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At least 37 records · Page 2

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

Turbulence and transport phenomena play a crucial role in the confinement and stability of tokamak plasmas. Turbulent fluctuations in certain physical quantities, such as density or temperature fluctuations, can have a wide range of spatial scales, and understanding their correlation length is important for predicting and controlling the behavior of the plasma. The correlation length in the radial direction is identified as the critical length in real space. The dynamics in real space are of significant interest because transport in configuration space is primarily focused on them. When investigating transport caused by the E×B drift, the correlation length in real space represents the size of E×B whirls. It was numerically discovered that in drift wave turbulence, this length is inversely proportional to the normalized mode number of the fastest growing mode relative to the drift frequency. Considerable time was required before a proper analytical derivation of this condition was accomplished. Therefore, a connection has been established between phenomena occurring in real space and those occurring in k-space. Although accompanied by a turbulent spectrum in k-space with a substantial width, transport in real space is uniquely determined by the correlation length, allowing for accurate transport calculations through the dynamics of a single mode. Naturally, the dynamics are subject to nonlinear effects, with resonance broadening in frequency being the most significant nonlinear effect. Thus, mode number space is once again involved. Resonance broadening leads to the detuning of waves from particles, permitting a fluid treatment. It should be emphasized that the consideration here involves the total electric field, including the induction part, which becomes particularly important at higher beta plasmas.

Weiland, Jan (ORCID:0000000253496025)↗

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

This research has focused on quantitative prediction of the stability, control, and equilibrium state evolution in toroidal burning plasmas. The stability of long pulse burning plasmas is highly sensitive to the physics of resonant layers in the plasma, sources of momentum and flow, kinetic effects of energetic particles, and boundary conditions at the wall, including feedback control and error fields. In ITER in particular, the low toroidal flow equilibrium state, sustained primarily by energetic alpha particles from fusion reactions, will require the consideration of all of these key elements to predict quantitatively the stability and evolution. The principal investigators on this proposal are leading experts in the relevant theoretical and computational areas, and aimed to perform computations guided by analytic modeling, to address this physics in realistic configurations. The overall goal is to understand the key physics mechanisms that describe resistive toroidal burning plasmas, surrounded by a resistive wall, under active feedback control. With the physics of the energetic ions, resonant layers, resistive wall, and toroidal momentum transport included, this study will extend from recent publications in theory and simulation of individual effects and move toward predictive modeling for burning plasmas.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Real-time observation of toroidal current redistributions induced by three-dimensional MHD phenomena triggering vertical displacement events in tokamak plasmas

Three-dimensional MHD instabilities, including edge-localized modes (ELMs) and internal reconnection events (IREs), have been observed to precipitate loss of vertical stability in tokamak plasmas, resulting in vertical displacement events (VDEs). This vertical destabilization can occur due to toroidal current redistributions and/or shape changes resulting from these phenomena. Using a recently introduced method for rapidly reconstructing the two-dimensional toroidal plasma current density profile in real-time, results are presented that demonstrate the specific current distribution changes that occur during ELMs (on KSTAR) and IREs (on MAST-U) that lead to loss of vertical control. The method most efficiently reconstructs the toroidal current density profile by doing so on a basis of principal components of historical profiles. These principal components isolate dominant current profile dynamics, improving interpretability, increasing speed, and reducing dimensionality of the profile computation. On KSTAR, this computation is executed in the real-time plasma control system at a rate of 10 kHz (limited by available CPU cycle times), allowing the current profile evolution to be assessed at several times over the course of each ELM event. Further, by incorporating the reconstructions into a novel vertical stability metric, the contribution of specific current profile dynamics to the loss of vertical stability can be assessed in real-time for VDE avoidance and improved understanding of the causal relationship between three-dimensional MHD phenomena and VDEs. The success of this method in approximating toroidal current density profiles from kinetic equilibrium reconstructions is also presented ($R^2=0.990$), along with its capability to produce other equilibrium quantities of interest in real-time at high time resolution.

edge-localized modes↗

Generation of localized lower-hybrid current drive by temperature perturbations

Despite high demonstrated efficiency, lower-hybrid current drive (LHCD) has not been considered localized enough for neoclassical tearing mode (NTM) stabilization in tokamaks. This assessment must be reconsidered in view of the radiofrequency current condensation effect. Here we show that an island with a central hot spot induces significant localization of LHCD. Furthermore, in steady state tokamaks where a significant amount of current is provided by LHCD, passive stabilization of NTMs may occur automatically, particularly as islands become large, without requiring precise aiming of the wave power.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Calculation of tearing mode stability in an inverse aspect-ratio expanded tokamak plasma equilibrium

The tearing mode stability of an inverse aspect-ratio expanded tokamak plasma equilibrium of general shape is investigated using asymptotic matching techniques. Particular emphasis is placed on the conservation of toroidal electromagnetic angular momentum. The TJ code, which is a specific implementation of the results of the investigation, is described.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

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

This research will focus on quantitative prediction of the stability, control, and equilibrium state evolution in toroidal burning plasmas. The stability of long pulse burning plasmas is highly sensitive to the physics of resonant layers in the plasma, sources of momentum and ow, kinetic effects of energetic particles, and boundary conditions at the wall, including feedback control and error fields. In ITER in particular, the low toroidal ow equilibrium state, sustained primarily by energetic alpha particles from fusion reactions, will require the consideration of all of these key elements to predict quantitatively the stability and evolution. The principal investigators on this proposal are leading experts in the relevant theoretical and computational areas, and aim to perform computations guided by analytic modeling, to address this physics in realistic configurations. The overall goal is to understand the key physics mechanisms that describe resistive toroidal burning plasmas, surrounded by a resistive wall, under active feedback control. With the physics of the energetic ions, resonant layers, resistive wall, and toroidal momentum transport included, this study will extend from recent publications in theory and simulation of individual effects and move toward predictive modeling for burning plasmas.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Macroscopic trends of neoclassical tearing stability in high-field H-mode tokamak pilot plants

The neoclassical tearing mode (NTM) stability metric—minimum marginally stable island width $w$$^{*}_{m}$—was compared across 14651 inductive high-field tokamak pilot plant equilibria. Larger devices with reduced elongation and/or increased minor radius demonstrated an order-of-magnitude increase in $w$$^{*}_{m}$, primarily due to a reduction in bootstrap drive. This work is part of an ongoing effort to ensure passive NTM-stability in the ARC tokamak, in which the technology to achieve active tearing-suppression with localised electron cyclotron current drive does not yet exist. The equilibrium scenarios in the database were Monte Carlo generated and normalised to the same >400MW fusion power, minimum pressure scenario at a range of plasma currents, before tearing analysis using the modified Rutherford equation was applied for all resonant poloidal and toroidal m, n modes up to n = 4. Single-helicity toroidal Δ' calculations in resistive DCON set the minimum marginally stable island width, and a simple modal scaling proportional to –m 2 n –1 was identified for high-m Δ' values. The dominant correlates of $w$$^{*}_{m}$ and Δ' across the database were analysed using interpretable machine learning techniques.

NTM seeding↗

Destabilizing effects of edge infernal components on resistive wall modes in advanced tokamak scenarios

The stability of the n = 1 resistive wall modes (RWMs) dominated by the pressure-driven infernal components is investigated using the ideal magnetohydrodynamics (MHD) code AEGIS for the advanced tokamak scenarios. Here, n is the toroidal mode number. In the advanced tokamak scenarios, due to the large fraction of bootstrap current contribution, the profile of safety factor q is deeply reversed in magnetic shear in the central core region and locally flattened within the edge pedestal. Consequently, the pressure-driven infernal components develop in the corresponding flat-q regions of both core and edge. However, the edge infernal components dominate the n = 1 RWM structure and lead to lower β N limits for the advanced tokamak scenarios. In the framework of ideal MHD, the edge rotation is found the most critical to the stabilization due to the dominant influence of the edge infernal components, which should be maintained sufficiently large in magnitude and range in order for the rotation alone to fully suppress the n = 1 RWM in typical advanced tokamak scenarios.

36 MATERIALS SCIENCE↗

Tokamak Plasmas with Density up to 10 Times the Greenwald Limit

Current-carrying, toroidal laboratory plasmas typically cannot be sustained with an electron density above the empirical Greenwald limit. Presented here are tokamak experiments in the Madison Symmetric Torus with a density up to an unprecedented level about ten times this limit. This is thought to be made possible in part by a thick, stabilizing, conductive wall, and a high-voltage, feedback-controlled power supply driving the plasma current. The radial profile of the toroidal current flattens around twice the limit, without the edge collapse routinely observed in other experiments.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Simultaneous access to high normalized density, current, pressure, and confinement in strongly-shaped diverted negative triangularity plasmas

Strongly-shaped diverted negative triangularity (NT) plasmas in the DIII-D tokamak demonstrate simultaneous access to high normalized density, current, pressure, and confinement. NT plasmas are shown to exist across an expansive parameter space compatible with high fusion power production, revealing surprisingly good core stability properties that compare favorably to conventional positive triangularity plasmas in DIII-D. Non-dimensionalizing the key parameters, expanded operating spaces featuring edge safety factors below 3, normalized betas above 3, Greenwald density fractions above 1, and high-confinement mode (H-mode) confinement qualities above 1 are observed, even simultaneously, and all with a robustly stable edge free from deleterious edge-localized mode instabilities. Scaling of the confinement time with engineering parameters reveals at least a linear dependence on plasma current although with significant power degradation, both in excess of expected H-mode scalings. These results increase confidence that NT plasmas are a viable approach to realize fusion power and open directions for future detailed study.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Asymptotic vacuum solution at tokamak X-point tip

In the H-mode regime of diverted tokamaks, the presence of strong pressure gradients in the pedestal gives rise to a sizable bootstrap current, together with the Ohmic and Pfirsch–Schlueter currents, close to the separatrix. For such equilibria, the presence of finite current density close to the separatrix requires the reexamination of equilibrium properties. It is almost universally assumed that the two branches of the separatrix (the stable and unstable manifolds) are straight as they cross at the X-point. However, the opposite angles of the plasma-filled segment and vacuum one cannot be equal if the current density does not vanish at the separatrix on the plasma side. We solve this difficulty by chipping off a thin layer of plasma edge so that the sharp corner of the plasma-filled segment becomes a hyperbola. Using the conformal transformation, we found that in the assumption of a hyperbolic boundary, the X point moves beyond the plasma boundary to fall in the vacuum region. An acute angle of the plasma-filled segment leads to an obtuse opposite angle of vacuum segment and vice versa. In the case of an acute angle of the plasma-filled segment, the new X point shifts inside the X point formed by the asymptotes of a hyperbolic boundary; in the case of an obtuse angle of the plasma-filled segment, the new X point shifts outside the X point formed by the asymptotes of a hyperbolic plasma boundary. Furthermore, the results are important for understanding the X point features, which affect the tokamak edge stability and transport.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Grassy ELM regime at low pedestal collisionality in high-power tokamak plasma

Spontaneous mitigation of giant ELMs and appearance of grassy ELMs have been observed repeatedly at low pedestal collisionality (${\nu }_{\mathrm{e},\mathrm{p}\mathrm{e}\mathrm{d}}^{{\ast}}\sim 0.15$) in the high-power (P inj > 13 MW) hybrid scenario in DIII-D. Higher β p and higher q 95 appear to be beneficial to achieving the grassy ELM regime. The grassy ELM H-mode plasma shows high energy confinement performance (H 98y2 up to over 1.5) under the conditions of high neutral beam torque and high core rotation. The pedestal width appears to exceed the EPED1.0 model prediction by more than 50%. Pedestal stability analysis performed with the ELITE code indicates that the stability against low-n kink/peeling modes is improved with increased auxiliary heating power and the operational point in the grassy ELM regime is located near the ballooning boundary. The pedestal stability characteristics during the grassy ELM crashes have been investigated in comparison with the giant ELM crashes based on plasma profiles experimentally measured with high resolution and accuracy. It has been found that the underlying mechanism for the observed small-amplitude ELM crashes is mainly the expansion of the ballooning stability boundary induced by an initial radially localized collapse in the pedestal, which helps to stop the growth of instabilities and further collapse of the pedestal. The effect of electron density pedestal on mitigating edge localized instabilities has been analyzed by numerical simulation, suggesting that the electron density pedestal characterized by high n e,sep /n e,ped and low density gradient helps to stabilize peeling-ballooning modes because of a low pressure pedestal gradient and to lower the ballooning boundary mainly because of a low ion diamagnetic frequency in the pedestal region, thus triggering ballooning instabilities and producing the intrinsic grassy ELMs. Numerical simulation of the Chinese fusion engineering test reactor (CFETR) with the SOLPS code indicates that the separatrix density might be insensitive to the electron diffusivity in the pedestal region and increase with the power flowing from the core region to the edge region. Furthermore, pedestal stability analysis suggests that the flat density pedestal with high separatrix density obtained in the high-power plasma in CFETR would make the operational point close to the ballooning boundary, which is considered to help destabilize ballooning instabilities and facilitate the access to the grassy ELM regime.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Comparison of MHD stability properties between QH-mode and ELMy H-mode plasmas by considering plasma rotation and ion diamagnetic drift effects

Magnetohydrodynamic (MHD) stability at tokamak edge pedestal in a quiescent H-mode (QH-mode) and type-I ELMy H-mode plasmas in DIII-D experiment was analyzed by considering plasma rotation and ion diamagnetic drift effects. QH-mode plasma is marginally stable to kink/peeling mode (K/PM), but ELMy H-mode one is almost unstable to peeling-ballooning mode (PBM). It was identified that there are three physics features responsible for the difference in the MHD stability properties between QH-mode plasma and ELMy H-mode one. These are the distance of pedestal foot from the last closed flux surface (LCFS), the amount of the ion diamagnetic drift frequency at pedestal, and impact of coupled rotation and ion diamagnetic drift effects. These features were confirmed through the numerical experiments that the stability properties of the QH-mode plasma can be changed to that of the ELMy H-mode one by shifting the plasma profiles inward in the radial direction and halving the ion diamagnetic drift frequency. The reasons of the change in the stability properties are thought as that K/PM is stabilized due to the inward shift of the bootstrap current profile, and PBM is destabilized due to the reduction of the coupled rotation and ion diamagnetic drift stabilizing effect. Importance of these features was validated through numerical experiments with experimental data of other QH-mode plasmas in DIII-D. All the results show that MHD stability properties of QH-mode plasma can be obtained in case that pedestal foot is close to LCFS, ion diamagnetic drift frequency is large due to high ion temperature, and strong rotation shear exists near pedestal.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Ideal MHD Limited Electron Temperature in Spherical Tokamaks

It is well documented that the central electron temperature in the national spherical torus experiment (NSTX) remains largely unchanged as the external heating power, and hence the normalized volume averaged plasma pressure β increases [Stutman, Phys. Rev. Lett. 102, 115002 (2009)]. Herein we present a hypothesis that low n, pressure driven ideal magnetohydrodynamic (MHD) instabilities that are nondisruptive, can break magnetic surfaces in the central region and thereby flatten the electron temperature profiles. We demonstrate this mechanism in a 3D resistive MHD simulation of a NSTX discharge. By varying the toroidal magnetic field strength, and/or the heating power, we show that there is a critical value of β, above which the central temperature profile no longer peaks on axis.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Multiscale Chirping Modes Driven by Thermal Ions in a Plasma with Reactor-Relevant Ion Temperature

A thermal ion driven bursting instability with rapid frequency chirping, considered as an Alfv´enic ion temperature gradient mode, has been observed in plasmas having reactor-relevant temperature in the DIII-D tokamak. The modes are excited over a wide spatial range from macroscopic device size to micro-turbulence size and the perturbation energy propagates across multiple spatial scales. The radial mode structure is able to expand from local to global in ~ 0.1 ms and it causes magnetic topology changes in the plasma edge, which can lead to a minor disruption event. Since the mode is typically observed in the high ion temperature ≳ 10 keV and high-! plasma regime, the manifestation of the mode in future reactors should be studied with development of mitigation strategies, if needed. In conclusion, this is the first observation of destabilization of the Alfv´en continuum caused by the compressibility of ions with reactor-relevant ion temperature.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Development and experimental qualification of novel disruption prevention techniques on DIII-D

Novel disruption prevention solutions spanning a range of control regimes are being developed and tested on DIII-D to enable ITER success. First, a new real-time control algorithm has been developed and tested for regulating nearness to stability limits and maintaining safety-margins. Its first application has been for reliable prevention of vertical displacement events (VDEs) by adjusting plasma elongation (κ) and the inner-gap between the plasma and inner-wall in response to real- time open-loop VDE growth rate (γ) estimators. VDEs were robustly prevented up to average open-loop growth rates of 800 rad/s with initial tunings, with only applying shape modification when near safety limits. Second, the disruption risk during fast, emergency shutdown after large tearing and locked modes can be significantly improved by transitioning to a limited topology during shutdown. More than 50% of emergency limited shutdowns after locked modes reach a final normalized current I_N < 0.3 before terminating, scaling to the 3 MA ITER requirement. Furthermore, this is in contrast to diverted shutdowns, the majority of which disrupt at I_N > 0.8. Despite improvements, these results highlight the critical importance of early prevention. Third, a novel emergency shut down method has been developed which excites instabilities to form a warm, helical core post-thermal quench. The current quench extends to ~100ms and avoids VDEs and runaway electron generation. Novel real-time machine learning disruption prediction has been integrated with the DIII-D proximity controller, and a real- time compatible multi-mode MHD spectroscopy technique has been developed. Results presented here were enabled by a focused effort, the Disruption Free Protocol, in DIII-D’s 2019-20 campaign to complement disruption prevention experiments with a large piggy-back program. In addition to testing novel techniques, it is estimated to have helped avoid 32 potential disruptions in piggyback operations with rapid, early shutdowns after large rotating n=1 or locked modes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Parallelized real-time physics codes for plasma control on DIII-D

A real-time safe multi-threading library was developed on the DIII-D plasma control system to optimize the real-time TORBEAM and real-time STRIDE physics codes. These physics codes are crucial for future fusion power plant operation as they provide information about electron cyclotron wave propagation and heating as well as inform about ideal plasma stability limits. The real-time TORBEAM code executed consistently in under 20 ms while the real-time STRIDE code computes in 100 ms. The multi-threading library developed in this work can be applied to other real-time physics-based codes that will be crucial for the next generation of fusion devices.

DIII-D↗

Asymptotic solutions and convergence studies of the resistive inner region equations

A recent publication presents a detailed prescription for constructing global eigenfunctions and complex growth rates for resistive instabilities in axisymmetric toroidal systems, using the method of matched asymptotic expansions. At each singular surface in the plasma, the small-x asymptotic solutions of the ideal MHD outer-region equations are matched to the large-x asymptotic solutions of the resistive inner-region equations, with x being the distance from the singular surface. The success of this method depends upon accurate asymptotic solutions of the resistive inner region equations. Extensive studies have shown that there are not only regimes of excellent agreement with straight-through methods, without asymptotic matching, but also regimes of strong disagreement. As such, in an effort to find the cause of this discrepancy, we present here a different method of constructing asymptotic solutions of the inner region equations and we study the convergence properties of the new and old solutions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗