A new method that solves concurrently the multi-fluid and Maxwell's equations has been developed for plasma simulations. By calculating the stress tensor in the multi-fluid momentum equation by means of computational particles moving in a self-consistent electromagnetic field, the kinetic effects are retained while solving the multi-fluid equations. The Maxwell's and multi-fluid equations are discretized implicitly in time enabling kinetic simulations over time scales typical of the fluid simulations. The fluid-kinetic Particle-in-Cell solver has been implemented in a three-dimensional electromagnetic code, and tested against the ion cyclotron resonance and magnetic reconnection problems. The new method is a promising approach for coupling fluid and kinetic methods in a unified framework.
We investigate the performance of a hybrid plasma solver on the test problem of an ion beam. The parallel solver is based on cell centered finite differences in space, and a predictor-corrector leapfrog scheme in time. The implementation is done in the FLASH software framework. It is shown that the solver conserves energy well over time, and that the parallelization is efficient (it exhibits weak scaling).
A general dispersion-relation solver that numerically evaluates the full propagation properties of all the waves in fluid plasmas is presented. The effects of anisotropic pressure, external magnetic fields and beams, relativistic dynamics, as well as local plasma inhomogeneity are included. [Computer Physics Communications, (2013); doi: 10.1016/j.cpc.2013.10.012; code: http://cpc.cs.qub.ac.uk/summaries/AERF\_v1\_0.html]
We present a solver of 3D two-fluid plasma model for the simulation of short-pulse laser interactions with plasma. This solver resolves the equations of the two-fluid plasma model with ideal gas closure. We also include the Bhatnagar-Gross-Krook collision model. Our solver is based on PseudoSpectral Time-Domain (PSTD) method to solve Maxwell's curl equations. We use a Strang splitting to integrate Euler equations with source term: while Euler equations are solved with a composite scheme mixing Lax-Friedrichs and Lax-Wendroff schemes, the source term is integrated with a fourth-order Runge-Kutt…
MITNS (Multiple-Ion Transport Numerical Solver) is a new numerical tool designed to perform 1D simulations of classical cross-field transport in magnetized plasmas. Its detailed treatment of multi-species effects makes it a unique tool in the field. We describe the physical model it simulates, as well as its numerical implementation and performance.
We describe the implementation of kinetic solvers in 1d2v phase space using adaptive Cartesian mesh. Spherical coordinates in velocity space are used to simplify the Lorentz and Fokker-Planck collisional operators. The key capabilities of the new solvers are illustrated for electron elastic scattering, acceleration, continuous energy loss in collisions, and ionization processes in weakly-ionized plasma. We have also implemented two-stream approach to reduce computational cost for studies of gas breakdown dynamics in the presence of runaway electrons. The benefits and limitations of the non-spl…
Continuum Vlasov simulations can be utilized for highly accurate modelling of fully kinetic plasmas. Great progress has been made recently regarding the applicability of the method in realistic plasma configurations. However, a reduction of the high computational cost that is inherent to fully kinetic simulations would be desirable, especially at high velocity space resolutions. For this purpose, low-rank approximations can be employed. The so far available low-rank solvers are restricted to either electrostatic systems or low dimensionality and can therefore not be applied to most space, astr…
We describe gas dynamic and plasma effects for transient plasma jets under different conditions. Our Unified Flow Solver (UFS) is evaluated for simulations of mixed continuum-rarefied flows, transient gas expansion dynamics and collisionless plasma expansion. We identify further advances that are required for hybrid fluid-kinetic simulations of laser-ablation and EEE-induced plasma jets.
A semi-implicit finite difference time domain (FDTD) numerical Maxwell solver is developed for full electromagnetic Particle-in-Cell (PIC) codes for the simulations of plasma-based acceleration. The solver projects the volumetric Yee lattice into planes transverse to a selected axis (the particle acceleration direction) that makes the scheme quasi-one-dimensional. The scheme removes the numerical dispersion of electromagnetic waves running parallel the selected axis. The fields locations in the transverse plane are selected so that the scheme is Lorentz-invariant for relativistic transformatio…
We present a new multi-fluid, multi-temperature plasma solver with adaptive Cartesian mesh (ACM) based on a full-Newton (non-linear, implicit) scheme for collisional low-temperature plasma. The particle transport is described using the drift-diffusion approximation for electrons and ions coupled to Poisson equation for electric field. In addition, the electron-energy transport equation is solved to account for electron thermal conductivity, Joule heating, and energy loss of electrons in collisions with neutral species. The rate of electron-induced ionization is a function of electron temperatu…
A general, fast, and effective approach is developed for numerical calculation of kinetic plasma dispersion relations. The plasma dispersion function is approximated by $J$-pole expansion. Subsequently, the dispersion relation is transformed to a standard matrix eigenvalue problem of an equivalent linear system. The result is accurate for $J=8$ except the solutions that are the little interesting heavily damped modes. In contrast to conventional approaches, such as Newton's iterative method, this approach can give either all the solutions in the system or a few solutions around the initial gue…
We show feasibility and benefits of porting an adaptive multi-scale kinetic-fluid code to CPU-GPU systems. Challenges are due to the irregular data access for adaptive Cartesian mesh, vast difference of computational cost between kinetic and fluid cells, and desire to evenly load all CPUs and GPUs. Our Unified Flow Solver (UFS) combines Adaptive Mesh Refinement (AMR) with automatic cell-by-cell selection of kinetic or fluid solvers based on continuum breakdown criteria. Using GPUs enables hybrid simulations of mixed rarefied-continuum flows with a million of Boltzmann cells with 24x24x24 veloc…
A large number of model particles is shown necessary for quantitatively correct simulations of the kinetic beam-plasma instability with the clouds-in-cells method. The required number of particles scales inversely with the expected growth rate, as in the kinetic regime only a narrow interval of beam velocities is resonant with the wave.
BO-PBK: A comprehensive solver for dispersion relations of obliquely propagating waves in magnetized multi-species plasma with anisotropic loss-cone drift product-bi-kappa distribution
The asymmetrically mounted flat plasma actuator is studied using a self-consistent 2-DIM fluid model at atmospheric pressure. The computational model use the drift-diffusion approximation and a simple plasma phenomenological kinetic model. It is investigated its electrical and kinetic properties, and calculated the charged species concentrations, surface charge density, electrohydrodynamic forces and gas speed. The present computational model contributes to understand the main physical mechanisms and methods to improve its performance.
A parallel, relativistic, three-dimensional particle-in-cell code SPACE has been developed for the simulation of electromagnetic fields, relativistic particle beams, and plasmas. In addition to the standard second-order Particle-in-Cell (PIC) algorithm, SPACE includes efficient novel algorithms to resolve atomic physics processes such as multi-level ionization of plasma atoms, recombination, and electron attachment to dopants in dense neutral gases. SPACE also contains a highly adaptive particle-based method, called Adaptive Particle-in-Cloud (AP-Cloud), for solving the Vlasov-Poisson problems…
We propose an asymptotic-preserving (AP), uniformly convergent numerical scheme for the relativistic collisional Drift-Kinetic Equation (rDKE) to simulate runaway electrons in axisymmetric toroidal magnetic field geometries typical of tokamak devices. The approach is derived from an exact Green's function solution with numerical approximations of quantifiable impact, and results in a simple, two-step operator-split algorithm, consisting of a collisional Eulerian step, and a Lagrangian orbit-integration step with analytically prescribed kernels. The AP character of the approach is demonstrated …
Continuum kinetic simulations of plasmas, where the distribution function of the species is directly discretized in phase-space, permits fully kinetic simulations without the statistical noise of particle-in-cell methods. Recent advances in numerical algorithms have made continuum kinetic simulations computationally competitive. This work presents the first continuum kinetic description of high-fidelity wall boundary conditions that utilize the readily available particle distribution function. The boundary condition is realized through a reflection function that can capture a wide range of cas…
A self-consistent model is presented for the simulation of a multi-component plasma in the tokamak boundary. A deuterium plasma is considered, with the plasma species that include electrons, deuterium atomic ions and deuterium molecular ions, while the deuterium atoms and molecules constitute the neutral species. The plasma and neutral models are coupled via a number of collisional interactions, which include dissociation, ionization, charge-exchange and recombination processes. The derivation of the three-fluid drift-reduced Braginskii equations used to describe the turbulent plasma dynamics …
With the advent of PW class lasers, the very large laser intensities attainable on-target should enable the production of intense high order Doppler harmonics from relativistic laser-plasma mirrors interactions. At present, the modeling of these harmonics with Particle-In-Cell (PIC) codes is extremely challenging as it implies an accurate description of tens of harmonic orders on a a broad range of angles. In particular, we show here that standard Finite Difference Time Domain (FDTD) Maxwell solvers used in most PIC codes partly fail to model Doppler harmonic generation because they induce num…
We consider the solution of the fully kinetic (including electrons) Vlasov-Ampère system in a one-dimensional physical space and two-dimensional velocity space (1D-2V) for an arbitrary number of species with a time-implicit Eulerian algorithm. The problem of velocity-space meshing for disparate thermal and bulk velocities is dealt with by an adaptive coordinate transformation of the Vlasov equation for each species, which is then discretized, including the resulting inertial terms. Mass, momentum, and energy are conserved, and Gauss's law is enforced to within the nonlinear convergence toleran…
The current paper reports on the implementation of a numerical solver on the Graphic Processing Units (GPU) to model reactive gas mixture with detailed chemical kinetics. The solver incorporates high-order finite volume methods for solving the fluid dynamical equations coupled with stiff source terms. The chemical kinetics are solved implicitly via an operator-splitting method. We explored different approaches in implementing a fast kinetics solver on the GPU. The detail of the implementation is discussed in the paper. The solver is tested with two high-order shock capturing schemes: MP5 (Sure…
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…
Force-free plasmas are a good approximation where the plasma pressure is tiny compared with the magnetic pressure, which is the case during the cold vertical displacement event (VDE) of a major disruption in a tokamak. On time scales long compared with the transit time of Alfven waves, the evolution of a force-free plasma is most efficiently described by the quasi-static magnetohydrodynamic (MHD) model, which ignores the plasma inertia. Here we consider a regularized quasi-static MHD model for force-free plasmas in tokamak disruptions and propose a mimetic finite difference (MFD) algorithm. Th…
The advent of massively parallel supercomputers, with their distributed-memory technology using many processing units, has favored the development of highly-scalable local low-order solvers at the expense of harder-to-scale global very high-order spectral methods. Indeed, FFT-based methods, which were very popular on shared memory computers, have been largely replaced by finite-difference (FD) methods for the solution of many problems, including plasmas simulations with electromagnetic Particle-In-Cell methods. For some problems, such as the modeling of so-called "plasma mirrors" for the gener…
There are many astrophysical and laboratory scenarios where kinetic effects play an important role. These range from astrophysical shocks and plasma shell collisions, to high intensity laser-plasma interactions, with applications to fast ignition and particle acceleration. Further understanding of these scenarios requires detailed numerical modelling, but fully relativistic kinetic codes are computationally intensive, and the goal of one-to-one direct modelling of such scenarios and direct comparison with experimental results is still difficult to achieve. In this paper we discuss the issues i…
A dynamic mode decomposition (DMD) based reduced-order model (ROM) is developed for tracking, detection, and prediction of kinetic plasma behavior. DMD is applied to the high-fidelity kinetic plasma model based on the electromagnetic particle-in-cell (EMPIC) algorithm to extract the underlying dynamics and key features of the model. In particular, the ability of DMD to reconstruct the spatial pattern of the self electric field from high-fidelity data and the effect of DMD extrapolated self-fields on charged particle dynamics are investigated. An in-line sliding-window DMD method is presented f…
In this study, a species-clustered ordinary differential equations (ODE) solver for chemical kinetics with large detailed mechanisms based on operator-splitting is presented. The ODE system is split into clusters of species by using graph partition methods which has been intensively studied in areas of model reduction, parameterization and coarse-graining, etc. , such as diffusion maps based on the concept of Markov random walk. Definition of the weight (similarity) matrix is application-driven and according to chemical kinetics. Each cluster of species is then integrated by VODE, an implicit …
Ergodic LLC（Ergodic有限责任公司）；University of Michigan（密歇根大学）
Plasma supports collective modes and particle-wave interactions that leads to complex behavior in inertial fusion energy applications. While plasma can sometimes be modeled as a charged fluid, a kinetic description is useful towards the study of nonlinear effects in the higher dimensional momentum-position phase-space that describes the full complexity of plasma dynamics. We create a differentiable solver for the plasma kinetics 3D partial-differential-equation and introduce a domain-specific objective function. Using this framework, we perform gradient-based optimization of neural networks th…
We present a new approach to find accurate solutions to the Poisson equation, as obtained from the steady-state limit of a diffusion equation with strong source terms. For this purpose, we start from Boltzmann's kinetic theory and investigate the influence of higher order terms on the resulting macroscopic equations. By performing an appropriate expansion of the equilibrium distribution, we provide a method to remove the unnecessary terms up to a desired order and show that it is possible to find, with high level of accuracy, the steady-state solution of the diffusion equation for sizeable Knu…
This paper describes the main features of a pioneering unsteady solver for simulating ideal two-fluid plasmas on unstructured grids, taking profit of GPGPU (General-purpose computing on graphics processing units). The code, which has been implemented within the open source COOLFluiD platform, is implicit, second-order in time and space, relying upon a Finite Volume method for the spatial discretization and a three-point backward Euler for the time integration. In particular, the convective fluxes are computed by a multi-fluid version of the AUSM+up scheme for the plasma equations, in combinati…
Effects induced by the finite number $N$ of particles on the evolution of a monochromatic electrostatic perturbation in a collisionless plasma are investigated. For growth as well as damping of a single wave, discrete particle numerical simulations show a $N$-dependent long time behavior which differs from the numerical errors incurred by vlasovian approaches and follows from the pulsating separatrix crossing dynamics of individual particles.
In this paper, the unified gas-kinetic wave-particle (UGKWP) method has been constructed on three-dimensional unstructured mesh with parallel computing for multiscale flow simulation. Following the direct modeling methodology of the unified gas-kinetic scheme (UGKS), the UGKWP method models the flow dynamics uniformly in different regime and gets the local cell's Knudsen number dependent numerical solution directly without the requirement of kinetic scale cell resolution. The UGKWP method is composed of evolution of deterministic wave and stochastic particles. With the dynamic wave-particle de…
