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At least 559 records · Page 31

Sparse regression for plasma physics

Many scientific problems can be formulated as sparse regression, i.e., regression onto a set of parameters when there is a desire or expectation that some of the parameters are exactly zero or do not substantially contribute. This includes many problems in signal and image processing, system identification, optimization, and parameter estimation methods such as Gaussian process regression. Sparsity facilitates exploring high-dimensional spaces while finding parsimonious and interpretable solutions. In the present work, we illustrate some of the important ways in which sparse regression appears in plasma physics and point out recent contributions and remaining challenges to solving these problems in this field. Further, a brief review is provided for the optimization problem and the state-of-the-art solvers, especially for constrained and high-dimensional sparse regression.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Experiments and Simulations of the Dusty Properties of Hypervelocity Impact Plasmas

Hypervelocity impacts, referring to impacts occurring at several times the speed of sound in the target, result in inertial stresses greatly exceeding the material strength and produce behavior that is not fully understood. These impact phenomena are seen in space through impacts of orbital debris and meteoroids on spacecraft and airless natural bodies but can also be produced in laboratory environments using light-gas guns and electrostatic dust accelerators. When a hypervelocity impact occurs, plasma is generated both from thermal ionization and from pressure ionization, producing a wide range of plasma densities depending on the impactor’s velocity. This plasma is initially formed in the warm dense matter (WDM) regime and governed by high energy density (HED) hydrodynamics before it rapidly expands and dissipates, spanning many orders of magnitude in density and length scale. The plasma can also contain a dust component, which is particularly relevant for the lower-velocity range of hypervelocity impacts with parameters that are particularly relevant to Tokamak plasmas. Therefore, the properties and dynamics of these plasmas cannot be fully characterized without considering dusty plasma effects, which are ubiquitous but poorly understood.

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Complete quasilinear model for the acceleration-driven lower hybrid drift instability and a computational assessment of its validity

A complete quasilinear model is derived for the electrostatic acceleration-driven lower hybrid drift instability in a uniform two-species low-beta plasma in which current is perpendicular to the background magnetic field. The model consists of coupled nonlinear velocity space diffusion equations for the volume-averaged ion and electron distribution functions. Each species' diffusion coefficient depends on a time-evolving spectral density of the electric-field energy per unit volume and a time-evolving dispersion relation. The dispersion relation is expressed analytically in integral form without the use of asymptotic limits and applies to arbitrary distribution functions, so long as they can be expressed as a function of one velocity coordinate, e.g., f⁡(vy) or f⁡(v⊥). The quasilinear model conserves energy and is complete in that it fully describes the evolution of the distribution functions, including resonant and nonresonant particle-wave interactions, while accounting for distribution-function-dependent mixed-complex frequencies. Further, the quasilinear diffusion model is solved numerically and self-consistently using a Crank-Nicolson temporal discretization and a second-order finite-volume velocity-space discretization. Numerical solutions are compared to nonlinear fourth-order accurate continuum kinetic Vlasov-Poisson simulations. Evolution of electric-field energy, growth rates, distribution functions, and diffusion coefficients are shown to be in agreement with Vlasov simulations. The quasilinear model is shown to predict anomalous transport terms, like resistivity and heating, to within a factor of order unity. Discrepancies between the quasilinear model and Vlasov simulations are assessed and attributed primarily to lack of damping in the quasilinear description and to the use of unperturbed-orbit susceptibilities in the linear theory dispersion relation. The results illuminate the predictive accuracy of the quasilinear model, place approximate bounds on its validity, and provide much needed vetting of quasilinear theory's ability to predict the nonlinear state of a microturbulent plasma.

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Experiment and model for a Stokes layer in a strongly coupled dusty plasma

A Stokes layer, which is a flow pattern that arises in a viscous fluid adjacent to an oscillatory boundary, was observed in an experiment using a two-dimensional strongly coupled dusty plasma. Liquid conditions were maintained using laser heating, while a separate laser manipulation applied an oscillatory shear that was localized and sinusoidal. The evolution of the resulting flow was analyzed using space-time diagrams. These figures provide an intuitive visualization of a Stokes layer, including features such as the depth of penetration and wavelength. Another feature, the characteristic speed for the penetration of the oscillatory flow, also appears prominently in space-time diagrams. To model the experiment, the Maxwell-fluid model of a Stokes layer was generalized to describe a two-phase liquid. In our experiment, the phases were gas and dust, where the dust cloud was viscoelastic due to strong Coulomb coupling. Furthermore, the model is found to agree with the experiment, in the appearance of the space-time diagrams, and in the values of the characteristic speed, depth of penetration, and wavelength.

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Kinetic simulations underestimate the effects of waves during magnetic reconnection

Collisionless plasma systems are often studied using fully kinetic simulations, where protons and electrons are treated as particles. Due to their computational expense, it is necessary to reduce the ion-to-electron mass ratio $m_i/m_e$ or the ratio between plasma and cyclotron frequencies in simulations of large systems. In this Letter we show that when electron-scale waves are present in larger-scale systems, numerical parameters affect their amplitudes and effects on the larger system. Using lower-hybrid drift waves during magnetic reconnection as an example, we find that the ratio between the wave electric field and the reconnection electric field scales as $\sqrt{m_i/m_e}$, while the phase relationship is also affected. The combination of these effects means that the anomalous drag that contributes to momentum balance in the reconnection region can be underestimated by an order of magnitude. The results are relevant to the coupling of electron-scale waves to ion-scale reconnection regions, and other systems such as collisionless shocks.

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Machine learning methods for probabilistic locked-mode predictors in tokamak plasmas

A rotating tokamak plasma can interact resonantly with the external helical magnetic perturbations, also known as error fields. This can lead to locking and then to disruptions. We leverage machine learning (ML) methods to predict the locking events. We use a coupled third-order nonlinear ordinary differential equation model to represent the interaction of the magnetic perturbation and the plasma rotation with the error field. This model is sufficient to describe qualitatively the locking and unlocking bifurcations. Here, we explore using ML algorithms with the simulation data and experimental data, focusing on the methods that can be used with sparse datasets. These methods lead to the possibility of the avoidance of locking in real-time operations. We describe the operational space in terms of two control parameters: the magnitude of the error field and the rotation frequency associated with the momentum source that maintains the plasma rotation. The outcomes are quan- tified by order parameters that completely characterize the state, whether locked or unlocked. We use unsupervised ML methods to classify locked/unlocked states and note the usefulness of a certain normalization of the order parameters. Three supervised ML classifiers are used in suite to estimate the probability of locking in the region of control parameter space with hysteresis, i.e., the set of control parameters for which both locked and unlocked states can exist. The results show that a neural network gives the best estimate of the locking probability. An analogy of the present locking model with the van der Waals equation of state is also provided.

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Novel soft x-ray multi-energy camera to study thermal plasmas on WEST

A multi-energy soft x-ray (SXR) pinhole camera has been built, calibrated and deployed on the WEST tokamak to aid the study of thermal plasmas. This novel imaging diagnostic technique employs a 2D pixelated x-ray detector in which the lower energy threshold for photon detection can be adjusted independently on each pixel. This innovation allows the simultaneous measurement of x-rays with space, time and energy resolution. Measurements at lower energy (2–6 keV) dominated by tungsten line emission are used to estimate the tungsten concentration and the plasma ΔZ eff . Measurements at higher energy (11–18 keV), where only continuum emission is present, are employed to infer the plasma electron temperature. Other applications of this powerful diagnostic include the determination of the plasma SXR centroid vertical position, characterization of tungsten UFOs and various real-time measurements.

electron temperature↗

Higher-order nonequilibrium term: Effective power density quantifying evolution towards or away from local thermodynamic equilibrium

A common approach to assess the nature of energy conversion in a classical fluid or plasma is to compare power densities of the various possible energy conversion mechanisms. A leading research area is quantifying energy conversion for systems that are not in local thermodynamic equilibrium (LTE), as is common in a number of fluid and plasma systems. Here we introduce the “higher-order nonequilibrium term” (HORNET) effective power density, which quantifies the rate of change of departure of a phase space density from LTE. It has dimensions of power density, which allows for quantitative comparisons with standard power densities. We employ particle-in-cell simulations to calculate HORNET during two processes, magnetic reconnection and decaying kinetic turbulence in collisionless magnetized plasmas, that inherently produce non-LTE effects. We investigate the spatial variation of HORNET and the time evolution of its spatial average. By comparing HORNET with power densities describing changes to the internal energy (pressure dilatation, Pi − D , and divergence of the vector heat flux density), we find that HORNET can be a significant fraction of these other measures (8% and 35% for electrons and ions, respectively, for reconnection; up to 67% for both electrons and ions for turbulence), meaning evolution of the system towards or away from LTE can be dynamically important. Applications to numerous plasma phenomena are discussed. Published by the American Physical Society 2024

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Finite spatial-grid effects in energy-conserving particle-in-cell algorithms

Finite-grid (or aliasing) instabilities are pervasive in particle-in-cell (PIC) plasma simulation algorithms, and force the modeler to resolve the smallest (Debye) length scale in the problem regardless of dynamical relevance. These instabilities originate in the aliasing of interpolation errors between mesh quantities and particles (which live in the space–time continuum). Recently, strictly energy-conserving PIC (EC-PIC) algorithms have been developed that promise enhanced robustness against aliasing instabilities. In this study, we confirm by analysis that EC-PIC is stable against aliasing instabilities for stationary plasmas. For drifting plasmas, we demonstrate by analysis and numerical experiments that, while EC-PIC algorithms are not free from these instabilities in principle, they feature a benign stability threshold for finite-temperature plasmas that make them usable in practice for a large class of problems (featuring ambipolarity and realistic ion-electron mass ratios) without the need to consider the size of the Debye length. We also demonstrate that this threshold is absent for the popular momentum-conserving PIC algorithms, which are therefore unstable for both drifting and stationary plasmas beyond a threshold in cell size compared to Debye length. Finite-grid (or aliasing) instabilities are pervasive in particle-in-cell (PIC) plasma simulation algorithms, and force the modeler to resolve the smallest (Debye) length scale in the problem regardless of dynamical relevance. These instabilities originate in the aliasing of interpolation errors between mesh quantities and particles (which live in the space–time continuum). Recently, strictly energy-conserving PIC (EC-PIC) algorithms have been developed that promise enhanced robustness against aliasing instabilities. In this study, we confirm by analysis that EC-PIC is stable against aliasing instabilities for stationary plasmas. For drifting plasmas, we demonstrate by analysis and numerical experiments that, while EC-PIC algorithms are not free from these instabilities in principle, they feature a benign stability threshold for finite-temperature plasmas that make them usable in practice for a large class of problems (featuring ambipolarity and realistic ion-electron mass ratios) without the need to consider the size of the Debye length. Finally, we also demonstrate that this threshold is absent for the popular momentum-conserving PIC algorithms, which are therefore unstable for both drifting and stationary plasmas beyond a threshold in cell size compared to Debye length.

97 MATHEMATICS AND COMPUTING↗

Payload concepts for investigations of electrostatic dust motion on the lunar surface

Significant experimental and computational investigations have explored the feasibility of electrostatically-motivated dust motion on the lunar surface. The motion of lunar dust influences our understanding of the evolution of the surface and may also present a hazard to future exploration vehicles and astronauts. The possibility of a sustained exploration presence on the lunar surface opens the door to long-term experiments on the lunar surface, akin to the science facilities on the International Space Station. We have identified four measurements/observations that would significantly advance our understanding of dust-plasma interactions on the lunar surface. In this context, we provide conceptual designs for payloads to obtain these observations: a Langmuir probe, dust deposit witness plate, regolith charge measurement instrument, and cameras to look for evidence of horizon glow. These payloads could deploy independently and sequentially, or together as a suite. The proposed payloads would provide key observations that would inform future modeling efforts and direct future in situ experiments to understand the dust-plasma environment, both for planetary science and spacecraft design applications.

42 ENGINEERING↗

A performant energy-conserving particle reweighting method for Particle-in-Cell simulations

A new particle-based reweighting method is developed and demonstrated in the Aleph Particle-in-Cell with Direct Simulation Monte Carlo (PIC-DSMC) program. Novel splitting and merging algorithms ensure that modified particles maintain physically consistent positions and velocities. This method allows a single reweighting simulation to efficiently model plasma evolution over orders of magnitude variation in density, while accurately preserving energy distribution functions (EDFs). Demonstrations on electrostatic sheath and collisional rate dynamics show that reweighting simulations achieve accuracy comparable to fixed weight simulations with substantial computational time savings. This highly performant reweighting method is recommended for modeling plasma applications that require accurate resolution of EDFs or exhibit significant density variations in time or space.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Large-scale tearing-mode hazard function analysis with standard matched equilibrium reconstructions

The association between features from standard tokamak equilibrium reconstructions and the onset of n = 1 tearing modes (TMs) is analyzed at scale. The TM onset rate is directly modeled with a ‘hazard’ function which gives the expected number of onsets (per unit time spent) in a given equilibrium parameter region. In particular the different statistical modeling performance achieved for magnetics-only reconstructions and motional Stark effect (MSE) enhanced reconstructions is studied. It is observed that a better hazard model for the TM onset rate can be built with the MSE-enhanced equilibria compared to the matched magnetics-only situation. This advantage disappears if internal profile details are withheld from the matched analysis. Plausibility of the hazard function is further demonstrated with visualizations of global trends in the operational space, and time-traces from specific tokamak discharges. As a result, TMs typically degrade tokamak plasma performance and may lead to plasma termination, motivating this statistical study.

equilibrium↗

Power balance and divertor asymmetries in the Super-X divertors of MAST-U using SOLPS-ITER

Spherical tokamaks (STs) present unique challenges and opportunities in the area of particle and power exhaust, intensified due to their more compact sizes. Substantial efforts are underway in STs to determine the limits in dissipative operational regimes and advanced divertor solutions, including at MAST-U which provides access to the Super-X divertor configuration. Power balance, and upper/lower divertor asymmetries have been studied using SOLPS-ITER simulations of the MAST-U Super-X divertor. A set of simulations with experimentally inferred transport coefficients with E x B and diamagnetic drifts activated, consisting of density and power scans, and high field side vs low field side gas puff locations, have been used for code experimentation to uncover trends beyond the current experimental parameter space. The upper biased asymmetry (U:L > 1) of the ratio of the peaks of the plasma energy flux densities at the outer targets increases with heating power and decreases with gas puff strength, going from symmetric to up to a factor of 15. The upper target electron temperature has been found to be a good ordering quantity for the magnitude of this asymmetry for all heating powers, gas puff strength, and gas puff locations. The lower divertor biased asymmetry (U:L < 1) of the radiation patterns processed through SOLPS-based bolometry synthetic diagnostics is in qualitative agreement with resistive bolometry experimental results, and it is in quantitative agreement with the trend of the total volume radiation within the divertors of SOLPS. However, radiation measurements alone are not sufficient to infer the magnitude of the asymmetry of the peaks of the power loads at the targets.

MAST-U↗

Piecewise Omnigenous Stellarators

In omnigenous magnetic fields, charged particles are perfectly confined in the absence of collisions and turbulence. For this reason, the magnetic configuration is optimized to be close to omnigenity in any candidate for a stellarator fusion reactor. However, approaching omnigenity imposes severe constraints on the spatial variation of the magnetic field. In particular, the topology of the contours of constant magnetic field strength on each magnetic surface must be such that there are no particles transitioning between different types of wells. This, in turn, usually leads to complicated plasma shapes and coils. This Letter presents a new family of optimized fields that display tokamak-like collisional energy transport while having transitioning particles. This result radically broadens the space of accessible reactor-relevant configurations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Transport Properties of Magnetized High-Energy Density Plasma (Final Project Report)

This report summarizes results of project DE-SC0016159 "Transport Properties of Magnetized High-Energy-Density Plasma,'' which ran from 7/15/2016 - 7/14/2021. The primary objectives of the work, as stated in the original proposal, were to develop a theory that describes transport coefficients in magnetized high energy density plasmas and to test the theory with molecular dynamics (MD) simulations. The science challenge is that strong ion coupling, strong magnetization of electrons, and partial degeneracy of electrons, cause the system to be in a regime that is not well described by current theory. The particular processes that were to be investigated include: ion stopping power, diffusion, electron-ion temperature relaxation, thermal conduction and viscosity. All of the primary research objectives were accomplished during the course of this work. In addition, some unexpected results were discovered along the way that led to new and productive research directions. This work resulted in 17 publications in well-respected peer-reviewed journals (primarily Physics of Plasmas and Physical Review E), and 2 more are being prepared for publication. A few of these were selected as Editor's Picks and one was published as a Rapid Communication. Highlights of the research results include: Transport phase space: The first identification of the parameter space that defines fundamental transport regimes in terms of the Coulomb coupling and magnetization parameters. Mean force kinetic theory: Systematic derivation of a kinetic theory for strongly coupled plasmas based on a new expansion parameter of the BBGKY hierarchy. This provided the derivation of a theory that we had previously posed phenomenologically, and also revealed a new term that captures the equation of state properties at all coupling strengths. Transverse friction force: Discovery that the friction force on a test charge in a strongly magnetized plasma includes a component that is perpendicular to the motion of the test charge in the plane defined by the velocity and magnetic field vectors. Gyrofriction force: Discovery that the friction force on a test charge in a plasma that is both strongly magnetized and strongly coupled includes a component of the force in the direction of the Lorentz force. Kinetic theory for warm dense matter: Extension of the mean force kinetic theory to include partial electron degeneracy, so that it applies to warm dense matter.

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Grad–Shafranov equilibria via data-free physics informed neural networks

A large number of magnetohydrodynamic (MHD) equilibrium calculations are often required for uncertainty quantification, optimization, and real-time diagnostic information, making MHD equilibrium codes vital to the field of plasma physics. In this paper, we explore a method for solving the Grad–Shafranov equation by using physics-informed neural networks (PINNs). For PINNs, we optimize neural networks by directly minimizing the residual of the partial differential equation as a loss function. We show that PINNs can accurately and effectively solve the Grad–Shafranov equation with several different boundary conditions, making it more flexible than traditional solvers. This method is flexible as it does not require any mesh and basis choice, thereby streamlining the computational process. We also explore the parameter space by varying the size of the model, the learning rate, and boundary conditions to map various tradeoffs such as between reconstruction error and computational speed. Additionally, we introduce a parameterized PINN framework, expanding the input space to include variables such as pressure, aspect ratio, elongation, and triangularity in order to handle a broader range of plasma scenarios within a single network. Parameterized PINNs could be used in future work to solve inverse problems such as shape optimization.

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On applications of quantum computing to plasma simulations

Quantum computing is gaining increased attention as a potential way to speed up simulations of physical systems, and it is also of interest to apply it to simulations of classical plasmas. However, quantum information science is traditionally aimed at modeling linear Hamiltonian systems of a particular form that is found in quantum mechanics, so extending the existing results to plasma applications remains a challenge. Here, we report a preliminary exploration of the long-term opportunities and likely obstacles in this area. First, we show that many plasma-wave problems are naturally representable in a quantumlike form and thus are naturally fit for quantum computers. Second, we consider more general plasma problems that include non-Hermitian dynamics (instabilities, irreversible dissipation) and nonlinearities. We show that by extending the configuration space, such systems can also be represented in a quantumlike form and thus can be simulated with quantum computers too, albeit that requires more computational resources compared to the first case. Third, we outline potential applications of hybrid quantum–classical computers, which include analysis of global eigenmodes and also an alternative approach to nonlinear simulations.

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Heat pump via charge incompressibility in a collisional magnetized multi-ion plasma

Stratification due to ion-ion friction in a magnetized multiple-ion species plasma is shown to be accompanied by a heat pump effect, identified for the first time here, transferring heat from one ion species to another as well as from one region of space to another. Here, the heat pump is produced via newly identified heating mechanisms associated with charge incompressibility and the Ettingshausen effect. Besides their academic interest, these new effects may have useful applications to plasma technologies that involve rotation or compression.

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