Machine Learning for Accelerating Direct-Simulation Monte-Carlo Collision Operators.
Abstract not provided.
Roberts, Nathaniel David↗
SEARCH · Engineering Papers
Results for “collision operators”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Neural-Network Based Collision Operators for the Boltzmann Equation.
Abstract not provided.
Cyr, Eric↗
Krash-ESL-Final report
During the period of the current Grant, the effort of the UCSD researchers was focused on: i) The application of the gyrokinetic code COGENT code to study the kinetic drift wave instability and its impact on blob dynamics, and ii) The modeling of edge plasma transport in collisional and semi-collisional regimes, and iii) Impurity transport in edge plasma and the incorporation of plasma-impurity collision operator (hereafter unlike particle collision operator) into COGENT. Over the years four UCSD graduate students (J. Angus, W. Lee, Y. Zhang, and A. Knyazev), funded under this Grant, contributed to the COGENT development/utilization and defended their PhD theses, which are based, partly, on their research related to the COGENT. Three of them (J. Angus, W. Lee, and Y. Zhang) have received “The Best MAE Graduate Student of the Year” awards. Whereas W. Lee after defending his PhD thesis returned back to his home country (South Korea), J. Angus, and Y. Zhang are continuing their research in plasma physics in the LLNL and LANL, whereas A. Knyazev currently is a postdoctoral fellow at Columbia University working on the theoretical aspects of advanced stellarators. The results obtained in our studies were disseminated in many papers published in first-class refereed scientific journals and presented on prestigious scientific meetings including the Annual APS DPP Meeting, Sherwood Fusion Theory Conference, IAEA Fusion Energy Conferences, International Conferences on Plasma-Surface Interactions in Controlled Fusion Devices, International Workshops on Edge Plasma Theory in Fusion Devices, etc. In what follows we highlight the major accomplishments of the UCSD Team in the main areas of our research.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Asymptotic-preserving dynamical low-rank method for the stiff nonlinear Boltzmann equation
In kinetic theory, numerically solving the full Boltzmann equation is extremely expensive. This is because the Boltzmann collision operator involves a high-dimensional, nonlinear integral that must be evaluated at each spatial grid point and every time step. The challenge becomes even more pronounced in the fluid (strong collisionality) regime, where the collision operator exhibits strong stiffness, causing explicit time integrators to impose severe stability restrictions. In this paper, we propose addressing this problem through a dynamical low-rank (DLR) approximation. The resulting algorithm requires evaluating the Boltzmann collision operator only r 2 times, where r, the rank of the approximation, is much smaller than the number of spatial grid points. We propose a novel DLR integrator, called the XL integrator, which reduces the number of steps compared to the available alternatives (such as the projector splitting or basis update & Galerkin (BUG) integrator). For a class of problems including the Boltzmann collision operator which enjoys a separation property between physical and velocity space, we further propose a specialized version of the XL integrator, called the sXL integrator. This version requires solving only one differential equation to update the low-rank factors. Furthermore, the proposed low-rank schemes are asymptotic-preserving, meaning they can capture the asymptotic fluid limit in the case of strong collisionality. Our numerical experiments demonstrate the efficiency and accuracy of the proposed methods across a wide range of regimes, from non-stiff (kinetic) to stiff (fluid).
97 MATHEMATICS AND COMPUTING↗
Semi-Lagrangian nodal discontinuous Galerkin method for the BGK model
In this work, we propose a semi-Lagrangian (SL) nodal discontinuous Galerkin (DG) solver for the BGK equation. The BGK model was introduced by Bhatnagar, Gross, and Krook [1] as a relaxation model for the fundamental Boltzmann equation [5], which describes the kinetic dynamic of rarefied gases with a probability distribution function. The challenges of designing efficient numerical schemes for the Boltzmann equation mainly come from its high dimensionality and complicated nonlinear collision operator. The BGK model gains interests since it has much lower computational cost, due to the relatively simple structure of the relaxation operator in replacement of the collision operator, while simultaneously preserving several important physical properties, such as macroscopic quantities and dissipation of entropy.
97 MATHEMATICS AND COMPUTING↗
Multi-species collisions for delta-f gyrokinetic simulations: Implementation and verification with GENE
A multi-species linearized collision operator based on the model developed by Sugama et al. has been implemented in the nonlinear gyrokinetic code, GENE. Such a model conserves particles, momentum, and energy to machine precision, and is shown to have negative definite free energy dissipation characteristics, satisfying Boltzmann’s H-theorem, including for realistic mass ratio. Finite Larmor Radius (FLR) effects have also been implemented into the local version of the code. For the global version of the code, the collision operator has been developed to allow for block-structured velocity space grids, allowing for computationally tractable collisional global simulations. The validity of the collision operator has been demonstrated by relaxation and conservation tests, as well as appropriate benchmarks. The newly implemented operator shall be used in future simulations to study magnetically confined fusion plasma turbulence and transport in more extreme regions with higher collisionality.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Fluid-Kinetic Coupling: Advanced Discretizations for Simulations on Emerging Heterogeneous Architectures (LDRD FY20-0643)
Plasma physics simulations are vital for a host of Sandia mission concerns, for fundamental science, and for clean energy in the form of fusion power. Sandia's most mature plasma physics simulation capabilities come in the form of particle-in-cell (PIC) models and magnetohydrodynamics (MHD) models. MHD models for a plasma work well in denser plasma regimes when there is enough material that the plasma approximates a fluid. PIC models, on the other hand, work well in lower-density regimes, in which there is not too much to simulate; error in PIC scales as the square root of the number of particles, making high-accuracy simulations expensive. Real-world applications, however, almost always involve a transition region between the high-density regimes where MHD is appropriate, and the low-density regimes for PIC. In such a transition region, a direct discretization of Vlasov is appropriate. Such discretizations come with their own computational costs, however; the phase-space mesh for Vlasov can involve up to six dimensions (seven if time is included), and to apply appropriate homogeneous boundary conditions in velocity space requires meshing a substantial padding region to ensure that the distribution remains sufficiently close to zero at the velocity boundaries. Moreover, for collisional plasmas, the right-hand side of the Vlasov equation is a collision operator, which is non-local in velocity space, and which may dominate the cost of the Vlasov solver. The present LDRD project endeavors to develop modern, foundational tools for the development of continuum-kinetic Vlasov solvers, using the discontinuous Petrov-Galerkin (DPG) methodology, for discretization of Vlasov, and machine-learning (ML) models to enable efficient evaluation of collision operators. DPG affords several key advantages. First, it has a built-in, robust error indicator, allowing us to adapt the mesh in a very natural way, enabling a coarse velocity-space mesh near the homogeneous boundaries, and a fine mesh where the solution has fine features. Second, it is an inherently high-order, high-intensity method, requiring extra local computations to determine so-called optimal test functions, which makes it particularly suited to modern hardware in which floating-point throughput is increasing at a faster rate than memory bandwidth. Finally, DPG is a residual-minimizing method, which enables high-accuracy computation: in typical cases, the method delivers something very close to the $L^2$ projection of the exact solution. Meanwhile, the ML-based collision model we adopt affords a cost structure that scales as the square root of a standard direct evaluation. Moreover, we design our model to conserve mass, momentum, and energy by construction, and our approach to training is highly flexible, in that it can incorporate not only synthetic data from direct-simulation Monte Carlo (DSMC) codes, but also experimental data. We have developed two DPG formulations for Vlasov-Poisson: a time-marching, backward-Euler discretization and a space-time discretization. We have conducted a number of numerical experiments to verify the approach in a 1D1V setting. In this report, we detail these formulations and experiments. We also summarize some new theoretical results developed as part of this project (published as papers previously): some new analysis of DPG for the convection-reaction problem (of which the Vlasov equation is an instance), a new exponential integrator for DPG, and some numerical exploration of various DPG-based time-marching approaches to the heat equation. As part of this work, we have contributed extensively to the Camellia open-source library; we also describe the new capabilities and their usage. We have also developed a well-documented methodology for single-species collision operators, which we applied to argon and demonstrated with numerical experiments. We summarize those results here, as well as describing at a high level a design extending the methodology to multi-species operators. We have released a new open-source library, MLC, under a BSD license; we include a summary of its capabilities as well.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
A Particle Method for the Multispecies Landau Equation
Abstract The multispecies Landau collision operator describes the two-particle, small scattering angle or grazing collisions in a plasma made up of different species of particles such as electrons and ions. Recently, a structure preserving deterministic particle method (Carrillo et al. in J. Comput. Phys. 7:100066, 2020) has been developed for the single species spatially homogeneous Landau equation. This method relies on a regularization of the Landau collision operator so that an approximate solution, which is a linear combination of Dirac delta distributions, is well-defined. Based on a weak form of the regularized Landau equation, the time dependent locations of the Dirac delta functions satisfy a system of ordinary differential equations. In this work, we extend this particle method to the multispecies case, and examine its conservation of mass, momentum, and energy, and decay of entropy properties. We show that the equilibrium distribution of the regularized multispecies Landau equation is a Maxwellian distribution, and state a critical condition on the regularization parameters that guarantees a species independent equilibrium temperature. A convergence study comparing an exact multispecies Bobylev-Krook-Wu (BKW) solution to the particle solution shows approximately 2nd order accuracy. Important physical properties such as conservation, decay of entropy, and equilibrium distribution of the particle method are demonstrated with several numerical examples.
Mathematics↗
Electron kinetics in a high- Z plasmoid
The problem of the electron dynamics on a closed magnetic field line passing through a high-Z plasmoid is considered. The electron kinetic equation is integrated over bounce motion and pitch angle, reducing the independent variables to a single adiabatic invariant plus time. Integration of the full Landau self-collision operator is carried out exactly, resulting in a nonlinear integro-differential operator in the new invariant. Conservation laws and the H theorem of the integrated self-collision operator are proven. Numerical solutions of the integrated kinetic equation are obtained with a self-consistent quasineutral electric potential, given the initial condition of a cold plasmoid immersed in a hot ambient plasma. The fact that cold electrons are deeply trapped in a potential with a parabolic peak leads to exactly 3/4 the usual rate of collisional heating by the ambient plasma, independent of any other parameters.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Importance of gyrokinetic exact Fokker-Planck collisions in fusion plasma turbulence
Gyrokinetic simulations of turbulence are fundamental to understanding and predicting particle and energy loss in magnetic fusion devices. Previous works have used model collision operators with approximate field-particle terms of unknown accuracy and/or have neglected collisional finite Larmor radius effects. This research moves beyond models to demonstrate important corrections using a gyrokinetic Fokker-Planck collision operator with the exact field-particle terms, in realistic simulations of turbulence in magnetically confined fusion plasmas. The exact operator shows significant corrections for temperature-gradient-driven trapped electron mode turbulence and zonal flow damping, and for microtearing modes in a Joint European Torus pedestal under ITER-like wall conditions. Analysis of the corrections using parameter scans motivates an accurate model which closely reproduces the exact results while reducing computational demands.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Numerical schemes for a multi-species BGK model with velocity-dependent collision frequency
Here, we consider a kinetic description of multi-species gas mixture modeled with Bhatnagar-Gross-Krook (BGK) collision operators, in which the collision frequency varies not only in time and space but also with the microscopic velocity. In this model, the Maxwellians typically used in standard BGK operators are replaced by a generalization of such target functions, which are defined by a variational procedure. In this paper we present a numerical method for simulating this model, which uses an Implicit-Explicit (IMEX) scheme to minimize a certain potential function, mimicking the Lagrange functional that appears in the theoretical derivation. We show that theoretical properties such as conservation of mass, total momentum and total energy as well as positivity of the distribution functions are preserved by the numerical method, and illustrate its usefulness and effectiveness with numerical examples.
97 MATHEMATICS AND COMPUTING↗
Relativistic approach to manipulating angular distribution of charged particles via kinetic equations
Deflection angles of charged particles interacting with materials play a critical role in various plasma applications. The development of a mathematically well-posed kinetic collision operator that accounts for deflection angles of strong Coulomb interactions remains a fundamental open problem. This paper presents a relativistic method for modifying the electromagnetic field in an anisotropic and adjustable manner to manipulate a system of charged particles, specifically by the transfer of angular momentum from a superluminal wave source to particles at specific times and locations. The method provides a mechanism to influence the scattering outcomes of strong interactions by manipulating the angular distribution of particles, and thus the deflection angles of their interactions with a solid surface, without requiring detailed knowledge of the kinetic collision operator. To this end, we demonstrate how a specific type of singularity, generated by Maxwell's equations for a superluminal wave source at the boundary of the plasma, can modify the electromagnetic field in a highly directional manner. The proposed method can lead to the development of novel approaches for controlling interactions of charged particles with a material in plasma systems. Published by the American Physical Society 2025
Moini, Nima (ORCID:0009000929568824)↗
Thermodynamics and collisionality in firehose-susceptible high- β plasmas
We study the evolution of collisionless plasmas that, due to their macroscopic evolution, are susceptible to the firehose instability, using both analytic theory and hybrid-kinetic particle-in-cell simulations. We establish that, depending on the relative magnitude of the plasma β, the characteristic time scale of macroscopic evolution and the ion-Larmor frequency, the saturation of the firehose instability in high-β plasmas can result in three qualitatively distinct thermodynamic (and electromagnetic) states. By contrast with the previously identified ‘ultra-high-beta’ and ‘Alfvén-inhibiting’ states, the newly identified ‘Alfvén-enabling’ state, which is realised when the macroscopic evolution time τ exceeds the ion-Larmor frequency by a β-dependent critical parameter, can support linear Alfvén waves and Alfvénic turbulence because the magnetic tension associated with the plasma’s macroscopic magnetic field is never completely negated by anisotropic pressure forces. We characterise these states in detail, including their saturated magnetic-energy spectra. The effective collision operator associated with the firehose fluctuations is also described; we find it to be well approximated in the Alfvén-enabling state by a simple quasi-linear pitch-angle scattering operator. The box-averaged collision frequency is ν eff ∼ β/τ, in agreement with previous results, but certain subpopulations of particles scatter at a much larger (or smaller) rate depending on their velocity in the direction parallel to the magnetic field. Our findings are essential for understanding low-collisionality astrophysical plasmas including the solar wind, the intracluster medium of galaxy clusters and black hole accretion flows. We show that all three of these plasmas are in the Alfvén-enabling regime of firehose saturation and discuss the implications of this result.
astrophysical plasmas↗
Quasilinear modelling of collisional trapped electron modes
The simplification of collision operators is necessary for quasilinear turbulence modelling used with integrated modelling frameworks, such as the gyrokinetic code QuaLiKiz. The treatment of collisions greatly impacts the accuracy of trapped electron mode (TEM) modelling, which is necessary to predict the electron heat flux and the balance between inward and outward particle fluxes. In particular, accurate particle flux predictions are necessary to successfully model density peaking in the tokamak core. We explored two ways of improving collisional TEM model reduction for tokamak core plasmas. First, we carried out linear GENE simulations to study the complex interplay between collisions and trapped electrons. We then used these simulations to define an effective trapped fraction to characterize the collisional TEM based on two key parameters, the local inverse-aspect ratio $\epsilon$ and the collisionality $\nu ^\ast$. One aspect missing from analytical TEM research is that the collisional frequency and the bounce-transit frequency are both velocity dependent; this effective trapped fraction takes both into account. In doing so, we determined that two parameters are not enough to model the collisional TEM, as an additional third free parameter was necessary. We determined that this model, as currently formulated, is not suitable for integrated modelling purposes. Second, we directly improved QuaLiKiz's Krook operator, which relies on two free parameters. We determined that these parameters required adjustments against higher-fidelity collisional models. In order to improve density profile predictions when paired with integrated models, we refined the Krook operator by using GENE simulations as a higher-fidelity point of comparison. We then demonstrate strong improvement of density peaking predictions of QuaLiKiz within the integrated modelling framework JETTO.
fusion plasma↗
Acceleration mechanisms of energetic ion debris in laser-driven tin plasma EUV sources
Laser-driven tin plasmas are driving new-generation nanolithography as sources of extreme ultraviolet (EUV) radiation centered at 13.5 nm. A major challenge facing industrial EUV source development is predicting energetic ion debris produced during the plasma expansion that may damage the sensitive EUV channeling multilayer optics. Gaining a detailed understanding of the plasma dynamics and ion acceleration mechanisms in these sources could provide critical insights for designing debris mitigation strategies in future high-power EUV sources. Here, we develop a fully kinetic model of tin-EUV sources using one-dimensional particle-in-cell simulations to study ion debris acceleration, which will be valuable for cross-validation of radiation-hydrodynamic simulations. An inverse-bremsstrahlung heating operator is used to model the interaction of a tin target with an Nd:YAG laser, and thermal conduction is included through a Monte Carlo Coulomb collision operator. While the large-scale evolution is in reasonable agreement with analogous hydrodynamic simulations, the significant timescale for collisional equilibration between electrons and ions allows for the development of prominent two-temperature features. A collimated flow of energetic ions is produced with a spectrum that is significantly enhanced at high energies compared to fluid simulations. The dominant acceleration mechanism is found to be a large-scale electric field supported mainly by the electron pressure gradient, which is enhanced in the kinetic simulations due to the increased electron temperature. We discuss the implications of these results for future modeling of tin-EUV sources and the development of debris mitigation schemes.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
The collisional particle-in-cell method for the Vlasov–Maxwell–Landau equations
We introduce an extension of the particle-in-cell method that captures the Landau collisional effects in the Vlasov–Maxwell–Landau equations. The method arises from a regularisation of the variational formulation of the Landau equation, leading to a discretisation of the collision operator that conserves mass, charge, momentum and energy, while increasing the (regularised) entropy. The collisional effects appear as a fully deterministic effective force, thus the method does not require any transport–collision splitting. The scheme can be used in arbitrary dimension, and for a general interaction, including the Coulomb case. We validate the scheme on scenarios such as the Landau damping, the two-stream instability and the Weibel instability, demonstrating its effectiveness in the numerical simulation of plasma.
Bailo, Rafael (ORCID:0000000180183799)↗
Landau Modes are Eigenmodes of Stellar Systems in the Limit of Zero Collisions
Abstract We consider the spectrum of eigenmodes in a stellar system dominated by gravitational forces in the limit of zero collisions. We show analytically and numerically using the Lenard–Bernstein collision operator that the Landau modes, which are not true eigenmodes in a strictly collisionless system (except for the Jeans unstable mode), become part of the true eigenmode spectrum in the limit of zero collisions. Under these conditions, the continuous spectrum of true eigenmodes in a collisionless system, also known as the Case–van Kampen modes, is eliminated. Furthermore, because the background distribution function in a weakly collisional system can exhibit significant deviations from a Maxwellian distribution function over long times, we show that the spectrum of Landau modes can change drastically even in the presence of slight deviations from a Maxwellian, primarily through the appearance of weakly damped modes that may be otherwise heavily damped for a Maxwellian distribution. Our results provide important insights for developing statistical theories to describe thermal fluctuations in a stellar system, which are currently a subject of great interest for N -body simulations as well as observations of gravitational systems.
79 ASTRONOMY AND ASTROPHYSICS↗
Conservative DG method for the micro-macro decomposition of the Vlasov–Poisson–Lenard–Bernstein model
The micro-macro (mM) decomposition approach is considered for the numerical solution of the Vlasov– Poisson–Lenard–Bernstein (VPLB) system, which is relevant for plasma physics applications. In the mM approach, the kinetic distribution function is decomposed as $f$ = $\mathscr{E}$[$ρ_f$] + g , where $\mathscr{E}$ is a local equilibrium distribution, depending on the macroscopic moments $ρ_f$ = $∫_{\mathbb{R}}$ $efdv$ = $\langle$$ef$$\rangle$$_{\mathbb{R}}$, where e = (1, $v$, $\frac{1}{2}$ $v^2$) T , and $g$, the microscopic distribution, is defined such that $\langle$$eg$$\rangle$$_{\mathbb{R}}$ = 0. We aim to design numerical methods for the mM decomposition of the VPLB system, which consists of coupled equations for $ρ_f$ and $g$. To this end, we use the discontinuous Galerkin (DG) method for phase-space discretization, and implicit-explicit (IMEX) time integration, where the phase-space advection terms are integrated explicitly and the collision operator is integrated implicitly. We give special consideration to ensure that the resulting mM method maintains the $\langle$$eg$$\rangle$$_{\mathbb{R}}$ = 0 constraint, which may be necessary for obtaining (i) satisfactory results in the collision dominated regime with coarse velocity resolution, and (ii) unambiguous conservation properties. The constraint-preserving property is achieved through a consistent discretization of the equations governing the micro and macro components. Here, we present numerical results that demonstrate the performance of the mM method. The mM method is also compared against a corresponding DG-IMEX method solving directly for $f$.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗