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Predictive simulations of heat and particle fluxes in the plasma boundary are a critical missing capability for magnetic fusion energy power plant design.
Generative deep learning techniques are employed in a novel framework for the construction of surrogate models capturing the spatiotemporal dynamics of 2D plasma turbulence. The proposed Generative Artificial Intelligence Turbulence (GAIT) framework enables the acceleration of turbulence simulations for long-time transport studies. GAIT leverages a convolutional variational auto-encoder and a recurrent neural network to generate new turbulence data from existing simulations, extending the time horizon of transport studies with minimal computational cost. The application of the GAIT framework to plasma turbulence using the Hasegawa–Wakatani (HW) model is presented, evaluating its performance via various analyses. Very good agreement is found between the GAIT and the HW models in the spatiotemporal Fourier and Proper Orthogonal Decomposition spectra, the flow topology characterized by the Okubo–Weiss parameter, and the time autocorrelation function of turbulent fluctuations. Excellent agreement has also been obtained in the probability distribution function of particle displacements and the effective turbulent diffusivity. In-depth analyses of the latent space of turbulent states, choice of hyperparameters and alternative deep learning models for the time prediction are presented. Our results highlight the potential of Artificial Intelligence-based surrogate models to overcome the computational challenges in turbulence simulation, which can be extended to other situations such as geophysical fluid dynamics.
Vlasov–Fokker–Planck simulation codes occupy an important niche in modeling laser-produced plasmas, since they are well suited to studying the effect of collisions on electron kinetic phenomena, especially energy transport. One of the most important elements of energy transport is the absorption of laser light by the plasma; however, simulating this in detail requires resolving oscillations of the laser light, whose characteristic timescale is orders of magnitude shorter than the simulation time needed to study transport physics. For this reason, most Vlasov–Fokker–Planck codes used to study electron transport in laser plasmas rely on simplified models of the laser–plasma coupling. Their underlying assumptions nominally preclude their use for modeling laser light having short-scale structure in space or time, such as broadband lasers. In this work, we derive a more general computational framework suitable for arbitrarily structured laser fields. Furthermore, our approach is based on an extended set of Vlasov–Fokker–Planck equations that separately solve for the low- and high-frequency plasma response. We implement these extended Vlasov–Fokker–Planck equations in the spherical harmonic code K2 and demonstrate the performance of the method on several laser absorption test problems, with particular attention to the judicious selection of time steps, time integrators, and spherical harmonic truncation, according to the intensity and spectrum of the laser light under consideration. Comparison with the widely used Langdon absorption operator shows the Langdon operator performs remarkably well for predicting laser heating in the simple cases considered here, even in situations that would seem to violate its underlying assumptions.
Numerical modeling of radio-frequency waves in plasma with sufficiently high spatial and temporal resolution remains challenging even with modern computers. However, such simulations can be sped up using quantum computers in the future. In this work, we propose how to do such modeling for cold plasma waves, in particular, for an X wave propagating in an inhomogeneous one-dimensional plasma. The wave system is represented in the form of a vector Schrödinger equation with a Hermitian Hamiltonian. Block encoding is used to represent the Hamiltonian through unitary operations that can be implemented on a quantum computer. To perform the modeling, we apply the so-called quantum signal processing algorithm and construct the corresponding circuit. Quantum simulations with this circuit are emulated on a classical computer, and the results show agreement with traditional classical calculations. We also discuss how our quantum circuit scales with the resolution.
The recent Parker Solar Probe observations of type III radio bursts show that the effects of the finite background magnetic field can be an important factor in the interpretation of data. In the present paper, the effects of the background magnetic field on the plasma-emission process, which is believed to be the main emission mechanism for solar coronal and interplanetary type III radio bursts, are investigated by means of the particle-in-cell simulation method. The effects of the ambient magnetic field are systematically surveyed by varying the ratio of plasma frequency to electron gyrofrequency. The present study shows that for a sufficiently strong ambient magnetic field, the wave–particle interaction processes lead to a highly field-aligned longitudinal mode excitation and anisotropic electron velocity distribution function, accompanied by a significantly enhanced plasma emission at the second-harmonic plasma frequency. For such a case, the polarization of the harmonic emission is almost entirely in the sense of extraordinary mode. On the other hand, for moderate strengths of the ambient magnetic field, the interpretation of the simulation result is less clear. The underlying nonlinear-mode coupling processes indicate that to properly understand and interpret the simulation results requires sophisticated analyses involving interactions among magnetized plasma normal modes, including the two transverse modes of the magneto-active plasma, namely, the extraordinary and ordinary modes, as well as electron-cyclotron-whistler, plasma oscillation, and upper-hybrid modes. At present, a nonlinear theory suitable for quantitatively analyzing such complex-mode coupling processes in magnetized plasmas is incomplete, which calls for further theoretical research, but the present simulation results could provide a guide for future theoretical efforts.
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Lasy is a Python library that facilitates numerical simulations of the interaction of complex laser pulses with plasmas. More specifically, lasy offers many ways to define complex laser pulses (e.g. from commonly-known analytical formulas, from experimental measurements, etc.) and then computes and saves the corresponding laser field in a standardized file. This file can then be read by external plasma simulation codes, that will then simulate the interaction between the complex laser pulse and a plasma. Lasy is useful for instance for numerical simulations of plasma-based particle accelerators, plasma-based laser amplification, etc. Lasy avoids having to duplicate the code that defines complex laser pulses in each plasma simulation codes, and instead provides a trusted, centralized implementation.
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. As we report here, 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 transient (e.g., ELM, disruption) and transport time-scale simulations.
Here, plasma-facing component (PFC) geometries are evaluated for a Fusion Nuclear Science Facility (FNSF) design to find solutions that are compatible with flowing liquid lithium components while satisfying requirements from the perspective of plasma and neutral particle transport. Flowing liquid metal (LM) divertor systems offer important advantages due to continual regeneration of the surface material, but may require modifications from standard optimized tokamak divertor designs. Scrape Off Layer Plasma Simulator for the International Thermonuclear Experimental Reactor (SOLPS-ITER) simulations are used to compare standard vertical target, open, and balanced baffled geometries. It is found that the open geometry offers little control of neutral particles and has narrow operating windows where the divertor fluxes can be lowered to acceptable levels, while maintaining the required upstream density. The addition of neutral baffles allows greater control over the divertor conditions with less impact on the upstream density. The divertor neutral pressure in the baffled geometry is slightly higher than the open divertor, but not as large with a vertical target. A first-pass coupling of the SOLPS solution with sheath and implantation/erosion models to compute the lithium emission shows that the lithium is largely confined to the near-surface region due to the small ionization mean free path and large main ion flow toward the surface. The lithium source was varied by three orders of magnitude. At the highest rate, when the sourced lithium approaches the level of the main ion recycling flux, a high core lithium concentration (~10%) is observed with only moderate power dissipation to affect the divertor plasma.
Abstract The trajectories and the ablation positions of boron dust particles dropped from an impurity powder dropper in the peripheral plasma in the Large Helical Device (LHD) were calculated using a three‐dimensional edge plasma simulation code (EMC3‐EIRENE) and a dust transport simulation code (DUSTT). The simulation shows that the trajectory of the boron dust particles is deflected at the upper divertor leg due to the effect of the hydrogen plasma flow, and the ablation positions of the dust particles in an ergodic layer change toward the outboard side of the torus for higher plasma densities. The effect of the boron ion flow in the divertor leg on the deflection is investigated by coupling the two codes self‐consistently. The simulation predicts that the boron ions in the divertor leg, which are produced by sputtering on the divertor plates, which do not affect the change in the ablation positions. It also shows that the ablation positions move toward the inboard side and approach the Last Closed Flux Surface (LCFS) in case of increased boron dust drop rates, which is caused by the lowered plasma flow in the upper divertor leg due to the lowered electron temperature by radiation cooling by the dropped dust particles.
Artificial heating in plasma simulations is a well-known phenomenon which occurs when, among other things, the Debye length is poorly resolved by the simulation mesh. Here, in this work, the degree to which numerical-heating occurs during a simulation of a nanosecond atmospheric pressure streamer discharge is examined. The streamer is simulated using a two-dimensional finite-element, particle-in-cell code Empire, which uses direct simulation Monte Carlo for binary particle interactions. Initially, an estimate of the numerical-heating rate applied to Empire is performed using a simple plasma model. Second, a positive atmospheric pressure streamer discharge simulation is performed to study the effects of numerical heating on plasma density, electron temperature, and streamer velocity. The nominal Debye length is approximately 1 μm and the amount of numerical heating introduced in the simulation is varied by using mesh sizes ranging from 2 μm to 20 μm. A measurable numerical heating quantity is proposed that can be used to estimate the appropriate element size and quantify the numerical-heating that can be expected over the simulation time for an atmospheric pressure streamer. In conclusion while Δx/λ D violations can be an issue it is not likely to be an issue with streamer discharges that are temporally short and occur in environments where collision frequencies are high. This result validates the rationale of grid size choices for a large amount of previously published works where Δx/λ D violation was not clearly addressed. Primary finding of this work is that numerical heating is of minor concern for plasma simulations where electron–neutral collisions are numerous such that multiple collisions can occur within a single plasma period.
The backward problem of plasma assisted combustion emphasizes evaluating the effect of the evolving thermochemical state on the plasma discharge. This paper investigates the dependence of avalanche to streamer to spark formation dynamics and kinetics on the gas composition and temperature at different points in an ammonia-air premixed laminar flame using a self-consistent multigrid-based 1D plasma solver. Different values of ..alpha.., the coefficient for effective ionization events per unit length, have been reported for electron avalanches in air and stoichiometric NH3-air mixtures. The streamer inception has been shown to obey the Meek's criterion. An exponential reduction in streamer and spark formation time has been observed from plasma simulations at different points in the unburnt, pre-heat zone, reaction zone and the fully burnt regions of the premixed flame. While the enhancement of the reduced electric field with increasing temperature affects effective ionization, there exists a minimum breakdown field for streamer formation, which does not vary proportionally with the changing number density of the gas. The change in the mixture from reactants (NH3, O2, N2) to products of complete combustion of ammonia in air (N2, H2O) has also been shown to affect the streamer and spark formation. Finally, the major pathways during the streamer and spark phases which are responsible for producing important radicals used in combustion of NH3 are also discussed.
We study classical lattice simulations of theories of electrodynamics coupled to charged matter at finite temperature, interpreting them using the higher-form symmetry formulation of magnetohydrodynamics (MHD). We compute transport coefficients using classical Kubo formulas on the lattice and show that the properties of the simulated plasma are in complete agreement with the predictions from effective field theories. In particular, the higher-form formulation allows us to understand from hydrodynamic considerations the relaxation rate of axial charge in the chiral plasma observed in previous simulations. A key point is that the resistivity of the plasma – defined in terms of Kubo formulas for the electric field in the 1-form formulation of MHD – remains a well-defined and predictive quantity at strong electromagnetic coupling. However, the Kubo formulas used to define the conventional conductivity vanish at low frequencies due to electrodynamic fluctuations, and thus the concept of the conductivity of a gauged electric current must be interpreted with care.
The design and optimization of radiofrequency-wave systems for fusion applications is often performed using ray-tracing codes, which rely on the geometrical-optics (GO) approximation. However, GO fails at wave cutoffs and caustics. To accurately model the wave behavior in these regions, more advanced and computationally expensive “full-wave” simulations are typically used, but this is not strictly necessary. A new generalized formulation called metaplectic geometrical optics (MGO) has been proposed that reinstates GO near caustics. The MGO framework yields an integral representation of the wavefield that must be evaluated numerically in general. We present an algorithm for computing these integrals using Gauss-Freud quadrature along the steepest-descent contours. Benchmarking is performed on the standard Airy problem, for which the exact solution is known analytically. Furthermore, the numerical MGO solution provided by the new algorithm agrees remarkably well with the exact solution and significantly improves on previously derived analytical approximations of the MGO integral.
We report the simplified δf mixed-variable/pullback electromagnetic simulation algorithm implemented in XGC for core plasma simulations by Cole et al. [Phys. Plasmas 28, 034501 (2021)] has been generalized to a total- f electromagnetic algorithm that can include, for the first time, the boundary plasma in diverted magnetic geometry with neutral particle recycling, turbulence, and neoclassical physics. The δf mixed-variable/pullback electromagnetic implementation is based on the pioneering work by Kleiber and Mischenko et al. [Kleiber et al., Phys. Plasmas 23, 032501 (2016); Mishchenko et al., Comput. Phys. Commun. 238, 194 (2019)]. An electromagnetic demonstration simulation is performed in a DIII-D-like, H-mode boundary plasma, including a corresponding comparative electrostatic simulation, which confirms that the electromagnetic simulation is necessary for a higher fidelity understanding of the electron particle and heat transport even at the low- β pedestal foot in the vicinity of the magnetic separatrix.
Mitigation of the multiple risks associated with disruptions and runaway electrons in tokamaks involves competing demands. Success requires that each risk be understood sufficiently that appropriate compromises can be made. Here the focus is on the interaction of short timescale magnetic-perturbations with the structure in ITER that is closest to the plasma, blanket modules covered by separated beryllium tiles. The effect of this tiled surface on the perturbations and on the forces on structures is subtle. Indeterminacy can be introduced by tile-to-tile shorting. A determinate subtlety is introduced because electrically separated tiles can act as a conducting surface for magnetic perturbations that have a normal component to the surface. A practical method for including this determinate subtlety into plasma simulations is developed. The shorter the timescales and the greater the localization, particularly in the toroidal direction, the more important the magnetic effects of the tiles become.
Finite-grid (or aliasing) instabilities are pervasive in particle-in-cell (PIC) plasma simulation algorithms, and force the modeler to resolve the smallest (Debye) length scale in the problem regardless of dynamical relevance. These instabilities originate in the aliasing of interpolation errors between mesh quantities and particles (which live in the space–time continuum). Recently, strictly energy-conserving PIC (EC-PIC) algorithms have been developed that promise enhanced robustness against aliasing instabilities. In this study, we confirm by analysis that EC-PIC is stable against aliasing instabilities for stationary plasmas. For drifting plasmas, we demonstrate by analysis and numerical experiments that, while EC-PIC algorithms are not free from these instabilities in principle, they feature a benign stability threshold for finite-temperature plasmas that make them usable in practice for a large class of problems (featuring ambipolarity and realistic ion-electron mass ratios) without the need to consider the size of the Debye length. We also demonstrate that this threshold is absent for the popular momentum-conserving PIC algorithms, which are therefore unstable for both drifting and stationary plasmas beyond a threshold in cell size compared to Debye length. Finite-grid (or aliasing) instabilities are pervasive in particle-in-cell (PIC) plasma simulation algorithms, and force the modeler to resolve the smallest (Debye) length scale in the problem regardless of dynamical relevance. These instabilities originate in the aliasing of interpolation errors between mesh quantities and particles (which live in the space–time continuum). Recently, strictly energy-conserving PIC (EC-PIC) algorithms have been developed that promise enhanced robustness against aliasing instabilities. In this study, we confirm by analysis that EC-PIC is stable against aliasing instabilities for stationary plasmas. For drifting plasmas, we demonstrate by analysis and numerical experiments that, while EC-PIC algorithms are not free from these instabilities in principle, they feature a benign stability threshold for finite-temperature plasmas that make them usable in practice for a large class of problems (featuring ambipolarity and realistic ion-electron mass ratios) without the need to consider the size of the Debye length. Finally, we also demonstrate that this threshold is absent for the popular momentum-conserving PIC algorithms, which are therefore unstable for both drifting and stationary plasmas beyond a threshold in cell size compared to Debye length.
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