb0.5O3−δ and BaTi0.5Ta0.5O3−δ. For both materials, a reversible temperature dependent phase transition (non-centrosymmetric to symmetric) is observed in the Raman spectrum in the region 533–583 K (260–310 °C); for Ba(Ti, Nb)O3, the onset is at 543 K (270 °C); and for Ba(Ti, Ta)O3, the onset is at 533 K (260 °C), which are comparable with 390–393 K (117–120 °C) for bulk BaTiO3. The crystal structure was resolved by examination of the powder x-ray diffraction and atomic pair distribution function (PDF) analysis of synchrotron total scattering data. It was postulated whether the structure adopted at the nanoscale was single or double perovskite. Double perovskites (A2B′B″O6) are characterized by the type and extent of cation ordering, which gives rise to higher symmetry crystal structures. PDF analysis was used to examine all likely candidate structures and to look for evidence of higher symmetry. The feasible phase space that evolves includes the ordered double perovskite structure Ba2(Ti, MV)O6 (M = Nb, Ta) Fm-3m, a disordered cubic structure, as a suitable high temperature analog, Ba(Ti, MV)O3Pm-3m, and an orthorhombic Ba(Ti, MV)O3Amm2, a room temperature structure that presents an unusually high level of lattice displacement, possibly due to octahedral tilting, and indication of a highly polarized crystal.

Chemistry↗
DOE OSTI2024

A transferable classical force field to describe glyme based lithium solvate ionic liquids

A non-polarizable force field for lithium (Li + ) and bis(trifluoromethanesulfonyl)imide (TFSI – ) ions solvated in diglyme at around 0.2 mol fraction salt concentration was developed based on ab initio molecular dynamics (AIMD) simulations and a modified polymer consistent force field model. A force–torque matching based scheme, in conjunction with a genetic algorithm, was used to determine the Lennard-Jones (LJ) parameters of the ion–ion and ion–solvent interactions. This force field includes a partial charge scaling factor and a scaling factor for the 1–4 interactions. The resulting force field successfully reproduces the radial distribution function of the AIMD simulations and shows better agreement compared to the unmodified force field. The new force field was then used to simulate salt solutions with glymes of increasing chain lengths and different salt concentrations. The comparison of the MD simulations, using the new force field, with experimental data at different salt concentrations and AIMD simulations on equimolar concentrations of the triglyme system demonstrates the transferability of the force field parameters to longer glymes and higher salt concentrations. Furthermore, the force field appears to reproduce the features of the experimental x-ray structure factors, suggesting accuracy beyond the first solvation shell, for equimolar salt solutions using both triglyme and tetraglyme as the solvent. Altogether, the new force field was found to accurately reproduce the molecular descriptions of LiTFSI-glyme systems not only at various salt concentrations but also with glymes of different chain lengths. Thus, the new force field provides a useful and accurate tool to perform in silico studies of this family of systems at the atomistic level.

25 ENERGY STORAGE↗
DOE OSTI2024

Helium metastable density determination in the COST reference source by absolutely calibrated optical emission spectroscopy

Helium metastable densities in the COST Reference Microplasma Jet are estimated for a variety of He/N2 admixtures and dissipated powers by applying a collisional-radiative model to absolutely calibrated optical emission spectroscopy measurements. This is accomplished by delineating the excitation mechanisms that result in the N2(C–B) and N2+(B–X) emission bands, the latter of which is strongly coupled to the presence of helium metastables. A number of other plasma parameters are established and discussed for each operating condition including the electron energy distribution function, reduced electric field, rate constants, and electron density. With these parameters, the reaction rates for the primary ionization pathways are also calculated, emphasizing the importance of helium metastables for discharge sustainment. Good agreement with the existing literature is found for most plasma parameters and for helium metastable densities, in particular. A clear [N2]−1 relationship between the nitrogen concentration and density of helium metastables is demonstrated, as has been identified in previous studies in analogous atmospheric pressure plasma jets. This validates the efficacy of this optical technique for determining helium metastable densities and establishes it as a viable, and in many cases, more accessible alternative to other means of quantifying helium metastables in low-temperature plasmas.

Physics↗
DOE OSTI2024

Thermal quasiparticle theory

The widely used thermal Hartree–Fock (HF) theory is generalized to include the effect of electron correlation while maintaining its quasi-independent-particle framework. An electron-correlated internal energy (or grand potential) is postulated in consultation with the second-order finite-temperature many-body perturbation theory (MBPT), which then dictates the corresponding thermal orbital (quasiparticle) energies in such a way that all fundamental thermodynamic relations are obeyed. The associated density matrix is of a one-electron type, whose diagonal elements take the form of the Fermi–Dirac distribution functions, when the grand potential is minimized. The formulas for the entropy and chemical potential are unchanged from those of Fermi–Dirac or thermal HF theory. The theory thus stipulates a finite-temperature extension of the second-order Dyson self-energy of one-particle many-body Green’s function theory and can be viewed as a second-order, diagonal, frequency-independent, thermal inverse Dyson equation. At low temperatures, the theory approaches finite-temperature MBPT of the same order, but it may outperform the latter at intermediate temperatures by including additional electron-correlation effects through orbital energies. Here, a physical meaning of these thermal orbital energies is proposed (encompassing that of thermal HF orbital energies, which has been elusive) as a finite-temperature version of Janak’s theorem.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2024

Ten-moment fluid model for low-temperature magnetized plasmas

In this paper, a one-dimensional 10-moment multi-fluid plasma model is developed and applied to low-temperature magnetized plasmas. The 10-moment model solves for six anisotropic pressure terms, in addition to density and three components of fluid momentum, which allows the model to capture finite kinetic effects. The results are benchmarked against a 5-moment model, which assumes that the gas constituents follow a Maxwellian velocity distribution function (VDF), and a particle-in-cell Monte Carlo collision model that allows for arbitrary non-Maxwellian VDFs. The models are compared in a one-dimensional, low-temperature, partially magnetized plasma test case. The 10-moment results accurately reproduce the anisotropic temperature profile in low-temperature magnetized plasmas, where shear gradients exist due to the E×B drift. We discuss the mechanisms by which the anisotropic pressure can be generated in low-temperature magnetized plasmas. In addition, the importance of a self-consistent heat flux closure to the 10-moment model is studied, showing consistency with other models only when the assumptions of the underlying model are met. The 10-moment model allows for study of electron inertia effects and non-Maxwellian VDFs without the need for kinetic methods that are more computationally expensive.

Kuldinow, Derek Amur (ORCID:0000000319730196)↗
DOE OSTI2025

Simulation of an inductively coupled plasma with a two-dimensional Darwin particle-in-cell code

A two-dimensional particle-in-cell code for the simulation of low-frequency electromagnetic processes in laboratory plasmas has been developed. The code uses the Darwin method omitting the electromagnetic wave propagation. The Darwin method separates the electric field into solenoidal and irrotational parts. The solenoidal electric field is calculated with a new algorithm based on the equation for the electric field vorticity. The system of linear equations in the new algorithm is readily solved using a standard iterative method. The irrotational electric field is the electrostatic field calculated with the direct implicit algorithm. The code is verified by reproducing the two-stream instability, electron electromagnetic waves, and shear Alfvén waves. The code is applied to simulate an inductively coupled plasma with the driving current flowing around the plasma region. In this simulation, a ring of dense plasma forms at the initial stage but then the density becomes maximal in the center and decays monotonically toward the walls. The skin effect is in the transitional mode between local and non-local, and the electron velocity distribution function is non-Maxwellian.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Structure–property relations of binary ferrite melts

Molten ferrite systems are used in the smelting and refining processes in steelmaking, to reduce the loss of metals in slags and to accelerate reaction rates. Here, high-energy x-ray diffraction experiments have been performed on aerodynamically levitated molten spheres of 43BaO–57FeO X and 43SrO–57FeO X at 1873 K using laser beam heating. The composition was varied within the range of x = 1–1.5 by changing the oxygen partial pressure of the levitation gas. The corresponding x-ray pair distribution functions have been interpreted using empirical potential structure refinement (EPSR) modeling. In oxygen-rich melts (x = 1.5), our EPSR models indicate very similar structures for the different alkaline-earth liquids, with both the Ba–O and Sr–O coordination numbers to be ∼8.4 and the total Fe–O coordination numbers ∼5.7. However, our models show that in reducing environments, the Fe 3+ and Fe 2+ ions exhibit very different behaviors in the Ba- and Sr-ferrite liquids. In the Ba-ferrite melt, the Fe 3+ –O coordination number decreases from 5.7 (at x = 1.5) to 5.2 (at x = 1.07), whereas Fe 2+ –O remains constant at ∼5.0 across the same compositional range. In the Sr melts, both the Fe 2+ –O and Fe 3+ –O coordination numbers rise from ∼5.7 (at x = 1.5) to 6.3 (at x = 1.07). All models show the structures to be heterogeneous with intertwined nanometer sized clusters or channels of Ba/Sr–O and Fe–O polyhedra that grow as oxygen content is reduced. Changes in the viscosity and electrical properties are interpreted in terms of the number of bridging and non-bridging oxygens associated with FeO 4 tetrahedra and concentration of charge carriers, respectively.

Benmore, Chris J. [Argonne National Laboratory (AN↗