Kinetic simulation technique for plasma flow in strong external magnetic field
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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.
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.
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.
Numerical simulations of the weak beam-plasma instability were done in the turbulent regime where small-scale trapping is a dominant feature of the instability, a regime with behavior not predicted by quasi-linear theory. The results of the simulations were compared with those of a specific model of the turbulence, the so-called 'turbulent trapping' model, which gives precise formulas for the particle correlation functions, and predicts a growth rate well enhanced over the quasi-linear value. It was found that the model gives accurate predictions for the correlation functions. On the other hand, while growth rates were enhanced over the quasi-linear values, the enhancements observed are smaller than expected from the quantitative predictions of the model.
In this report we discuss the ion velocity distribution dynamics from the 3D hybrid simulation. In our model the background, pickup, and ionospheric ions are considered as a particles, whereas the electrons are described as a fluid. Inhomogeneous photoionization, electron-impact ionization and charge exchange are included in our model. We also take into account the collisions between the ions and neutrals. The current simulation shows that mass loading by pickup ions H(+); H2(+), CH4(+) and N2(+) is stronger than in the previous simulations when O+ ions are introduced into the background plasma. In our hybrid simulations we use Chamberlain profiles for the atmospheric components. We also include a simple ionosphere model with average mass M = 28 amu ions that were generated inside the ionosphere. The moon is considered as a weakly conducting body. Special attention will be paid to comparing the simulated pickup ion velocity distribution with CAPS T9 observations. Our simulation shows an asymmetry of the ion density distribution and the magnetic field, including the formation of the Alfve n wing-like structures. The simulation also shows that the ring-like velocity distribution for pickup ions relaxes to a Maxwellian core and a shell-like halo.
Ion-driven destabilization of a toroidal electron plasma in a small aspect ratio axisymmetric toroidal device is reported for A r + ions of different initial density values using a high fidelity 3D3V PIC solver. Stability of a recently discovered quiescent quasi-steady state (QQS) of a toroidal electron plasma obtained from “seed” solution as a result of entropy extremization at zero inertia is addressed in the presence of a small ion population. An initial value (f0) of the ion fraction (f = n i / n e) and the corresponding secondary electrons are “preloaded” into the system after the electron plasma attains a QQS state. This procedure is regarded as a proxy to the conventional production of ions in the experimental devices via impact ionization. The resulting electron plasma exhibits destabilized “center of charge motion” (m = 1) along with higher order harmonics with dominant power in the second harmonic. Gradual loss of ions (and also electrons) is observed resulting in time varying f values. Beyond a certain value of f0 (≥ 0.005), growth in wall probe current is observed, which saturates at later simulation time due to the loss of particles. In conclusion, trajectories of ion particles indicate ion trapping in the potential well, which is qualitatively similar to the ion resonance instability in pure electron plasmas.
The gyrokinetic particle simulation is a powerful tool for studies of transport, nonlinear phenomenon, and energetic particle physics in tokamak plasmas. While most gyrokinetic simulations make use of the scalar and vector potentials, a new model (GK-E&B) has been developed by using the E and B field in a general form and has been implemented in simulating kinetic Alfvén waves in uniform plasma. In our work, the Chen et al. GK-E&B model has been expressed, in general, tokamak geometry using the local orthogonal coordinates and general tokamak coordinates. Its reduction for uniform plasma is verified, and the numerical results show good agreement with the original work. The theoretical dispersion relation and numerical results in the local model in screw pinch geometry are also in excellent agreement. Numerical results show excellent performance in a realistic parameter regime of burning plasmas with high values of β/(M e k$^{2}_{⊥}$ρ$^{2}_{i}$), which is a challenge for traditional methods due to the “cancellation” problem. As one application, the GK-E&B model is implemented with kinetic electrons in the local single flux surface limit. With the matched International Tokamak Physics Activity-Toroidicity-induced Alfvén Eigenmodes parameters adopted, numerical results show the capability of the GK-E&B in treating the parallel electron Landau damping for realistic tokamak plasma parameters. As another application, the global GK-E&B model has been implemented with the dominant electron contribution in the cold electron limit. Its capability in simulating the finite E || due to the finite electron mass is demonstrated.
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A new technology for developing fusion energy is to use hydrogen isotopes i.e., deuterium (D) and tritium (T) which is a combine effort for building up of International Thermonuclear Reactor (ITER) named as Tokamak, which will come into operation in 2020. Handsome amount of work has already been done by many researchers contingent with plasma shape, halo current and plasma equilibrium properties by numerical techniques. Halo current calculation is the most important work in fusion reactors. In this paper, we have calculated halo current and plasma cross-section energy. The research covers calculation of plasma energy and determines the force on the vessel by magnetic field transformation method, which is the essential part of calculating halo current. Further, we have developed VDE up/down halo current models. These models give total magnetic field, asymmetric forces, conducting points and poloidal halo current. Confined plasma by magnetic field is considered to be an abundant and durable source of energy for future aspects. In this paper, plasma magnetic field of each cross section was calculated by using energy integral. Transformation method has been successfully applied which provides the connection between major sideways forces acting on the plasma. Theoretical investigation and analyses of halo current have successfully been done. Two observations were analyzed, large ratio of halo current during VDE down and cancellation of specific forces at conducting point. The results obtained will be useful for equalizing the simulation and experimental results. The research will be extended to developed new models for future fusion research. (authors)