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At least 649 records · Page 36

Development of a reduced model for energetic particle transport by sawteeth in tokamaks

We report that the sawtooth instability is known for inducing transport and loss of energetic particles (EPs), and for generating seed magnetic islands that can trigger tearing modes. Both effects degrade the overall plasma performance. Several theories and numerical models have been previously developed to quantify the expected EP transport caused by sawteeth, with various degrees of sophistication to differentiate the response of EPs at different energies and on different orbits (e.g. passing vs. trapped), although the analysis is frequently limited to a single time slice during a tokamak discharge. This work describes the development and initial benchmark of a framework that enables a reduced model for EP transport by sawteeth retaining the full EP phase-space information. The model, implemented in the ORBIT hamiltonian particle-following code, can be used either as a standalone post-processor taking input data from codes such as TRANSP, or as a pre-processor to compute transport coefficients that can be fed back to TRANSP for time-dependent simulations including the effects of sawteeth on EPs. The advantage of the latter approach is that the evolution of the EP distribution can be simulated quantitatively for sawtoothing discharges, thus enabling a more accurate modeling of sources, sinks and overall transport properties of EP and thermal plasma species for comprehensive physics studies that require detailed information of the fast-ion distribution function and its evolution over time.

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Verification of an improved equation-free projective integration method for neoclassical plasma-profile evolution in tokamak geometry

A brute-force, long-time gyrokinetic simulation of plasma profile evolution in magnetic fusion devices is not desirable due to large computational resource requirements and a possible accumulation of numerical error. The equation-free projective integration method of Keverekidis et al. [Commun. Math. Sci. 1(4), 715–762 (2003)] is one of the outstanding candidates in projecting micro-scale simulations to a longer timescale. However, its application to tokamak plasma has not been fruitful due to the appearance of spurious transient oscillations in the lifting process, which are present when the kinetic simulations are initialized with a simplified model distribution function and which make the kinetic simulations to deviate from the desired paths. In this work, a kinetically informed lifting algorithm is added to the equation-free projective integration method, which is then verified in the electrostatic gyrokinetic particle-in-cell code XGCa [R. Hager and C. S. Chang, Phys. Plasmas 23, 042503 (2016)] for a neoclassical ion heat transport problem with adiabatic electrons. This new lifting operator is demonstrated to control spurious transients, enabling an over four-times reduction in the overall computing time in the time-evolution of the ion temperature profile in an axisymmetric toroidal plasma. Further reduction in the computing time is found to be limited due to the stability properties of the linear least squares projective integrator.

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Disruption event characterization and forecasting in tokamaks

Disruption prediction and avoidance is a critical need for next-step tokamaks, such as ITER. Disruption Event Characterization and Forecasting (DECAF) research fully automates analysis of tokamak data to determine chains of events that lead to disruptions and to forecast their evolution allowing sufficient time for mitigation or complete avoidance of the disruption. Disruption event chains related to local rotating or global magnetohydrodynamic (MHD) modes and vertical instability are examined with warnings issued for many off-normal physics events, including density limits, plasma dynamics, confinement transitions, and profile variations. Along with Greenwald density limit evaluation, a local radiative island power balance theory is evaluated and compared to the observation of island growth. Automated decomposition and analysis of rotating tearing modes produce physical event chains leading to disruptions. A total MHD state warning model comprised of 15 separate criteria produces a disruption forecast about 180 ms before a standard locked mode detector warning. Single DECAF event analyses have begun on KSTAR, MAST, and NSTX/-U databases with thousands of shot seconds of device operation using from 0.5 to 1 × 10 6 tested sample times per device. An initial multi-device database comparison illustrates a highly important result that plasma disruptivity does not need to increase as βN increases. Global MHD instabilities, such as resistive wall modes (RWMs), can give the briefest time period of warning before disruption compared to other physics events. In an NSTX database with unstable RWMs, the mode onset, loss of boundary and current control, and disruption event warnings are found in all cases and vertical displacement events are found in 91% of cases. An initial time-dependent reduced physics model of kinetic RWM stabilization created to forecast the disruption chain predicts instability 84% of the time for experimentally unstable cases with a relatively low false positive rate. Instances of the disruption event chain analysis illustrate dynamics including H–L back transitions for rotating MHD and global RWM triggering events. Furthermore, disruption warnings are issued with sufficient time before the disruption (on transport timescales) to potentially allow active profile control for disruption avoidance, active mode control, or mitigation.

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Editorial for the 28th Workshop on Magnetohydrodynamic (MHD) Stability Control

This special issue contains four papers which were presented at the 28th Workshop on Magnetohydrodymanic (MHD) Stability Control. The workshop was held at Auburn University and on Zoom from 3–5 October 2024. Furthermore, this annual workshop covers the active and passive control of MHD instabilities such as kink, tearing and edge-localized modes in tokamaks, reversed field pinches, spherical tori or other magnetic confinement devices.

Yang, J. [Princeton Plasma Physics Laboratory (PPP↗

Frontier system-on-chip (SoC) technology for microwave diagnostics (invited)

The next generation of fusion reactors, exemplified by projects such as the Demonstration Power Plant following the International Thermonuclear Experimental Reactor, faces the monumental challenge of proving the viability of generating electricity through thermonuclear fusion. This pursuit introduces heightened complexities in diagnostic methodologies, particularly in microwave-based diagnostics. The increased neutron fluence necessitates significant reductions in vessel penetrations and the elimination of internal diagnostics, posing substantial challenges. SoC technology offers a promising solution by enabling the miniaturization, modularization, integration, and enhancing the reliability of microwave systems. After seven years of research, our team successfully pioneered the V- and W-band system-on-chip approach, leading to the development of active transmitters and passive receiver modules applied in practical settings, notably within the DIII-D tokamak project. Arrays of these modules have supported microwave imaging diagnostics. New physics measurement results from the Electron Cyclotron Emission Imaging system on DIII-D provide compelling evidence of improved diagnostics following the adoption of SoC technology. Furthermore, we achieved a breakthrough in developing an F-band SoC, advancing higher frequency capabilities for fusion devices. These achievements represent a significant leap forward in fusion diagnostic technology, marking substantial progress toward establishing reliable and efficient plasma diagnostics for future fusion reactors.

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Axisymmetric simulations of vertical displacement events in tokamaks: A benchmark of M3D-C 1 , NIMROD, and JOREK

A benchmark exercise for the modeling of vertical displacement events (VDEs) is presented and applied to the 3D nonlinear magnetohydrodynamic codes M3D-C 1 , JOREK, and NIMROD. The simulations are based on a vertically unstable NSTX equilibrium enclosed by an axisymmetric resistive wall with a rectangular cross section. A linear dependence of the linear VDE growth rates on the resistivity of the wall is recovered for sufficiently large wall conductivity and small temperatures in the open field line region. We report the benchmark results show good agreement between the VDE growth rates obtained from linear NIMROD and M3D-C 1 simulations and from the linear phase of axisymmetric nonlinear JOREK, NIMROD, and M3D-C 1 simulations. Axisymmetric nonlinear simulations of a full VDE performed with the three codes are compared, and an excellent agreement is found regarding the plasma location and plasma currents, as well as eddy and halo currents in the wall.

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Fuel recycling control in long pulse operation with full tungsten divertors in EAST tokamak

Fuel recycling control in long pulse discharges is studied in EAST tokamak with tungsten divertors by particle balance. Double null configuration, proper Resonant Magnetic Perturbation (RMP), divertor cryopumps and realtime lithium injection, are all very effective for recycling control. High heating power discharge leads to low recycling due to the enhancement of particle exhausting. High external gas injection is required in a low fuel recycling discharge to keep a constant density, and Dα emission is increased by external injection, therefore a higher Dα emission may indicate low fuel recycling for the same plasma density. Reproducible long pulse discharges of over 100 s with core electron temperature >10 keV, and 1056 s discharge with ~1.5 MW heating power were obtained in the EAST 2021 campaign, fuel recycling was well controlled by divertor cryopumps and realtime lithium injection. The results provide a valuable reference for the high power and long pulse operation in future fusion reactors, such as ITER and CFETR.

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Application of machine learning and artificial intelligence to extend EFIT equilibrium reconstruction

Recent progress in the application of machine learning (ML)/artificial intelligence (AI) algorithms to improve the Equilibrium Fitting (EFIT) code equilibrium reconstruction for fusion data analysis applications is presented. A device-independent portable core equilibrium solver capable of computing or reconstructing equilibrium for different tokamaks has been created to facilitate adaptation of ML/AI algorithms. A large EFIT database comprising of DIII-D magnetic, motional Stark effect, and kinetic reconstruction data has been generated for developments of EFIT model-order-reduction (MOR) surrogate models to reconstruct approximate equilibrium solutions. Furthermore, a neural-network MOR surrogate model has been successfully trained and tested using the magnetically reconstructed datasets with encouraging results. Other progress includes developments of a Gaussian process Bayesian framework that can adapt its many hyperparameters to improve processing of experimental input data and a 3D perturbed equilibrium database from toroidal full magnetohydrodynamic linear response modeling using the Magnetohydrodynamic Resistive Spectrum - Feedback (MARS-F) code for developments of 3D-MOR surrogate models.

Gaussian process↗

Design and Analysis of Liquid Lithium Plasma Facing Components

In this study, liquid metal (LM) on plasma-facing components (PFCs) creates a renewable protective cover enhancing power exhaust and protecting the solid substrate. Additionally, energy confinement improvement through particle pumping can be achieved in the case of liquid lithium (LL). A new variant of PFCs was recently introduced at Princeton Plasma Physics Laboratory (PPPL) where a porous wall is used to stabilize the LM surface, while using magnetohydrodynamic (MHD) drive to push the LM flow inside the component. This arrangement allows efficient heat exhaust, and enhanced control of the LM surface temperature, leading to spatial control of evaporation and condensation of LL on the plasma interface. This feature is particularly attractive when vapor shielding is introduced to allow heat flux redistribution. This system has the advantage that as the heat flux increases, the evaporation rate will increase, while decreasing heat flux will decrease the evaporation rate of lithium, ideally creating a feedback effect which could self-regulate the amount of lithium evaporated. Analytical and numerical models for LL PFCs were developed in PPPL. To calculate the target temperature distribution for the case of evaporation from the divertor, we apply an iterative process allowing two-way coupling between the fluid-kinetic analysis of plasma using SOLPS-ITER code and the flow and heat transfer analysis of the PFC using an analytical model. In the last stage, the results are validated using computational fluid dynamics (CFD) analysis with customized version of the CFX code from ANSYS. CFX was modified at PPPL to allow MHD analysis at the high magnetic field typical for fusion applications. Results of the analysis for NSTX-U tokamak conditions will be presented.

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Effects of equilibrium pressure on plasma response to RMPs in a spherical tokamak

This study presents a comprehensive analysis of the equilibrium pressure on the plasma response to resonant magnetic perturbations (RMPs) in the spherical tokamak (ST) MAST-U, employing both single-fluid and MHD-kinetic hybrid models (implemented via the MARS-F/K codes). As a key finding, the study identifies two different pressure-driven eigenmodes, exhibiting Sturmian property, that affect the Troyon no-wall limits for the onset of the n = 1 and n = 2 ( n is the toroidal mode number) ideal external kink instabilities as well as the corresponding plasma response to the applied RMP. With increasing equilibrium pressure, the plasma response to RMPs is significantly enhanced in the ST plasma, particularly in the high-pressure regime where kinetic effects strongly stabilize the external kink instability. The Troyon no-wall limit divides the plasma response into two regions: well below the limit, the response amplitudes and trends (versus pressure) are similar between the fluid and kinetic models; as the equilibrium pressure approaches the Troyon limit, the kinetic model predicts significant amplification of the RMP field, up to 30 times for cases considered. A relatively weak dependence of the optimal coil phasing on the equilibrium pressure is computed in this ST plasma, similar to the trend obtained for the conventional aspect ratio devices. These findings underscore the importance of incorporating kinetic effects in accurate prediction of the plasma response to RMPs in high-pressure ST tokamak plasmas and provide a theoretical basis for optimizing RMP-based control of the edge-localized modes in future ST devices.

RMP↗

Plasma shape and position control development for NSTX-U using the GSEvolve plasma simulator

NSTX-U discharges have been reproduced using the GSEvolve plasma simulator in order to improve their control and reduce oscillations during the plasma current (Ip) ramp-up phase, and with the ultimate goal of enabling reliable H-mode access with a double-null shape at high elongation, low internal inductance, and high plasma performance. The control objective is to eliminate undesired oscillations in the plasma shape and vertical position that start when the plasma diverts during the Ip ramp-up phase, and that happened recurrently during the first NSTX-U experimental campaign. Model-based control solutions have been developed, including alternative H-mode access recipes and a Multi-Input Multi-Output (MIMO) decoupling controller. These solutions have demonstrated their capability to reduce or eliminate the aforementioned oscillations in GSEvolve simulations, enabling reproducible H-mode access. The results of this work aim to inform NSTX-U experimental operations on potential control developments to maximize its scientific output, and highlight the powerful capabilities of high-fidelity control-simulation frameworks like GSEvolve.

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Modeling q 95 windows for the suppression of edge localized modes by resonant magnetic perturbations in the DIII-D tokamak

A toroidal asymptotic matching model of the response of a tokamak plasma to a static resonant magnetic perturbation (RMP) is used to simulate the n = 3 RMP-induced edge-localized-mode-suppression windows in q 95 that are evident when the plasma current is slowly ramped in DIII-D discharge #145380. All quantities employed in the simulation are derived from experimental measurements, apart from the neutral particle data. Three cases are considered. In the first case, the natural frequencies of tearing modes resonant in the plasma are determined by the ion flows at the corresponding resonant surfaces, which is the prediction of nonlinear tearing mode theory. In the second case, the natural frequencies are determined by the local E x B velocities at the resonant surfaces. In the third case, the natural frequencies are determined by the electron flows at the resonant surfaces, which is the prediction of linear tearing mode theory. The second case gives the best agreement between the simulations and the experimental observations. The first and third cases only lead to partial agreement between the simulations and the observations. In the first case, the lack of complete agreement may be a consequence of using an inaccurate assumption for the neutral particle distribution in the pedestal. In the third case, the lack of complete agreement is probably due to the fact that the response of a tokamak plasma to an RMP is not accurately described by linear tearing mode theory.

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Effects of divertor electrical drifts on particle distribution and detachment near the divertor target plate in DIII-D

Strong impacts of drifts on the divertor plasma in–out asymmetry and detachment are demonstrated in DIII-D with an open divertor configuration. For forward toroidal field, B T , i.e., with the ion B × ∇B drift toward the divertor, the particle flux to the inner divertor, as represented by the Langmuir probe measured ion saturation current (J sat ), exhibits a double peak structure, with electron temperature, lower at the inner target. Reversing the B T direction reverses both the radial and poloidal E × B flows, leading to a broad particle flux profile in the outboard scrape-off layer (SOL) with a similar double-peak structure to that observed at the inner target with forward B T . The correlation of a double peak structure with divertor temperature profiles confirms physical coupling between the drift flow and sheath boundary condition and their strong impact on divertor profiles. In addition, under reversed B T conditions, increasing the density flattens the target temperature profile. However, J sat remains high away from the strike point, rendering it difficult to achieve an “effective” detached plasma, i.e., with effective reduction in both peak heat flux and peak temperature (in the far SOL). In contrast, divertor detachment with a cold and flat temperature profile can be achieved at both target plates with the forward B T .

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Computation of the Biot–Savart line integral with higher-order convergence using straight segments

One common approach to computing the magnetic field produced by a filamentary current-carrying coil is to approximate the coil as a series of straight segments. The Biot–Savart field from each straight segment is analytically known. However, if the endpoints of the straight segments are chosen to lie on the coil, then the accuracy of the Biot–Savart computation is generally only the second order in the number of endpoints. In this work, we propose a simple modification: shift each end point of the coil in the outward normal direction by an amount proportional to the local curvature. With this modification, the Biot–Savart accuracy increases to the fourth order and the numerical error is dramatically reduced for a given number of discretization points.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Extension of the flux fit method for estimating power deposition profiles

The flux fit method is used to self-consistently estimate the power deposition profile and heat transport profiles from temperature measurements originating from perturbative experiments with a modulated source. Furthermore, this letter improves on this method by addressing the limitations and assumptions. The most crucial improvement is the additional freedom in the source deposition profile. Allowing for a variable central deposition location and height and including a skewness parameter produces deposition profiles more consistent with the measurement data, but still wider than equilibrium ray tracing in two different DIII-D discharges. Moreover, we show that the quality of the estimated deposition profile is key to the accuracy of diffusivity and connectivity estimates, but inversely, the estimated transport parameters hardly affect the quality of the power deposition estimate. Using this method, we show that the power deposition profile estimate is broadened with respect to ray-tracing by about 1.7-1.8 times in two DIII-D discharges.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Testing the conservative character of particle simulations: I. Canonical and noncanonical guiding center model in Boozer coordinates

The guiding center (GC) Lagrangian in Boozer coordinates for toroidally confined plasmas can be cast into canonical form by eliminating terms containing the covariant component B Ψ P of the magnetic field vector with respect to the poloidal flux function Ψ P . In an unperturbed plasma, B Ψ P can be eliminated via exact coordinate transformations, but, in general, one relies on approximations, assuming that the effect of B Ψ P is small. In this work, we are interested in the question whether Hamiltonian conservation laws are still satisfied when B Ψ P is retained in the presence of fluctuations. Considering fast ions in the presence of a shear Alfvén wave field with fixed amplitude, fixed frequency, and a single toroidal mode number n, we show that simulations using the code ORBIT with and without B Ψ P yield practically the same resonant and nonresonant GC orbits. The numerical results are consistent with theoretical analyses (presented in the appendix), which show that the unabridged GC Lagrangian with B Ψ P retained yields equations of motion that possess two key properties of Hamiltonian flows: (i) phase space conservation and (ii) energy conservation. As counter-examples, we also show cases where energy conservation (ii) or both conservation laws (i) and (ii) are broken by omitting certain small terms. When testing the conservative character of the simulation code, it is found to be beneficial to apply perturbations that do not resemble normal (eigen) modes of the plasma. The deviations are enhanced and, thus, more easily spotted when one inspects wave-particle interactions using nonnormal modes.

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The infrared imaging video bolometer at Wendelstein 7-X

The radiated power distribution is a crucial aspect of heat transport, heat load mitigation, and plasma exhaust performance. An imaging video bolometer camera has been installed to measure the plasma radiated power in the divertor region of the Wendelstein 7-X (W7-X) stellarator. This diagnostic offers a wide-angle (40° × 68°) sampling of the plasma volume in both the poloidal and toroidal directions. The field-of-view is covered with a large number (> 500) of bolometer channels, providing imaging capability. The diagnostic design is introduced here together with its data analysis procedure. A set of laboratory experiments is performed to assess the thermal properties of the gold absorber foil and their spatial uniformity. Following installation, a heat source originating from the inertially cooled front of the diagnostic is identified and filtered out. The discharge data indicate a satisfactory signal-to-noise ratio as well as spatiotemporal resolution. These represent the first toroidally resolved images of the line-integrated radiated power in the W7-X island divertor. The diagnostic was then upgraded with a thinner platinum absorber and adjusted mirrors. Early data from the most recent experimental campaign employing the upgraded design show a considerable improvement in the diagnostic performance with more bolometer channels (> 1400), extended coverage, and increased spatial resolution.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Excitation of whistler and slow-X waves by runaway electrons in a collisional plasma

Runaway electrons are known to provide robust ideal or collisionless kinetic drive for plasma wave instabilities in both the whistler and slow-X branches, via the anomalous Doppler-shifted cyclotron resonances. In a cold and dense post-thermal-quench plasma, collisional damping of the plasma waves can compete with the collisionless drive. Previous studies have found that, due to their higher wavelength and frequency, slow-X waves suffer stronger collisional damping than the whistlers, while the ideal growth rate of slow-X modes is higher. Here, we study runaway avalanche distributions that maintain the same eigen distribution and increase only in magnitude over time. The distributions are computed from the relativistic Fokker–Planck–Boltzmann solver, upon which a linear dispersion analysis is performed to search for the most unstable or least damped slow-X and whistler modes. Taking into account the effect of plasma density, plasma temperature, and effective charge number, we find that the slow-X modes tend to be excited before the whistlers in a runaway current ramp-up. Furthermore, even when the runaway current density is sufficiently high that both branches are excited, the most unstable slow-X mode has a much higher growth rate than the most unstable whistler mode. The qualitative and quantitative trends uncovered in the current study indicate that even though past experiments and modeling efforts have concentrated on whistler modes, there is a compelling case that slow-X modes should also be a key area of focus in the runaway self-mediation through wave instabilities.

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