Edge localized modes (ELMs) are effectively suppressed in the ‘quasi-snowflake’ (QSF) divertor discharges, which has been observed in the Experimental Advanced Superconducting Tokamak (EAST). To obtain the physical mechanism of ELM suppression, the numerical simulations are carried out using the BOUT++ turbulence model. The simulations reveal that the large local magnetic shear near the outer mid-plane (OMP) induced by QSF divertor plays a key role in the ELM suppression. Using the EFIT code, a series of plasma equilibria with different 2nd X-points and nearly fixed last closed flux surfaces (LCFSs) are generated to analyze the effects of the different magnetic configurations on ELMs. Here we mainly discuss the standard single-null (SN), snowflake plus (SF+), and snowflake minus (SF-) divertors. The simulation results indicate that: (1) for linear instability, compared to SN, SF+ is more unstable, while SF- is more stable. Essentially, the local magnetic shear formed by different divertor geometries can alter the growth rate of the peeling-ballooning (P-B) mode. Through statistical analysis, there is an inverse correlation between the strength of local magnetic shear and the growth rate of P-B mode; (2) for ELM energy loss, SN is 4.60%, SF+ is 7.50%, and SF- is 0.35%. The SF+ divertor triggers a larger ELM, which is consistent with the TCV experiments; while the SF- divertor reduces the ELM amplitude, which is similar to the QSF experiments in EAST. Further analysis shows that the Reynolds stress determines the ELM size under different divertor configurations. The Reynolds stress can redistribute energy to fluctuations and cause the growth of low- n modes. What’s more, the SF- divertor not only suppresses the radial transport, but also has large magnetic flux expansion and connection length, which can reduce the target heat flux effectively. The conclusion of this paper shows that the advanced divertor configurations are promising for the future fusion.

A general phenomenon that the edge localized modes (ELMs) can be effectively mitigated with the enhanced coherent modes (CMs) has been observed on EAST. For this phenomenon, the experimental statistical analysis and electromagnetic (EM) simulations have been performed. There is a threshold value of the CM intensity in the experiments, which plays a key role in ELMs mitigation. Through the ELITE and conventional BOUT++ analysis, we found that when the insignificant ELM and enhanced CM co-exist, the pedestal is located in unstable P–B region and the ELM is relatively large. The simulation results only using the experimental profiles without considering other factors cannot reproduce the no significant ELM experiment. The CM enhances the edge turbulence, which can control ELMs. Therefore, the effects of CM are considered to explain the ELM mitigation. Modifying the three-field reduced model in BOUT++, an imposed perturbation is added as the CM. The simulation results indicate that: without the CM, the ELM size belongs to the relative large ELM region; after considering the CM, the ELM is mitigated and the energy loss is reduced by about 44.5%. Analysis shows that the CM enhances the three-wave nonlinear interactions in the pedestal and reduces the phase coherence time (PCT) between the pressure and potential, which lead the perturbation to tend to be ‘multiple-mode’ coupling. The competition of free energy between the multiple modes leads to the lack of obvious filament structures and the decreased energy loss. The above reveals that there is a competitive relationship between turbulence and ELMs, and the CM-enhanced turbulence can effectively reduce ELM energy loss. In addition, through the parameter scanning, there is a threshold of the amplitude A, which is consistent with the statistical results in the experiments.

Edge localized modes (ELMs) are completely suppressed by ion cyclotron resonant heating (ICRH) during H-mode discharge, which is first observed in the Experimental Advanced Superconducting Tokamak (EAST). The electromagnetic turbulence model in the BOUT++ framework is applied to the simulations, with the aim of obtaining the key physics mechanisms of ELM suppression by ICRH. The simulations, for the EAST experiment with no ELMs after ICRH, reveal that the radio frequency (RF) sheath plays a key role in the suppression of ELMs. The simulation results show that: (a) using the flow-balanced electric field, the ELM sizes are about 3.4% before ICRH, and 2.1% after ICRH. Although the smaller ELM is obtained with ICRH, it still belongs to relatively large ELMs; (b) instead of the flow-balance condition, the radial electric field E r is calculated using the RF sheath model, and the ELM size is about 0.36% with ICRH, much closer to the small/no ELM regime. After considering the effect of ICRH, the larger E × B shear rate in the pedestal and scrape-off layer induced by the RF sheath reduces the linear growth rate, and enhances the nonlinear mode coupling. Furthermore, we find that there is an effective range of the sheath potential, in which the ELM can be well suppressed, but beyond this range the ELM may be only mitigated rather than suppressed. This can reasonably explain why the probability of ELM suppression by ICRH appearing in the experiments is low.

The EAST coherent modes (CMs) during the inter-ELM phase are simulated by the electromagnetic six-field two-fluid module in BOUT++ framework. The fluctuation level of the electrostatic potential, electron pressure and density perturbations are comparable to the experiments, and the simulated electrostatic perturbation is around two orders of magnitude larger than the magnetic one in EAST CM. The frequency and poloidal wave number are consistent with experiments in the simulations of EAST CM equilibriums. The energy transfer between three-wave coupling indicates that the energy tends to transfer from medium-n to low-n modes in the early nonlinear phase, and the modes coupling effect in the nonlinear saturation phase is larger than that in the early nonlinear phase. Both the energy transfer and bispectral analysis show that the Ni fluctuation tends to generate the 'single-mode' coupling and Te tends to be 'multiple-mode', which indicates that the collapse of the density profile is larger than the electron temperature. The relative phase analysis is applied to evaluate whether the turbulence can extract the energy from density and temperature profiles. The result indicates that the density profile provides much more energy to drive the turbulence than electron temperature. The kinetic and magnetic energy transfer rates are used to understand the instability and turbulence driving mechanisms of the EAST CM. In the linear phase of the nonlinear simulation, the instability is driven by the peeling-ballooning mode and drift-Alfven wave (DAW), and the radial electric field and shear Alfven wave have large suppressing effects. The turbulence of EAST CM is a predominantly electrostatic mode, which corresponds to the Reynolds stress seven times larger than Maxwell stress. In addition, the effect of the electrostatic part in DAW is much larger than the electromagnetic one.

A test particle module is developed under BOUT++ framework. The guiding-center orbits in real divertor geometry can be calculated. The turbulence transport is implemented by random walk model. Impurity migration patterns under different turbulence transport levels are simulated by this module. As transport increase, migration pattern is modified significantly. More particles are lost and the lost at low field side boundary increase significantly.

To study the evolution and distribution of the transient particle and heat fluxes during the edge-localized modes (ELMs) burst on the experimental advanced superconducting tokamak (EAST), the BOUT++ six-field two-fluid model with sheath boundary conditions (SBCs) and magnetic flutter terms in the parallel thermal conduction is used to simulate the evolution of the profiles and growing process of the fluxes at divertor targets. Although SBCs hardly play a role in the linear phase, in the nonlinear phase both SBCs and magnetic flutter can change the dominant toroidal mode. SBCs are able to broaden the frequency distribution of the turbulence. The magnetic flutter increases the ELM size from 2.8% to 8.4%, and it doubles the amplitudes of the radial heat and particle transport coefficients at outer midplane (OMP), at around 1.0 m(2)s(-1). It is then able to increase the particle and heat flux at the divertor targets and to broaden the radial distribution of the parallel heat flux towards the targets.

In the previous simulations on the divertor heat fluxes of C-Mod and EAST, the inverse proportional to the plasma current I-p or poloidal magnetic field B-p trend of Eich's Scaling is well reproduced by the BOUT+ + simulations. However, the simulated SOL width lambda(q) is only half of the value realized in EAST measurements. The reason is believed to be the lack of RF heating scheme in the simulations. The RF heating on EAST, especially lower hybrid wave (LHW), is considered to change the boundary topology and increase the flux expansion. To prove the topology change effects of LHW in the scraped-off layer (SOL), a modeled helical current filament (HCF) due to LHW in SOL, which has the same amplitude of 13 kA to the experiments, is added as the force-free form into the 6-field 2-fluid module of BOUT++. The radial magnetic field induced by this HCF could be much smaller than the perturbed field induced by the edge tubulence or ELM, but it is able to force the perturbations of the turbulence or ELM with the same toroidal mode number to grow up at the start of the linear phase during the simulations. This forced mode is effective to compete with the spontaneous fluctuations and change their linear properties, which leads to the suppression of the divertor heat flux and the broadening of SOL width. The modeling results imply that the HCF with the toroidal mode number n(NCF) = 5 is able to increase the SOL, width by similar to 25%, and the peak parallel heat flux towards divertor target is decreased by similar to 32%. The scan of the toroidal mode number of HCF indicates that the smaller n(HCF) could generate the broader SOL width and lower peak heat flux. The modeled broadening of the particle flux by HCF clearly shows the secondary striate filaments on divertor target, which is similar to the splitting of the strike point observed in the measurements by the divertor probes.

The steady state radial electric field (Er) is calculated by coupling a plasma transport model with the quasi-neutrality constraint and the vorticity equation within the BOUT++ framework. Based on the experimentally measured plasma density and temperature profiles in Alcator C-Mod discharges, the effective radial particle and heat diffusivities are inferred from the set of plasma transport equations. The effective diffusivities are then extended into the scrape-off layer (SOL) to calculate the plasma density, temperature and flow profiles across the separatrix into the SOL with the electrostatic sheath boundary conditions (SBC) applied on the divertor plates. Given these diffusivities, the electric field can be calculated self-consistently across the separatrix from the vorticity equation with SBC coupled to the plasma transport equations. The sheath boundary conditions act to generate a large and positive Er in the SOL, which is consistent with experimental measurements. The effect of magnetic particle drifts is shown to play a significant role on local particle transport and Er by inducing a net particle flow in both the edge and SOL regions.

The equilibrium electric field that results from an imposed DC bias potential, such as that driven by a radio frequency (RF) sheath, is calculated using a new minimal two-field model in the BOUT++ framework. Biasing, using an RF-modified sheath boundary condition, is applied to an axisymmetric limiter, and a thermal sheath boundary is applied to the divertor plates. The penetration of the bias potential into the plasma is studied with a minimal self-consistent model that includes the physics of vorticity (charge balance), ion polarization currents, force balance with E x B, ion diamagnetic flow (ion pressure gradient) and parallel electron charge loss to the thermal and biased sheaths. It is found that a positive radial electric field forms in the scrape-off layer and it smoothly connects across the separatrix to the force-balanced radial electric field in the closed flux surface region. The results are in qualitative agreement with the experiments. Plasma convection related to the E x B net flow in front of the limiter is also obtained from the calculation.

The linear analysis of the influence of diamagnetic effect and toroidal rotation at the edge of tokamak plasmas with BOUT++ is discussed in this paper. This analysis is done by solving the dispersion relation, which is calculated through the numerical integration of the terms with different physics. This method is able to reveal the contributions of the different terms to the total growth rate. The diamagnetic effect stabilizes the ideal ballooning modes through inhibiting the contribution of curvature. The toroidal rotation effect is also able to suppress the curvature-driving term, and the stronger shearing rate leads to a stronger stabilization effect. In addition, through linear analysis using the energy form, the curvature-driving term provides the free energy absorbed by the line-bending term, diamagnetic term and convective term.

The mitigating impact of thermal and rectified radio frequency (RF) sheath potentials on the peeling-ballooning modes is studied non-linearly by employing a two-fluid three-field simulation model based on the BOUT++framework. Additional shear flow and the Kelvin-Helmholtz effect due to the thermal and rectified RF sheath potential are induced. It is found that the shear flow increases the growth rate while the K-H effect decreases the growth rate slightly when there is a density gradient, but the energy loss of these cases is suppressed in the nonlinear phase. The stronger external electrostatic field due to the sheaths has a more significant effect on the energy loss suppression. From this study, it is found the growth rate in the linear phase mainly determines the onset of edge-localized modes, while the mode spectrum width in the nonlinear phase has an important impact on the turbulent transport. The wider mode spectrum leads to weaker turbulent transport and results in a smaller energy loss. Due to the thermal sheath and rectified RF sheath potential in the scrape-off-layer, the modified shear flow tears apart the peeling-ballooning filament and makes the mode spectrum wider, resulting in less energy loss. The perturbed electric potential and the parallel current near the sheath region is also suppressed locally due to the sheath boundary condition. (C) 2014 AIP Publishing LLC.

This paper reports on the theoretical and simulation results of a gyro-Landau-fluid extension of the BOUT++ code, which contributes to increasing the physics understanding of edge-localized-modes (ELMs). Large ELMs with low-to-intermediate-n peeling-ballooning (P-B) modes are significantly suppressed due to finite Larmor radius (FLR) effects when the ion temperature increases. For type-I ELMs, it is found from linear simulations that retaining complete first order FLR corrections as resulting from the incomplete “gyroviscous cancellation” in Braginskii's two-fluid model is necessary to obtain good agreement with gyro-fluid results for high ion temperature cases (Ti≽3 keV) when the ion density has a strong radial variation, which goes beyond the simple local model of ion diamagnetic stabilization of ideal ballooning modes. The maximum growth rate is inversely proportional to Ti because the FLR effect is proportional to Ti. The FLR effect is also proportional to toroidal mode number n, so for high n cases, the P-B mode is stabilized by FLR effects. Nonlinear gyro-fluid simulations show results that are similar to those from the two-fluid model, namely that the P-B modes trigger magnetic reconnection, which drives the collapse of the pedestal pressure. Due to the additional FLR-corrected nonlinear E × B convection of the ion gyro-center density, for a ballooning-dominated equilibrium the gyro-fluid model further limits the radial spreading of ELMs. In six-field two fluid simulations, the parallel thermal diffusivity is found to prevent the ELM encroachment further into core plasmas and therefore leads to steady state L-mode profiles. The simulation results show that most energy is lost via ion channel during an ELM event, followed by particle loss and electron energy loss. Because edge plasmas have significant spatial inhomogeneities and complicated boundary conditions, we have developed a fast non-Fourier method for the computation of Landau-fluid closure terms based on an accurate and tunable approximation. The accuracy and the fast computational scaling of the method have been demonstrated.