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At least 19 records

Validation of an integrated modeling framework for investigating 3D plasma responses in tokamak plasmas

As contemporary experimental tokamaks are pushed toward reactor-relevant operation, they provide essential testbeds for demonstrating and exploring ELM control strategies for deployment in future fusion pilot plants. Accurate predictions of full plasma responses are essential to guide and optimize these demonstrations. This paper introduces and validates an integrated modeling framework over a historical range of DIII-D operational space. The integrated modeling framework uses only scalar plasma parameters and optional reference boundary to self-consistently and flexibly scan through tokamak operational space and estimate the corresponding ELM-suppression relevant plasma response over 3D coil phase space. The framework generates tightly converged equilibria that satisfy a target set of plasma parameters (I p , β N , l i ), with kinetic profiles constrained by an EPED(NN)-computed pedestal and empirical core model. The plasma response of these modeled equilibria is calculated with GPEC. Validated against 55 distinct DIII-D equilibria, the framework consistently reproduces experimentally constrained equilibrium pressure, q, and other representative profiles using the time-varying information from only evolving scalar plasma parameters; plasma response validation is performed for the n=3 perturbation. In particular, the plasma response of a DIII-D discharge scanning q 95 in search of ELM suppression windows is quantitatively reproduced. By accurately reproducing experimental equilibria and plasma responses across wide parameter variation, the framework supports potential for synthetic parameter scans in key operational, stability, and plasma response dimensions to investigate RMP ELM-suppression experiments and inform predictive RMP scenario optimization.

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Machine learning methods for probabilistic locked-mode predictors in tokamak plasmas

A rotating tokamak plasma can interact resonantly with the external helical magnetic perturbations, also known as error fields. This can lead to locking and then to disruptions. We leverage machine learning (ML) methods to predict the locking events. We use a coupled third-order nonlinear ordinary differential equation model to represent the interaction of the magnetic perturbation and the plasma rotation with the error field. This model is sufficient to describe qualitatively the locking and unlocking bifurcations. Here, we explore using ML algorithms with the simulation data and experimental data, focusing on the methods that can be used with sparse datasets. These methods lead to the possibility of the avoidance of locking in real-time operations. We describe the operational space in terms of two control parameters: the magnitude of the error field and the rotation frequency associated with the momentum source that maintains the plasma rotation. The outcomes are quan- tified by order parameters that completely characterize the state, whether locked or unlocked. We use unsupervised ML methods to classify locked/unlocked states and note the usefulness of a certain normalization of the order parameters. Three supervised ML classifiers are used in suite to estimate the probability of locking in the region of control parameter space with hysteresis, i.e., the set of control parameters for which both locked and unlocked states can exist. The results show that a neural network gives the best estimate of the locking probability. An analogy of the present locking model with the van der Waals equation of state is also provided.

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Evidence of nonlinear coupling in the edge harmonic oscillation sustaining quiescent high confinement in a tokamak plasma

In a tokamak plasma, we measure nonlinear coupling between harmonics comprising a saturated edge oscillation, as predicted by nonlinear magnetohydrodynamic simulations. The coherent structure formed by this coupling suppresses bursty edge-localized modes that cause energy and particle loss. We also measure nonlinear coupling of the edge harmonic oscillation to core-resonant magnetic tearing modes. When tearing modes are present, the edge oscillation harmonics decouple, and edge-localized modes return. In this article, we conclude that nonlinear interaction with tearing modes interrupts the formation of the edge harmonic oscillation.

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Modelling of the electron cyclotron emission burst from a laboratory tokamak plasma with loss-cone maser instability

The maser instability associated with the loss-cone distribution has been widely invoked to explain the radio bursts observed in the astrophysical plasma environment, such as aurora and corona. In the laboratory plasma of a tokamak, events reminiscent of these radio bursts have also been frequently observed as an electron cyclotron emission (ECE) burst in the microwave range (~2f ce near the last closed flux surface) during transient magnetohydrodynamic events. These bursts have a short duration of ~10 μs and display a radiation spectrum corresponding to a radiation temperature T e,rad of over 30 keV while the edge thermal electron temperature T e is only in the range of 1 keV. Suprathermal electrons can be generated through magnetic reconnection, and a loss-cone distribution can be generated through open stochastic field lines in the magnetic mirror of the near-edge region of a tokamak plasma. Radiation modelling shows that a sharp distribution gradient ∂f/∂v ⊥ > 0 at the loss-cone boundary can cause a negative absorption of ECE radiation through the maser instability. The negative absorption then amplifies the radiation so that the microwave intensity is significantly stronger than the thermal value. The significant T e,rad from the simulations suggests the potential role of the loss-cone maser instability in generating the ECE burst in a tokamak.

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Self-organized magnetic equilibria in tokamak plasmas with very low edge safety factor

Tokamak plasmas often exhibit self-organizing behavior in which internal modes shape the toroidal current density profile, a common example being the sawtooth instability. However, such behavior has not been studied in detail for edge safety factor below 2 due to disruptive kink instabilities that typically prevent operation in this regime. Now, steady tokamak plasmas with an edge safety factor down to 0.8 have been created in the Madison Symmetric Torus, where disruptions are prevented due to a thick, conductive wall and a feedback power supply that sustains the plasma current. Internal measurements and nonlinear magnetohydrodynamic modeling reveal a family of safety factor profiles with a central value clamped near unity as the edge safety factor decreases, indicating current profile broadening through a relaxation process. Furthermore, as the safety factor decreases, the magnetic fluctuations become irregular, and the electron energy confinement time decreases.

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Intrinsic Toroidal Rotation Driven by Turbulent and Neoclassical Processes in Tokamak Plasmas from Global Gyrokinetic Simulations

Gyrokinetic tokamak plasmas can exhibit intrinsic toroidal rotation driven by the residual stress. While most studies have attributed the residual stress to the parallel-momentum flux from the turbulent E × B motion, the parallel-momentum flux from the drift-orbit motion (denoted $Π^D_\parallel$) and the E × B-momentum flux from the E × B motion (denoted $Π_{E×B}$) are often neglected. Here, we use the global total-f gyrokinetic code XGC to study the residual stress in the core and the edge of a DIII-D H-mode plasma. Numerical results show that both $Π^D_\parallel$ and $Π_{E×B}$ make up a significant portion of the residual stress. In particular, $Π^D_\parallel$ in the core is higher than the collisional neoclassical level in the presence of turbulence, while in the edge it represents an outflux of countercurrent momentum even without turbulence. Using a recently developed “orbit-flux” formulation, we show that the higher-than-neoclassical-level $Π^D_\parallel$ in the core is driven by turbulence, while the outflux of countercurrent momentum from the edge is mainly due to collisional ion orbit loss. In conclusion, these results suggest that $Π^D_\parallel$ and $Π_{E×B}$ can be important for the study of intrinsic toroidal rotation.

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Generation and suppression of runaway electrons in MST tokamak plasmas

This paper discusses the behavior of runaway electrons in tokamak plasmas at low electron density, plasma current, and magnetic field using experimental data from the Madison Symmetric Torus and computational data from the NIMROD nonlinear resistive 3D MHD code. Density thresholds for the onset and suppression of runaway electrons are determined experimentally in steady tokamak plasmas, and in plasmas with a population of runaway electrons, resonant magnetic perturbations with different poloidal mode numbers are applied. Poloidal mode number m = 3 perturbations suppress the runaway electrons, while perturbations with m = 1 have little effect. This difference is consistent with the difference in computed magnetic topologies. The m = 1 RMP has minimal effect on the topology, while the m = 3 RMP produces a broad region of stochasticity, which can allow for rapid loss of the runaway electrons.

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Stability and Control of Burning Tokamak Plasmas with Resistive Walls (Final Report)

Work supported by the grant, "Stability and Control of Burning Tokamak Plasmas with Resistive Walls" in the period Aug 2017 to 2023 can be cast in three general categories: (1) linear tearing regimes and the effects on the response to error fields and resistive walls: (2) nonlinear tearing modes in the presence of error fields, with locking; and (3) energetic particle effects. In the first category, we have completed a study of tearing mode regimes with extended MHD effects, including parallel dynamics and toroidal effects, notably favorable average curvature. This work has been presented at the 2018 Sherwood Conference. This work has been published in the ArXiv and is being prepared for publication in Physics of Plasmas. A systematic study of shaping in a tokamak plasma with resistive tearing layers and a resistive wall has been presented in the PhD dissertation by Dov Rhodes, a student of Andrew Cole at Columbia University. John Finn was on Rhodes's PhD committee, and was a co-author of a paper published in Physics of Plasmas on that work. A detailed study of nonlinear tearing modes in the presence of finite beta, favorable average curvature, and an error field has been nearly completed. In this study it was found that the response to an error field with real frequency a tearing layer agreed with analytic results, and that tearing mode saturation by flattening of the current profile as well as destabilization due to flattening of the pressure profile were important factors in the locking process. This work was presented at the 2017 APS/DPP Conference and at the 2018 Sherwood Conference. The effects of energetic ions on tearing modes was presented at the 2017 APS/DPP Conference and in the PhD dissertation of Michael Halfmoon. John Finn served as a committee member on Halfmoon's PhD committee. Extensions to this work including two fluid effects were performed and presented at the APS/DPP Conference in 2017.

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Influence of anomalous perpendicular transport on linear tearing mode dynamics in tokamak plasmas

The analysis of a previous paper [A. Cole and R. Fitzpatrick, Phys. Plasmas 13, 032503 (2006)] that maps out all of the two-fluid response regimes of a linear tearing layer interacting with an externally generated resonant magnetic perturbation, in a large aspect-ratio tokamak plasma, is generalized to take into account realistic levels of perpendicular particle transport. A new response-regime map is obtained that differs substantially, in many respects, from the old one. The improved analysis is first employed to find all of the two-fluid growth-rate regimes of a non-interacting low-mode-number tearing mode in a large aspect-ratio tokamak plasma. The analysis is then used to determine the scaling of the error-field penetration threshold with machine parameters in large aspect-ratio tokamak plasmas.

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Local transport dynamics of cold pulses in tokamak plasmas

Abstract For over two decades, our fundamental understanding of energy transport dynamics in the core of tokamak plasmas had been challenged by the striking observation of temperature perturbation reversals following the injection of cold pulses at the plasma edge. These phenomena were first discovered by Gentle et al. (Phys. Rev. Lett. 74(18):3620–3623, 1995) in 1995 and had long been suggested to be evidence of nonlocal transport effects. In recent years, a new explanation to these phenomena has emerged, fully consistent with the theory of turbulent transport in magnetized plasmas and in remarkable agreement with experiment. This article reviews the experimental observation of temperature reversals in tokamak plasmas and presents the explanation based on local transport physics.

Rodriguez-Fernandez, P. (ORCID:0000000273611131)↗

Projected global stability of high beta MAST-U spherical tokamak plasmas

Assessment of the limits of stability of tokamak plasmas is essential to operation in high fusion performance ranges without disruption of the plasma current. Projected equilibria have been generated for the MAST-U spherical tokamak experiment, an upgrade of the previous MAST device, in order to prepare for operation. These equilibria are scanned in pressure and current profiles, and assessed with the DCON and MARS-F stability codes to find the so-called 'no-wall' beta limit, above which resistive wall mode instabilities can be expected in the absence of other stabilising effects. The no-wall limit was generally found to increase as plasma internal inductance increased. The equilibria are also assessed for the 'with-wall' limit, theoretically the highest achievable performance point, again with the DCON and MARS-F codes, including different approximate axisymmetric walls, and with the VALEN code which includes a 3D model of the surrounding conducting structure. Similar limits were found, despite the difference between the 2D and 3D codes in the treatment of the wall. Conducting passive stabilisation plates, which were newly installed in MAST-U, are in a region of significant mode perturbation when the plasma β N is sufficiently high and eddy currents are driven in these structures. Due to the increased stabilising effect of the wall in MAST-U vs. MAST, a significant gap exists between the approximate no-wall limits of β N / l i = 6.71 and 7.13, found from DCON and MARS-F respectively, and the with-wall limits of β N / l i = 8.23 and 8.53 for the equilibrium profiles analysed in this study. This opens a region of high beta operating space in MAST-U for potentially stable operation if non-ideal effects or active control can stabilise the resistive wall mode.

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An E and B gyrokinetic simulation model for kinetic Alfvén waves in tokamak 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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Bifurcated merging operations of two spherical tokamak plasmas for reconnection heating and magnetic helicity injection

In tokamak plasma merging experiments, high-power ion heating is achieved only when the current sheet thickness is compressed to ion gyroradius ρ i . The magnetic reconnection converts 40%–50% of the reconnecting magnetic field energy (B rec 2 /2μ 0 ) into the ion heating energy (W i ) with the scaling law of W i proportional to B rec 2 . If the compressed current sheet thickness is larger than ρ i the magnetic reconnection converts only 5%–10% of B rec 2 /2μ 0 into W i . Finally, the high-power ion heating can be understood from the experimental finding that the poloidal electric field due to electrostatic quadrupolar potential in the downstream region increases linearly with both B rec and the guide field B t .

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Faraday-effect polarimetry for current profile measurement in the tokamak plasma edge

Toroidal current profile measurements in the tokamak plasma edge are critical for fusion plasma physics research and model validation. A three-wave Faraday-effect polarimeter-interferometer with a sub-centimeter spatial resolution is proposed on the DIII-D tokamak to determine the edge current profile via Abel inversion. By using probe beams with 316 µm wavelength, a low-field-side, vertical-view, single-pass optical layout covering the plasma edge region (R = 2.15–2.27 m) is assessed. Measurements with no greater than 0.1° polarimetric systematic uncertainty, no greater than 0.01° polarimetric root-mean-square noise (1 kHz bandwidth), and a 0.8 cm radial chord spacing are considered feasible based on the achieved performance of existing systems using similar wavelengths on fusion devices. Furthermore, synthetic diagnostic calculations taking various factors into account, such as diagnostic uncertainty and quality of magnetic flux surfaces, find that the edge current profile can be determined with up to 0.12 MA/m 2 uncertainty, or about 10% of the peak current density in the pedestal of an investigated high-confinement plasma.

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Physics of the thermal quench in MST tokamak plasmas (Final Technical Report)

This project at the University of Wisconsin-Madison targeted measurements in tokamak plasmas in the Madison Symmetric Torus (MST) to help elucidate the physics of the tokamak disruption. We intended to focus on the thermal quench, during which energy is lost from the plasma in a very short time. Understanding and ultimately mitigating the thermal quench are among the highest priority research thrusts for ITER, a large international fusion experiment presently under construction. The measurements in MST exploited an advanced set of diagnostics for internal measurements with high time resolution, targeting linear and nonlinear magnetohydrodynamic (MHD) activity as well as the electron temperature and density profiles. We also exploited other features of the MST device, including very flexible power supplies for the toroidal magnetic field and toroidal plasma current that are capable of producing almost arbitrary waveforms. While the work funded by this project was purely experimental, we continued and expanded an existing collaboration with UW-Madison experts in nonlinear MHD computational modeling of tokamak plasmas. That modeling incorporated realistic, experimentally measured parameters. The results of the modeling were anticipated to deepen considerably our understanding of the experimental measurements, and in turn, the experimental measurements were anticipated to help validate the modeling results. The science of transients such as disruptions is one of the highest priority research areas in the U.S. and international fusion programs. The work carried out in this project was targeted to help advance the science of tokamak disruptions which will in turn contribute to the success of ITER.

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Generalized kinetic equation for tokamak plasma equilibrium distribution function

A generalised kinetic equation for the equilibrium distribution function in a finite beta, arbitrary tokamak plasma is derived. The equation is correct to second order in ρ/L (ρ is the particle Larmor radius and L is the system size). Resolving finite Larmor radius length scales with no restriction on the ratio of poloidal to total equilibrium magnetic field, B $\vartheta$ /B, it generalises the drift kinetic theory of [Hazeltine Phys. Plasmas 15 (1973) 77] to the limit of B $\vartheta$ /B ~ 1 (e.g. to ensure validity for spherical tokamaks). Two cases are considered. The first provides the equilibrium distribution function, consistent with the generalised gyrokinetic formalism of [Dudkovskaia et al. Plasma Phys. Control. Fusion 65 (2023) 045010], derived specifically to capture neoclassical equilibrium currents in gyrokinetic stability analyses in strong gradient regions. The second assumes short length scales in the direction perpendicular to the magnetic field, which can occur as a result of small coherent magnetic structures in the plasma, such as neoclassical tearing mode magnetic islands close to threshold. This then extends the drift island equations of [Dudkovskaia et al. Nucl. Fusion 63 (2023) 016020] for the plasma response to magnetic islands to a spherical tokamak plasma configuration. In conclusion, resolving ρ ~ ρ $\vartheta$ (or B $\vartheta$ ~ B), where ρ $\vartheta$ is the particle poloidal Larmor radius, is also expected to influence calculations of the magnetic island propagation frequency and the associated contributions to the island onset conditions.

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Internal measurement of magnetic turbulence in ELMy H-mode tokamak plasmas

Magnetic turbulence is directly observed internally in the pedestal of ELMy H-mode tokamak plasmas using a newly developed Faraday-effect polarimetry measurement. Fluctuation amplitude is δb r ≥ 15 G (150–500 kHz), with a ratio of magnetic to density fluctuation |δb r /B|/|δn/n|≥0.15. Here, magnetic turbulence is identified as resulting from micro-tearing-instability and mode growth accompanied by degraded plasma confinement is observed.

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Combined Influence of Rotation and Scrape-Off Layer Drifts on Recycling Asymmetries in Tokamak Plasmas

Coupled 2D fluid-kinetic simulations of a DIII-D high confinement tokamak plasma show that plasma rotation coupled with drift effects near the plasma edge play a significant role in the creation of the observed poloidal distribution of neutrals. It is observed that including either drift or rotation effects enhances particle flux at the inner target in the case of ion 𝐵×∇𝐵 drift toward the 𝑋-point. However, the particle flux asymmetry is significantly higher with the combination of drifts and rotation than either effect alone. The heightened particle flux asymmetry allows for improved simulation of the strong in-out asymmetry of the Lyman-𝛼 brightness profiles measured in the experiment. Enhancement of radial transport of parallel momentum changes the upstream scrape-off layer flow pattern, increasing the fraction of deuterium flux that reaches the inboard divertor entrance while lowering that which arrives at the outboard. In conclusion, this Letter indicates that by combining drifts, rotation, and viscous coupling, existing boundary plasma models can achieve a satisfactory agreement with experimentally measured neutral asymmetries.

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