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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Flexible, integrated modeling of tokamak stability, transport, equilibrium, and pedestal physics

The STEP (Stability, Transport, Equilibrium, and Pedestal) integrated-modeling tool has been developed in OMFIT to predict stable, tokamak equilibria self-consistently with core-transport and pedestal calculations. STEP couples theory-based codes to integrate a variety of physics, including magnetohydrodynamic stability, transport, equilibrium, pedestal formation, and current-drive, heating, and fueling. The input/output of each code is interfaced with a centralized ITER-Integrated Modelling & Analysis Suite data structure, allowing codes to be run in any order and enabling open-loop, feedback, and optimization workflows. This paradigm simplifies the integration of new codes, making STEP highly extensible. STEP has been verified against a published benchmark of six different integrated models. Core-pedestal calculations with STEP have been successfully validated against individual DIII-D H-mode discharges and across more than 500 discharges of the H98,y2 database, with a mean error in confinement time from experiment less than 19%. STEP has also reproduced results in less conventional DIII-D scenarios, including negative-central-shear and negative-triangularity plasmas. Predictive STEP modeling has been used to assess performance in several tokamak reactors. Simulations of a high-field, large-aspect-ratio reactor show significantly lower fusion power than predicted by a zero-dimensional study, demonstrating the limitations of scaling-law extrapolations. STEP predictions have found promising scenarios for an EXhaust and Confinement Integration Tokamak Experiment, including a high-pressure, 80%-bootstrap-fraction plasma. ITER modeling with STEP has shown that pellet fueling enhances fusion gain in both the baseline and advanced-inductive scenarios. Finally, STEP predictions for the SPARC baseline scenario are in good agreement with published results from the physics basis.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Early internal detection of magnetic tearing and implications for tokamak magnetohydrodynamic stability

Internal fluctuation measurements with Faraday-effect polarimetry in the DIII-D tokamak reveal the onset of a tearing mode with toroidal mode number n = 3 well before it is detected by the sensing coils external to the plasma. This mode appears before the n = 2, 1 modes and is first detected with internal measurements at a lower value of the ideal-wall kink beta limit than is indicated at the time of first detection by the sensing coils. When the mode is first detected, the linear resistive stability parameter, Δ′, indicates marginal stability and continues to do so until later when the mode amplitude begins increasing linearly with time—together suggesting a neoclassical origin for this mode.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Effect of negative triangularity on tearing mode stability in tokamak plasmas

Abstract The influence of negative triangularity (NT) of the plasma shape on the n = 1 (n is the toroidal mode number) tearing mode (TM) stability has been numerically investigated, with results compared to that of the positive triangularity (PT) counterpart. By matching the safety factor profile for a series of toroidal equilibria, several important plasma parameters, including the triangularity, the plasma equilibrium pressure, the plasma resistivity as well as the toroidal rotation, have been varied. The TM localized near the plasma edge is found to be more unstable in the NT plasmas as compared to the PT counterpart. The fundamental reason for this difference is the lack of favorable average curvature stabilization in NT configurations. Direct comparison of the Mercier index corroborates this conclusion. For the core-localized mode, where the difference in the local triangularity between NT and PT becomes small and the curvature stabilization is significantly reduced, larger Shafranov shift in the plasma core associated with the NT configuration results in more stable TM. The plasma toroidal flow generally stabilizes the TM in plasmas with both NTs and PTs. The flow stabilization is however weaker in the case of negative triangularity with finite plasma pressure.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

The theory of kinetic effects on resistive wall mode stability in tokamaks

Tokamak fusion plasmas benefit from high pressures but are then susceptible to modes of instability. These magnetohydrodynamic (MHD) modes are macroscopic distortions of the plasma, but certain collective motions of individual particles can provide stabilizing effects opposing them. The presence of a resistive wall slows the mode growth, converting a kink to a resistive wall mode (RWM). A kinetic MHD model includes Maxwell's equations, ideal MHD constraints, and kinetic effects included through the pressure tensor, calculated with the perturbed drift-kinetic distribution function of the particles. The kinetic stabilizing effects on the RWM arise through resonances between the plasma rotation and particle drift motions: precession, bounce, and transit. A match between particle motions and the mode allows efficient transfer of energy that would otherwise drive the growth of the mode, thus damping the growth. The first approach to calculating RWM stability is to write a set of equations for the complex mode frequency in terms of known quantities and then to solve the system. The “energy principle” approach, which has the advantage of clarity in distinguishing the various stabilizing and destabilizing effects, is to change the force balance equation into an equation in terms of changes of kinetic and potential energies, and then to write a dispersion relation for the mode frequency in terms of those quantities. These methods have been used in various benchmarked codes to calculate kinetic effects on RWM stability. Importantly, the theory has illuminated the important roles of plasma rotation, energetic particles, and collisions in RWM stability.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Demonstration of tokamak vertical stability control based on non-inductive Faraday-effect polarimetry measurements

Long-pulse or steady-state fusion reactors are envisioned to control vertical stability based on non-inductive measurements, i.e. that do not rely on temporal change of magnetic field. For the first time, vertical stability control using non-inductive Faraday-effect polarimetry measurements has been demonstrated. The Radial Interferometer-Polarimeter system on DIII-D is capable of microsecond resolution and was used to absolutely determine the vertical position of the plasma magnetic axis Z 0 . A vertical stability controller was developed to robustly stabilize diverted plasmas using Faraday-based measurements. The system was able to stabilize against vertical displacement events with growth rates up to 350 s -1 in elongated and elliptical plasma shapes, and instabilities with even higher growth rates are likely to be controllable with further improvements to controller tuning. Tests show that the Faraday-based controller remains effective and is capable of recovering from loss of control even when the plasma vertical position is far from the region where the linear model used to calculate Z 0 is most valid. Faraday control has also been activated during plasma ramp-up, demonstrating the robustness of the technique to larger systematic diagnostic uncertainty at low electron density.

Faraday-effect polarimetry↗
DOE OSTI2020

CAKE: Consistent Automatic Kinetic Equilibrium reconstruction

Magnetohydrodynamic equilibrium reconstructions with kinetic constraints are an essential input of many tokamak stability and transport analysis work- flows. The reconstructions themselves also contain useful information about pressure and current density distributions within the plasma which can be used to drive other calculations. While standardized magnetic-only, and partially kinetic equilibrium reconstruction is widely available and used, re- constructions for well diagnosed machines such as DIII-D, that incorporates a large and heterogeneous set of internal diagnostic measurements yet robustly reaching high numerical accuracy have been a time intensive, manual process. The Consistent Automatic Kinetic Equilibrium reconstruction tool (CAKE) has been developed and implemented at DIII-D for producing low error, kinetically constrained reconstructions without human intervention, and to identify strategies for doing so that would be broadly applicable. Here, the techniques employed to allow CAKE to handle data of limited quality and availability, as well as the full automation of the workflow may assist future efforts to form kinetic constraint profiles in real time plasma control applications.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Stability of a tokamak plasma with diffuse toroidal rotation

The present work considers the stability of a high- $\beta$ , large aspect ratio, circular plasma with diffuse profiles for the safety factor and the angular toroidal frequency (López & Guazzotto, Phys. Plasmas , vol. 24, 032501). An application of the Frieman–Rotenberg formalism results in a system of scalar eigenmode equations whose coupling is retained at the plasma–vacuum transition but is disregarded across the plasma column, which is a standard practice. The solution technique consists of a multidimensional shooting method for the poloidal harmonics; robust initial guesses are constructed by solving the dispersion relation in the static scenario with vanishing magnetic shear. Flow shear appears as a high- $\beta$ toroidal contribution, and we illustrate its destabilizing influence on $n=1$ external kink modes in the presence of ideal and resistive walls. Internal resonances are avoided by means of the selection of appropriate equilibrium parameters. The stabilizing influence of a finite positive average magnetic shear is also exemplified.

Physics↗
DOE OSTI2021

Hybrid simulations of sub-cyclotron compressional and global Alfvén eigenmode stability in spherical tokamaks

A comprehensive numerical study has been conducted in order to investigate the stability of beam-driven, sub-cyclotron-frequency compressional Alfvén eigenmodes (CAEs) and global Alfvén eigenmodes (GAEs) in low-aspect-ratio plasmas for a wide range of beam parameters. The presence of CAEs and GAEs has previously been linked to anomalous electron temperature profile flattening at high beam powers in NSTX experiments, prompting a further examination of the conditions necessary for their excitation. Linear simulations have been performed with the hybrid MHD–kinetic initial value code HYM in order to capture the general Doppler-shifted cyclotron resonance that drives the modes. Additionally, three distinct types of modes were found in the simulations—co-CAEs, cntr-GAEs, and co-GAEs—with differing spectral and stability properties. The simulations revealed that unstable GAEs are more ubiquitous than unstable CAEs, which is consistent with experimental observations, as they are excited at lower beam energies and generally have larger growth rates. Local analytic theory is used to explain key features of the simulation results, including the preferential excitation of different modes based on beam injection geometry and the growth rate dependence on the beam injection velocity, critical velocity, and degree of velocity space anisotropy. The background damping rate is inferred from the simulations and analytically estimated for relevant sources absent from the simulation model, indicating that co-CAEs are closer to marginal stability than modes driven by the cyclotron resonances.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Hybrid simulations of sub-cyclotron compressional and global Alfven Eigenmode stability in spherical tokamaks

A comprehensive numerical study has been conducted in order to investigate the stability of beam-driven, sub-cyclotron frequency compressional (CAE) and global (GAE) Alfven Eigenmodes in low aspect ratio plasmas for a wide range of beam parameters. The presence of CAEs and GAEs has previously been linked to anomalous electron temperature profile flattening at high beam power in NSTX experiments, prompting further examination of the conditions for their excitation. Linear simulations are performed with the hybrid MHD-kinetic initial value code HYM in order to capture the general Doppler-shifted cyclotron resonance that drives the modes. Three distinct types of modes are found in simulations -- co-CAEs, cntr-GAEs, and co-GAEs -- with differing spectral and stability properties. The simulations reveal that unstable GAEs are more ubiquitous than unstable CAEs, consistent with experimental observations, as they are excited at lower beam energies and generally have larger growth rates. Local analytic theory is used to explain key features of the simulation results, including the preferential excitation of different modes based on beam injection geometry and the growth rate dependence on the beam injection velocity, critical velocity, and degree of velocity space anisotropy. The background damping rate is inferred from simulations and estimated analytically for relevant sources not present in the simulation model, indicating that co-CAEs are closer to marginal stability than modes driven by the cyclotron resonances.

Compressional Alfven Eigenmodes↗
DOE OSTI2021

Magnetic-Confinement Fusion—Plasma Theory: Tokamak Magnetohydrodynamic Equilibrium and Stability

Magnetohydrodynamics (MHD) provides a useful model to describe the crucial plasma macroscopic equilibrium and stability behaviors in toroidal tokamak devices by considering the plasma as a conducting fluid interacting with a surrounding confining electromagnetic field. MHD is the most basic plasma model, incorporating most large-scale phenomena, including plasma equilibrium and all major instabilities. MHD equations are obtained by taking moments of the Boltzmann equations for different plasma species. They provide a set of comprehensive physics constrains to compute and optimize the equilibrium plasma shape and pressure and current profiles that are critical to its stability and performance. In the ideal case, the equations have special properties that lead to efficient numerical calculation schemes, the most important of which is the ideal MHD energy principle for linear stability against small departures from equilibrium. In a tokamak plasma, equilibrium pressure is mostly destabilizing for MHD modes, whereas equilibrium current is also often a major driving force. Plasma resistivity creates new freedom for a MHD instability to grow, but there are also cases where the plasma resistivity plays a stabilizing role. Equilibrium toroidal flow and/or flow shear can affect MHD instabilities. Principal MHD instabilities include the internal kink mode, sawtooth, fishbone, external kink, resistive wall mode, resistive interchange, tearing and neoclassical tearing modes (NTMs), locked modes, toroidal Alfven eigenmodes (TAEs), and edge localized modes (ELMs). Fast-growing MHD instabilities can lead to an abrupt plasma disruption and termination that can potentially damage the device plasma facing components (PFCs) and in-vessel structures. Furthermore, an important MHD application is to develop robust techniques to mitigate and control MHD instabilities.

Dispersive pellet injection↗
DOE OSTI2024

MHD stability of spherical tokamak equilibria with non-monotonic q-profiles

We use the 3D magnetohydrodynamic (MHD) code M3D-C1 [Jardin et al., Comput. Sci. Discovery 5, 014002 (2012)] to examine the MHD stability and subsequent evolution of NSTX shot 129169. This discharge had a period with a non-monotonic safety factor profile, q (reversed shear), which was terminated by a MHD event that abruptly lowered the central safety factor, q0, and greatly reduced the peakedness of the pressure profile. We show that the equilibrium just before the MHD event occurred was linearly unstable to many pressure-driven infernal modes. Modes with toroidal mode number n≥3 all had rational surfaces very close to the minimum value of q. However, a non-resonant pressure-driven (1, 1) mode was also present, and this dominated the nonlinear evolution. The final state in the simulation, after the MHD activity subsided, had a reduced and flattened pressure profile and a nearly monotonic q-profile, in qualitative agreement with experimental results. The initial state was also unstable to the resistive interchange criteria in the reversed-shear region, but the final state was stable everywhere. The “double tearing mode” (DTM) does not appear to play a role in the MHD activity of this discharge. In Appendix A, we show that in a torus, the DTM is strongly stabilized by pressure, but it is destabilized in cylindrical geometry (which has been the most extensively analyzed in the literature).

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Visualization of fast ion phase-space flow in plasmas well-below, near and well-above Alfvén eigenmode stability threshold in tokamak

Abstract Transport of fast ions along certain local phase space paths, referred to as fast ion phase-space flow, has been systematically measured by an imaging neutral particle analyzer (INPA) in three plasma regimes, which are well-below, near, and well-above the Alfvén eigenmode stability threshold (Du et al 2021 Phys. Rev. Lett. 127 235002). (1) In plasmas well-below the Alfvén eignenmodes (AE) stability threshold, fast ions are well-confined on passing particle orbits without noticeable transport over the phase space. The observed INPA images agree well with the synthetic INPA images, using the fast ion distribution predicted by neoclassical theory. (2) In plasmas near the AE stability threshold, INPA images in the presence of AE activity moderately deviate from those without AE activity. The image difference can be well interpreted by AE-driven, phase-space fast ion flow. Paths of this flow over the velocity space (or streamlines) are reconstructed by the intersection lines of curved E ʹ and µ surfaces, referred to as E ʹ and µ line (where E ′ ≡ E − ( ω / n ) P ζ ; E , P ζ and µ are the energy, canonical toroidal momentum and magnetic moment of ions; ω and n are the angular frequency and toroidal mode number of AEs, respectively). Resonant fast ions move radially inward by gaining energy and move radially outward by losing energy and the trajectory well aligns with the E ʹ and µ lines that pass through the mode resonances near the injection energy of neutral beams. (3) In plasmas well-above the AE stability threshold, fast ion phase-space dynamics shows additional features. Fast ions are transported out of the birth positions so promptly along the streamlines that the slowing-down process from the injection energy is not observable, exhibiting strong critical gradient behavior at local phase space. As a result, the increase of electron temperature is very small, in spite of an increase of beam power by ∼ 45 % . It should be emphasized that the directions of phase-space transport, induced by AEs with different frequencies, structures and mode numbers, do not largely differ.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

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.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

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.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Stability evaluation and mitigation strategies in advanced tokamaks using 3D MHD spectroscopy

Multi-modal, active 3D MHD spectroscopy is applied in high-performance advanced tokamak scenarios to study their stability time evolution, revealing an intriguing dependence on both and . A tailored applied 3D field provides a 3D plasma response to extract the growth rate of the least stable mode. The estimated growth rate finds a decrease in stability when the minimum in the safety factor (q) passes through 2.0 and reveals inherent risks of crossing an additional rational surface at integer q min , even above the usual q = 1 sawtooth condition. Based on this result, the potential scenario in which q min ~ 2 can be safely crossed during a more stable lower β N phase was investigated, and the improved stability of this scenario is confirmed by the estimated growth rate. This shows that 3D MHD spectroscopy can offer insights into strategies for improving stability by identifying the vulnerable aspects of such scenarios. In addition, the method highlights its potential for instability avoidance by enabling early detection of multiple modes, even before magnetic coils can measure them. The measured growth rate by the 3D MHD spectroscopy shows its reliability by exhibiting a correlation with the programmed rises in plasma beta across various high β N and high q min discharges. In addition, this method is successfully applied during rapidly evolving I p ramp-up phases, a key part of the scenario development. By achieving reasonable growth rate measurements at high-performance scenario developments, this technique contributes to the development of advanced diagnostic tools for tokamak scenario stability, which will help identify an effective pathway to stable, high-performance scenarios.

Yang, S. M. [Princeton Plasma Physics Laboratory (↗
DOE OSTI2024

ELM-free H-mode phase and decoupling of peeling–ballooning stability boundary in the MAST Upgrade tokamak

A linear magnetohydrodynamic (MHD) peeling–ballooning stability analysis of the edge-localized mode (ELM)-free phase of a MAST Upgrade (MAST-U) H-mode plasma is presented. In contrast to other similar discharges, #47018 is found to have a significantly higher and wider pedestal during its ELM-free H-mode phase that lasts for approximately 80 ms; this is made possible by the reduced core MHD mode activity on the q = 2 surface. During this period, there is sustained decoupling of peeling and ballooning branches of the stability boundary on J–α space, opening an access channel to the second stability regime with higher peaks in pedestal current density $J_{\mathrm{N,ped}}$ and pressure gradient (α). Such decoupling of the stability boundary has not previously been observed in MAST-U H-modes, and if such a condition can be readily reproduced, it opens a wide range of opportunities for MAST-U to explore low-collisionality peeling-limited pedestal regimes as well as advanced scenarios such as quiescent H-modes that are relevant to future reactors such as STEP and ITER.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Development of a neural network model for peeling–ballooning stability analysis in the KSTAR tokamak pedestals

The neural network model, MISHKA-NN is developed to mitigate the computational burden associated with the linear ideal magnetohydrodynamic (MHD) stability analysis of the pedestal based on the peeling–ballooning (P–B) model. By utilizing both 1D plasma profiles (current density, pressure gradient, and safety factor) and 0D parameters (plasma geometry, total current, and toroidal mode number), the model predicts linear growth rate of edge-localized ideal MHD instability in a given equilibrium state. By enabling the prediction of each instability within a second, the model reduces the time required for plotting a pedestal P–B stability diagram (j - α diagram) from approximately 100 CPU hours to a few CPU minutes. Notably, even with the utilization of parametric pressure and current profiles and plasma boundary shapes for the training dataset, the model shows a satisfactory level of performance in benchmarking the j - α diagram for the reconstructed equilibrium from a KSTAR tokamak experiment. We anticipate the model to serve as a versatile alternative to 2D linear MHD stability codes, alleviating numerical costs.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗