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DOE OSTI2021

The data-driven future of high-energy-density physics

High-energy-density physics is the field of physics concerned with studying matter at extremely high temperatures and densities. Such conditions produce highly nonlinear plasmas, in which several phenomena that can normally be treated independently of one another become strongly coupled. The study of these plasmas is important for our understanding of astrophysics, nuclear fusion and fundamental physics—however, the nonlinearities and strong couplings present in these extreme physical systems makes them very difficult to understand theoretically or to optimize experimentally. Here we argue that machine learning models and data-driven methods are in the process of reshaping our exploration of these extreme systems that have hitherto proved far too nonlinear for human researchers. Furthermore, from a fundamental perspective, our understanding can be improved by the way in which machine learning models can rapidly discover complex interactions in large datasets. From a practical point of view, the newest generation of extreme physics facilities can perform experiments multiple times a second (as opposed to approximately daily), thus moving away from human-based control towards automatic control based on real-time interpretation of diagnostic data and updates of the physics model. To make the most of these emerging opportunities, we suggest proposals for the community in terms of research design, training, best practice and support for synthetic diagnostics and data analysis.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1986

Computer models of the spacecraft wake

Until recently, computations of space plasma flow over a spacecraft have been unstable for ratios of spacecraft dimension to Debye length typical of the low Earth orbit environment. Calculations are presented of the spacecraft/environment interaction based on two computer codes, MACH and POLAR. MACH, an inside-out particle tracking code, was developed for the purpose of validating the physics of POLAR in regimes where these are no comprehensive theoretical or experimental results. While the spacecraft which can be treated by MACH are restricted to simple geometries, the methodology is more fundamental than POLAR. MACH generates self-consistent solutions within the context of quasisteady Vlasov plasma flow and achieves Debye ratios previously unobtainable. POLAR uses a three-dimensional finite-element representation of the vehicle in a staggered mesh. The plasma sheath is modeled by outside-in particle tracking. Solutions for the plasma flow, wake and vehicle charging are obtained by Vlasov-Poisson iteration; charge stabilization techniques make the results virtually insensitive to the Debye ratio. POLAR reproduces the Laframboise static plasma solutions for sperical probes and fits the Makita-Kuriki probe data for spheres in a flowing plasma in regions where comparisons are valid. POLAR and MACH solutions for the particle and electrostatic potential structure of the wake of a charged disk in a low-altitude flow are shown for Mach numbers 4, 5, and 8. New features of the solutions include ion focussing in the wake and a definitive determination of the sheath edge in the wake which shows that the sheath is not an equipotential.

Rubin, A. G.↗

DOE OSTI2023

Constructing the space of quasisymmetric stellarators through near-axis expansion

Abstract A simplified view of the space of optimised stellarators has the potential to guide and aid the design efforts of magnetic confinement configurations suitable for future fusion reactors. We present one such view for the class of quasisymmetric stellarators based on their approximate description near their centre (magnetic axis). The result is a space that captures existing designs and presents new ones, providing a common framework to study them. Such a simplified construction offers a basic topological approach, guided by certain theoretical and physical choices, which this paper presents in detail.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Adiabatic behavior of an elliptical vortex in a time-dependent external strain flow

The adiabatic behavior of two-dimensional (2D) fluid vortices subject to slowly varying, time-dependent external strain flows is studied theoretically, and experimentally using magnetized non-neutral electron plasmas. Here the E × B drift dynamics of the electrons perpendicular to the magnetic field are analogous to the motion of fluid vorticity under the 2D Euler equations describing ideal fluids. A low-dimensional elliptical vortex patch model is used along with a WKB approximation to derive a formula for the breaking of an adiabatic invariant due to the changing external flow. The invariant is interpreted as the amplitude of a perturbative oscillation about a stable fixed point corresponding to a steady elliptical vortex. Smooth, hyperbolic tangent and piecewise linear ramp functions are considered for the external strain time dependence. Standard exponential breaking is observed in the former case, whereas the latter exhibits a power-law breaking curve with periodic modulation. It is found that a driving term in the equations of motion contributes the majority of the breaking whereas the frequency variation plays a weaker, but significant role. The experimental data agree closely with the theoretical model. The most significant deviation is due to inviscid damping behavior associated with the smooth edges of the experimental vortices, which tends to reduce the amplitude of the oscillation. Finally, the results are compared and contrasted with other related experimental, numerical, and theoretical work.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Fast ion stabilization of tilt in large radius FRCs

The field reversed configuration (FRC) has been a curious case in plasma physics research in that early MHD analysis suggested FRCs should be grossly unstable, while experimental results contradicted that prediction. Later, this theory was able to resolve this contradiction by understanding that finite Larmor radius effects largely negated the MHD predictions. Similarly, previous theoretical studies of beam driven FRCs predicted that such system would be unstable to beam driven modes while, again, experimental results indicated the contradiction. In this paper, we reconcile the theoretical understanding of beam driven modes with experimental observations of stability in these systems. By self-consistently capturing fast ion generation from neutral beam injection and its impact on the plasma equilibrium, we show that low amplitude perturbations in the magnetic field, driven by betatron particles, modify the precession frequencies of the betatron particles such that the drive for compressional Alfvén waves in the thermal plasma is reduced. Finally, we are able to demonstrate, for the first time, stable beam driven FRC evolution at high S*/E in 3D kinetic simulations.

Betatrons↗

DOE OSTI2024

Richtmyer–Meshkov instability when a shock is reflected for fluids with arbitrary equation of state

First predicted by Richtmyer in 1960 and experimentally confirmed by Meshkov in 1969, the Richtmyer–Meshkov instability (RMI) is crucial in fields such as physics, astrophysics, inertial confinement fusion and high-energy-density physics. These disciplines often deal with strong shocks moving through condensed materials or high-pressure plasmas that exhibit non-ideal equations of state (EoS), thus requiring theoretical models with realistic fluid EoS for accurate RMI simulations. Approximate formulae for asymptotic growth rates, like those proposed by Richtmyer, are helpful but rely on heuristic prescriptions for compressible materials. These prescriptions can sometimes approximate the RMI growth rate well, but their accuracy remains uncertain without exact solutions, as the fully compressible RMI growth rate is influenced by both vorticity deposited during shock refraction and multiple sonic wave refractions. This study advances previous work by presenting an analytic, fully compressible theory of RMI for reflected shocks with arbitrary EoS. It compares theoretical predictions with heuristic prescriptions using ideal gas, van der Waals gas and three-term constitutive equations for simple metals, the latter being analysed with detailed and simplified ideal-gas-like EoS. We additionally offer an alternative explicit approximate formula for the asymptotic growth rate. The comprehensive model also incorporates the effects of constant-amplitude acoustic waves at the interface, associated with the D'yakov–Kontorovich instability in shocks.

Napieralski, Mario (ORCID:0009000692344901)↗

DOE OSTI2024

Energetic Particles - microturbulence interaction thrust (EP SIWG white paper)

This white paper outlines a strategic approach to Energetic Particle (EP) research, aimed at applying the results to the future burning devices such as ITER. Our goal is to deepen the understanding of the interplay between plasma background microturbulence and diverse species of energetic ions in burning plasma devices. This strategy is poised to advance our knowledge in this crucial area of fusion science, paving the way for significant breakthroughs in plasma physics and fusion energy research. We consider the confinement of energetic ions such as auxiliary heating beams, minority ions from ICRH, and fusion product alpha particles. Recent studies have underscored the potential of EP/microturbulence interaction to enhance fusion plasma performance by stabilizing microturbulence. However, it also poses risks, such as exacerbating Alfvénic eigenmode (AE) instabilities, which could compromise the sustainability of plasma discharge by causing EP losses. The interplay between EPs and background microturbulence is evident in the phenomenon of effective pitch angle scattering, a crucial aspect of the quasilinear (QL) theory. This theory is integral to developing numerically-efficient yet comprehensive and self-consistent approaches, recently employed to investigate the relaxation of energetic particle populations in the holistic modeling of fusion-grade plasmas. The primary objectives of this white paper thrust encompass a dual focus. First is that we need to delve into the mechanisms through which microturbulence engenders effective pitch angle scattering. This investigation will entail the examination of the presence of known or self-consistently predicted spectra of modes accountable for microturbulence. In these explorations, electrostatic microturbulence serves as a logical initial stride towards achieving the trust's objectives. This endeavor is anticipated to yield formulations expressing the parametric dependencies of the effective pitch angle scattering frequency on variables such as thermal plasma electron and/or ion temperatures, as well as their respective thermal conductivities. In our second objective, we aim to delve into the intricate formation of zonal flow (ZF) structures amidst the complex interplay of microturbulence and Alfvenic eigenmodes (AEs). This endeavor poses greater challenges as we seek to unravel the macroscopic manifestations influenced by microturbulence, termed as zonal structures (ZS), stemming from microturbulence-induced ZF. Drawing from this understanding, we anticipate employing a QL approach to yield comprehensive insights into the distribution function of energetic particles (EP) within phase space. This method entails resolving the dominant multidimensional phase space diffusion processes while effectively averaging over the rapid ballistic responses. Nevertheless, substantial strides remain imperative to realize a comprehensive whole-device modeling framework. This entails meticulous verification and validation exercises against experimental observations, as well as rigorous benchmarking against theoretical frameworks and numerical simulations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

The X-Ray Emission Effectiveness of Plasma Mirrors: Reexamining Power-Law Scaling for Relativistic High-Order Harmonic Generation

Ultrashort pulsed lasers provide uniquely detailed access to the ultrafast dynamics of physical, chemical, and biological systems, but only a handful of wavelengths are directly produced by solid-state lasers, necessitating efficient high-power frequency conversion. Relativistic plasma mirrors generate broadband power-law spectra, that may span the gap between petawatt-class infrared laser facilities and x-ray free-electron lasers; despite substantial theoretical work the ultimate efficiency of this relativistic high-order-harmonic generation remains unclear. We show that the coherent radiation emitted by plasma mirrors follows a power-law distribution of energy over frequency with an exponent that, even in the ultrarelativistic limit, strongly depends on the ratio of laser intensity to plasma density and exceeds the frequently quoted value of -8/3 over a wide range of parameters. The coherent synchrotron emission model, when adequately corrected for the finite width of emitting electron bunches, is not just valid for p-polarized light and thin foil targets, but generally describes relativistic harmonic generation, including at normal incidence and with finite-gradient plasmas. Our numerical results support the ω-4/3 scaling of the synchrotron emission model as a limiting efficiency of the process under most conditions. The highest frequencies that can be generated with this scaling are usually restricted by the width of the emitting electron bunch rather than the Lorentz factor of the fastest electrons. The theoretical scaling relations developed here suggest, for example, that with a 20-PW 800-nm driving laser, 1 TW/harmonic can be produced for 1-keV photons.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1975

Denouement of Jovian radiation belt theory

Predictions of theoretical models of Jupiter's radiation belts are compared with Pioneer 10 measurements. A brief quasi-historical review is given of the evolution of the basic theoretical ideas with emphasis on the three physical processes that were believed to be dominant in the Jovian electron fluxes: radial-diffusion transport, limitation of particle fluxes by plasma wave turbulence, and particle losses from collisional sweep-up by the Galilean satellites. Pioneer 10 data on the inner zone are discussed which yield the clearest evidence for radial diffusion being the dominant transport process, the synchrotron flux density is estimated using Pioneer 10 measurements, and the observed outer-zone electron fluxes are favorably compared with the qualitative and quantitative predictions of the whistler-mode stable-trapping model. The outer-zone electron-precipitation flux is estimated, and it is suggested that precipitation could affect the structure of the Jovian ionosphere. Satellite sweep-up is shown to be less severe than had been anticipated.

Coroniti, F. V.↗

NASA NTRS1983

Positron-electron pairs in astrophysics; Proceedings of the Workshop, Greenbelt, MD, January 6-8, 1983

Astrophysical sources of positron-electron-pair annihilation radiation are characterized in reviews and reports of observational and theoretical investigations. Topics examined include gamma-ray lines from solar flares, gamma-ray bursts, pulsars, the Galactic center, active galaxies, and physical processes in relativistic and magnetized plasmas. Spectra, historgrams, graphs, and diagrams are provided.

Burns, M. L.↗

NASA NTRS2020

X-ray Spectra of the Fe-L Complex II: Atomic Data Constraints from the EBIT Experiment and X-Ray Grating Observations of Capella

The Hitomi results for the Perseus cluster have shown that accurate atomic models are essential to the success of X-ray spectroscopic missions and just as important as the store of knowledge on instrumental calibration and astrophysical modeling. Preparing the models requires a multifaceted approach, including theoretical calculations, laboratory measurements, and calibration using real observations. In a previous paper, we presented a calculation of the electron impact cross sections on the transitions forming the Fe-L complex. In the present work, we systematically tested the calculation against cross-sections of ions measured in an electron beam ion trap experiment. A two-dimensional analysis in the electron beam energies and X-ray photon energies was utilized to disentangle radiative channels following dielectronic recombination, direct electron-impact excitation, and resonant excitation processes in the experimental data. The data calibrated through laboratory measurements were further fed into a global modeling of the Chandra grating spectrum of Capella. We investigated and compared the fit quality, as well as the sensitivity of the derived physical parameters to the underlying atomic data and the astrophysical plasma modeling. We further list the potential areas of disagreement between the observations and the present calculations, which, in turn, calls for renewed efforts with regard to theoretical calculations and targeted laboratory measurements.

Liyi Gu↗

DOE OSTI2020

Quantitative metrics for evaluating thermonuclear design codes and physics models applied to the National Ignition Campaign

In this study, physics models and design codes for hot dense plasmas undergoing thermonuclear burn are evaluated objectively using statistical metrics that compare the difference between calculations and data relative to the experimental uncertainties. The analysis is applied to the National Ignition Campaign (NIC) because it is relevant, comprehensive, and well documented. The statistics confirm that a key process afflicting NIC performance is mix driven by hydrodynamic instabilities as approximated here using the KL model [G. Dimonte and R. Tipton, Phys. Fluids 18, 085101 (2006)]. New physics models are also presented for instability-driven magnetic fields [B. Srinivasan et al., Phys. Rev. Lett. 108, 165002 (2012)] and the Coulomb logarithm for electron–ion thermal relaxation [G. Dimonte and J. Daligault, Phys. Rev. Lett. 101, 135001 (2008)]. The plasma-generated magnetic fields improve the agreement between code and data in a statistically significant manner by reducing the electron thermal conduction in the hot-spot via the Hall term. The Coulomb logarithm is presented in a numerically practical form that incorporates recent theoretical advances. However, it does not improve the agreement between the code and data because the thermal relaxation is so fast in non-ignited NIC plasmas that the typical 20% error does not change the tight coupling between electrons and ions. Even with these improved physics models, the one-dimensional simulations presented here are not able to describe the high-convergence NIC implosions in a statistically acceptable manner. Of the heroic multi-dimensional simulations of Clark et al. [Phys. Plasmas 23, 056302 (2016)], only those in three-dimensions satisfy the statistical acceptance criterion.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Particle collisionality in scaled kinetic plasma simulations

Kinetic plasma processes, such as magnetic reconnection, collisionless shocks, and turbulence, are fundamental to the dynamics of astrophysical and laboratory plasmas. Simulating these processes often requires particle-in-cell (PIC) methods, but the computational cost of fully kinetic simulations can necessitate the use of artificial parameters, such as a reduced speed of light and ion-to-electron mass ratio, to decrease expense. While these approximations can preserve overall dynamics under specific conditions, they introduce nontrivial impacts on particle collisionality that are not yet well understood. In this work, we develop a method to scale particle collisionality in simulations employing an artificial speed of light and/or an artificial ion-to-electron mass ratio. By introducing species-dependent scaling factors, we independently adjust inter- and intra-species collision rates to better replicate the collisional properties of the physical system. Our approach maintains the fidelity of electron and ion transport properties while preserving critical relaxation rates, such as energy exchange timescales, within the limits of weakly collisional plasma theory. Furthermore, we demonstrate the accuracy of this scaling method through benchmarking tests against theoretical relaxation rates and connecting to fluid theory, highlighting its ability to retain key transport properties. Existing collisional PIC implementations can be easily modified to include this scaling, which will enable deeper insights into the behavior of marginally collisional plasmas across various contexts.

Totorica, S. R. [Princeton Univ., NJ (United State↗

NASA NTRS2012

Doubly-Shadowed Regions in Lunar Polar Craters: Hydrogen Accumulation in the Presence of Recursive Plasma Wakes

Permanently shadowed regions (PSRs) of the Moon have been identified as unique environments of extreme cold and comprise a natural cold trap for sequestering volatiles [Paige et al. 2010]. The diverse chemical composition of the LCROSS impact plume provided evidence for a volatile-rich and chemically-complex PSR environment [Cola prete et al. 2010, Schultz et al. 2010]. Additionally, the polar electrostatic environment is highly complex, with the possibility of strong, localized electric fields that divert solar wind ions directly into polar cold traps [Farrell et al. 2010, Zimmerman et al. 2011]. Thus, regional plasma physics processes couple directly with volatile sequestration. In the present work, kinetic simulations show that recursive plasma wake structure arises in the presence of step-like topographic features (Le. doubly-shadowed craters). Combining the plasma code with a numerical sputtering model demonstrates that solar wind protons can be either a hydrogen source via implantation or a volatile loss mechanism via sputtering, depending on properties of the regolith and solar wind. The present model provides a novel theoretical pathway toward understanding the lunar surface/solar wind physical and chemical interactions for complex topography near the poles.

Zimmerman, Michael I.↗

DOE OSTI2021

Simulating Boundary Region Plasma Instabilities

The boundary regions of low-temperature plasmas are known to be susceptible to kinetic instabilities, which can affect the energies and fluxes of particles directed at the material boundary. For example, both the ion acoustic instability as well as an instability near the electron plasma frequency have been observed. Particle-in-cell (PIC) simulation is a tool that, alongside experiments, can capture the effects these instabilities have on the particle distribution functions. Ultimately, simulations can determine under what conditions these effects are significant by comparing to theoretical predictions and explore conditions unamenable to experiments.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1983

Plasma physics on auroral field lines - The formation of ion conic distributions

The formation of the conical distribution function and the acceleration of ions on aurora field lines are considered. Ion cyclotron waves were assumed to be excited by drifting electrons associated with the return current in the auroral zone. A theoretical analysis of ion cyclotron waves is given, and a simulation model is described. Simulation results are presented. The heating of ions and the evolution of ion cyclotron waves on auroral field lines and in the magnetosphere are discussed.

Ashour-Abdalla, M.↗

NASA NTRS1994

Hard X-rays from NGC 4151: A thermal origin?

We present a model for explaining the recent combined X-ray and low-energy gamma-ray observations of the Seyfert galaxy NGC 4151. According to this model, soft photons become Comptonized in a hot spot producing simultaneously the low-energy power law as observed by Ginga and the high-energy cutoff observed by the Oriented Scintillation Spectrometer Experiment (OSSE). Implementing recently developed theoretical calculations toward a generalized theory of Comptonization, we were able to find fits to the observations using only two parameters which characterize the physical quantities of the emission region: the plasma cloud optical depth and its temperature. We find that there is no need for additional nonthermal, reflection, or higher temperature thermal components to fit the aforementioned OSSE and Ginga observations. We derive in addition the size of the photon region and the temperature of the upscattered soft photons. We should emphasize, also, that any attempt at fitting only the high-energy parts of the spectrum (photon energies greater than 60 keV) by the Sunyaev & Titarchuk (1980) nonrelativistic Comptonization model leads to an underestimate of the Comptonization parameter y (or, equivalently, to an overestimation of the X-ray power-law spectral slope) and leads, as a result, to incorrect proportions between the low-energy and high-energy parts of the spectrum.

Titarchuk, Lev↗

DOE OSTI2020

Dissertation Proposal: Innovations in Pulsed Power and Plasma Science Theory Simulation and Experiment

Pulsed power and plasma physics are topics of great study at both Sandia National Laboratories (SNL or Sandia) and the University of New Mexico (UNM). The goal of this research is to further knowledge and understanding of these fields using the resources of both SNL and UNM in three ways. The first way is through the comprehension, application, and testing of theory. Reading and analytically deriving theoretical solutions of problems both real-world and simplified will allow for a fresh perspective and the furthering of the theory. One such theory is Ottinger's generalized theory for voltage measurement in magnetically insulated transmission lines (MITLs). By working through the math, a deeper understanding of the theory is gained from which one may add more physically accurate and/or more detailed physics into the theory. Additionally, understanding the theory lays a good foundation from which one can analyze, test, and compare results to the theory in the following two ways that will advance the fields of pulsed power and plasma physics. The second way is through the modeling and simulation of real-world and simplified problems that utilize and test the afore mentioned theories. Theory can be applied to a simulation domain by using the unstructured time-domain electromagnetic (UTDEM) codes EMPHASIS and EMPIRE as well as the physical modeling software CUBIT, all of which were developed at SNL. Problems such as the modeling and design of the extended MITL on HERMES III, the understanding of space-charge-limited emission from vacuum cathodes, and the interaction between a relativistic electron beam and an ideal gas can all be modeled, simulated, and analyzed with this set of codes. Here the advantage is three-fold. Firstly, theory that describes our understanding of these problems can be put to the test and advanced through iterative simulation and analysis. Secondly, the understanding of these problems will have a positive impact on national security through the advancement of the technological capability of the United States of America. Thirdly, and not unrelated to the prior advantage, is the validation and verification of EMPIRE and EMPHASIS. This segues into the third way, which is through experiment and the comparison of experiment to simulated and theoretical results. Performing experimental comparisons completes the scientific method and grounds all of the work in reality. Being able to physically test theory and simulation is necessary for any real conclusions to be drawn. Another advantage for carrying out experimental work is to advance the physical testing capabilities of SNL. Several systems will be developed and tested through the course of this work that positively impact technological advancement of Sandia National Labs. Lastly, all of the above work will converge to yield a well-rounded perspective that ties the three categories of research together.

42 ENGINEERING↗