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At least 469 records · Page 26
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

On the relationship between the multi-region relaxed variational principle and resistive inner-layer theory

We show that the variational energy principle of the multi-region relaxed magnetohydrodynamic (MRxMHD) model can be used to predict finite-pressure linear tearing instabilities. In this model, the plasma volume is sliced into sub-volumes separated by 'ideal interfaces', and in each volume the magnetic field relaxes to a Taylor state, where the pressure gradient $\nabla p = 0$. The MRxMHD model is implemented in the Stepped-Pressure Equilibrium Code (SPEC) so that the equilibrium solution in each region is computed while preserving the force balance across the interfaces. As SPEC computes the Hessian matrix (a discretized stability matrix), the stability of an MRxMHD equilibrium can also be computed with SPEC. In this article, using SPEC, we investigate the effect of local pressure gradients and the $\nabla p = 0$ in the vicinity of the resonant surface of a tearing mode. For low-beta plasma, we have been able to illustrate a relationship between the resistive singular-layer theory (Coppi et al 1966 Nucl. Fusion6 101; Glasser et al 1975 Phys. Fluids18 875–88) and the MRxMHD model. Within the singular layer, the volume-averaged magnetic helicity and the flux-averaged toroidal flux are shown to be the invariants for the linear tearing modes in SPEC simulations. Our technique to compute MRxMHD stability is first tested numerically in a cylindrical tokamak and its application in toroidal geometry is demonstrated. We demonstrate an agreement between the stability boundary obtained with SPEC simulation and the resistive inner-layer theories.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

MST resistive wall tearing mode simulations

Here, the Madison Symmetric Torus (MST) is a toroidal device that, when operated as a stan dard tokamak, does not have major disruptions. Unlike most tokamaks, the MST plasma is surrounded by a close fitting highly conducting wall, with a resistive wall penetration time two orders of magnitude longer than in JET or DIII-D, and three times longer than in ITER. The MST can operate with edge q a ⩽ 2, unlike standard tokamaks. Simulations presented here indicate that the MST is unstable to resistive wall tearing modes (RWTMs) and resistive wall modes (RWMs). They could in principle cause disruptions, but the predicted thermal quench time is much longer than the experimental pulse time. If the MST thermal quench time were comparable to measurements in JET and DIII-D, theory and simulations predict that disruptions would have been observed in MST. This is consistent with the modeling herein, predicting that disruptions are caused by RWTMs and RWMs. In the low q a ~ 2 regime of MST, the RWTM asymptotically satisfies the RWM dispersion relation. The transition from RWTM to RWM occurs smoothly at q a = m/n, where m, n are poloidal and toroidal mode numbers.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Verification of gyrokinetic particle simulations of neoclassical tearing modes in fusion plasmas

Abstract The ability to simulate neoclassical tearing modes (NTMs) in the gyrokinetic toroidal code (GTC) has been developed and verified, in which ions are treated with a gyrokinetic model and electrons are treated as a resistive fluid. The simulation results demonstrate that the neoclassical bootstrap current effect can destabilize an otherwise stable classical tearing mode. In the cylindrical geometry, GTC simulations in the magnetohydrodynamic limit show quantitative agreement with the modified Rutherford theory, both in terms of the scaling law in the small island limit and in terms of the saturation level and pressure flattening effect in the large island limit. The toroidal effects are slightly destabilizing for the NTM, while the kinetic effects of thermal ions are stabilizing for the NTM and increase its excitation threshold.

Physics↗
DOE OSTI2024

Macroscopic trends of linear tearing stability in cylindrical current profiles

Abstract The likelihood of realising tokamak power-plants will be greatly improved by the discovery of high-gain equilibria that resist the formation of small islands and hence avoid the disruptive neoclassical tearing mode. We propose a series of studies to understand how simple tokamak design can leverage aspects of tearing onset physics to maximise passive resistance to island formation. Here we investigate the variation that current profiles can bring about in preventing tearing onset through the cylindrical linear tearing stability parameter Δ ′ . A database of 159148 realistic pilot-plant current profiles was generated with Monte Carlo sampling, and the distribution of Δ ′ values was linked with interpretable profile characteristics. In agreement with prior theoretical and experimental studies, Δ ′ was found to be strongly correlated with the existence and steepness of a local toroidal current well or hill, with the former destabilising and the latter stabilising. In the absence of these two cases, the remaining Δ ′ values were linearly bounded by the toroidal current gradient at the rational surface.

Physics↗
DOE OSTI2024

First observation of RMP ELM mitigation on MAST Upgrade

Abstract The first experimental attempts at controlling edge localised modes (ELMs) via the application of resonant magnetic perturbations on the MAST Upgrade tokamak are reported. Using the linear MHD model MARS-F, the phase shift between the upper and lower coil rows ΔΦ was optimised for toroidal mode number n = 1 and n = 2 fields, to provide forward guidance to experiments. In low β N discharges, the application of n = 1 3D fields caused the ELM frequency f E L M to increase by over a factor 20 relative to the reference, and also induced a locked mode, which did not cause a plasma termination nor an H-L back transition. However when β N was raised, this induced locked mode caused plasma termination which precluded mitigation access. Initially, applying a numerically optimised n = 2 field had no effect. However applying a rigid toroidal shift to this field caused a locked mode disruption, demonstrating the presence of a substantial n = 2 error field. Coil current ramps were conducted with ΔΦ set at 6 different values, resulting in either locked mode disruptions or no effect, but mitigation with n = 2 fields was not established.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Experimental progress and future plans on spherical tokamak, QUEST

QUEST (Q-shu university experiment with steady state spherical tokamak) aims at effective plasma current start-up and stable maintenance of plasma discharge. To solve the inherent problems in a spherical tokamak (ST) arising from insufficient space for placing the inductive center solenoid, electron cyclotron current drive (ECCD) and transient coaxial helicity injection (T-CHI) are implemented as a non-inductive plasma start-up method in QUEST. Efficient ECCD assisted by energetic electrons could be achieved. By combining control of the wave injection angle and application of a negative toroidal electric field, the bulk electron temperature could be raised up to 1 keV due to selective wave power absorption in the bulk electrons. The plasma current of over 50 kA contained within the closed flux surface could be obtained with a floating single biased electrode placed on lower divertor plates for T-CHI. Long-pulse operations on QUEST are impeded frequently due to wall saturation and subsequent density runaway caused by fuel particle imbalance. Since 2014, a unique tool called the ‘hot wall’ has been implemented to overcome the imbalance. The hot wall has a capability to regulate its surface temperature using a heater and two water cooling channels. With the help of the hot wall, 6 h discharges were obtained in 2020. Cooling down of the surface of the hot wall was significantly effective in recovering the wall pumping and was useful to extend the pulse duration. Augmentation of the toroidal magnetic field, B T up to 0.5 T from 0.25 T and a continuous wave (CW) gyrotron of 28 GHz are planned for QUEST in the near future. As raising B T provides a fundamental resonance of electron cyclotron waves (ECWs) with 28 GHz, more effective plasma current start-up and heating will be performed. Long-pulse operations with higher plasma parameters are expected.

QUEST↗
DOE OSTI2025

Stability analysis of Alfvén eigenmodes excited by ion cyclotron resonance heating on EAST

Alfvén wave instabilities driven by energetic particles are common in fusion devices. Understanding their behavior is essential for the good confinement of fusion plasma. For this purpose, a series of experiments are performed on EAST to investigate the excitation of toroidal Alfvén eigenmodes (TAEs). Experimentally, it was found that AEs with frequencies around 80, 134, 157 kHz are excited by ion cyclotron resonance heating (ICRH) hydrogen minority heating scenario. Moreover, the excitation of AEs is independent of the wall-coating materials, but determined with the generation and confinement of the fast ions. Statistical analysis suggests that the TAEs can only be excited when the ICRH power is larger than 2 MW and the H 98 factor is larger than 1.15. In line with the experiments, a set of simulations using TORIC, ASCOT, and NOVA-C is performed. The simulation results show that with the experimental density profile and safety factor, the measured TAE with frequency of 134 kHz is well reproduced by taking into account the plasma toroidal rotation frequency. However, the appearance of the 80 kHz mode cannot be captured in the simulations. The ICRH-generated fast hydrogen ions mainly have banana orbits and that their perpendicular velocity is much larger than that of the parallel ions. The stability analysis with NOVA-C suggests that the radial gradient of the fast H ion distribution is the only driving source of TAEs. For TAEs locate in the center of Alfvén continuum, the D ion Landau damping is the dominant damping term; For most other TAEs which have intersections with the continuum boundary, the continuum damping becomes the dominant damping mechanism.

Alfvén eigenmodes↗
DOE OSTI2026

Drift-kinetic effects of tungsten on plasma response to RMP in ITER

Here, effects of high- Z ( Z is the particle charge number) tungsten impurity ions on the plasma response to the resonant magnetic perturbation (RMP) field are numerically investigated for the ITER 15 MA baseline scenario, where the tungsten contribution to the plasma response is computed with a drift-kinetic model while the bulk thermal particle contributions follow the fluid approximation. The study yields three highlights: (i) the drift-kinetic contribution of the tungsten impurity exerts minor influence on the plasma response compared to that computed by the pure fluid model without tungsten; (ii) a new figure of merit, based on the resonant spectrum perturbation at the plasma boundary surface, results in different optimal coil phasing compared to that previously obtained by maximizing the edge-peeling plasma response; (iii) the optimal $n = 3$ RMP (for edge localized mode (ELM) control, $n$ is the toroidal mode number) is found to induce a large tungsten particle influx near the plasma edge associated with the neoclassical toroidal viscosity. The study thus provides useful data on the compatibility of the full tungsten wall with RMP ELM control in ITER.

ITER↗
DOE OSTI2020

Predicting the rotation profile in ITER

Determining the toroidal rotation for future tokamaks like ITER is a challenging and important problem. By combining empirical scalings for the intrinsic rotation at the top of the pedestal with the expected neutral beam torque and modeling of momentum transport, the toroidal rotation profile for ITER is predicted with TGYRO using TGLF (SAT0 and SAT1). On axis rotation exceeds 20 krad s –1 and the E x B shear is significant enough to reduce turbulent transport and significantly increase confinement and fusion power when comparing to cases that ignore the effect of rotation. Here, the prediction of the rotation at the top of the pedestal is made with increased confidence due to experiments and modeling in DIII-D that have determined the importance of fast-ion and neutral particle transport effects on intrinsic rotation at this location. In particular, the effect of neutral particles on momentum transport in the pedestal region is found to be insignificant.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Nonlinear modeling of the scaling law for the m/n = 3/2 error field penetration threshold

The scaling law for the m/n=3/2 error field (EF) penetration threshold is predicted numerically based on nonlinear single-fluid and two-fluid modeling using the TM1 code. The simulated penetration threshold of radial magnetic field b r at the plasma edge is scaled to the electron density n e , temperature T e , viscous time τ μ , toroidal field B t and the natural frequency ω in the form of b r /B t ∝n e αn T e αT τ μ αμ B t αB ω αω by scanning these parameters separately. Here, α n , α T , α μ , α B and α ω are the scaling coefficients on n e , T e , τ μ , B t and ω, respectively. Single-fluid modeling shows that the 3/2 EF threshold scales as b r /B t ∝n e 0.56 T e 0.6 τ μ -0.59 B t -1.15 ω, which is similar with the analytical scaling law in both the Rutherford and visco-resistive regimes. Yet, two-fluid modeling shows that the scaling law differs significantly in particular regarding the dependence on plasma rotation. In detail, the scaling coefficient α n on density decreases from 0.67 to 0.56 and α T on temperature decreases from 0.67 to 0.32, while α μ on viscous time is around -0.45 and α B on toroidal field decreases slightly from -1.15 to -1, when the ratio |ω E /ω *e | between plasma rotation frequency ω E and diamagnetic drift frequency ω *e varies from 0 to 10. Scans of the plasma rotation reveals that the penetration threshold linearly depends on the perpendicular rotation frequency (or natural frequency) ω ⊥e =ω E +ω *e , and there is a minimum in the required field amplitude when ω ⊥e 0. In addition, the enduring mystery of non-zero penetration threshold at zero plasma natural frequency in EF experiments is resolved by two-fluid simulations. We report that the very small island and smooth bifurcation in EF penetration near zero frequency is hard to detect in the experiment, leading to a finite penetration threshold within the capability of the experimental measurements.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Creation and sustainment of wide pedestal quiescent H-mode with zero net neutral beam torque

Recent experiments on DIII-D have shown it is possible to create and sustain wide pedestal quiescent H-mode (QH-mode) plasmas with zero net torque from neutral beam injection (NBI) for the full discharge duration. Wide pedestal QH-mode has many of the features of the previously investigated QH-mode while having the advantage of increased edge pedestal pressure and excellent energy confinement time. Both QH-mode variants operate without edge localized modes. Accordingly, these discharges demonstrate that significant input torque is not essential to the exploitation of wide pedestal QH-mode in future devices that are expected to have small or nonexistent NBI torque. In conclusion, developing operating conditions that allowed net zero torque access to wide pedestal QH-mode required implementing several techniques to avoid locked modes including minimizing intrinsic error fields, avoiding large sawteeth, and driving toroidal rotation via neoclassical toroidal viscosity.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Geometric concepts for stellarator permanent magnet arrays

The development of stellarators that use permanent magnet arrays to shape their confining magnetic fields has been a topic of recent interest, but the requirements for how such magnets must be shaped, manufactured, and assembled remain to be determined. To address these open questions, we have performed a study of geometric concepts for magnet arrays with the aid of the newly developed MAGPIE code. A proposed experiment similar to the National Compact Stellarator Experiment (NCSX) is used as a test case. Here, two classes of magnet geometry are explored: curved bricks that conform to a regular grid in cylindrical coordinates, and hexahedra that conform to the toroidal plasma geometry. In addition, we test constraints on the magnet polarization. While magnet configurations constrained to be polarized normally to a toroidal surface around the plasma are unable to meet the required magnetic field parameters when subject to physical limitations on the strength of present-day magnets, configurations with unconstrained polarizations are shown to satisfy the physics requirements for a targeted plasma.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Modeling of the ECCD injection effect on the Heliotron J and LHD plasma stability

The aim of the study is to analyze the stability of the energetic particle modes (EPM) and Alfven Eigenmodes (AE) in Helitron J and LHD plasma if the electron cyclotron current drive (ECCD) is applied. Additionally, the analysis is performed using the code FAR3d that solves the reduced MHD equations describing the linear evolution of the poloidal flux and the toroidal component of the vorticity in a full 3D system, coupled with equations of density and parallel velocity moments for the energetic particle (EP) species, including the effect of the acoustic modes. The Landau damping and resonant destabilization effects are added via the closure relation. The simulation results show that the n = 1 EPM and n = 2 global AE (GAE) in Heliotron J plasma can be stabilized if the magnetic shear is enhanced at the plasma periphery by an increase (co-ECCD injection) or decrease (ctr-ECCD injection) of the rotational transform at the magnetic axis ($\rlap{-} \iota_{0}$). In the ctr-ECCD simulations, the EPM/AE growth rate decreases only below a given $\rlap{-} \iota_{0}$, similar to the ECCD intensity threshold observed in the experiments. In addition, ctr-ECCD simulations show an enhancement of the continuum damping. The simulations of the LHD discharges with ctr-ECCD injection indicate the stabilization of the n = 1 EPM, n = 2 toroidal AE (TAE) and n = 3 TAE, caused by an enhancement of the continuum damping in the inner plasma leading to a higher EP β threshold with respect to the co- and no-ECCD simulations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Study of the Alfven eigenmodes stability in CFQS plasma using a Landau closure model

The aim of this study is to analyze the stability of the Alfven eigenmodes (AE) in the Chinese First Quasi-axisymmetric Stellarator (CFQS). The AE stability is calculated using the code FAR3d that solves the reduced MHD equations to describe the linear evolution of the poloidal flux and the toroidal component of the vorticity in a full 3D system, coupled with equations of density and parallel velocity moment for the energetic particles (EP) species including the effect of the helical couplings and acoustic modes. The Landau damping and resonant destabilization effects are added in the model by a given closure relation. The simulation results indicate the destabilization of n = 1 to 4 AEs by EP during the slowing down process, particularly n = 1 and n = 2 toroidal AEs (TAE), n = 3 elliptical AE (EAE) and n = 4 non circular AE (NAE). If the resonance is caused by EPs with an energy above 17 keV (weakly thermalized EP), n = 2 EAEs and n = 3 NAEs are unstable. On the other hand, EPs with an energy below 17 keV (late thermalization stage) lead to the destabilization of n = 3 and n = 4 TAEs. The simulations for an off-axis NBI injection indicate the further destabilization of n = 2 to 4 AEs although the growth rate of the n = 1 AEs slightly decreases, so no clear optimization trend with respect to the NBI deposition region is identified. In addition, n = 2, 4 helical AE (HAE) are unstable above an EP β threshold. Also, if the thermal β of the simulation increases (higher thermal plasma density) the AE stability of the plasma improves. Overall, the simulations including the effect of the finite Larmor radius and electron-ion Landau damping show the stabilization of the n = 1 to 4 EAE/NAEs as well as a decrease of the growth rate and frequency of the n = 1 to 4 BAE/TAEs.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Microtearing modes as the source of magnetic fluctuations in the JET pedestal

Abstract We report on a detailed study of magnetic fluctuations in the JET pedestal, employing basic theoretical considerations, gyrokinetic simulations, and experimental fluctuation data to establish the physical basis for their origin, role, and distinctive characteristics. We demonstrate quantitative agreement between gyrokinetic simulations of microtearing modes (MTMs) and two magnetic frequency bands with corresponding toroidal mode numbers n = 4 and 8. Such disparate fluctuation scales, with substantial gaps between toroidal mode numbers, are commonly observed in pedestal fluctuations. Here we provide a clear explanation, namely the alignment of the relevant rational surfaces (and not others) with the peak in the ω * profile, which is localized in the steep gradient region of the pedestal. We demonstrate that a global treatment is required to capture this effect. Nonlinear simulations suggest that the MTM fluctuations produce experimentally-relevant transport levels and saturate by relaxing the background electron temperature gradient, slightly downshifting the fluctuation frequencies from the linear predictions. Scans in collisionality are compared with a simple MTM dispersion relation. At the experimental points considered, MTM growth rates can either increase or decrease with collision frequency depending on the parameters thus defying any simple characterization of collisionality dependence.

Physics↗
DOE OSTI2021

The interaction of the ITER first wall with magnetic perturbations

Mitigation of the multiple risks associated with disruptions and runaway electrons in tokamaks involves competing demands. Success requires that each risk be understood sufficiently that appropriate compromises can be made. Here the focus is on the interaction of short timescale magnetic-perturbations with the structure in ITER that is closest to the plasma, blanket modules covered by separated beryllium tiles. The effect of this tiled surface on the perturbations and on the forces on structures is subtle. Indeterminacy can be introduced by tile-to-tile shorting. A determinate subtlety is introduced because electrically separated tiles can act as a conducting surface for magnetic perturbations that have a normal component to the surface. A practical method for including this determinate subtlety into plasma simulations is developed. The shorter the timescales and the greater the localization, particularly in the toroidal direction, the more important the magnetic effects of the tiles become.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

MARS-Q modeling of kink-peeling instabilities in DIII-D QH-mode plasma

In quiescent H-mode (QH-mode) regime, edge harmonic oscillations (EHOs) are believed to provide necessary radial transport to prevent occurrence of large edge localized modes. A systematic modeling study is performed here on the low- n EHOs in a DIII-D QH-mode plasma (Chen et al 2016 Nucl. Fusion 56 076011), by utilizing the MARS-Q code (Liu et al 2013 Phys. Plasmas 20 042503). Both the n = 1 and n = 2 instabilities are found to be strongly localized near the plasma edge, exhibiting the edge-peeling characteristics. The DIII-D resistive wall is found to have minor effects on these instabilities. The plasma resistivity is found to strongly modify the mode growth rate. Assuming the Spitzer model for the plasma resistivity, the computed mode growth rate scales as S sup>-1/3 with S being the Lundquist number. Toroidal flow of the plasma slightly stabilizes these edge localized kink-peeling modes. Drift kinetic effects all have a destabilization effect on these modes. Non-perturbative magneto-hydrodynamic-kinetic hybrid computations find that the drift kinetic effects associated with thermal particle species push the peak location of the eigenmode radially inward but still in the pedestal region. The modeled plasma temperature and density fluctuations in the plasma edge region, as well as the poloidal magnetic field perturbations along both the low and high field sides of the plasma surface, are in good agreement with experimental measurements. Finally, the quasi-linear initial value simulations find a strong non-linear interplay between the kink-peeling instability and the toroidal flow near the plasma edge. The combined effect of the damping of the flow amplitude and change of the edge flow shear is found to be the stabilizing factor for the kink-peeling mode, leading to the mode saturation and thus EHOs.

Physics↗
DOE OSTI2021

Pedestal stability analysis on MAST in preparation for MAST-U

In preparation for the upcoming MAST-U campaign, pedestal stability of spherical tokamaks is revisited by investigating standard H-mode discharges on MAST. As a step beyond previous studies, both ion and electron profiles are used for obtaining equilibria and a diverse set of pedestals is evaluated. Stability analysis with the ELITE and CGYRO codes shows that MAST pedestals are constrained by kinetic ballooning modes and medium toroidal mode number peeling-ballooning modes, with most unstable modes ranging from n = 25 to n = 45. In discharges with a steep q profile at the edge a larger number of poloidal harmonics is excited for each toroidal mode. In conclusion, a comparison with discharges on DIII-D with matched shape and similar non-dimensional parameters indicates that the increased shear at lower aspect ratio stabilizes low n peeling modes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗