Low-n Modes Research Articles

Evaluation of core beta effects on pedestal MHD stability in ITER and consequences for energy confinement

The maximum stable pedestal pressure has been shown to increase with core pressure and, in combination with core transport effects, this can lead to a positive feedback mechanism. However, the effect is shown to saturate for a high β in ASDEX-Upgrade simulations [Wolfrum et al. “Impact of wall materials and seeding gases on the pedestal and on core plasma performance,” Nucl. Mater. Energy 12, 18 (2017)]. In this paper, it is numerically investigated whether this effect appears in ITER plasmas, using ideal MHD numerical codes HELENA and MISHKA for different ITER scenarios, in a range of plasma conditions: two inductive scenarios at 7.5 MA/2.65 T and 15 MA/5.3 T and one steady-state scenario at 10 MA/5.3 T. For all scenarios, reference cases for ITER plasmas were taken as a starting point. No pedestal pressure saturation is found for the inductive scenarios, gradually growing up to the global βN limit, which is determined by the Troyon limit. On the contrary, for the 10 MA/5.3 T steady-state scenario, the maximum stable pedestal pressure does not depend on the total β and it is limited by low-n kink-peeling modes, as opposed to high-n peeling-ballooning modes that limit the maximum attainable pedestal height in the inductive scenarios. This core-edge MHD stability feedback loop has been investigated for two assumptions regarding the scaling of the pedestal width with βp,ped¯, using either a constant pedestal width or when scaling it as ΔψN∝βp,ped¯1/2. A stronger core-edge MHD stability feedback is observed for the varying pedestal width for the inductive plasma scenarios, which is closer to the experimental results from JET [Challis et al. “Improved confinement in JET high plasmas with an ITER-like wall,” Nucl. Fusion 55(5), 053031 (2015)], but not for the steady-state one. Finally, the pressure achieved according to this core-edge feedback stability analysis is compared to the plasma pressure achievable on the basis of the energy confinement IPB98(y,2) scaling for various assumptions regarding the scaling of core plasma confinement with heating power.

Low-n global ideal MHD instabilities in the CFETR baseline scenario

This article reports an evaluation on the linear ideal magnetohydrodynamic (MHD) stability of the China Fusion Engineering Test Reactor (CFETR) baseline scenario for various first-wall locations. The initial-value code NIMROD and eigen-value code AEGIS are employed in this analysis. Despite the distinctly different approaches in modeling the scrape off layer region, the dominant growth in each of the low-n (n = 1 − 10) modes are consistent between the two codes. The higher-n modes are dominated by ballooning modes and localized in the pedestal region, while the lower-n modes have more prominent external kink components and broader mode profiles. The influence of the plasma-vacuum profile and wall shape are also examined using NIMROD. In the presence of a resistive wall, the low-n ideal MHD instabilities are further studied using AEGIS. For the designed first-wall location, the n = 1 resistive wall mode is found to be unstable, which could be fully stabilized by uniform toroidal rotation above the 2.9% core Alfvén speed.

Stabilizing effect of enhanced resistivity on peeling-ballooning instabilities on EAST

Previous stability analysis of NSTX equilibrium with lithium-conditioning demonstrates that enhanced resistivity due to the increased effective charge number Zeff (i.e. increased impurity level) can provide a stabilizing effect on low-n edge localized modes (Banerjee et al 2017 Nucl. Fusion 24 054501). This paper extends the resistivity stabilizing effect to the intermediate-n peeling-ballooning (PB) instabilities with the linear stability analysis of EAST high-confinement mode equilibria in NIMROD two-fluid calculations. However, the resistivity stabilizing effect on PB instabilities in the EAST tokamak appears weaker than that found in NSTX. This work may provide better insight into the physical mechanism behind the beneficial effects of impurities on pedestal stability.

Nonlinear simulation and energy analysis of the EAST coherent mode

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.

Divertor currents during type-I edge-localized modes on the DIII-D tokamak

Measurements of divertor currents on DIII-D lead to new insights in nonlinear edge-localized mode (ELM) dynamics and a possible mechanism to explain their explosive growth. Rapidly oscillating currents flowing into the divertor before a significant increase in divertor heat flux occurs are measured with an array of shunted tiles and characterized. Extrapolation results in total n = 0 currents of 5–10 kA flowing into a concentric circle near the strike point. The detected Fourier harmonics appear consistent with a mix of low-n modes (n < 4) with currents up to 4 kA. A heuristic framework for ELM currents is developed based on thermoelectric origin of the tile currents with flow through regions inside of the nominal separatrix and found consistent with the current measurements. A current flow through the confined plasma leading to increased stochasticity and transport at the plasma edge could provide a mechanism for additional nonlinear growth as sought for in computational ELM simulations. Results also imply that ELM currents may open the possibility to manipulate the ELM character by perturbations through non-axisymmetric divertor bias or tile insulation.

Helical equilibrium magnetohydrodynamic flow effects on the stability properties of low-n ideal external-infernal modes in weak shear tokamak configurations

The impact of equilibrium helical flows on the stability properties of low shear tokamak plasmas is assessed. The corrections due to such helical flow to the equilibrium profiles (mass density, pressure, Shafranov shift, magnetic fluxes) are computed by minimising order by order the generalised Grad–Shafranov equation. By applying the same minimisation procedure, a set of three coupled equations, suitable for the study of magnetohydrodynamic perturbations localised within core or edge transport barriers is derived in circular tokamak geometry. We apply these equations to modelling the impact of strong poloidal flow shear in the edge region caused by a radial electric field on the stability of edge infernal modes retaining vacuum effects. Due to the poloidal flow shearing, the effect of plasma rotation is not simply a Doppler shift of the eigenfrequency. Stabilisation is found even for weak flow amplitude.

Study on edge localized mode during plasma vertical swing in HL-2A tokamak

An experiment on edge localized modes (ELMs) during the vertical swing is performed in HL-2A tokamak. ELM mitigation is observed when the plasma moves upward. The plasma column expands accompanied by a decrease in both lower triangularity and the absolute value of local magnetic shear at the outer mid-plane during the upward moving. The critical pressure gradient in pedestal is reduced for the mitigating case according to the linear simulation based on peeling-ballooning theory. The physics of the ELM crash process is also explored through nonlinear simulation. For the mitigating case, small current drive for low-n modes and a weak ion diamagnetic effect on high-n modes lead to a higher dominant mode and a wider growth rate spectrum, which result in weak turbulence transport and a small ELM size.

Experimental study on the magnetic coherent mode in the H-mode pedestal of EAST

Here we report the experimental analysis on the low-n (mostly n = 1, sometimes n = 2) magnetic coherent mode (MCM) at a characteristic frequency 20–, which has been frequently observed in various H-mode discharges on EAST. This mode can be easily identified in the magnetic fluctuations measured by the fast Mirnov coils mounted on the vacuum vessel wall, but is detected by the local measurements of edge electrostatic fluctuations only when the mode is sufficiently strong. The apperance of the MCM is summarized covering broad ranges of discharge parameters, in particular, the different heating schemes including pure neutral beams injected in either co- or counter-current direction as well as pure ratio-frequency waves. This may rule out the possibility of fast particle driven modes. Radial distribution and poloidal propagation of the MCM are investigated using the Doppler backscattering system and Langmuir probes inserted at the outer midplane, respectively. Temporal evolution of MCM amplitude during large ELM crashes is evaluated in detail, may suggesting the mode is closely correlated with pedestal buildup. Dedicated experiments reveal the possible correlations of MCM’s frequencies with edge line-averaged density and edge safety factor q95. We also present the observation of multi MCMs at relatively high q95, which are speculated locating at different rational surfaces in the pedestal via analyzing their mode structures and nonlinear interactions. Finally, effect of the MCM on edge particle transport is explored via surveying the correlation between the intermittent events of the mode and the particle fluxes deposited on the divertor target plates, utilizing the conditional analysis method. Corresponding results suggest that the MCM seems to primarily result in a notable poloidal redistribution of the divertor particle flux, rather than a considerable net increase of the total flux.

Grassy-ELM regime with edge resonant magnetic perturbations in fully noninductive plasmas in the DIII-D tokamakaaEdge-localized-mode.

Resonant magnetic perturbations (n = 3 RMPs) are used to suppress large amplitude ELMs and mitigate naturally occurring ‘grassy’-ELMs in DIII-D plasmas relevant to the ITER steady-state mission. Fully non-inductive discharges in the ITER shape and pedestal collisionality ( ≈ 0.05–0.15) are routinely achieved in DIII-D with RMP suppression of the Type-I ELMs. The residual grassy-ELMs deliver a low peak heat flux to the divertor as low as 1.2× the inter-ELM heat flux in plasmas with sustained high H-factor (H98y2 ≈ 1.2). The operating window for the RMP grassy-ELM regime is q95 = 5.3–7.1 and external torque in the range 9–0.7 Nm in the co-Ip direction, which is in the range required for a steady-state tokamak reactor. The RMP grassy-ELM regime is associated with a two-step pedestal, with strong flattening of the density around the zero crossing in the E × B shear. The edge magnetic response of the plasma to the n = 3 RMP is found to be ≈2–3× larger than for comparable ITER baseline plasmas (βN ≈ 1.8, q95 ≈ 3.1). The amplification of the RMP is consistent with the weak magnetic perturbation level (δB/B ≈ 1 × 10−4) required for effective Type-I ELM suppression. Cyclic variations in the pedestal pressure, width, and toroidal rotation are observed in these plasmas, correlated with cyclic variations in the strength and frequency of the grassy-ELMs. Extended MHD analysis and magnetic measurements indicate that these pedestal pulsations are driven by cyclic variations in the resonant field strength at the top of the pedestal. These pedestal pulsations reveal that the grassy-ELMs is correlated with the proximity of the pedestal to the low-n peeling-ballooning mode stability boundary. The use of low amplitude magnetic fields to access grassy-ELM conditions free of Type-I ELMs in high beta poloidal plasmas (βP ≈ 1.5–2.0) opens the possibility for the further optimization of the steady-state tokamak by use of edge resonant magnetic perturbations.

Impact of bootstrap current and Landau-fluid closure on ELM crashes and transport

Results presented here are from 6-field Landau-Fluid simulations using shifted circular cross-section tokamak equilibria on BOUT++ framework. Linear benchmark results imply that the collisional and collisionless Landau resonance closures make a little difference on linear growth rate spectra which are quite close to the results with the flux limited Spitzer-Härm parallel flux. Both linear and nonlinear simulations show that the plasma current profile plays dual roles on the peeling-ballooning modes that it can drive the low-n peeling modes and stabilize the high-n ballooning modes. For fixed total pressure and current, as the pedestal current decreases due to the bootstrap current which becomes smaller when the density (collisionality) increases, the operational point is shifted downwards vertically in the Jped – α diagram, resulting in threshold changes of different modes. The bootstrap current can slightly increase radial turbulence spreading range and enhance the energy and particle transports by increasing the perturbed amplitude and broadening cross-phase frequency distribution.

Modelling of NSTX hot vertical displacement events using M3D-C1

The main results of an intense vertical displacement event (VDE) modelling activity using the implicit 3D extended MHD code M3D-C1 are presented. A pair of nonlinear 3D simulations are performed using realistic transport coefficients based on the reconstruction of a so-called NSTX frozen VDE where the feedback control was purposely switched off to trigger a vertical instability. The vertical drift phase is solved assuming axisymmetry until the plasma contacts the first wall, at which point the intricate evolution of the plasma, decaying to large extent in force-balance with induced halo/wall currents, is carefully resolved via 3D nonlinear simulations. The faster 2D nonlinear runs allow to assess the sensitivity of the simulations to parameter changes. In the limit of perfectly conducting wall, the expected linear relation between vertical growth rate and wall resistivity is recovered. For intermediate wall resistivities, the halo region contributes to slowing the plasma down, and the characteristic VDE time depends on the choice of halo temperature. The evolution of the current quench and the onset of 3D halo/eddy currents are diagnosed in detail. The 3D simulations highlight a rich structure of toroidal modes, penetrating inwards from edge to core and cascading from high-n to low-n mode numbers. The break-up of flux-surfaces results in a progressive stochastisation of field-lines precipitating the thermalisation of the plasma with the wall. The plasma current then decays rapidly, inducing large currents in the halo region and the wall. Analysis of normal currents flowing in and out of the divertor plate reveals rich time-varying patterns.

Dynamics of an n = 1 explosive instability and its role in high-β disruptions

Some low-n kink-ballooning modes not far from marginal stability are shown to exhibit a bifurcation between two very distinct nonlinear paths that depends sensitively on the background transport levels and linear perturbation amplitudes. The particular instability studied in this work is an mode dominated by an component. It is driven by a large pressure gradient in weak magnetic shear and can appear in various high- hybrid/advanced scenarios. Here it is investigated in reversed shear equilibria where the region around the safety-factor minimum provides the low-shear conditions necessary for instability. For a certain range of parameters, a relatively benign path results in a saturated ‘long-lived mode’ (LLM) that causes little confinement degradation. At the other extreme, the quadrupole geometry of the perturbed pressure field evolves into a ballooning finger that subsequently transitions from exponential to explosive growth. The finger eventually leads to a fast disruption with precursors too short for any mitigation effort. Interestingly, the saturated LLM state is found to be metastable; it also can be driven explosively unstable by finite-amplitude perturbations. Similarities to some high-β disruptions in reversed-shear discharges are discussed.

Ideal MHD stability and characteristics of edge localized modes on CFETR

Investigation on the equilibrium operation regime, its ideal magnetohydrodynamics (MHD) stability and edge localized modes (ELM) characteristics is performed for the China Fusion Engineering Test Reactor (CFETR). The CFETR operation regime study starts with a baseline scenario (R = 5.7 m, BT = 5 T) derived from multi-code integrated modeling, with key parameters varied to build a systematic database. These parameters, under profile and pedestal constraints, provide the foundation for the engineering design. The long wavelength low-n global ideal MHD stability of the CFETR baseline scenario, including the wall stabilization effect, is evaluated by GATO. It is found that the low-n core modes are stable with a wall at r/a = 1.2. An investigation of intermediate wavelength ideal MHD modes (peeling ballooning modes) is also carried out by multi-code benchmarking, including GATO, ELITE, BOUT++ and NIMROD. A good agreement is achieved in predicting edge-localized instabilities. Nonlinear behavior of ELMs for the baseline scenario is simulated using BOUT++. A mix of grassy and type I ELMs is identified. When the size and magnetic field of CFETR are increased (R = 6.6 m, BT = 6 T), collisionality correspondingly increases and the instability is expected to shift to grassy ELMs.

E × B flow shear drive of the linear low-n modes of EHO in the QH-mode regime

A new model for the edge harmonic oscillations (EHOs) in the quiescent H-mode regime has been developed, which successfully reproduces the recent observations in the DIII-D tokamak. In particular, at high E × B flow shear only a few low-n kink modes remain unstable at the plasma edge, consistent with the EHO behavior, while at low E × B flow shear, the unstable mode spectrum is significantly broadened, consistent with the low-n broadband electromagnetic turbulence behavior. The model is based on a new mechanism for destabilizing low-n kink/peeling modes by the E × B flow shear, which underlies the EHOs, separately from the previously found Kelvin–Helmholtz drive. We find that the differential advection of mode vorticity by sheared E × B flows modifies the 2D pattern of mode electrostatic potential perpendicular to the magnetic field lines, which in turn causes a radial expansion of the mode structure, an increase of field line bending away from the mode rational surface, and a reduction of inertial stabilization. This enhances the kink drive as the parallel wavenumber increases significantly away from the rational surface at the plasma edge where the magnetic shear is also strong. This destabilization is also shown to be independent of the sign of the flow shear, as observed experimentally, and has not been taken into account in previous pedestal linear stability analyses. Verification of the veracity of this EHO mechanism will require analysis of the nonlinear evolution of low-n kink/peeling modes so destabilized in the linear regime.

Bifurcation of quiescent H-mode to a wide pedestal regime in DIII-D and advances in the understanding of edge harmonic oscillations

New experimental studies and modelling of the coherent edge harmonic oscillation (EHO), which regulates the conventional Quiescent H-mode (QH-mode) edge, validate the proposed hypothesis of edge rotational shear in destabilizing the low-n kink-peeling mode as the additional drive mechanism for the EHO. The observed minimum edge E × B shear required for the EHO decreases linearly with pedestal collisionality , which is favorable for operating QH-mode in machines with low collisionality and low rotation such as ITER. In addition, the QH-mode regime in DIII-D has recently been found to bifurcate into a new ‘wide-pedestal’ state at low torque in double-null shaped plasmas, characterized by increased pedestal height, width and thermal energy confinement (Burrell 2016 Phys. Plasmas 23 056103, Chen 2017 Nucl. Fusion 57 022007). This potentially provides an alternate path for achieving high performance ELM-stable operation at low torque, in addition to the low-torque QH-mode sustained with applied 3D fields. Multi-branch low-k and intermediate-k turbulences are observed in the ‘wide-pedestal’. New experiments support the hypothesis that the decreased edge E × B shear enables destabilization of broadband turbulence, which relaxes edge pressure gradients, improves peeling-ballooning stability and allows a wider and thus higher pedestal. The ability to accurately predict the critical E × B shear for EHO and maintain high performance QH-mode at low torque is an essential requirement for projecting QH-mode operation to ITER and future machines.

Impact of E × B shear flow on low-n MHD instabilities.

Recently, the stationary high confinement operations with improved pedestal conditions have been achieved in DIII-D [K. H. Burrell et al., Phys. Plasmas 23, 056103 (2016)], accompanying the spontaneous transition from the coherent edge harmonic oscillation (EHO) to the broadband MHD turbulence state by reducing the neutral beam injection torque to zero. It is highly significant for the burning plasma devices such as ITER. Simulations about the effects of E × B shear flow on the quiescent H-mode (QH-mode) are carried out using the three-field two-fluid model in the field-aligned coordinate under the BOUT++ framework. Using the shifted circular cross-section equilibriums including bootstrap current, the results demonstrate that the E × B shear flow strongly destabilizes low-n peeling modes, which are mainly driven by the gradient of parallel current in peeling-dominant cases and are sensitive to the Er shear. Adopting the much more general shape of E × B shear ([Formula: see text]) profiles, the linear and nonlinear BOUT++ simulations show qualitative consistence with the experiments. The stronger shear flow shifts the most unstable mode to lower-n and narrows the mode spectrum. At the meantime, the nonlinear simulations of the QH-mode indicate that the shear flow in both co- and counter directions of diamagnetic flow has some similar effects. The nonlinear mode interaction is enhanced during the mode amplitude saturation phase. These results reveal that the fundamental physics mechanism of the QH-mode may be shear flow and are significant for understanding the mechanism of EHO and QH-mode.

Benchmark studies of the gyro-Landau-fluid code and gyro-kinetic codes on kinetic ballooning modes

A Gyro-Landau-Fluid (GLF) 3 + 1 model has been recently implemented in BOUT++ framework, which contains full Finite-Larmor-Radius effects, Landau damping, and toroidal resonance [Ma et al., Phys. Plasmas 22, 055903 (2015)]. A linear global beta scan has been conducted using the JET-like circular equilibria (cbm18 series), showing that the unstable modes are kinetic ballooning modes (KBMs). In this work, we use the GYRO code, which is a gyrokinetic continuum code widely used for simulation of the plasma microturbulence, to benchmark with GLF 3 + 1 code on KBMs. To verify our code on the KBM case, we first perform the beta scan based on “Cyclone base case parameter set.” We find that the growth rate is almost the same for two codes, and the KBM mode is further destabilized as beta increases. For JET-like global circular equilibria, as the modes localize in peak pressure gradient region, a linear local beta scan using the same set of equilibria has been performed at this position for comparison. With the drift kinetic electron module in the GYRO code by including small electron-electron collision to damp electron modes, GYRO generated mode structures and parity suggest that they are kinetic ballooning modes, and the growth rate is comparable to the GLF results. However, a radial scan of the pedestal for a particular set of cbm18 equilibria, using GYRO code, shows different trends for the low-n and high-n modes. The low-n modes show that the linear growth rate peaks at peak pressure gradient position as GLF results. However, for high-n modes, the growth rate of the most unstable mode shifts outward to the bottom of pedestal and the real frequency of what was originally the KBMs in ion diamagnetic drift direction steadily approaches and crosses over to the electron diamagnetic drift direction.

Nonlinear MHD simulations of Quiescent H-mode plasmas in DIII-D

In the Quiescent H-mode (QH-mode) regime, the edge harmonic oscillation (EHO), thought to be a saturated kink-peeling mode (KPM) driven unstable by current and rotation, is found in experiment to provide sufficient stationary edge particle transport to avoid the periodic expulsion of particles and energy by edge localized modes (ELMs). In this paper, both linear and nonlinear MHD modelling of QH-mode plasmas from the DIII-D tokamak have been investigated to understand the mechanism leading to the appearance of the EHO in QH-mode plasmas. For the first time nonlinear MHD simulations with low-n modes both with ideal wall and resistive wall boundary conditions have been carried out with the 3D non-linear MHD code JOREK. The results show, in agreement with the original conjectures, that in the non-linear phase, kink peeling modes are the main unstable modes in QH-mode plasmas of DIII-D and that the kink-peeling modes saturate non-linearly leading to a 3D stationary state. The characteristics of the kink-peeling modes, in terms of mode structure and associated decrease of the edge plasma density associated with them, are in good agreement with experimental measurements of the EHO in DIII-D. The effect of plasma resistivity, the role of plasma parallel rotation as well as the effect of the conductivity of the vacuum vessel wall on the destabilization and saturation of kink-peeling modes have been evaluated for experimental QH-mode plasma conditions in DIII-D.

Characteristics of MHD instabilities limiting the beta value in LHD

Effects of low-n magnetohydrodynamic instabilities on plasma performance have been assessed in the regime where an achieved beta value is limited by instabilities. The unstable regime of an ideal interchange mode is characterized by enhanced magnetic hill and reduced magnetic shear. Experiments have clarified that (i) low-n modes are significantly destabilized in the ideal-unstable configurations and lead to degradation of central beta by at most 60%, and (ii) the degree of their damages strongly depends on the mode rotation velocity. The occurrence of the minor collapse is independent of an existence of an error field.

Multimode excitation during the inter-ELM-crash periods in KSTAR H-mode plasma

Temporal and spatial modulation of the edge localized mode (ELM) structure has been observed during the inter-ELM-crash period by toroidally-separated two electron cyclotron emission imaging systems. The observed modulation is interpreted as a beat wave of two modes with adjacent toroidal mode number. An additional assumption is that each mode has to have a different poloidal rotation speed. In nonlinear simulation, the low-n mode can be driven by locking between the dominant modes. The modulation is reconstructed using beat waves not the locking of modes.