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Verification methods for drift–diffusion reaction models for plasma simulations
Abstract Compared to other computational physics areas such as codes for general computational fluid dynamics, the documentation of verification methods for plasma fluid codes remains under developed. Current analytical solutions for plasma are often highly limited in terms of testing highly coupled physics, due to the harsh assumptions needed to derive even simple plasma equations. This work highlights these limitations, suggesting the method of manufactured solutions (MMSs) as a potential option for future verification efforts. To demonstrate the flexibility of MMS in verifying these highly coupled systems, the Multiphysics Object-Oriented Simulation Environment (MOOSE) framework was utilized. Thanks to the MOOSE framework’s robustness and modularity, as well as to its physics module capabilities and ecosystem applications (i.e. Zapdos and the chemical reaction network) developed for plasma physics modeling and simulation, this report lays the groundwork for a structured method of conducting plasma fluid code verification.
Workshop Goals
The goals are: 1. Report and document recent progress on radiation belt model and plasma model development. Metrics for past and current programs. 2. Complete a roadmap for the development of new standard radiation belt and space plasma models for spacecraft engineering: input to agencies for future investments, interagency cooperation.
Multi-machine validation of plasma initiation modelling and prospects for future devices: Predicting plasma initiation using only hardware design and control room input data
This paper reports on the generic prediction capability of full electromagnetic plasma initiation modelling with DYON, which was carried out for the first time in fusion research by the joint modelling of the International Tokamak Physics Activity—Integrating Operation Scenario group. The following devices were included in the experiment database: VEST (spherical torus, copper coils, Stainless steel wall, R/a = 0.3 m/0.2 m, V v = 3.7 m 3 ), MAST-U (spherical torus, copper coils, C wall, R/a = 0.7 m/0.5 m, V v = 55 m 3 ), EAST (conventional tokamak, superconducting coils, metallic wall, R/a = 1.85 m/0.5 m, V v = 38 m 3 ), DIII-D (conventional tokamak, copper coils, C wall, R/a = 1.67 m/0.65 m, V v = 35 m 3 ), and KSTAR (conventional tokamak, superconducting coils, C wall, R/a = 1.8 m/0.5 m, V v = 55 m 3 ). Despite the different hardware features of the devices, the required operating spaces of the loop voltage induction and prefill gas pressure for inductive plasma initiation in each device were successfully reproduced by the predictive simulations with DYON using only the individual hardware design and the control room input data for each discharge. This successful validation across multiple machines demonstrates that the full electromagnetic DYON modelling can capture the essential physics of inductive plasma initiation. The simulation settings commonly employed for all modelling and the modifications necessary to account for the discrepancies between individual devices are reported. Predictions for ITER based on the multi-machine validation indicate that a wide range of prefill gas pressures exists for the Townsend breakdown and the plasma burn-through (0.01–1.5 mPa).
EISCAT velocity patterns for theoretical plasma convection models
Theoretical line-of-sight velocities, as would be observed by the EISCAT radar, are computed for idealized models of plasma convection in the polar ionosphere. The calculations give the velocity as a function of range and Universal Time. For several variants of the Volland and Heelis convection models, how the maxima, minima and reversals of velocity depend on beam azimuth is examined. The analysis is designed to be applied to data from the UK-POLAR experiment, an example of which is shown.
Quasilinear theory: the lost ponderomotive effects and why they matter
Quasilinear theory (QLT) has been used for modeling wave–plasma interactions for decades but remains largely heuristic. Plasma inhomogeneity, ponderomotive effects, microscopic fluctuations, and collisions are not easily accommodated from first principles in QLT, and typically are ignored entirely, due to the limitations of the standard Fourier–Laplace global-mode approach. This results in inconsistencies, for example, violation of the action conservation for nonresonant waves. However, these issues can be avoided, and the theory can be substantially generalized and corrected, if QLT is formulated using more suitable analytical tools, particularly, the Weyl symbol calculus. Here, an attempt is made to deliver an accessible review of this modern formulation, provide intuitive calculations for special cases, and elaborate on the connection with the ‘oscillation-center QLT’ originally proposed by Dewar (Phys Fluids 16:1102, 1973). A Fokker–Planck equation for a ‘dressed’ distribution is derived from the Klimontovich equation and captures quasilinear diffusion, ponderomotive forces, and interactions with background fields for a generic Hamiltonian, so many known formulations of QLT for specific plasma models become corollaries of a single unifying theory. Also, waves are allowed to be off-shell (not constrained by a dispersion relation), which allows them to accommodate microscopic fluctuations. This leads to a collision integral of the Balescu–Lenard type that has all the usual properties but is not restricted to any specific plasma model. For on-shell waves, a generalized version of the classic oscillation-center QLT is obtained. Finally, combined with the wave-kinetic equation, this formulation not only conserves particles, momentum, and energy, like the classic QLT but also reinstates the action conservation for nonresonant waves.
Kinetic modeling of the Saturn ring-ionosphere plasma environment
A time-independent kinetic plasma model was developed on the basis of the Li et al. (1988) semikinetic plasma model and was used to study the interaction of the Saturnian ionosphere and ring plasma. The model includes the gravitational magnetic mirror and centripetal and ambipolar electric forces, and the effect of the mixing of two plasma populations. The results obtained indicate that the density, temperature, and composition of plasma near the rings changing in the direction from the inner C ring to the outer A ring, due to the fact that the predominant source of plasma changes from the ionosphere to the rings. The model results also suggest that the outflow of hydrogen from the ionosphere to the rings may be shut off for field lines passing through the outer B and A ring, due to the ambipolar electric field set up by the warm ring plasma trapped near the ring plane by the centipetal force. In these regions, there will be a net flux of O(+) ions from the rings to the ionosphere.
Plasma Reactor Modeling and Validation Experiments
Plasma processing is a key processing stop in integrated circuit manufacturing. Low pressure, high density plum reactors are widely used for etching and deposition. Inductively coupled plasma (ICP) source has become popular recently in many processing applications. In order to accelerate equipment and process design, an understanding of the physics and chemistry, particularly, plasma power coupling, plasma and processing uniformity and mechanism is important. This understanding is facilitated by comprehensive modeling and simulation as well as plasma diagnostics to provide the necessary data for model validation which are addressed in this presentation. We have developed a complete code for simulating an ICP reactor and the model consists of transport of electrons, ions, and neutrals, Poisson's equation, and Maxwell's equation along with gas flow and energy equations. Results will be presented for chlorine and fluorocarbon plasmas and compared with data from Langmuir probe, mass spectrometry and FTIR.
A quantitative model of plasma in Neptune's magnetosphere
A model encompassing plasma transport and energy processes is applied to Neptune's magnetosphere. Starting with profiles of the neutral densities and the electron temperature, the model calculates the plasma density and ion temperature profiles. Good agreement between model results and observations is obtained for a neutral source of 5 x 10 exp 25/s if the diffusion coefficient is 10 exp -8 L3R(N)/2s, plasma is lost at a rate 1/3 that of the strong diffusion rate, and plasma subcorotates in the region outside Triton.
Elucidating key reducing species beyond ions in hydrogen plasma smelting reduction of iron ore
Hydrogen plasma smelting reduction (HPSR) of iron ore has attracted significant attention over the past decade due to its high-temperature operation, rapid plasma mediated reduction kinetics, and simpler density-based separation of molten iron product, compared to H2-based solid-state reduction. All of these attributes enable processing of low-grade ores for downstream use in electric-arc furnaces, as virgin iron with low gangue content is required for high quality steel and improved furnace operation. While positive ions exist within the plasma arc, this work demonstrates that near the anodic ore surface, hydrogen radicals and vibrationally excited hydrogen species dominate and their densities correlate well with observed reduction rates. Species concentrations in the transferred plasma arc and at the plasma-ore interface are evaluated using coupled thermal plasma and near-wall non-equilibrium plasma models. The thermal plasma model is validated against experimental voltage data and spectroscopic measurements of plasma temperature and density for varying current inputs. Modeling of the near surface thermochemical non-equilibrium and micrometer scale anode sheath layer reveals, in addition to the expected H + , significant concentrations of ArH + and H$^+_3$ ions, typically not observed in thermal plasmas under thermodynamic equilibrium. Our results show that the inverted sheath structure at the anodic ore surface strongly suppresses reactive positive ion fluxes, while non-equilibrium electron-impact processes generate abundant hydrogen radicals and vibrationally excited species. These findings highlight the critical role of non-equilibrium effects in hydrogen arc-driven iron ore reduction and advance understanding beyond prevailing hypotheses centered on hydrogen ion-driven mechanisms.
Apparatus for calibration of on-board instruments and laboratory modelling of rarefied plasma flows past models
Problems of laboratory simulation of artificial earth satellite flight conditions in the ionosphere are examined, and a setup capable of reproducing the basic parameters of ion flows (with energies of 5-10 eV, energy spectrum width approximately 2x5 eV, and an intensity of 10 to the minus 8th power a/cm/2) past measurement instruments and satellite models is described. Possibilities for further improvement of the apparatus are discussed.
A new model for plasma transport and chemistry at Saturn
A model of plasma transport and chemistry is described which calculates the evolution of a plasma population in latitude and radial distance. This model is applied to the magnetosphere of Saturn, where it is used to fit the density profile of the heavy ions assuming both satellite and ring sources of plasma. Use of an extended source region is found to significantly alter the resulting plasma profile. Water ions cannot fit the observed density profile inside L = 6 even with a large ring source. Oxygen ions can fit the density profile throughout the region inside L = 12 given a suitable profile of neutral hydrogen; a suitable profile contains up to 5 H/cu cm outside L = 4 with the number increasing inside this. Preferred values of K are 1-3 x 10 exp -10 R(S)2/s, but any value K less than 10 exp -9 R(S)2/s can be accommodated. The temperature profile is shown to favor models invoking in situ plasma formation and loss as opposed to models where transport is important.
Excited-state potentials for modelling dense plasmas from first principles
The modelling of dense plasmas using finite-temperature density functional theory has proven very successful in determining transport properties and the equation of state of systems where quantum many-body effects and correlations play a key role in their structure. Here we show how excited-state projector augmented- wave potentials can be used to extend these calculations to explicitly model core-hole states, allowing for the calculation of the electronic structure of a range of integer charge configurations embedded in a dense plasma environment. Our excited-state potentials show good agreement with all-electron calculations at finite-temperatures, motivating their use as an efficient approach in modelling from first principles both the structure of strongly-coupled non-equilibrium plasmas and their interaction with intense X-rays.
A Coupled Plasma-Sheath Model for High Density Sources
High density, low pressure plasmas are used for etching and deposition in microelectronics fabrication processes. The process characteristics are strongly determined by the ion energy distribution (IED) and the ion flux arriving at the substrate that are responsible for desorption of etch products and neutral dissociation at the surface. The ion flux and energy are determined by a self- consistent modeling of the bulk plasma, where the ions and the neutral radicals are produced, and the sheath, where the ions are accelerated. Due to their widely different time scales, it is a formidable task to self-consistently resolve non-collisional sheath in a high density bulk plasma model. In this work, we first describe a coupled plasma-sheath model that attempts to resolve the non-collisional sheath in a reactor scale model. Second, we propose a semianalytical radio frequency (RF) sheath model to improve ion dynamics.
Title: Benchmarking of High-performance Low-temperature Plasma Particle-in-cell Codes for Modeling Magnetized Plasmas
Understandinrelationships between magnetic field and plasma conditions
An implicit-explicit time splitting strategy for the far SOL plasma fluid model with DG-FEM discretization
We consider a far scrape-off layer (SOL) plasma fluid model of ions that is governed by a Braginskiitype model: a one-dimensional, nonlinear system of advection-diffusion equations coupled with a diffusion equation for neutral particles. Our motivation for studying this system arises from the coupling between the edge plasma and radio-frequency (RF) heating, where solving a far SOL plasma fluid model provides critical insights into edge plasma dynamics. Numerical simulations of plasma fluid models require advanced computational techniques to achieve both efficiency and accuracy, especially when resolving the boundary layer in magnetically confined plasmas. In this work, we propose an implicit-explicit time operator splitting strategy that allows for an efficient solution algorithm, where the diffusive terms are treated semi-implicitly requiring only a linear solve, while the advection part is handled explicitly using a strong-stability-preserving Runge-Kutta (SSP-RK3) scheme. This leads to a fully decoupled system in which the diffusion and advection sub-problems can be solved separately, simplifying the overall solution procedure and allowing for efficient parallelization, which is particularly relevant for exploring the impact of RF heating on the SOL plasma. The main challenge of the discretization is due to the strong coupling between diffusion and advection, particularly through the boundary conditions. This makes implementation of such a scheme in an accurate and stable manner nontrivial. We discuss in detail how to split the equations and manage boundary conditions to maintain stability and well-posedness for each subsystem. We also describe a spatial discretization approach, based on the discontinuous Galerkin finite element method (DG-FEM) and present numerical results for a one-dimensional system.
Short Wavelength Electromagnetic Perturbations Excited Near the Solar Probe Plus Spacecraft in the Inner Heliosphere: 2.5D Hybrid Modeling
A 2.5D numerical plasma model of the interaction of the solar wind (SW) with the Solar Probe Plus spacecraft (SPPSC) is presented. These results should be interpreted as a basic plasma model derived from the SW-interaction with the spacecraft (SC), which could have consequences for both plasma wave and electron plasma measurements on board the SC in the inner heliosphere. Compression waves and electric field jumps with amplitudes of about 1.5 V/m and (12-18) V/m were also observed. A strong polarization electric field was also observed in the wing of the plasma wake. However, 2.5D hybrid modeling did not show excitation of whistler/Alfven waves in the upstream connected with the bidirectional current closure that was observed in short-time 3D modeling SPPSC and near a tether in the ionosphere. The observed strong electromagnetic perturbations may be a crucial point in the electromagnetic measurements planned for the future Solar Probe Plus (SPP) mission. The results of modeling electromagnetic field perturbations in the SW due to shot noise in absence of SPPSC are also discussed.
Inductive Pulsed Plasma Thruster Model with Time-Evolution of Energy and State Properties
A model for pulsed inductive plasma acceleration is presented that consists of a set of circuit equations coupled to both a one-dimensional equation of motion and an equation governing the partitioning of energy. The latter two equations are obtained for the plasma current sheet by treating it as a single element of finite volume and integrating the governing equations over that volume. The integrated terms are replaced where necessary by physically-equivalent quantities that are calculated through the solution of other parts of the governing equation set. The model improves upon previous one-dimensional performance models by permitting the time-evolution of the energy and state properties of the plasma, the latter allowing for the tailoring of the model to different gases that may be chosen as propellants. The time evolution of the various energy modes in the system and the associated plasma properties, calculated for argon propellant, are presented to demonstrate the efficacy of the model. The model produces a result where efficiency is maximized at a given value of the electrodynamic scaling term known as the dynamic impedance parameter. Qualitatively and quantitatively, the model compares favorably with performance measured for two separate inductive pulsed plasma thrusters, with disagreements attributable to simplifying assumptions employed in the generation of the model solution.