Session ZO07: MFE: Pedestal Physics

The simulation of ELMs mitigation by pedestal coherent mode in EAST using BOUT++

A general phenomenon that the edge localized modes (ELMs) can be effectively mitigated/suppressed by the enhanced coherent mode (CM) intensity has been observed on EAST. For this phenomenon, the experimental statistical analysis and the electromagnetic (EM) simulations have been performed. There is a threshold value of the CM intensity in the experiments, which plays a key role in the ELM mitigation. Using the ELITE and BOUT++ analysis, we found that the pedestal is located outside the P-B boundary when the ELM mitigation and the enhanced CM co-exit. It is inconsistent with the experiment. Therefore, the effects of the CM are considered to explain the mitigation/suppression of ELM.

Modifying the three-filed reduced model in BOUT++, an imposed perturbation is added as the CM effect. The simulation results indicate that: without considering the CM, the ELM size belongs to the large ELM region; after considering the CM effect, the ELM is effectively mitigated and the ELM size is reduced by about 44.5%. Analysis shows that the CM can enhance the three-wave nonlinear interactions in the pedestal and reduce the phase coherence time (PCT) between the pressure and potential, which lead the perturbation to tend to be ‘multiple-mode’ coupling. The multiple modes compete with each other for the free energy, resulting in no obvious filament structure generation and decreased energy loss. The above reveals that there is a competitive relationship between turbulence and ELMs, and the CM can effectively regulate the edge energy loss. In addition, through the parameter scanning, we found that there is a threshold of the amplitude, which is consistent with the statistical results in the experiments.   

Role of Edge Stochastic Layer in Density Pump-out by Resonant Magnetic Perturbations

The role of the edge stochastic layer on particle transport is addressed in DIII-D plasmas with applied Resonant Magnetic Perturbations (RMPs) causing density pumpout. Using an analytical model that adds the stochastic parallel transport of electrons [R. Harvey et. al., 1981 Phys. Rev. Lett. 47 (1981)] to the fluid equations the ambipolar radial electric field and particle flux are calculated self-consistently. In this model the nonambipolar electron particle flux, driven by the stochastic magnetic field, is predominantly balanced by the nonambipolar perpendicular ion flux, driven by toroidal viscosity, across a narrow stochastic layer of order 2 percent of the plasma radius (0.98   

Exploiting the Plasma Response to Maximize Access to RMP-ELM Control in Tokamaks

Plasma response modeling captures the optimum applied spectrum to experimentally access RMP-ELM suppression over a wide range of operating currents in EAST, and provides a hypothesis for why an optimum in triangularity is found in DIII-D and AUG. Analysis of both RMP coupling to the edge resonant surfaces and extraction of multiple eigenmodes through singular value decomposition capture the optimal spectrum for RMP-ELM control over a wide range of operating currents in EAST. This confirms that the plasma response near the pedestal top is consistent with the observed RMP-ELM control sensitivities. The 3D plasma response provides explanation for the inability to access ELM suppression at high triangularity in DIII-D, namely that the resonant coupling is reduced at high triangularity as compared to that at low triangularity. This is validated through targeted comparisons with experiments across devices. These findings indicate that the plasma shape should be taken into consideration when designing a tokamak suitable for RMP-ELM control, and that predictive plasma response calculations can be used to maximize access to RMP-ELM control in future devices by maximizing the coupling between coils and the plasma.   

Recent progress on ELM suppression in hydrogen and helium at DIII-D and ASDEX Upgrade

ITER pre-fusion power operation (PFPO) phase operating with hydrogen (H) and helium (He) will be the first opportunity to study suppression of edge-localized modes (ELMs) by magnetic perturbations (MP). ELM suppression has been demonstrated on many tokamaks, however, only in deuterium (D). Recently, ELM suppression has been investigated in H at DIII-D and ASDEX Upgrade.

We find that on DIII-D in H plasmas a weak MP field causes a H-L transition. Diluting the H plasma moderately with He prevents the backtransition and the MP field leads to a weak density pump-out. As such, the density cannot be reduced significantly below the critical density for ELM suppression and, therefore no ELM suppression has been observed in H or H+He plasmas in DIII-D or ASDEX Upgrade.

Progress has been made extending the work reported in [1], which showed ELM suppression at a high density in a low power He plasma. Key signatures characteristic of ELM suppression in D are discovered in He such as an increase of the plasma response to the MP field, a narrowing of the pedestal and increased density fluctuations.

[1] T. Evans et al, Nucl. Fusion 57 (2017) 086016   

Characteristics of EAST grassy ELMs and its impact on the divertor heat flux width*

For a 60s steady-state long pulse high β_p EAST grassy ELM discharge, BOUT++ linear simulations show that the unstable modes cover a range from low-n (n=10~15) with characteristics of peeling-ballooning modes (P-B) to high-n (n=40~80) modes driven by drift-Alfvén instabilities (DAI). Even though the DAI dominate the linear growth phase with a wide n-spectrum and the fluctuation peaks on high-field side, nonlinear simulations show that the ELM crash is trigged by P-B modes on low-field side while the DAI delays the onset of the ELM and enhances the energy transport. The fluctuation amplitude drops by an order of magnitude and the ELM crashes disappear if the peeling drive is removed. The temporal evolution of the power loading shows no obvious decay from the maximum of the ELM power pulse after the onset of the ELM power and the elm size is small (< 2%). The turbulence thermal diffusivity is larger than the critical value indicating grassy ELM falls into the turbulence dominated regime. The divertor heat flux width is 2 times larger than the estimates based on the HD model and the Eich’s ITPA multi-tokamak scaling. The heat flux width is inversely proportional to Er-shear due to the enhancement of the SOL parallel transport and suppression of radial transport.   

Radial Structure and Fluxes Associated with the Low Frequency Edge Oscillation in Alcator C-Mod I-Mode Plasmas

The role of the Low Frequency Edge Oscillation (LFEO) in regulating particle transport in Alcator C-Mod I-mode plasmas has been investigated via direct measurement of the density and poloidal electric field fluctuations, and resulting fluxes, using the scanning Mirror Langmuir Probe (MLP) on Alcator C-Mod. I-mode on Alcator C-Mod is often accompanied by the LFEO below 40 kHz in addition to the ubiquitous Weakly Coherent Mode at ~200 kHz on C-Mod. Understanding its nature and role is of interest as I-Mode’s high energy confinement without the presence of Edge Localized Modes make it an attractive regime for a reactor. The MLP measurements indicate the LFEO is often associated with significant outward particle flux near the separatrix which can be observed in divertor LP measurements. The LFEO’s radial structure has also been investigated by synchronizing a Gas Puff Imaging system and the MLP. This has revealed a radial zonal structure for the electric potential and density fluctuations consistent with a radially propagating GAM, in agreement with work by Cziegler et. al. The LFEO frequency is shown to be modulated by the Sawtooth Cycle, consistent with the GAM’s Te^(1/2) frequency dependence, and impacted by Impurities. Supported by US DoE award SC0014264.   

Importance of non-ideal effects for peeling-ballooning stability thresholds in spherical tokamaks

It is shown that non-ideal physics can crucially alter peeling-ballooning (PB) stability limits in spherical torus (ST) configurations. Emphasis is placed on identifying conditions under which these extended-MHD effects become important. Ideal-MHD has been successful in predicting PB stability thresholds [and associated edge-localized modes (ELMs)] in conventional aspect ratio tokamaks. Although ideal-MHD finds agreement with observations of ELMs in STs in some cases, such as some ballooning-limited cases in MAST, its success in describing stability limits in STs is far more limited than in conventional aspect ratio tokamaks. We employ the extended-MHD code M3D-C1 to investigate macroscopic edge stability in ELMing and ELM-free discharges in NSTX and MAST. It is found that PB growth rates in ELMing NSTX discharges tend to exhibit a strong scaling with resistivity, especially in kink-peeling limited regimes, while in ELM-free scenarios and in the considered MAST discharge this happens to a lesser extent. We present analysis to determine under what conditions non-ideal MHD effects are required to accurately describe PB stability. These results constitute a valuable basis for the development of a predictive model for ELMs in STs, which is an important step towards a compact fusion power plant.   

Gyrokinetic prediction of microstability and transport in NSTX H-mode pedestals

Gyrokinetic analysis (CGYRO) predicts that a variety of NSTX H-modes are within 10% of kinetic ballooning mode (KBM) stability thresholds across the entire pedestal. This is true from narrow ELMy to wide-pedestal ELM-free cases, indicating that KBM remains a viable candidate for constraining the maximum pressure gradient at low aspect ratio where EPED predictions have yet to be successfully validated. Other transport mechanisms are likely responsible for establishing profiles prior to their reaching KBM limits, as the ratio of experimental electron particle to thermal diffusivity is much smaller than that predicted for KBM. Microtearing mode (MTM) and trapped electron mode instabilities are also unstable across the pedestals, while the electron temperature gradient (ETG) instability is unstable in the outer half of the pedestals. Electron heat flux predicted from nonlinear ETG simulations approaches experimental values in some cases. An ETG pedestal transport model is presented, integrating similar results from conventional aspect ratio analysis. Nonlinear MTM simulations are progressing to determine how much transport they contribute. This work supported by the U.S. Department of Energy under DE-AC02-09CH11466, DE-FC02-04ER54698 and DE-AC02-05CH11231.   

Investigation of Pedestal Bifurcations in Hybrid Plasmas on DIII-D

Experiments with double null divertor (DND) on DIII-D have achieved hybrid plasmas with bifurcated pedestals yielding moderate pedestal pressures around 7 kPa or high pressures up to 18 kPa [F. Turco APS 2020, C. Petty IAEA 2020]. The plasmas have a safety factor range q₉₅ = 5-6, with combined neutral beam and electron cyclotron heating powers up to 15 MW. Due to a pedestal bifurcation between a lower state and a higher state, correlated with a 2 MW heating power change, the confinement factors and normalized beta have a wide range H₉₈ = 1.1–1.8 and β_N = 2.5–4.1 [T. Petrie NF 57 (2017) 086004]. The cause of the confinement transition and pedestal bifurcation is investigated by analyzing pedestal stability and inspecting the role of ion diamagnetic stabilization, ExB shear contributions and ratio of separatrix to pedestal density. In some discharges, the higher pedestal state is found to be consistent with the entry region to a Super H-mode channel. The pedestal contribution to βN and E in the high confinement regime is about 10 %. Since the hybrid is a leading candidate for advanced tokamak operational regimes, strategies using plasma current ramps based on Super H-mode experience are developed to extend the hybrid parameter space and raise performance via pedestal optimization.   

Role of multi-scale MHD/turbulence in pedestal stability and transport of wide-pedestal QH-mode

Wide-pedestal QH-mode discovered on DIII-D is an attractive scenario for future fusion reactors as it exists with low edge rotation and good H-mode confinement without ELMs. Two experimental observed scale-separated MHD/turbulence modes are identified in BOUT++ reduced MHD model linear and nonlinear simulations: a) low frequency, low k peeling mode rotates in the ion diamagnetic drift direction; b) higher frequency, intermediate-high k electron drift wave propagates in the electron diamagnetic drift direction. In the experiments it was observed that ELMs could occur in wide-pedestal QH-mode with an increase of the amplitude of the low k mode and a decrease of the intermediate-high k mode. This indicates that the intermediate-high k electron drift wave could have an impact on the low k peeling mode and thus an impact on the ELM dynamics. BOUT++ simulation with only low k initial perturbation leads to ELM crash as linear peeling-ballooning theory predicted; meanwhile the all-scale simulation forms a "turbulence mixed" state with no ELM crash, which indicates a novel nonlinear criterion for the onset of ELMs. This work presents improved physics understanding on the connection between multi-scale MHD/turbulence and the existence of wide-pedestal QH-mode.   

Single particle finite orbit width effects and the H-mode edge transport barrier

Full-orbit single particle simulations using the SPIRAL code [1] have been performed to study the effects of finite orbit widths on the steep edge gradient region of H-mode plasmas.  It was found that finite orbit width effects of the thermal ions create an edge parallel current in the plasma current direction and a surface current perpendicular to the magnetic field lines. These edge ion-currents cannot be canceled by equivalent electron currents because of the large difference between ion and electron orbit widths. The surface current is equivalent with a poloidal flow that creates an inwardly directed electric field. After including scattering of test particles inside and charge exchange effects outside the plasma, simulation results are compared with experimental result showing that finite ion orbit width effects create the edge radial electric field which is important for the H-mode transport barrier.

[1] G.J. Kramer et al. Plasma Phys. Control.Fusion 55 (2013) 025013   

Effects of collisional ion-orbit loss on neoclassical tokamak radial electric fields

Ion-orbit loss is considered important to the radial electric fields Er of tokamak edge plasmas. In neoclassical equilibria, collisions can scatter ions onto the loss orbits and generate a steady-state radial current, which may drive the edge Er away from its neoclassical value. To quantitatively measure this effect, an ion-orbit-flux diagnostic [1,2] has been implemented in the axisymmetric version of the gyrokinetic particle-in-cell code XGC [3]. The validity of the diagnostic is demonstrated  by studying the collisional relaxation of Er in the core plasmas. Then, the ion orbit-loss effect is numerically measured at the edge for an H-mode plasma in the DIII-D geometry. It is found that the steady-state collisional ion orbit loss is not significant enough to drive Er away from its neoclassical value with the given plasma parameters.    

ELM mitigation with high-frequency lithium granules gravitational injection in EAST

Large edge-localized modes (ELMs) were mitigated by gravitational injection of lithium (Li) granules (0.7mm nominal diameter) into the upper X-point region of the EAST device, which has tungsten plasma-facing components (PFCs) [1]. The maximum ELM size was reduced by ~ 70% in Type-1 ELMy H-mode plasmas. Large ELMs were stabilized for up to ~ 40 energy confinement times. Constant core radiated power held constant, and there was no evidence of impurity accumulation. The Li granule injection reduced the edge plasma pedestal electron density and temperature, and also their gradients, due to increased edge radiation and reduced recycling. ELITE code calculations indicate that the stabilization of large ELMs correlates with improved stability of intermediate-n peeling-ballooning modes, due to reduced edge current resulting from the relaxation of edge profile gradients. The pedestal pressure reduction was partially offset by a core density increase, with the net result of a modest ~ 7% drop in core stored energy and normalized energy confinement. We surmise that the remnant small ELMs are triggered by the penetration of multiple Li granules just past the separatrix, similar to small ELMs triggered by deuterium.

[1] Z. Sun et al., 2021 Nucl. Fusion 61 066022   

Experimental Particle Transport Coefficient Evaluation in the Pedestal Region Utilizing Lyman-alpha Measurements

New high resolution measurements of main chamber Lyman-α radiation in the pedestal region have allowed direct evaluation of the Deuterium (D) or Hydrogen particle source for quantitative experimental examination of pedestal particle transport on DIII-D. Absolutely calibrated brightness measurements from the Ly-α Measurement Apparatus (LLAMA) allow quantitative evaluation of ionization rate and neutral density profiles. Using 1D geometry the particle fluxes and effective diffusion coefficient (Deff) can be evaluated from the ionization rate profile. During stationary periods in discharges, decreasing D_eff from ∼0.1-0.01 m²/s is observed as the density pedestal increases due to  varied plasma current and edge opacities. LLAMA has also been utilized to monitor the source during dynamic events such as ELMs and gas puff modulation. During ELM cycles, for ∼5 ms after the ELM onset, LLAMA measurements show increased D neutral density inside the separatrix while the electron density pedestal gradient is reduced. Then the density gradient saturates while the pedestal top electron density continues to evolve which is accompanied by increased ionization rate in the confined plasma region.