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A special issue of Plasma (ISSN 2571-6182).

Deadline for manuscript submissions: 31 December 2024 | Viewed by 13008

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Dr. Tariq Rafiq

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Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, PA 18015, USA
Interests: plasma magnetic confinement; plasma instabilities; turbulence and transport; theoretical modeling; integrated whole device modeling; verification and validation of developed models; fusion energy; tokamaks

Special Issue Information

Dear Colleagues,

First-principles-based heat, particle, and momentum transport models for thermal and energetic particles in magnetic fusion devices are complex and computationally intensive, making them almost impossible to use for predictions and control. Therefore, there is a need for reduced models that can provide efficient and accurate predictions of transport while retaining the essential physics. This strategy is currently being used to develop and improve transport models. The developed reduced transport models are validated against the results of first-principles codes and experimental data from many different types of discharges and different tokamaks, including existing conventional and spherical tokamaks. The model predictions have been compared with the measured quantities, such as rotation, diffusivities, fluxes, and plasma profiles. The agreement between the model and experimental data is used to assess the accuracy and reliability of the model. Once the model is validated, it is then used to simulate the future performance of burning plasmas in ITER and the next-step fusion pilot plant. Physics-based integrated-modeling simulations based on reduced models are used to gain a deeper understanding of the physics underlying different types of instabilities as well as energy and particle confinement in current and future tokamak fusion reactors. This facilitates the identification of particular transport driving mechanisms and provides a foundation for describing and regulating transport in tokamaks. Simulations are used to analyze interactions between a variety of related physical processes, to develop scenarios, to improve the performance of tokamak discharges, to plan new experiments, or to extrapolate them to future planned devices.

Dr. Tariq Rafiq
Guest Editor

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Keywords

reduced transport models
thermal and energetic particle confinement
integrated whole device modeling simulation
verification and validation
microinstabilities and associated transport
modeling of core–edge coupling
neural network models
magnetically confined fusion devices
ITER and fusion pilot plant

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Published Papers (10 papers)

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Research

16 pages, 1608 KiB

Open AccessArticle

Control-Oriented Free-Boundary Equilibrium Solver for Tokamaks

by Xiao Song, Brian Leard, Zibo Wang, Sai Tej Paruchuri, Tariq Rafiq and Eugenio Schuster

Plasma 2024, 7(4), 842-857; https://doi.org/10.3390/plasma7040045 - 23 Oct 2024

Viewed by 486

Abstract

A free-boundary equilibrium solver for an axisymmetric tokamak geometry was developed based on the finite difference method and Picard iteration in a rectangular computational area. The solver can run either in forward mode, where external coil currents are prescribed until the converged magnetic [...] Read more.

ψ (R, Z)

map is achieved, or in inverse mode, where the desired plasma boundary, with or without an X-point, is prescribed to determine the required coil currents. The equilibrium solutions are made consistent with prescribed plasma parameters, such as the total plasma current, poloidal beta, or safety factor at a specified flux surface. To verify the mathematical correctness and accuracy of the solver, the solution obtained using this numerical solver was compared with that from an analytic fixed-boundary equilibrium solver based on the EAST geometry. Additionally, the proposed solver was benchmarked against another numerical solver based on the finite-element and Newton-iteration methods in a triangular-based mesh. Finally, the proposed solver was compared with equilibrium reconstruction results in DIII-D experiments. Full article

(This article belongs to the Special Issue New Insights into Plasma Theory, Modeling and Predictive Simulations)

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16 pages, 3663 KiB

Open AccessArticle

Energy Efficiency of Plasma Jets: Electrical Modeling Based on Experimental Results

by Achraf Hani, Karim Saber, Alyen Abahazem and Nofel Merbahi

Plasma 2024, 7(4), 826-841; https://doi.org/10.3390/plasma7040044 - 23 Oct 2024

Viewed by 503

Abstract

This paper focuses on the determination of and improvement in the energy efficiency of plasma jets. To achieve this goal, an equivalent electrical model of a discharge reactor was developed, incorporating variable electrical parameters. The evolution of these parameters was determined by a mathematical identification method based on the recursive least squares algorithm (RLSA). The good agreement between the measured currents and those calculated using our electrical circuit, as well as the significant shapes of the estimated parameters, confirmed the accuracy of the parameter estimation method. This allowed us to use these parameters to determine the energy delivered to the reactor and that used during the discharge. This made our reactor controllable at the energy level. Thus, the ratio between these two energies allowed us to calculate the energy efficiency of plasma jets at each discharge instant. We also studied the effect of the applied voltage on efficiency. We found that efficiency was increased from 75% to 90% by increasing the voltage from 6 kV to 8 kV. All the results found in this work were interpreted and compared with the discharge behavior. This proposed model will help us to choose the right operating conditions to reach the maximum efficiency. Full article

(This article belongs to the Special Issue New Insights into Plasma Theory, Modeling and Predictive Simulations)

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13 pages, 601 KiB

Open AccessArticle

Exploring Experimental Isotope Scaling and Density Limit in Tokamak Transport

by Jan Weiland, Tariq Rafiq and Eugenio Schuster

Plasma 2024, 7(3), 780-792; https://doi.org/10.3390/plasma7030041 - 23 Sep 2024

Viewed by 559

Abstract

As it turns out, both isotope scaling and density limits are phenomena closely linked to fluid closure. The necessity to include ion viscosity arises for both phenomena. Thus, we have added ion viscosity to our model. The experimental isotope scaling has been successfully recovered in our fluid model through parameter scans. Although ion viscosity typically exerts a small effect, the density limit is manifested by increasing the density by approximately tenfold from the typical experimental density. In our case, this increase originates from the density in the Cyclone base case. Notably, these phenomena would not manifest with a gyro-Landau fluid closure. The isotope scaling is nullified by the addition of a gyro-Landau term, while the density limit results from permitting ion viscosity to become comparable to the gyro-Landau term. The mechanism of zonal flows, demonstrated analytically for the Dimits upshift, yields insights into the isotope scaling observed in experiments. In our approach, ion viscosity is introduced in place of the Landau fluid resonances found in some fluid models. This implies that the mechanism of isotope scaling operates at the level of fluid closure in connection with the generation of zonal flows. The strength of zonal flows in our model has been verified, particularly in connection with the successful simulation of the nonlinear Dimits shift. Consequently, a role is played by our approach in the temperature perturbation part of the Reynolds stress. Full article

(This article belongs to the Special Issue New Insights into Plasma Theory, Modeling and Predictive Simulations)

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14 pages, 1127 KiB

Open AccessArticle

Analysis of ICRF Heating Schemes in ITER Non-Active Plasmas Using PION+ETS Integrated Modeling

by Tomas Bensadon, Mervi J. Mantsinen, Thomas Jonsson, Dani Gallart, Xavier Sáez and Jordi Manyer

Plasma 2024, 7(3), 517-530; https://doi.org/10.3390/plasma7030028 - 19 Jul 2024

Viewed by 785

Abstract

The PION code has been integrated into the European Transport Solver (ETS) transport workflow, and we present the first application to model Ion Cyclotron Resonance Frequency (ICRF) heating scenarios in the next-step fusion reactor ITER. We present results of predictive, self-consistent and time-dependent simulations where the resonant ion concentration is varied to study its effects on the performance, with a special emphasis on the resulting bulk ion heating and thermal ion temperature. We focus on two ICRF heating schemes, i.e., fundamental H minority heating in a ⁴He plasma at 2.65 T/7.5 MA and a three-ion ICRF scheme consisting of fundamental ³He heating in a H-⁴He plasma at 3.3 T/ 8.8 MA. The H minority heating scenario is found to result in strong absorption by resonant H ions as compared to competing absorption mechanisms and dominant background electron heating for H concentrations up to 10%. The highest H absorption of ∼80% of the applied ICRF power and highest ion temperature of ∼15 keV are obtained with an H concentration of 10%. For the three-ion scheme in 85%:15% H:⁴He plasma, PION+ETS predicts ³He absorption in the range of 21–65% for ³He concentrations in the range of 0.01–0.20%, with the highest ³He absorption at a ³He concentration of 0.20%. Full article

(This article belongs to the Special Issue New Insights into Plasma Theory, Modeling and Predictive Simulations)

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12 pages, 3932 KiB

Open AccessArticle

Spatial Distribution Analyses of Axially Long Plasmas under a Multi-Cusp Magnetic Field Using a Kinetic Particle Simulation Code KEIO-MARC

by Ryota Nishimura, Tomohiro Seino, Keigo Yoshimura, Hiroyuki Takahashi, Akinobu Matsuyama, Kazuo Hoshino, Tetsutarou Oishi and Kenji Tobita

Plasma 2024, 7(1), 64-75; https://doi.org/10.3390/plasma7010005 - 22 Jan 2024

Viewed by 1523

Abstract

To realize the development of a long plasma source with a uniform electron density distribution in the axial direction, the spatial distribution of plasma under a multi-cusp magnetic field was analyzed using a KEIO-MARC code. Considering a cylindrical plasma source with an axial length of 3000 mm and a cross-sectional diameter of 100 mm, in which the filament electrode was the electron source, the electron density distribution was calculated using the residual magnetic flux density, B_res, and the number of permanent magnets installed at different locations surrounding the device, N_mag, as design parameters. The results show that both B_res and N_mag improved the uniformity of the electron density distribution in the axial direction. The maximum axial electron density decreased with increasing N_mag and increased with increasing B_res. These trends can be explained by considering the nature of the multi-cusp field, where particles are mainly confined to the field-free region (FFR) near the center of the plasma column, and the loss of particles due to radial particle transport. The use of multiple filaments at intervals shorter than the plasma decay length dramatically improved axial uniformity. To further improve axial uniformity, the filament length and FFR must be properly set so that electrons are emitted inside the FFR. Full article

(This article belongs to the Special Issue New Insights into Plasma Theory, Modeling and Predictive Simulations)

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13 pages, 1417 KiB

Open AccessArticle

Effects of Non-Thermal Plasma on the Transition from Nano-Crystalline to Amorphous Structure in Water and Subsequent Effects on Viscosity

by Joshua Ginzburg, Mobish Shaji, Alexander Rabinovich, Dmitri Vainchtein, Christopher Sales and Alexander Fridman

Plasma 2024, 7(1), 16-28; https://doi.org/10.3390/plasma7010002 - 21 Dec 2023

Viewed by 1742

Abstract

Recent studies have demonstrated that the physical properties of water treated with non-thermal plasma, or plasma-activated water (PAW), significantly differ from those of distilled water. For example, contrary to expectation, the viscosity of PAW becomes lower than that of distilled water at certain temperatures. This study developed a model to explain these differences by combining the two-state model of ordinary water, which describes water as a combination of nano-crystalline clusters and amorphous, free-floating molecules, using the Debye–Huckel theory for a fluid containing ions. A model for the viscosity of PAW was then developed from the general model. It explains how PAW has a lower viscosity than distilled water as the temperature decreases and why this effect is stronger than the colligative effect for ideal solutions. Finally, the viscosity model is compared to the experimental measurements of PAW treated with gliding arc plasma, showing that the data match the predicted values quite well. The model of PAW developed here can be used to understand other physical properties beyond viscosity, such as the surface tension, contact angle, electric conductivity, heat capacity, isothermal compressibility, and density, potentially facilitating new applications of PAW. Full article

(This article belongs to the Special Issue New Insights into Plasma Theory, Modeling and Predictive Simulations)

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12 pages, 3536 KiB

Open AccessArticle

Investigation of Plasma Propagation in Packed-Bed Dielectric Barrier Discharge Based on a Customized Particle-in-Cell/Monte Carlo Collision Model

by Xufeng Li, Leiyu Zhang, Aamir Shahzad, Pankaj Attri and Quanzhi Zhang

Plasma 2023, 6(4), 637-648; https://doi.org/10.3390/plasma6040044 - 13 Oct 2023

Cited by 1 | Viewed by 1778

Abstract

This study investigates the propagation dynamics of plasma streamers in a packed-bed dielectric barrier discharge using a 2D particle-in-cell/Monte Carlo collision model. To accurately simulate the high-intensity discharge and streamer propagation mechanism at atmospheric pressure, additional algorithms for particle merging and a new electron mechanism are incorporated into the traditional particle-in-cell/Monte Carlo collision model. To validate the accuracy of this improved model, qualitative comparisons are made with experimental measurements from the existing literature. The results show that the speed of streamer propagation and the distribution of plasma are strongly influenced by the dielectric constant of the packed pellet, which is commonly used as a catalyst. In cases with a moderate dielectric constant, the presence of a strong electric field between the pellet and dielectric layer on the electrode significantly enhances the discharge. This enables the streamer to propagate swiftly along the pellet surface and results in a wider spread of plasma. Conversely, a very high dielectric constant impedes streamer propagation and leads to localized discharge with high intensity. The improved model algorithms derived from this research offer valuable insights for simulating high-density plasma discharge and optimizing plasma processing applications. Full article

(This article belongs to the Special Issue New Insights into Plasma Theory, Modeling and Predictive Simulations)

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12 pages, 1213 KiB

Open AccessEditor’s ChoiceArticle

Comparison of Saturation Rules Used for Gyrokinetic Quasilinear Transport Modeling

by Scott E. Parker, Calder S. Haubrich, Stefan Tirkas, Qiheng Cai and Yang Chen

Plasma 2023, 6(4), 611-622; https://doi.org/10.3390/plasma6040042 - 12 Oct 2023

Cited by 2 | Viewed by 1978

Abstract

Theory-based transport modeling has been widely successful and is built on the foundations of quasilinear theory. Specifically, the quasilinear expression of the flux can be used in combination with a saturation rule for the toroidal mode amplitude. Most transport models follow this approach. Saturation rules are heuristic and difficult to rigorously derive. We compare three common saturation rules using a fairly accurate quasilinear expression for the fluxes computed using local linear gyrokinetic simulation. We take plasma parameters from experimental H-mode profiles and magnetic equilibrium and include electrons, deuterium, and carbon species. We find that the various saturation rules provide qualitatively similar behavior. This may help to explain why the different theory-based transport models can all predict core tokamak profiles reasonably well. Comparisons with nonlinear local and global gyrokinetic simulations are discussed. Full article

(This article belongs to the Special Issue New Insights into Plasma Theory, Modeling and Predictive Simulations)

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7 pages, 281 KiB

Open AccessCommunication

Unveiling the Significance of Correlations in K-Space and Configuration Space for Drift Wave Turbulence in Tokamaks

by Jan Weiland, Tariq Rafiq and Eugenio Schuster

Plasma 2023, 6(3), 459-465; https://doi.org/10.3390/plasma6030031 - 27 Jul 2023

Viewed by 967

Abstract

Turbulence and transport phenomena play a crucial role in the confinement and stability of tokamak plasmas. Turbulent fluctuations in certain physical quantities, such as density or temperature fluctuations, can have a wide range of spatial scales, and understanding their correlation length is important for predicting and controlling the behavior of the plasma. The correlation length in the radial direction is identified as the critical length in real space. The dynamics in real space are of significant interest because transport in configuration space is primarily focused on them. When investigating transport caused by the

E \times B

drift, the correlation length in real space represents the size of

E \times B

whirls. It was numerically discovered that in drift wave turbulence, this length is inversely proportional to the normalized mode number of the fastest growing mode relative to the drift frequency. Considerable time was required before a proper analytical derivation of this condition was accomplished. Therefore, a connection has been established between phenomena occurring in real space and those occurring in k-space. Although accompanied by a turbulent spectrum in k-space with a substantial width, transport in real space is uniquely determined by the correlation length, allowing for accurate transport calculations through the dynamics of a single mode. Naturally, the dynamics are subject to nonlinear effects, with resonance broadening in frequency being the most significant nonlinear effect. Thus, mode number space is once again involved. Resonance broadening leads to the detuning of waves from particles, permitting a fluid treatment. It should be emphasized that the consideration here involves the total electric field, including the induction part, which becomes particularly important at higher beta plasmas. Full article

(This article belongs to the Special Issue New Insights into Plasma Theory, Modeling and Predictive Simulations)

24 pages, 2059 KiB

Open AccessEditor’s ChoiceArticle

Validating the Multi-Mode Model’s Ability to Reproduce Diverse Tokamak Scenarios

by Tariq Rafiq, Zibo Wang, Shira Morosohk, Eugenio Schuster, Jan Weiland, Wilkie Choi and Hyun-Tae Kim

Plasma 2023, 6(3), 435-458; https://doi.org/10.3390/plasma6030030 - 24 Jul 2023

Cited by 4 | Viewed by 1589

Abstract

A large-scale validation exercise was conducted to assess the multi-mode model (MMM) anomalous transport model in the integrated modeling code TRANSP. The validation included 6 EAST discharges, 17 KSTAR discharges, 72 JET ITER-like wall D-D discharges, and 4 DIII-D fusion plasma discharges. Using the MMM, the study computed anomalous thermal, particle, impurity, and momentum transport within TRANSP. Simulations for EAST, KSTAR, and JET focused on electron and ion temperatures and safety factor profiles, while DIII-D simulations also considered electron density, toroidal rotation frequency, and flow shear. The predicted profiles were compared to experimental data at the diagnostic time, quantifying the comparison using root-mean-square (RMS) deviation and relative offsets. The study found an average RMS deviation of 9.3% for predicted electron temperature and 10.5% for ion temperature, falling within the experimental measurement error range 20%. The MMM model demonstrated computational efficiency and the ability to accurately reproduce a wide range of discharges, including various scenarios and plasma parameters, such as plasma density, gyroradius, collisionality, beta, safety factor and heating method variations. Full article

(This article belongs to the Special Issue New Insights into Plasma Theory, Modeling and Predictive Simulations)

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