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The data in this repository correspond to the figures of the paper "A study of resistive peeling-ballooning modes across spherical tokamaks" published in the journal Plasma Physics and Controlled Fusion. The figures are created based on simulations with the M3D-C1 and NIMROD codes using Python post-processing tools.
A number of important physics effects on the stability of relatively high-n (n is the toroidal mode number) peeling-ballooning modes (PBMs) are investigated based on an equilibrium reconstructed from a NSTX discharge, utilizing extended magnetohydrodynamic (MHD) eigenvalue solvers. For a given toroidal mode number n, multiple branches of instabilities are computed, with the total number of unstable branches roughly linearly scaling with n. Most of the unstable branches are located in the plasma core region, but edge-localized branches, i.e., PBMs, are also identified at higher n-numbers. For the single-fluid-wise most unstable PBM with n = 19, stabilizing/destabilizing effects due to various physics beyond ideal MHD are systematically investigated. Plasma toroidal flow is found to be weakly stabilizing. Local flow shear is generally stabilizing as well, with the degree of stabilization depending on the initial growth rate (without flow shear) of the mode. The plasma resistivity can strongly destabilize the PBM within the single-fluid framework. Anisotropic thermal transport, strong parallel sound wave damping, as well as two-fluid effects are all stabilizing to the mode. In particular, diamagnetic stabilization (within the two-fluid model) is found to be very strong for this mode.
Linear magnetohydrodynamic (MHD) simulations for the SMall Aspect Ratio Tokamak (SMART) have been carried out for the first time, for both positive (PT) and negative triangularity (NT) shaped plasmas using the MARS-F code. The MHD stability of projected SMART plasmas against internal kinks, infernal modes and edge peeling-ballooning modes have been analyzed for a wide range of realistic equilibria. A stabilization of internal kinks and infernal modes is observed when increasing the safety factor profile and reducing plasma beta. PT shaped plasmas are more stable against both internal kinks and infernal modes than their counterpart NT shaped plasmas. Toroidal flows have little impact on the MHD stability of the internal kinks, but they have a strong stabilizing effect on infernal modes, which can be further mitigated in NT shaped plasmas. The MHD stability of peeling-ballooning modes is reduced in NT shaped plasmas, as observed in conventional tokamaks.
High pressure, peeling limited pedestals with pedestal normalized beta β N,ped >2 and pedestal top density n ped at or above the Greenwald density nG have been achieved in DIII-D high poloidal beta plasmas, with high global normalized beta β N >3 and energy confinement H 98 ~1.2-1.7. Higher β N allows higher pedestal density above the Greenwald value and higher pedestal pressure, even with a low injected torque. MHD modeling confirms that the experimental profiles lie near the peeling-mode unstable boundary with high normalized pressure gradient βMHD and high edge current density. Experimental analysis and stability calculations indicate that the high poloidal beta with strong Shafranov shift, high βMHD and weak/negative magnetic shear improves the pedestal stability by decoupling the peeling and ballooning modes and stabilizing the ballooning modes, thus facilitating access to the second stable region of peeling-ballooning mode. The access to the second stable peeling-ballooning stability region opens Super-H-like channels without extremely strong shaping or strong torque injection. The high-pressure peeling pedestal allows the pedestal density to go beyond the Greenwald limit with strong ExB shear maintained: pedestal pressure increases with pedestal density even when n ped >n G , until reaching the ideal MHD instability boundary, where giant ELMs occur. The giant ELMs are dominated by a strong n=1 component and cause a large reduction of the edge pressure, but a negligible change of the core pressure, consistent with kink/peeling-mode induced instability. The pedestal recovers from the collapse and typically sustains a high baseline density, around the Greenwald limit, during the whole discharge duration. Experiments also found that internal transport barriers and n ped ~0.9nG, peeling limited pedestals could be simultaneously achieved in high β N plasmas, while an internal feedback between ITB strength and pedestal performance is found.
A central challenge in fusion energy is reconciling the high-confinement mode required for reactor performance with the intense intermittent relaxation events it produces, known as edge-localized modes. These instabilities arise in the steep pressure pedestal at the plasma edge when magnetohydrodynamic thresholds are crossed, inflicting damaging heat loads on reactor components. Here, we show that multiscale interactions between microscopic turbulence and macroscopic magnetohydrodynamic modes provide encouraging prospects for self-organized edge-localized modes regulation. Using direct quantitative measurements of multiscale modes, eddy dynamics, and turbulent flux, we show that small-scale electron drift wave turbulence actively scatters the large-scale peeling-ballooning modes. This scattering decorrelates the pressure and velocity fields of the instability, so arresting its growth. Our modeling and theoretical analysis confirm this suppression mechanism is effective even when conventional linear stability thresholds are exceeded. This work establishes a nonlinear principle for edge-localized modes stability, revealing how ambient micro-turbulence can be leveraged to maintain a macro-stable, high-performance pedestal for future fusion reactors.
In this work, the dominant unstable magnetohydrodynamic mode and its stable region in the pedestal of the China Fusion Engineering Test Reactor are studied by numerical modeling with the peeling-ballooning theory over a wide range of triangularities (δ) and collisionalities (υ*). A new accessible stable region is found at δ<−0.1 for large βN,ped and υ*. This new stable region expands toward lower βN,ped and υ* with decreasing δ and is totally covered by the peeling unstable region with δ=−0.5 because of the increasing trapped particle fraction (ft,eff). The sensitivity of this new stable region to the kinetic ballooning mode constraint and elongation is studied. For negative and low δ<0.1, the boundary of the first stable region is determined from the ballooning mode. For δ>0.1, the peeling mode becomes dominant as the boundary approaches low s with low υ*, while the ballooning mode is still dominant at the boundary with high υ*. When δ increases beyond 0.46, the first stable region is expanded, and access to the second stable region of the ballooning mode opens up. The entire newly connected region of the first and second stable regions keeps expanding with further increases in δ until δ=0.6. Beyond this value, the ballooning mode becomes more unstable with increasing δ, while the peeling mode is approximately unchanged with increasing δ in this range. The change in the dominant mode and the stable region with increasing δ can be explained by the trade-off between the stabilization effect from the deeper poloidal magnetic well and destabilization due to the enlarged drive term.
The flux coordinates with dual-region safety factor (q) in the poloidal direction are developed in this work. The X-point effects on the ideal MHD modes in tokamaks are then analyzed using this coordinate system. Since the X-point effects mainly affect the edge region, the modes localized at the tokamak edge are particularly examined. Two types of modes are studied. The first is related to the conventional peeling or peeling-ballooning modes. The mode existence aligned with the local magnetic field in the poloidally core region as observed experimentally is confirmed. The X points are shown to contribute to a stabilizing effect for the conventionally treated modes with the surface-averaged q and with the tokamak edge portion truncated. The other is the axisymmetric modes localized in the vicinity of X points, which can affect the cross-field-line transport near the X points. The existence of axisymmetric modes points to the possibility of applying a toroidally axisymmetric resonant magnetic perturbation (RMP) in the X-point area for mitigating the edge localized modes, which can be an alternative to the current RMP design. The dual q description also has important implications for the existing non-axisymmetric RMP concept. It helps to understand why the RMP suppression of edge localized modes is difficult to achieve in the double-null tokamak configurations and points to the possibility of further improving the current RMP concept by considering the alignment to the local q.
The steep plasma pressure gradient that forms at the edge of the high confinement, H-mode regime of tokamak operation provides free energy to drive electromagnetic micro-instabilities that are widely believed to influence the transport processes in this so-called pedestal region. This high pressure gradient also provides a high current density (bootstrap current), known to influence ballooning mode stability and to be important for driving kink modes in the ideal magneto-hydrodynamic plasma model (so-called peeling-ballooning modes). Furthermore, efficient, steady state future tokamak power plants must operate with a large bootstrap current in the core and especially concerning spherical tokamaks, confinement will be influenced by electromagnetic turbulence. To accommodate these important situations, conventional electromagnetic gyrokinetic theory is extended to incorporate neoclassical effects in the equilibrium drives, allowing $B_{\vartheta} ~ B_0$ (B0 is the confining magnetic field, and $B_{\vartheta}$ is its poloidal component). This provides a global gyrokinetic model that self-consistently captures the consequences of large bootstrap current fractions on the equilibrium distribution functions.
Stability of edge-localized modes (ELMs) in spherical tokamaks is explored using the extended MHD model. Linear NIMROD simulations have been performed for three NSTX discharges 132543, 132588, and 141133, to investigate the role of resistivity, diffusivity, and shear flows on the onset of ELMs. The first discharge represents the wide pedestal regime and the later two discharges represent ELM-free enhanced pedestal H-mode. We first present the effect of toroidal rotation shear and find a flow shear destabilizing effect in these NSTX discharges. Simulations are also extended to include the two-fluid and ion gyroviscosity effects. Simulations show that the flow shear can shift the mode spectrum and alter the critical condition of ELM onset. We also uncover that ELM onset prediction in spherical tokamaks requires effects beyond MHD, in particular gyroviscosity and diamagnetic terms could stabilize Peeling-Ballooning modes consistent with the experimental observation of ELM-free regimes in NSTX. The findings give new insight into the nature of the interplay between resistivity, flows, and diamagnetic stabilization in ELM suppression and have potential applications to ELM control schemes in NSTX-U and next-generation spherical tokamaks. This study identifies the essential physical effects that must be included in future predictive and validation simulations.
We report fully suppressing edge-localized modes (ELMs), e.g., with resonant magnetic perturbations (RMPs), is essential to reach and sustain high-performance steady-state H-mode plasmas because large ELMs can significantly reduce the lifetime of divertor components in future tokamak reactors. RMP-driven ELM suppression in KSTAR has been modeled by coupling the neoclassical transport code PENTRC to the nonlinear 3D MHD code JOREK. We have found that the radial transport from the combined effects of the kink-peeling, tearing response, and neoclassical toroidal viscosity can explain the pedestal degradation observed in experiments. In addition, it has been found that the RMP response can increase the inter-ELM heat flux on the lower outer divertor by redistributing the heat transport between the divertor plates. In addition to the degraded pedestal, ELM suppression is also attributable to the RMP-induced mode interactions. While the linear stability of peeling-ballooning mode (PBMs) improves owing to the degraded pedestal, the PBM and RMP interaction increases the spectral transfer between edge harmonics, preventing catastrophic growth and the crash of unstable modes. Here, it turns out that the magnetic islands near the pedestal top can play a vital role in mediating the mode interactions.
Abstract Coupling a high-performance core to a low heat flux divertor is a crucial step for ITER and a Fusion Pilot Plant or DEMO. Experiments in DIII-D recently expanded the steady-state hybrid scenario to high density and divertor impurity injection to study the feasibility of a radiating mantle solution. This work presents the physics basis for trade-offs between density, current drive and stability to tearing modes (TMs) at high β. EC power is crucial to tailor the plasma profiles into a passively stable state, and to eject impurities from the core. Off-axis EC depositions decrease the heating efficiency, but calculated electron heat transport coefficients show that this effect is partially mitigated by improved confinement inside the EC deposition. Additionally, the reduction in pressure is recovered by increasing the density. This favourable scaling of confinement with density was observed in high power plasmas for years, and this work provides a comprehensive explanation. ELITE predictions indicate that a path in peeling-ballooning stability opens up for certain conditions of density, power, q 95 and shaping, allowing the edge pressure to continue increasing without encountering a limit. In the core, calculated anomalous fast-ion diffusion coefficients are consistent with density fluctuation measurements in the toroidicity-induced Alfvén eigenmode range, showing that smaller fast-ion losses contribute to the enhanced confinement at high density. The edge integration study shows that divertor heat loads can be reduced with Ne and Ar injection, but this eventually triggers a cascade of n = 1, 2, 3 core TMs. We can now show that impurity radiation in the core is small and it is not the cause for the drop in confinement at high Ar and Ne injection rates. The overlap between the core TMs is consistent with the loss of pressure as estimated by the Belt model for the coupled rational surfaces. Optimization of these trade-offs has achieved plasmas with sustained H 98y2 = 1.7, f GW = 0.7 and ∼85% mantle radiation. The scenario and its variations at higher density and on- vs off-axis EC heating has been studied as a candidate for an integrated solution for several reactor designs, such as ITER, ARC, and the ARIES-ACT1 case, showing promising results in terms of fusion power and gain.
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.
Abstract Predictions of heat load widths λ q based on particle orbits alone are very pessimistic. This paper shows that pedestal peeling-ballooning (P-B) magnetohydrodynamic (MHD) turbulence broadens the stable scrape-off layer (SOL) by the transport, or spreading, of fluctuation energy from the pedestal. λ q is seen to increase with Γ ε , the fluctuation energy density flux. We elucidate the fundamental physics of the spreading process. Γ ε increases with pressure fluctuation correlation length. P-B turbulence is seen to be especially effective at spreading, on account of its large effective mixing length. Spreading is shown to be a multiscale process, which is enhanced by the synergy of large and small-scale modes. Pressure fluctuation skewness correlates well with the spreading flux–with the zero crossing of skewness and Γ ε spatially coincident–suggesting the role of coherent fluctuation structures and the presence of intermittency in λ q broadening. λ q ∼ B p − 1 scaling persists for the broadened SOL. We show that the spreading flux increases for increasing pedestal pressure gradient ∇ P 0 and for decreasing pedestal collisionality υ ped ∗ . This trend is due to the dominance of peeling modes for large ∇ P 0 and low υ ped ∗ . Ultimately, we see that a state of weak MHD turbulence, as for small ELMs, is very attractive for heat load management. Our findings have transformative implications for future fusion reactor designs and call for experimental investigations to validate the observed trends.
Experiments on ASDEX Upgrade (AUG) in 2021 and 2022 have addressed a number of critical issues for ITER and EU DEMO. A major objective of the AUG programme is to shed light on the underlying physics of confinement, stability, and plasma exhaust in order to allow reliable extrapolation of results obtained on present day machines to these reactor-grade devices. Concerning pedestal physics, the mitigation of edge localised modes (ELMs) using resonant magnetic perturbations (RMPs) was found to be consistent with a reduction of the linear peeling-ballooning stability threshold due to the helical deformation of the plasma. Conversely, ELM suppression by RMPs is ascribed to an increased pedestal transport that keeps the plasma away from this boundary. Candidates for this increased transport are locally enhanced turbulence and a locked magnetic island in the pedestal. The enhanced D-alpha (EDA) and quasi-continuous exhaust (QCE) regimes have been established as promising ELM-free scenarios. Here, the pressure gradient at the foot of the H-mode pedestal is reduced by a quasi-coherent mode, consistent with violation of the high-n ballooning mode stability limit there. This is suggestive that the EDA and QCE regimes have a common underlying physics origin. In the area of transport physics, full radius models for both L- and H-modes have been developed. These models predict energy confinement in AUG better than the commonly used global scaling laws, representing a large step towards the goal of predictive capability. A new momentum transport analysis framework has been developed that provides access to the intrinsic torque in the plasma core. In the field of exhaust, the X-Point Radiator (XPR), a cold and dense plasma region on closed flux surfaces close to the X-point, was described by an analytical model that provides an understanding of its formation as well as its stability, i.e., the conditions under which it transitions into a deleterious MARFE with the potential to result in a disruptive termination. With the XPR close to the divertor target, a new detached divertor concept, the compact radiative divertor, was developed. Here, the exhaust power is radiated before reaching the target, allowing close proximity of the X-point to the target. No limitations by the shallow field line angle due to the large flux expansion were observed, and sufficient compression of neutral density was demonstrated. With respect to the pumping of non-recycling impurities, the divertor enrichment was found to mainly depend on the ionisation energy of the impurity under consideration. In the area of MHD physics, analysis of the hot plasma core motion in sawtooth crashes showed good agreement with nonlinear 2-fluid simulations. This indicates that the fast reconnection observed in these events is adequately described including the pressure gradient and the electron inertia in the parallel Ohm’s law. Concerning disruption physics, a shattered pellet injection system was installed in collaboration with the ITER International Organisation. Thanks to the ability to vary the shard size distribution independently of the injection velocity, as well as its impurity admixture, it was possible to tailor the current quench rate, which is an important requirement for future large devices such as ITER. Progress was also made modelling the force reduction of VDEs induced by massive gas injection on AUG. The H-mode density limit was characterised in terms of safe operational space with a newly developed active feedback control method that allowed the stability boundary to be probed several times within a single discharge without inducing a disruptive termination. Regarding integrated operation scenarios, the role of density peaking in the confinement of the ITER baseline scenario (high plasma current) was clarified. The usual energy confinement scaling ITER98(p,y) does not capture this effect, but the more recent H20 scaling does, highlighting again the importance of developing adequate physics based models. Advanced tokamak scenarios, aiming at large non-inductive current fraction due to non-standard profiles of the safety factor in combination with high normalised plasma pressure were studied with a focus on their access conditions. A method to guide the approach of the targeted safety factor profiles was developed, and the conditions for achieving good confinement were clarified. Based on this, two types of advanced scenarios (‘hybrid’ and ‘elevated’
Abstract The first pedestal stability and structure analysis on the new MAST Upgrade (MAST-U) spherical tokamak H-mode plasmas is presented. Our results indicate that MAST-U pedestals are close to the low toroidal mode number ( n ) peeling branch of the peeling-ballooning instability, in contrast with MAST H-mode pedestals which were deeply in the high- n ballooning branch. This offers the possibility of reaching the ELM-free quiescent H-mode (Burrell et al 2005 Plasma Phys. Control. Fusion 47 B37–B52) or high-performance super H-mode (Snyder et al 2015 Nucl. Fusion 55 083026; Snyder et al 2019 Nucl. Fusion 59 086017) regimes. In addition, the coupling between the peeling and ballooning branches is weak in MAST-U, suggesting that a path to very high pedestal pressure gradient at high density may exist with sufficient heating power. A possible explanation for the differences between MAST and MAST-U pedestal stability is given in terms of plasma shaping parameters, in particular squareness and elongation, as well as the pedestal top temperature and collisionality.
A BOUT ++ three-field magnetohydrodynamic model is employed to study the triggering and evolution of edge localized mode (ELM) by Li pellets injected along the outer mid-plane in the EAST configuration. The linear simulation shows that compared with a large deposition on the pedestal top (scenario I), a smaller deposition within the steep-gradient pedestal region (scenario II) can stimulate much larger linear growth rates of all-n peeling-ballooning modes (PBMs). The nonlinear simulation shows that there exists a pellet size threshold for ELM triggering for two deposition locations; the threshold for scenario I predicted in the present study matches the EAST observation well. Comparison of the two scenarios reveals that a smaller deposition is sufficient to trigger an ELM in a much shorter time in scenario II, whose ELM size is comparable to that in scenario I. This conclusion confirms previous DIII-D and ASDEX-Upgrade observations, suggesting that the steep-gradient pedestal region is a favorable deposition location for ELM triggering with minimum pellet size. Simulation analyses also find that the positive radial gradient of the hump-like pressure profile in the outer mid-plane induced by the pellet deposition plays a different role in the two scenarios. In scenario I, the force resulting from the gradient hinders the outflow of core plasmas and in return, the perturbation is suppressed from spreading inwards after ELM crashes. In scenario II, with a sizable deposition, the gradient results in another competitive perturbation growth region during the linear phase, thus dispersing the free energy and reducing the efficiency of destabilizing PBMs by pellet injection. The suppressing effect of saturated zonal flow on other modes, the short ELM fast crash phase, and the restricting transport effect of the positive radial pressure gradient work together to constrain the pedestal energy loss, especially when the pellet deposition amount is high.
Abstract Integration of transient and steady-state divertor heat fluxes control with a high-performance core is necessary for future fusion reactors. In recent DIII-D high- β p experiments, divertor detachment and simultaneous edge localized mode (ELM) suppression are demonstrated while the plasma confinement quality is maintained high in ITER-similar shape. By optimizing the neon injection in high- β p scenario with ITER-similar shape, deep detachment and ELM suppression are achieved with a high-performance core ( β N ∼ 2.8, β p ∼ 2.3) at q 95 ∼ 7.5. Partial divertor detachment and suppression of large ELMs are achieved at q 95 ∼ 6. The stability analyses suggest that with low neon injection, the density pedestal becomes higher and steeper and the T i profile also increases, therefore the increased edge pressure and higher current density destabilize the Peeling-Ballooning mode (PBM), which would lead to a large ELM collapse. With strong neon gas puffing, the significantly reduced pedestal pressure and current density, due to the degraded T e pedestal, lead to the stabilization of PBM and ELMs are suppressed. For both cases, the coupling between the large radius internal transport barrier (ITB) and edge pedestal is the key reason for maintaining high global performance. The formation of large radius ITB compensates for pedestal degradation. Such results could provide an attractive scenario to well control the transient and steady-state heat flux onto the divertor plates while maintaining good plasma performance, which is an important step toward the steady-state operation of future fusion reactors.
A simple impurity model has been developed under the BOUT++ framework to investigate the Li-pellet triggered edge localized mode (ELM) in EAST configuration. The present impurity model decouples the ion pressure enhancement effect (IPEE) (which affects radial E X B flow shear and gyro-viscosity of deuterium ions and is implicitly included in our previous work) to make the simulation of Li pellet injection more physically reasonable. In addition, the present impurity model also includes the impurity equilibrium effect (IEE) (which induces modifications on vorticity and gyro-viscosity). The simulation results show that without IPEE a turbulent ELM induced by Li pellet is triggered by multiple peeling-ballooning modes (PBMs) rather than by a single dominant mode, and the simultaneous growth of multiple modes is conducive to reducing the time for pedestal entering the energy loss state. When a turbulent ELM occurs, the nonlinearly dominant modes undergo a secondary fast growth during fast crash phase. The finding explains the secondary increase of D α emission observed in the DIII-D Li injection experiments. During the evolution of a turbulent ELM, the continuous pedestal collapse dominates the pedestal energy loss in turbulent transport phase; however, in saturation phase, the stabilizing effects on PBMs (n ≠ 0) by n = 0 mode and radial E X B flow shear within the steepest gradient region are more prominent. It is also found that with IEE and without IPEE, the size threshold of ELM triggering and the magnitude of ELM sizes both show a good agreement with EAST and DIII-D experimental observations.