Accurate modeling of heat flux in inertial confinement fusion plasmas requires closures that remain predictive far from local equilibrium and across disparate spatial and temporal resolutions. We develop a resolution-independent machine-learning heat flux closure trained on particle-in-cell simulations using a Fourier Neural Operator. Two nonlocal electron thermal conduction models are trained and tested. When embedded self-consistently into the electron energy equation, the learned closure faithfully reproduces the temperature evolution and shows good temporal extrapolation and generalization capability. Remarkably, models trained on coarse-resolution data accurately predict heat flux when deployed in substantially finer-resolution implicit, iterative solvers of the energy equation, significantly enhancing the practicality of embedding data-driven closures into partial differential equation solvers. These results establish a data-driven closure that bridges kinetic and fluid descriptions and provides a viable pathway for treating machine learning as an iterative solver within the radiation-hydrodynamic simulations of ICF plasma.
In this paper we study the influence of the magnetised thermal conductivity on the propagation of a nanosecond $10^{14} \mathrm{Wcm}^{-2}$ laser in an underdense plasma by performing simulations of a paraxial model laser in a plasma with the full Braginskii magnetised transport coefficients. Analytic theory and simulations show the shortening of the self-focal length of a laser beam in a plasma as a result of the reduction of the plasma thermal conductivity in a magnetic field. Furthermore the filamentation of a laser via the thermal mechanism is found to have an increased spatial growth rate …
Investigation of Laser Plasma Instabilities driven by Coupled High-Power Laser Beams in Magnetized Underdense Plasmas
University of Bordeaux（波尔多大学）；INRS EMT（国家研究研究所电磁学与技术中心）；Laboratoire pour l’Utilisation des Lasers Intenses, UMR 7605 CNRS-CEA-École Polytechnique- Université Paris VI（高强度激光利用实验室）；CNRS, LNCMI, Univ Toulouse 3, INSA Toulouse, Univ Grenoble Alpes, EMFL（法国国家科学研究中心低磁场强电流实验室）；ELI-NP, ”Horia Hulubei” National Institute for Physics and Nuclear Engineering（极高性能激光设施-核物理与工程霍里亚·胡卢贝伊国家研究所）；Sorbonne Université, Observatoire de Paris, Université PSL（索邦大学、巴黎天文台、巴黎文理研究大学）
The genesis of the ion axial velocity distribution function (VDF) is analyzed for collisionless Hall thruster discharges. An analytical form for the VDF is obtained from the Vlasov equation, by applying the Tonks-Langmuir theory in the thruster channel, under the simplifying assumptions of monoenergetic creation of ions and steady state. The equivalent set of 1D unsteady anisotropic moment equations is derived from the Vlasov equation, and simple phenomenological closures are formulated, assuming a polynomial shape for the ions VDF. The analytical results and the anisotropic moment equations a…
Recent efforts to include kinetic effects in fluid simulations of plasmas have been very promising. Concerning collisionless magnetic reconnection, it has been found before that damping of the pressure tensor to isotropy leads to good agreement with kinetic runs in certain scenarios. An accurate representation of kinetic effects in reconnection was achieved in a study by Wang et al. (Phys. Plasmas, volume 22, 2015, 012108) with a closure derived from earlier work by Hammett and Perkins (PRL, volume 64, 1990, 3019). Here, their approach is analyzed on the basis of heat flux data from a Vlasov s…
Counter-streaming heat-flux closure for electron-only collisionless magnetic reconnection
University of California, Los Angeles（加州大学洛杉矶分校）；Massachusetts Institute of Technology（麻省理工学院）；University of Maryland, College Park（马里兰大学帕克分校）；Universidade de Lisboa（里斯本大学）
A Fokker-Planck model for the interaction of fast ions with the thermal electrons in a quasi-neutral plasma is developed. When the fast ion population has a net flux (i.e. the distribution of the fast ions is anisotropic in velocity space) the electron distribution function is significantly perturbed from Maxwellian by collisions with the fast ions, even if the fast ion density is orders of magnitude smaller than the electron density. The Fokker-Planck model is used to derive classical electron transport equations (a generalized Ohm's law and a heat flow equation) that include the effects of t…
Ion parallel closures are obtained for arbitrary atomic weights and charge numbers. For arbitrary collisionality, the heat flow and viscosity are expressed as kernel-weighted integrals of the temperature and flow-velocity gradients. Simple, fitted kernel functions are obtained from the 1600 parallel moment solution and the asymptotic behavior in the collisionless limit. The fitted kernel parameters are tabulated for various temperature ratios of ions to electrons. The closures can be used conveniently without solving the kinetic equation or higher order moment equations in closing ion fluid eq…
A Neural Operator Closure for Landau Damping in Electrostatic Plasma
Queen Mary University of London（伦敦大学玛丽女王学院）；University of Colorado, Boulder（科罗拉多大学博尔德分校）；Institute for Plasma Science and Technology, Consiglio Nazionale delle Ricerche（意大利国家研究委员会等离子科学与技术研究所）
Simulations of large-scale plasma systems are typically based on a fluid approximation approach. These models construct a moment-based system of equations that approximate the particle-based physics as a fluid, but as a result lack the small-scale physical processes available to fully kinetic models. Traditionally, empirical closure relations are used to close the moment-based system of equations, which typically approximate the pressure tensor or heat flux. The more accurate the closure relation, the stronger the simulation approaches kinetic-based results. In this paper, new closure terms ar…
A fluid description for collisionless magnetized plasmas that takes into account the effect of cyclotron resonance has been developed. Following the same approach as the Landau fluid closure, the heat flux components associated with transverse electromagnetic fluctuations are approximated by a linear combination of lower-order moments in wavenumber space. The closure successfully reproduces the linear cyclotron resonance for electromagnetic waves propagating parallel to the ambient magnetic field. In the presence of finite temperature anisotropy, the model gives approximately correct predictio…
A two-fluid model is derived from the plasma kinetic equations using the moment model reduction method. The moment method we adopt was recently developed with a globally hyperbolic regularization where the moment model attained is locally well-posed in time. Based on the hyperbolic moment model with well-posedness, the Maxwellian iteration method is utilized to get the closure relations for the resulted two-fluid model. By taking the Shakhov collision operator in the Maxwellian iteration, the two-fluid model inherits the correct Prandtl number from the plasma kinetic equations. The new model i…
We consider a reduced dynamics for the first four fluid moments of the onedimensional Vlasov-Poisson equation, namely, the fluid density, fluid velocity, pressure and heat flux. This dynamics depends on an equation of state to close the system. This equation of state (closure) connects the fifth order moment-related to the kurtosis in velocity of the Vlasov distribution-with the first four moments. By solving the Jacobi identity, we derive an equation of state which ensures that the resulting reduced fluid model is Hamiltonian. We show that this Hamiltonian closure allows symmetric homogeneous…
A baffled Snowflake Minus Low-Field Side (SF-LFS) is geometrically-optimised in TCV, increasing divertor neutral pressure, to evaluate the roles of divertor closure (comparing with an unbaffled SF-LFS) and magnetic geometry (comparing with a baffled Single Null, SN) in power exhaust and core-divertor compatibility. Ohmically-heated L-mode discharges in deuterium, with a line-averaged core density of approximately 4x10(19) m-3, are seeded with nitrogen to approach detached conditions. Baffles in the SF-LFS configuration are found to reduce the peak outer target heat flux by up to 23%, without s…
We report on the first steady-state simulations of strong plasma shocks with fully kinetic ions and electrons, independently confirmed by two fully kinetic codes (an Eulerian continuum and a Lagrangian particle-in-cell). While kinetic electrons do not fundamentally change the shock structure as compared with fluid electrons, we find an appreciable rearrangement of the preheat layer, associated with nonlocal electron heat transport effects. The electron heat flux profile qualitatively agrees between kinetic and fluid electron models, suggesting a certain level of "stiffness", though substantial…
We study the validity of the time-dependent asymptotic $P_N$ approximation in radiative transfer of photons. The time-dependent asymptotic $P_N$ is an approximation which uses the standard $P_N$ equations with a closure that is based on the asymptotic solution of the exact Boltzmann equation for a homogeneous problem, in space and time. The asymptotic $P_N$ approximation for radiative transfer requires careful treatment regarding the closure equation. Specifically, the mean number of particles that are emitted per collision ($ω_{\mathrm{eff}}$) can be larger than one due to inner or outer radi…
We study the effects of heat flows and velocity shear on the parallel firehose instability in weakly collisional plasma flow. For this purpose we apply an anisotropic 16-moments MHD fluid closure model that takes into account the pressure and temperature anisotropy, as well as the effect of anisotropic heat flux. The linear stability analysis of the firehose modes is carried out in the incompressible limit, where the MHD flow is parallel to the background magnetic field, while the velocity is sheared in the direction transverse to the flow direction. It seems that an increase of the velocity s…
Recently the drift-reduced Landau fluid six-field turbulence model within the BOUT++ framework has been upgraded. In particular, this new model employs a new normalization, adds a volumetric flux-driven source option, the Landau fluid closure for parallel heat flux and a Laplacian inversion solver which is able to capture n=0 axisymmetric mode evolution in realistic tokamak configurations. These improvements substantially extended model's capability to study a wider range of tokamak edge phenomena, and are essential to build a fully self-consistent edge turbulence model capable of both transie…
Based on a 14-moment closure for non-resistive (general-) relativistic viscous plasmas, we describe a new numerical scheme that is able to handle all first-order dissipative effects (heat conduction, bulk and shear viscosities), as well the anisotropies induced by the presence of magnetic fields. The latter is parameterized in terms of a thermal gyrofrequency or, equivalently, a thermal Larmor radius and allows to correctly capture the thermal Hall effect. By solving an extended Israel-Stewart-like system for the dissipative quantities that enforces algebraic constraints via stiff-relaxation, …
