Session CO04: Fundamental Plasmas: Modeling and Machine Learning

Theory of the Ion-Electron Temperature Relaxation Rate in Strongly Magnetized Plasmas

Recent works have shown that strongly magnetized plasmas characterized by having a gyrofrequency greater than the plasma frequency exhibit novel transport properties. One example is that the friction force on a test charge shifts, obtaining components perpendicular to its velocity in addition to the typical stopping power component antiparallel to its velocity. Here, we apply a recent generalization of the Boltzmann equation for strongly magnetized plasmas to calculate the ion-electron temperature relaxation rate. Strong magnetization is generally found to increase the temperature relaxation rate perpendicular to the magnetic field, and to cause the temperatures parallel and perpendicular to the magnetic field to not relax at equal rates. This, in turn, causes a temperature anisotropy to develop during the equilibration. Strong magnetization also breaks the symmetry of independence of the sign of the charges of the interacting particles on the collision rate, commonly known as the ``Barkas effect". It is found that the combination of oppositely charged interaction and strong magnetization causes the ion-electron parallel temperature relaxation rate to be significantly suppressed, scaling inversely proportional to the magnetic field strength.   

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The effects of the external AC electric field on self-diffusion coefficients in perpendicular and parallel directions are investigated using the Stokes-Einstein (S-E) and Green-Kubo (G-K) formulas. For this, we employed the molecular dynamics (MD) simulations method for three-dimensional (3D) one-component plasmas (OCPs) to compute the perpendicular (D┴) and parallel (D_║) diffusion coefficients. The effects of uniaxial (z-axis) AC electric field (M_T) on diffusive characteristics for OCPs have been investigated along with various values of plasma Coulomb coupling and M_T. The new MD outcomes demonstrate that the D_┴ decreased under the intermediate to large M_T strength, and D_║ increased with an increase under moderate M_T strength. Both D_┴ and D_║ and remained nearly constant for low M_T values. It is also observed the S-E and G-K relations provide near-similar results for the entire similar parameters. The investigations show that the current EMD scheme is more efficient for noni-deal gas-like, liquid-like, and solid-like states of strongly coupled OCPs. These investigations are significant to understand the diffusivity, phase transitions and rheological behaviors for the systems of charged particles, colloidal suspensions, and dusty plasma systems.   

A multi-GPU accelerated Vlasov-Poisson solver for microturbulence studies

Microphysics plays a critical role in collisionless plasma transport and affects macroscopic properties like resistivity.

A kinetic description is required to model these anomalous transport phenomena.

The challenge of using kinetic simulations is the immense computational cost associated with accurately modeling the evolution of the species distribution functions in position-velocity phase space.

To address this challenge, new algorithms and techniques are developed to extend the CPU-based VCK continuum kinetic Vlasov-Poisson solver to utilize multiple GPUs.

This code uses a finite-volume discretization to facilitate noise-free fourth-order accurate solutions with robust convergence properties and portable performance across a wide variety of GPU architectures.

Key algorithmic advances include efficient moment integration and techniques for minimizing data communication costs.

In this talk we present the capabilities of the multi-GPU code and include performance metrics on a wide set of problem sizes.

The order of magnitude speedup from the multi-GPU accelerated code enables the study of parameter regimes that are practically inaccessible to the CPU-based version. These advances facilitate more comprehensive studies of microturbulence, including capturing dynamics for realistic electron-proton mass ratios.

The new capabilities from GPU acceleration are leveraged to characterize collisionless resistivity induced by the lower hybrid drift instability in pulsed power inertial confinement fusion experiments.   

Verification, Validation, and Uncertainty Quantification for Computational Plasma Physics

Verification, Validation, and Uncertainty Quantification (VVUQ) is effectively the scientific method applied to computational sciences and provides the paradigm shift necessitated to effectively leverage modern computational methods within the experimental design cycle. In this talk, we examine how advanced tools for computational plasma physics are both being developed and applied to enable deep understanding the physics at working within integrated plasma physics experiments. We will describe development of model formulations and verification hierarchies and examine how these will be assessed on realistic integrated plasma physics experiments.   

Modeling Strongly-Correlated Plasmas With Hydrodynamic Density Functional Theory

Strongly-coupled plasmas, such as ultracold neutral plasmas, dusty plasmas and warm dense matter, can be difficult model, as a complete understanding of the physics relies on both the dynamics and the underlying particle correlations. Density functional theory (DFT) is a natural formalism for describing such correlations but is limited to equilibrium systems. For non-equilibrium systems, hydrodynamic DFT (HDFT) provides a dynamic generalization of DFT that has recently been applied to plasmas and other fluids [1, 2]. One of the primary advantages of HDFT is that it establishes a direct connection to atomic-scale correlations self-consistently and without the need for an ad hoc equation of state. We extend the HDFT model to include the dynamics of a temperature field, which can be highly relevant to the description of plasmas, as well as examine various choices of correlation functionals in the HDFT model. The governing equations are solved numerically, and we address both the computational challenges that arise from the nonlocal correlation effects as well as the theoretical challenges associated with heterogeneous and strongly-coupled systems. Finally, we explore the role that correlations play in plasma waves.

[1] A. J. Archer, J. Chem. Phys., 130(1), 014509 (2009).

[2] A. Diaw and M. S. Murillo, Phys. Rev. E, 92(1), 013107 (2015).   

Decay of Mechanically Driven Axial Counter-Current in a High Speed Rotating Cylinder Using DSMC Simulations

The decay of mechanically driven axial counter-current along the axial direction in a high speed rotating cylinder is studied for wall pressure P_w in the range 20 to 100 m-bar using two dimensional Direct Simulation Monte Carlo (DSMC) simulations. The shape & magnitude of the radial-profile of the axial mass flux is investigated quantitatively at various axial locations and the axial-decay is characterized by a universal exponential function with varying exponent & pre-exponential factor based on the wall pressure and hence the hold up. The analysis shows that as the wall pressure is increased from 20 to 100 m-bar, the shift in the inversion point (corresponds to zero axial mass flux) along the axial length is significant ((Pradhan & Kumaran, J. Fluid Mech., vol. 686, 2011, pp. 109-159); (Kumaran & Pradhan, J. Fluid Mech., vol. 753, 2014, pp. 307-359)). The analysis further indicates that the decay of axial counter-current influences both the flow profile efficiency (E_F) and the circulation efficiency (E_C) to a great extent, and plays an important role in deciding the separation performance of the gas centrifuge machine. The DSMC simulation results are compared with the analytical results for the decay length based on Dirac equation of high speed approximation ( Z_D = (1/ 2η) (1/(4.82 A⁶)) ((P_wall M_W)/(R_g T)) (V_θ R²_wall ) [ 1 + (((γ-1) M_W V_θ²)/(4 γ R_g T))² ] ^1/2 , and found good agreement (error within 15%). Here, Z_D is the decay length, η is the gas viscosity, A is the stratification parameter A= (M_W V_θ²/(2 R_g T))^1/2, P_wall is the wall pressure, M_W is the molecular weight, R_g is the universal gas constant, T is the uniform gas temperature, V_θ is the peripheral velocity, R_wall is the radius of the cylinder, γ is the specific heat ratio (C_P/C_V), and the parameter B = (((γ-1) M_W V_θ²)/(4 γ R_g T)) represents the ratio of adiabatic force to angular momentum force.

  

Explicit relativistic energy-conserving PIC scheme and conservative particle down-sampling

The absence of exact preservation of energy and other physically conserved quantities in PIC simulations is known to enable numerical heating, instabilities and other artefacts that must be restrained, sometimes at the cost of excessive computational demands. For example, the conservation of energy can be enforced in implicit relativistic or semi-implicit non-relativistic schemes. Highly scalable explicit relativistic PIC simulations commonly require high-order weighting, current smoothing and a large number of particles per cell, as well as small time and space steps that can be much smaller than the spatiotemporal scales of interest. Another example concerns the problem of down-sampling particle ensembles in case of growing number of particles due to ionization, pair production or other processes. Particle merging may smoothen particle distributions, while thinning may cause a local violation of conservation laws with difficult-to-assess consequences. We propose methods for solving the outlined problems. The first method provides a way to enforce an exact energy conservation in explicit relativistic PIC method and thereby eliminates the related excessive computational demands [Gonoskov arXiv:2302.01893 (2023)]. The second method provides a way to reduce the number of macroparticles without any systematic influence on distribution functions, while locally preserving any number of conserved quantities and central moments [Gonoskov Comput. Phys. Commun. 271, 108200 (2022)].   

Accelerating Kinetic Simulations of Electrostatic Plasmas with Reduced-Order Modeling

We present a cost-effective method for collisionless electrostatic plasma kinetics based on the Vlasov-Poisson equation. Eulerian simulations are computationally expensive due to high dimensionality, while particle-based methods suffer from statistical noise and require many particles. Our reduced-order modeling (ROM) approach projects the equation onto a linear subspace spanned by major proper orthogonal decomposition (POD) modes. We introduce a tensorial approach to efficiently update the nonlinear term using a precomputed third-order tensor. To capture multi-scale behaviors with a few POD modes, we decompose the solution into multiple time windows, constructing a temporally-local ROM. Demonstrated on 1D--1V simulations with a prescribed electric field and the benchmark two-stream instability case, our tensorial approach solves the equation about 100 times faster than Eulerian simulations. Time-windowing significantly improves the ROM performance, especially for nonlinear simulations.   

Learning the Dynamics of a 1D Plasma Electrostatic Sheet Model with Graph Neural Networks

Graph neural network-based simulators have been proposed as an alternative to model multiscale fluid and rigid body dynamics [1-3]. Their main advantages are the flexibility to operate on both mesh and particle-based simulations, the possibility of enforcing known physics constraints into the graph construction, and the capability of utilizing coarser grids and larger time steps when trained on subsampled data from high-fidelity simulations. In this talk, we explore the possibility of using this class of graph-based models to fully replace a kinetic plasma physics simulator. We show that our model learns the kinetic plasma dynamics of the one-dimensional plasma model, a predecessor of contemporary kinetic plasma simulation codes, introduced by J. Dawson [4]. Our model is capable of recovering well-known kinetic plasma processes, including plasma thermalization, electrostatic fluctuations about thermal equilibrium, and the drag on a fast sheet and a Fourier mode (Landau damping).  We compare the performance against the original plasma model in terms of run time, conservation laws, and temporal evolution of key physical quantities. The main challenges faced to obtain the required generalization capabilities are also addressed, and possible directions for higher-dimensional surrogate models for kinetic plasmas are outlined.

[1] P. Battaglia et al., arXiv:1806.01261 (2018)

[2] A. Sanchez-Gonzalez et al., PMLR 119 (2020)

[3] T. Pfaff et al., ICLR (2021)

[4] J. Dawson, Phys. Fluids 5(4) (1962)   

Data-driven, multi-moment fluid modeling of Landau damping using machine learning

Kinetic approaches are generally accurate in dealing with microscale plasma physics problems but are computationally expensive for large-scale and multi-scale systems. One of the long-standing problems in plasma physics is the integration of kinetic effects into fluid models, which is often achieved through analytical closure terms. In this work, data-driven approaches are adopted to incorporate fluid closures in a multi-moment fluid model, and consequently, it can accurately capture the collisionless Landau damping. We investigate two different machine learning approaches 1) the mPDE-Net architecture with an explicitly formulated fluid closure and 2) the physics-informed neural network (PINN) with an implicit fluid closure. The learned multi-moment fluid models are constructed from and tested against fully kinetic Vlasov simulation data. The newly constructed fluid models can successfully capture the time evolution of the electric field energy, including its damping rate. This work sheds light on the accurate and efficient modeling of large-scale systems, which can be extended to complex multiscale laboratory, space, and astrophysical plasma physics problems.   

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Plasma X-ray spectra contain rich information and features, such as line intensities and widths, which can be used to deduce plasma properties such as temperature and density, however, inferring this information typically requires time-consuming expert analysis coupled with detailed atomic kinetics and/or radiation hydrodynamics simulations. “Big data” generated by ensemble simulations and high-repetition-rate (HRR, >1 Hz) experiments at ultra-intense laser facilities can be coupled through machine learning in order to transform the way that atomic physics is studied in high-energy-density plasma systems. Such an approach could dramatically increase the speed of analysis and fold in uncertainties due to plasma spatio-temporal gradients and evolution. Here we present progress in developing multi-modal, neural-network-based analysis models for rapid analysis of X-ray spectra with confidence bounds to enable temperature and density parameter scans in short-pulse laser experiments.   

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Cold atmospheric plasma (CAP) refers to a non-thermal plasma encountered in ambient air, with diverse applications in cancer therapy, wound treatment, sterilization, agriculture, and air and water purification. These applications critically depend on CAP chemistry, specifically the presence of reactive oxygen and nitrogen species. However, the comprehensive measurement of the numerous species involved in CAP chemistry, which involves complex dynamic chemical reactions, poses a significant challenge for traditional experimental approaches. Additionally, numerical simulations encounter computational costs due to the vast disparity in timescales between sub-nanosecond inelastic collisions (chemical reactions) and the millisecond to minute timescales of CAP operation. In this study, we propose a novel approach that combines physics-based data-driven modeling and advanced machine-learning techniques to overcome these challenges. Our methodology employs a physics-informed neural network (PINN) that is trained using constraints derived from physical laws and experimental measurements. The trained PINN provides a holistic understanding of species concentrations, aligning with physical laws and real-world observations. By integrating experimental measurements with machine learning numerical simulations, our approach presents a general methodology to address the multiscale nature of microscopic plasma chemistry coupled with macroscopic gas flows.   

Dynamics of the Meissner effect: how superconductors expel magnetic fields

Dynamics of the Meissner effect: how superconductors expel magnetic fields

A normal metal cooled into the superconducting state expels the magnetic field from its interior. How does this happen? I have understood it several years ago and have attempted to explain it to solid state physicists [1], however solid state physicists believe that it is already explained by BCS theory [2] and are not receptive to alternative explanations. The fact however is, BCS theory only describes the final state but not the process. The Meissner effect results from outward flow of a perfectly conducting fluid that carries the magnetic field lines with it. This should be intuitively obvious to plasma physicists, what is not so obvious is (a) what is the nature of this fluid, that cannot carry either charge or mass, since if it did it would lead to a charge and/or mass imbalance, (b) what drives the outward flow, and (c) how is angular momentum conserved, since there is angular momentum in the Meissner current in the final state and there was none in the initial state. I will provide answers to these questions using standard concepts of plasma physics that are not commonly used in solid state physics, combined with standard concepts of solid state physics that are not commonly used in plasma physics.

[1] J. E. Hirsch, Phys. Rev. B 95, 014503 (2017).

[2] J. Bardeen, L. N. Cooper, and J. R. Schrieffer, Phys. Rev. 108, 1175 (1957).    

Nonthermal Proton-Boron11 Fusion

Maintaining nonthermal ion populations can facilitate economical proton-Boron11 fusion [1.2].  Suppressing electron radiation by deconfinement of fast electrons in a mirror-like geometry [3-5] might also be useful.  The charged particle traffic described here might be regulated in part by ponderomotive effects [6-7].

[1] E. J. Kolmes, I. E. Ochs, and N. J. Fisch, Wave-Supported Hybrid Beam-Thermal pB11 Fusion, Phys. Plasma 29, 110701 (2022).

[2] I. E. Ochs et al., Improving the Feasibility of Economical Proton-Boron 11 Fusion via Alpha Channeling with a Hybrid Fast and Thermal Proton Scheme, Phys. Rev. E 106 055215 (2022).

[3] M. E. Mlodik et al., Sensitivity of synchrotron radiation to the superthermal electron population in mildly relativistic plasma, Phys. Plasma 30, 043301 (2023).

[4] I. E. Ochs et al., Confinement time and ambipolar potential in a relativistic mirror-confined plasma, Phys. Plasma 30, 052508 (2023).

[5] V. R. Munirov and N. J. Fisch, Suppression of Bremsstrahlung losses from relativistic plasma with energy cutoff, Phys. Rev. E 107, 065205 (2023).

[6] T. Rubin et al., Magnetostatic ponderomotive potential in rotating plasma, Phys. Plasma 30, 052501 (2023).

[7] I. E. Ochs, and N. J. Fisch , The Critical Role of Potential Surfaces in Static Ponderomotive End Plugs, arxiv:2305.09768 (2023).