Particle-in-cell Simulations of Decaying Plasma Turbulence: Linear Instabilities versus Nonlinear Processes in 3D and 2.5D Approximations
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The goal of the present work is to better understand and develop a predictive capability for when approaching and crossing a MHD linear instability boundary leads to a thermal quench and subsequent disruption (hard limit), and when it just leads to increased transport or small amplitude oscillations(soft). Understanding the difference between hard and soft limits is crucial for effective disruption prediction and avoidance. We present several examples of both hard and soft beta limits.
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Gyrokinetic simulations of the fishbone instability in DIII-D tokamak plasmas find that self-generated zonal flows can dominate the nonlinear saturation by preventing coherent structures from persisting or drifting in the energetic particle phase space when the mode frequency down-chirps. Results from the simulation with zonal flows agree quantitatively, for the first time, with experimental measurements of the fishbone saturation amplitude and energetic particle transport. Moreover, the fishbone-induced zonal flows are likely responsible for the formation of an internal transport barrier that was observed after fishbone bursts in this DIII-D experiment. Finally, gyrokinetic simulations of a related ITER baseline scenario show that the fishbone induces insignificant energetic particle redistribution and may enable high performance scenarios in ITER burning plasma experiments. Published by the American Physical Society 2024
The final technical report for project DE‐FG02‐08ER54954 “Gyrokinetic Simulation of Tokamak Fusion Plasmas”. This report covers the entire period of the sponsored project. This grant supported in part the salary, travel, and research supplies for the principal investigator Scott E. Parker, graduate research associate Stefan Tirkas, who is a Ph.D. graduate student in the Physics Department. Postdoctoral Scholar Dr. Neeraj Kumar is also collaborating on this project. The main goals of the project are to investigate the nonlinear saturation of electron scale turbulence using gyrokinetic theory and simulation and to investigate impurity transport in the edge pedestal region.
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.
We describe a simple practical numerical method for simulating plasma driven within a vacuum chamber by a pulsed power generator. Typically, in this type of simulation, the vacuum region adjacent to the plasma is approximated as a highly resistive, light fluid; this involves computationally expensive solvers describing the diffusion of the magnetic field through this fluid. Instead, we provide a recipe for coupling pulsed power generators to the magnetohydrodynamics (MHD) domain by approximating the perfectly insulating vacuum as a light, perfectly conducting, inviscid MHD fluid and discuss the applicability of this counter-intuitive technique. This much more affordable ideal MHD representation is particularly useful in situations where a plasma exhibits interesting three-dimensional phenomena, either due to the design of the experiment or due to developing instabilities. We verified that this coupling recipe works by modeling an exactly solvable flux compression generator as well as a self-similar Noh-like solution and demonstrated convergence to the theoretical solution. We also showed examples of simulating complex three-dimensional pulsed power devices with this technique. We release our code implementation to the public.
A one-dimensional electronegative plasma situated between two symmetrical parallel electrodes under DC bias is studied by Particle-In-Cell simulation with Monte Carlo Collisions. By varying the electronegativity {alpha}{identical_to}n{sub -}/n{sub e} from the limit of electron-ion plasmas (negative ion free) to ion-ion plasmas (electron free), the sheaths formation, the negative ion flux flowing towards the electrodes, and the particle velocities at the sheath edges are investigated. Depending on {alpha}, it is shown that the electronegative plasma behavior can be described by four regimes. In the lowest regime of {alpha}, i.e., {alpha} < 50, negative ions are confined by two positive sheaths within the plasma, while in the higher regimes of {alpha}, a negative sheath is formed and the negative ion flux can be extracted from the bulk plasma. In the two intermediate regimes of {alpha}, i.e., 50 < {alpha} < 10{sup 5}, both the electron and the negative ion fluxes are involved in the neutralization of the positive ions flux that leaves the plasma. In particular, we show that the velocity of the negative ions entering the negative sheath is affected by the presence of the electrons, and is not given by the modified Bohm velocity generally accepted for electronegative plasmas. For extremely high electronegativity, i.e., {alpha} > 10{sup 5}, the presence of electrons in the plasma is marginal and the electronegative plasma can be considered as an ion-ion plasma (electron free).
A 3-dimensional particle-in-cell/Monte Carlo collision simulation that is fully implemented on a graphics processing unit (GPU) is described and used to determine low-temperature plasma characteristics at high reduced electric field, E/n, in nitrogen gas. Details of implementation on the GPU using the NVIDIA Compute Unified Device Architecture framework are discussed with respect to efficient code execution. The software is capable of tracking around 10 × 10{sup 6} particles with dynamic weighting and a total mesh size larger than 10{sup 8} cells. Verification of the simulation is performed by comparing the electron energy distribution function and plasma transport parameters to known Boltzmann Equation (BE) solvers. Under the assumption of a uniform electric field and neglecting the build-up of positive ion space charge, the simulation agrees well with the BE solvers. The model is utilized to calculate plasma characteristics of a pulsed, parallel plate discharge. A photoionization model provides the simulation with additional electrons after the initial seeded electron density has drifted towards the anode. Comparison of the performance benefits between the GPU-implementation versus a CPU-implementation is considered, and a speed-up factor of 13 for a 3D relaxation Poisson solver is obtained. Furthermore, a factor 60 speed-up is realized for parallelization of the electron processes.
External biasing of the Large Plasma Device (LAPD) and its impact on plasma flows and turbulence are explored for the first time in 3D simulations using the Global Braginskii Solver code. Without external biasing, the LAPD plasma spontaneously rotates in the ion diamagnetic direction. The application of a positive bias increases the plasma rotation in the simulations, which show the emergence of a coherent Kelvin Helmholtz (KH) mode outside of the cathode edge with poloidal mode number m≃6. Negative biasing reduces the rotation in the simulations, which exhibit KH turbulence modestly weaker than but otherwise similar to unbiased simulations. Biasing either way, but especially positively, forces the plasma potential inside the cathode edge to a spatially constant, KH-stable profile, leading to a more quiescent core plasma than the unbiased case. A moderate increase in plasma confinement and an associated steepening of the profiles are seen in the biasing runs. The simulations thus show that the application of external biasing can improve confinement while also driving a Kelvin-Helmholtz instability. Ion-neutral collisions have only a weak effect in the biased or unbiased simulations.
One of the main challenges in the increase of luminosity of circular colliders is the control of the beam-beam effect. In the process of exploring beam-beam mitigation methods using plasma, we evaluated the possibility of plasma generation via ionization of neutral gas by proton beams, and performed highly resolved simulations of the beam-plasma interaction using SPACE, a 3D electromagnetic particle-in-cell code. The process of plasma generation is modelled using experimentally measured cross-section coefficients and a plasma recombination model that takes into account the presence of neutral gas and beam-induced electromagnetic fields. Numerically simulated plasma oscillations are consistent with theoretical analysis. In the beam-plasma interaction process, high-density neutral gas reduces the mean free path of plasma electrons and their acceleration. A numerical model for the drift speed as a limit of plasma electron velocity was developed. Simulations demonstrate a significant reduction of the beam electric field in the presence of plasma. Preliminary simulations using fully-ionized plasma have also been performed and compared with the case of beam-induced plasma.
Equilibrium molecular dynamics simulations are used to calculate the thermal conductivity of the onecomponent plasma via the Green-Kubo formalism over a broad range of Coulomb coupling strength, 0.1 ≤ Γ ≤180. These simulations address previous discrepancies between computations using equilibrium versus nonequilibrium methods. Analysis of heat flux autocorrelation functions show that very long (6×10 5 $ω^{-1}_{p}$) time series are needed to reduce the noise level to allow ≲2% accuracy. The simulations provide accurate data for Γ ≲ 1. Furthermore, this enables a test of the traditional Landau-Spitzer theory, which is found to agree with the simulations for Γ ≲ 0.3. It also enables tests of theories to address moderate and strong Coulomb coupling. Two are found to provide accurate extensions to the moderate coupling regime of Γ ≲ 10, but none are accurate in the Γ ≳ 10 regime where potential energy transport and coupling between mass flow and stress dominate thermal conduction.
The effect of a pressure gradient (∼133 Pa–0.133 Pa) on electron and ion energy distributions in a radiofrequency (rf at 13.56 MHz) argon plasma jet is studied using a 1D-3v Particle In Cell (PIC) simulation. The PIC domain is three times that of the 0.018 m long plasma cavity and the total simulation time is 1 ms. Ion heating and acceleration up to a drift velocity about 2000 m s{sup −1} are measured along the jet's main expansion axis. Elastic and charge exchange ion-neutral collisions histograms computed at equilibrium during 0.74 ms show that charge exchange collisions act as the main neutral heating mechanism.