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Kinetic ballooning mode (KBM) instability in tokamak plasmas is studied with gyrokinetic theory. It extends and improves on the theory of higher order KBM which is not subject to second stabilization (Hirose et al 1994 Phys. Rev. Lett. 72 3993). It is verified that increasing ion temperature gradient (η i ) significantly enhances the instability of KBMs, and causes extended instability in the second MHD stable regime. Especially when η i ≳ 1, the mode is unstable almost in the whole β space from an experimental point of view, here β is the ratio of kinetic pressure to magnetic pressure. It is found that for the case with a relatively low safety factor (1 ≲ q ≲ 2) and η i ≈ 0, which is generally in the central regions of a tokamak plasma, the KBM instability can also be extended to the region of β or α far beyond the second MHD stability boundary due only to impurity effect, here α = −Rq 2(dβ/dr). It has characteristics similar to the extended instability induced by η i , while its instability window is narrower than the latter. From the observations, the unstable window of extended instability is finite. As the safety factor q and magnetic shear s ^ (≡ r dq/q dr) increases, the ‘theoretical’ critical β of the second stable regime decreases and the α threshold increases. When the impurity effect is combined with the η i effect, the unstable window of the extended instability induced by η i can be greatly reduced by the former. In some cases, for instance as η i ≳ 1 and q is larger, and in the presence of impurity with mediate mass number, the impurity effect can even make the second stable regime of ‘experimental significance’ re-appear in KBMs. The influence of η i and impurity effects on broadening mode structure of KBMs are smaller than q and s ^ . The stability boundary based on s ^ – α plane confirms the above results.

Direct causality analysis of the multi-scale interactions among macro-scale tearing mode (TM), meso-scale geodesic acoustic mode (GAM) and small-scale turbulence in the edge plasma of the HL-2A tokamak utilizing transfer entropy (TE) method is reported. Experimental results have demonstrated that the (m/n) = (2/1) (with m and n being the poloidal and toroidal mode numbers, respectively) TM modulates the turbulence with the frequency range of f = 50–150 kHz and the GAM mainly modulates that with higher frequencies. The TM has both amplitude and phase modulation on turbulence energy while the GAM has only amplitude regulation effect. TE analyses have shown that both TM and GAM will modulate the turbulence energy during which the impact of the former is of about an order magnitude larger than the latter, whereas the causal effect of TM on particle transport is about twice that of the GAM, which is due to the different causal effects on density and electric field fluctuations caused by TM and GAM, respectively. It is suggested that the magnetic fluctuation strongly modulates the Reynolds stress which serves as a mediator, leading to a cooperative interaction between TM and GAM in the edge of tokamak plasmas.

Since the last IAEA Fusion Energy Conference in 2018, significant progress of the experimental program of HL-2A has been achieved on developing advanced plasma physics, edge localized mode (ELM) control physics and technology. Optimization of plasma confinement has been performed. In particular, high-β N H-mode plasmas exhibiting an internal transport barrier have been obtained (normalized plasma pressure β N reached up to 3). Injection of impurity improved the plasma confinement. ELM control using resonance magnetic perturbation or impurity injection has been achieved in a wide parameter regime, including types I and III. In addition, impurity seeding with supersonic molecular beam injection or laser blow-off techniques has been successfully applied to actively control the plasma confinement and instabilities, as well as plasma disruption with the aid of disruption prediction. Disruption prediction algorithms based on deep learning are developed. A prediction accuracy of 96.8% can be reached by assembling a convolutional neural network. Furthermore, transport resulting from a wide variety of phenomena such as energetic particles and magnetic islands has been investigated. In parallel with the HL-2A experiments, the HL-2M mega-ampere class tokamak was commissioned in 2020 with its first plasma. Key features and capabilities of HL-2M are briefly presented.

The control of edge localized mode(ELM) in tokamaks has been intensively investigated with different techniques. Recently, ELM control with impurity seeding has also raised to be a hot topic. This paper reports the effect of the laser blow-off(LBO) impurity seeding on the pedestal turbulence and ELMs. It has been found that the seeded impurity could have dual impacts on pedestal instabilities, depending on the quantity of the injected impurity. The impurity enhances the pedestal turbulence and further mitigates the ELMs when its quantity exceeds a lower threshold. Instead, the impurities suppress the pedestal turbulence and suppress ELMs when the quantity of the injected particles reaches a second higher threshold. It has also been observed that the ion toroidal velocity increases due to the impurity seeding while the collision rate is increasing. In addition, the impurities reduce the velocity shear rate by changing the toroidal velocity term rather than by changing the pressure gradient term as observed in ELM mitigation with LHCD. The reduction of the E×B velocity shear rate enhances the pedestal turbulence possibly through the turbulence spectral shift process during ELM mitigation.

This article assesses current understanding of hysteresis in transport relations, and its impact on the field. The rapid changes of fluxes compared to slow changes of plasma parameters are overviewed for both core and edge plasmas. The modulation ECH experiment is explained, in which the heating power cycles on-and-off periodically, revealing hysteresis and fast changes in the gradient–flux relation. The key finding is that hystereses were observed simultaneously in both the the gradient–flux and gradient–fluctuation relations. Hysteresis with rapid timescale exists in the channels of energy, electron and impurity densities, and plausibly in momentum. Advanced methods of data analysis are explained. Transport hysteresis can be studied by observing the higher harmonics of temperature perturbation in heating modulation experiments. The hysteresis introduces the term , which depends on the harmonic number m in an algebraic manner (not exponential decay). Next, the causes of hysteresis and its fast timescale are discussed. The nonlocal-in-space coupling works here, but does not suffice. One mechanism for 'the heating heats turbulence' is that the external source S in phase space for heating has its fluctuation in turbulent plasma. This coupling can induce the direct input of heating power into fluctuations. The height of the jump in transport hysteresis is smaller for heavier hydrogen isotopes, and could be one of the origins of isotope effects on confinement. Finally, the impacts of transport hysteresis on the control system are assessed. Control systems must be designed so as to protect the system from sudden plasma loss.

Author(s): Zhao, KJ; Chen, ZP; Shi, Y; Diamond, PH; Dong, JQ; Chen, ZY; Ding, YH; Zhuang, G; Liu, YB; Zhang, HQ; Chen, YQ; Liu, H; Cheng, J; Nie, L; Rao, B; Cheng, ZF; Gao, L; Zhang, XQ; Yang, ZJ; Wang, NC; Wang, L; Li, JQ; Jin, W; Xu, JQ; Yan, LW; Liang, YF; Xie, YY; Liu, B | Abstract: Enhancements of residual Reynolds stresses and symmetry breaking with resonant magnetic perturbations (RMPs) are presented. These experiments were performed using a Langmuir probe array in the edge plasmas of the J-TEXT tokamak. This study aims to explain the mechanisms for generating residual stresses and intrinsic rotations. It is observed that with RMPs, peaked residual stresses, steeper pressure gradients and stronger shear layers all appear around the resonant surface. The toroidal rotation is accelerated in the direction of the plasma current and shows a correlation with turbulence and the measured residual stresses near the resonant surfaces of RMPs. Symmetry breaking induced by magnetic islands is proposed as a new mechanism, which qualitatively explains the enhanced residual stresses and the acceleration of the toroidal rotation. The changes to the residual stresses and symmetry breaking with RMPs near the last closed surface are also discussed.

The impact of supersonic molecular beam injection (SMBI) fuelling on plasma turbulence and shear flows, which forms a self-consistent state, has been studied in the HL-2A tokamak. The SMBI flattens the shear layer by collisional flow damping and increases the turbulence intensity. It is found that the SMBI can enhance the nonlinear regulation dynamics and acts as an external tool for turbulence quench via stimulating two dynamic processes. The SMBI-stimulated nonlinear interactions facilitate the L-H transition at the marginal heating power for accessing the H-mode. The effective reduction of the H-mode power threshold by SMBI is demonstrated. The result suggests that the SMBI could be a general tool for realization of controllable L-H transition via reducing the H-mode power threshold in future devices.

For the first time supersonic molecular beam injection (SMBI) and cluster jet injection (CJI) were applied to mitigate edge-localized modes (ELMs) in HL-2A successfully. The ELM frequency increased by a factor of 2–3 and the heat flux on the divertor target plates decreased by 50% on average after SMBI or CJI. Energetic particle induced modes were observed in different frequency ranges with high-power electron cyclotron resonance heating (ECRH). The high frequency (200–350 kHz) of the modes with a relatively small amplitude was close to the gap frequency of the toroidicity-induced Alfven eigenmode. The coexistent multi-mode magnetic structures in the high-temperature and low-collision plasma could affect the plasma transport dramatically. Long-lived saturated ideal magnetohydrodynamic instabilities during strong neutral beam injection heating could be suppressed by high-power ECRH. The absolute rate of nonlinear energy transfer between turbulence and zonal flows was measured and the secondary mode competition between low-frequency (LF) zonal flows (ZFs) and geodesic acoustic modes (GAMs) was identified, which demonstrated that ZFs played an important role in the L–H transition. The spontaneously generated E × B shear flow was identified to be responsible for the generation of a large-scale coherent structure (LSCS), which provided unambiguous experimental evidence for the LSCS generation mechanism. New meso-scale electric potential fluctuations (MSEFs) at frequency f ∼ 10.5 kHz with two components of n = 0 and m/n = 6/2 were also identified in the edge plasmas for the first time. The MSEFs coexisted and interacted with magnetic islands of m/n = 6/2, turbulence and LF ZFs.

New mesoscale electric fluctuations (MSEFs) are identified in the edge plasmas of the HL-2A tokamak using multiple Langmuir probe arrays. The MSEFs, resulting from the synchronization and having components of dominant geodesic acoustic mode (GAM) and m/n = 6/2 potential fluctuations, are found at the same frequency as that of the magnetic fluctuations of m/n = 6/2 (m and n are poloidal and toroidal mode numbers, respectively). The temporal evolutions of the MSEFs and the magnetic fluctuations clearly show the frequency entrainment and the phase lock between the GAM and the m/n = 6/2 magnetic fluctuations. The results indicate that GAMs and magnetic fluctuations can transfer energy through nonlinear synchronization. The nonlinear coupling analyses show that the MSEFs couple to turbulence and low frequency zonal flows (LFZFs). This suggests that the MSEFs may contribute to the LFZF formation, reduction of turbulence level, and thus confinement regime transitions. The analysis of the envelope modulation demonstrates that both the MSEFs and the LFZFs modulate the turbulence while the MSEFs are modulated by the LFZFs.

Author(s): Xu, M; Duan, XR; Liu, Y; Song, XM; Liu, DQ; Wang, YQ; Lu, B; Yang, QW; Zheng, GY; Ding, XT; Dong, JQ; Hao, GZ; Zhong, WL; Shi, ZB; Yan, LW; Zou, XL; Liu, YQ; Chen, W; Xiao, GL; Zhang, YP; Jiang, M; Hou, YM; Cheng, J; Liang, AS; Bai, XY; Cao, JY; Cao, Z; Chen, HT; Cui, CH; Cui, ZY; Delpech, L; Diamond, PH; Ekedahl, A; Feng, BB; Giruzzi, G; Gong, SB; He, HM; Hoang, T; Huang, M; Huang, Y; Ida, K; Inagaki, S; Isobe, M; Itoh, K; Itoh, SI; Ji, XQ; Ke, R; Kobayashi, M; Lei, GJ; Li, B; Li, GS; Li, HJ; Li, JQ; Li, Q; Li, Q; Li, XD; Li, YG; Li, Y; Mao, WC; Mazon, D; McKee, GR; Morita, S; Nie, L; Peng, JF; Peysson, Y; Rao, J; Ren, Y; Tynan, GR; Wang, HX; Wang, QM; Wei, HL; Xia, F; Xiao, XP; Xuan, WM; Yan, Z; Yao, K; Yu, LM; Yu, Y; Yu, DL; Yuan, BD; Yuan, BS; Zhang, JH; Zhou, Y; Liu, Y | Abstract: The mission of HL-2A is to explore the key physical topics relevant to ITER and to the advanced tokamak operation (e.g. the operation of future HL-2M), such as the access of H-mode, energetic particle physics, edge-localized mode (ELM) mitigation/suppression and disruption mitigation. Since the 2016 Fusion Energy Conference, the HL-2A team has focused on the investigations on the following areas: (i) pedestal dynamics and L-H transition, (ii) techniques of ELM control, (iii) turbulence and transport, (iv) energetic particle physics. The HL-2A results demonstrated that the increase of mean shear flow plays a key role in triggering L-I and I-H transitions, while the change of flow is mainly induced by the ion pressure gradient. Both mitigation and suppression of ELMs were realized by laser blow-off seeded impurity (Al, Fe, W). The 30% Ne mixture supersonic molecular beam injection seeding also robustly induced ELM mitigation. The ELMs were mitigated by low-hybrid current drive. The stabilization of m/n = 1/1 ion fishbone activities by electron cyclotron resonance heating was found on the HL-2A. A new m/n = 2/1 ion fishbone activity was observed recently, and the modelling indicated that passing fast ions dominantly contribute to the driving of 2/1 fishbone. The non-linear coupling between the toroidal Alfven eigenmode and tearing mode (TM) led to the generation of a high frequency mode with the toroidal mode number n = 0. The turbulence was modulated by TM when the island width exceeds a threshold and the modulation is localized merely in the inner area of the islands. Meanwhile, turbulence radial spread took place across the island region.

We theoretically investigate turbulence in high-confinement mode (H-mode) plasmas with the pressure gradient and the mean flow. The toroidal flow, which is induced by the poloidal mean flow so as to satisfy the divergence free condition, exists in the H-mode, thus the effect of the toroidal return flow on instabilities is considered. The proposed model self-consistently includes not only the destabilization of the drift wave and the parallel flow shear instability, called the D'Angelo mode, but also the stabilization due to the poloidal flow shear. Depending on the strength of the flow shear or on the magnetic geometrical parameter, we obtain the stabilization of the drift wave and the destabilization of the D'Angelo mode. The competition between different instabilities through coupling of the poloidal flow with the toroidal return flow could be a key concept for understanding the turbulence in the H-mode. The characteristics of the instabilities are similar to the observations of the precursor of the type-III edge-localized mode.

Two different directions of scale-to-scale energy transfer that corresponds to forward and inverse energy cascades, respectively, were clarified in toroidal plasma turbulence by means of experimental analysis. In the present work we first report the evidence that the turbulence dominated by broad wavenumber spectrum was developed under the action of forward (direct) energy cascade in a reversed field pinch (RFP) plasma, while the generation of GAM zonal flow (ZF) was related with the energy concentrating into low frequency region from higher frequency region due to inverse energy cascade in a tokamak plasma. The two evidences are compared. The results indicate a modulation mechanism in turbulence which is relative to the generation or development of specific turbulent flows. This hints a correlation between energy transfer and the development of toroidal plasma turbulence.

Divertor heat flux mitigation has been achieved using the Supersonic Molecular Beam Injection (SMBI) in type-III ELMy H-mode plasmas on the HL-2A tokamak. After an SMBI, ELM mitigation occurs and is characterized by an ELM frequency increase by a factor of 2–3 and an amplitude decrease by 30–40%. The corresponding confinement has a little degradation (stored energy drops is smaller than 7%). The burst rate of smaller-scale filament (density amplitude σ ) increases by 20–30%, and the divertor heat flux decreases by 40–50%, which is consistent with an increase in radiation power loss. This observation indicates that SMBI should be a good candidate for ELM mitigation.

The acceleration of the co-current toroidal rotations around resonant surfaces by resonant magnetic perturbations (RMPs) through turbulence is presented. These experiments were performed using a Langmuir probe array in the edge plasmas of the J-TEXT tokamak. This study aims at understanding the RMP effects on edge toroidal rotations and exploring its control method. With RMPs, the flat electron temperature T e profile, due to magnetic islands, appears around resonant surfaces (Zhao et al 2015 Nucl. Fusion 55 073022). When the resonant surface is closer to the last closed flux surface, the flat T e profile vanishes with RMPs. In both cases, the toroidal rotations significantly increase in the direction of the plasma current around the resonant surfaces with RMPs. The characteristics of turbulence are significantly affected by RMPs around the resonant surfaces. The turbulence intensity profile changes and the poloidal wave vector k θ increases with RMPs. The power fraction of the turbulence components in the ion diamagnetic drift direction increases with RMPs. The measurements of turbulent Reynolds stresses are consistent with the toroidal flows that can be driven by turbulence. The estimations of the energy transfer between the turbulence and toroidal flows suggest that turbulence energy transfers into toroidal flows. The result has the implication of the intrinsic rotation being driven by RMPs via turbulence.

Blob birth and propagation characteristics have been investigated on the HL-2A tokamak using the novel probe combination of a radial eight-probe array and a poloidal ten-probe array toroidally separated by 210 cm. Outside of the separatrix, close zero parallel wave number along a magnetic field line was found. Inside the separatrix 4–8 mm, density gradient has a maximum and the skewness is close to zero. Blob poloidal velocity changes its direction across the separatrix, which is consistent with E × B driven mechanism. Based on the significant correlation along a magnetic line, blob propagation across the separatrix in poloidal–radial plane is clearly observed with condition average. At the far SOL, blob radial velocity is 0.5–0.6 km/s, which dominates the particle loss in the SOL.

Isotope effects on instabilities driven by ion temperature gradient (ITG) and impurities in tokamak plasmas in the presence of tungsten ions are numerically studied. It is revealed that the tungsten ions significantly modify the isotope scaling of the maximum growth rates of the instabilities with respect to the main or effective ion mass number or M eff [=(1 − f z )M i + f z M z ] with (=Zn z /n e ) being impurity charge concentration. The most reasonable scaling is deduced as with , for ITG driven modes, whilst holds with , for tungsten impurity modes, in significant contrast with the case of light or intermediate impurities where the scaling is and for ITG and impurity modes, respectively. These results suggest that existence of tungsten impurity would enhance (weaken) the isotope effect of instability driven by ITG (tungsten impurity ions), which is beneficial (harmful) for improvement of confinement when hydrogen isotopes are used in plasmas. The results might also provide hints on studies of particle and energy transports and discharge performance, particularly, in ITER-like wall machines.

Dynamics of the pedestal between type-III ELMs have been studied by a particular designed four-step probe array on HL-2A tokamak. The recovery of the edge transport barrier (ETB) can be divided clearly into three different phases. Inconsistent with the dynamics during the type I ELMy discharge, our results on HL-2A show that the (electron) temperature pedestal is recovered first, well before the ELM crash, while the density and pressure pedestals are still evolving slowly until the next ELM. The fast recovery of the temperature pedestal can trigger a low-frequency electrostatic coherent mode (LFM) (20–120 kHz) in the edge plasma. Direct and indirect measurements reveal that the LFM can drive strong inward particle flux. After the excitation, the LFM can slow down the further recovery of the temperature pedestal. Yet, the excitation of the LFM may help the recovery of the density pedestal. The structure and excitation studies indicate that the LFM may be the ion temperature gradient driving mode (ITG) excited in the edge plasma and plays a critical role in the recovery of pedestal between type-III ELMs.

A novel design of the three-step Langmuir probe (TSLP) array has been developed to investigate the zonal flow (ZF) physics in the HL-2A tokamak. Three TSLP arrays are applied to measure the three-dimensional (3D) features of ZFs. They are separated by 65 mm in the poloidal and 800 mm in the toroidal directions, respectively. The 3D properties of the geodesic acoustic mode (GAM) ZFs are presented. The poloidal and toroidal modes of the radial electric fields of the GAM perturbations are simultaneously determined in the HL-2A tokamak for the first time. The modes have narrow radial wave numbers (kr ρi = 0.03–0.07) and short radial scale lengths (2.4–4.2 cm). High coherence of both the GAM and the ambient turbulence separated by toroidal 22.5 ◦ along a magnetic field line is observed, which contrasts with the high coherence of the GAM and the low coherence of the ambient turbulence apart from the field line. The nonlinear three wave coupling between the turbulent fluctuations and the ZFs is a plausible mechanism for flow generation. The skewness and kurtosis spectra of the probability distribution function of the potential perturbations are contrasted with the corresponding bicoherence for the first time, which support the three wave coupling mechanism.

Recent experiment results from the HL-2A tokamak are presented in this paper. Supersonic molecular beam injection (SMBI) with liquid nitrogen temperature propellant is used. Low temperature SMBI can form hydrogen clusters that penetrate into the plasma more deeply and efficiently. Particle diffusion coefficient and convection velocity (D = 0.5?1.5?m2?s?1 and Vconv < 40?m?s?1, respectively) are obtained at the plasma periphery using modulated SMBI. Multi-probe measurements reveal the m = 0?1, n = 0 symmetries of directly measured low frequency (7?9?kHz) electric potential and field are simultaneously observed for the first time. Impurity transport is determined with the laser blow-off system and transport code. A disruption predictor has been derived based on MHD activity observations and statistical analysis. Sawtooth characteristics during ECRH are investigated and coupling between m = 1 and m/n = 2/1 modes is studied. Detachment features of HL-2A divertor are numerically and experimentally studied using the code SOLPS5.0 and measured data. The long divertor legs and thin divertor throats in HL-2A pose MHD shaping problems resulting in momentum losses even at low densities and strongly enhanced main chamber losses.

Strong m = 1 MHD activities are observed in the HL-1M tokamak during off-axis electron cyclotron resonance heating (ECRH) when the cyclotron resonance location is placed just outside the q = 1 surface at the high-magnetic-field side of the magnetic surface. Addition of lower-hybrid waves to ECRH significantly enhances the MHD excitation, but lower-hybrid waves alone cannot excite or sustain the mode. This result is a clear demonstration of the suprathermal trapped electron effect on the instability because of the absence of energetic ions in the plasma.

We report an experimental result on the stabilization of the energetic–ion driven internal kink mode (ion fishbone) by electron cyclotron resonance heating (ECRH), observed for the first time in a toroidal plasma. The mode asserts itself a resistive branch close to the marginal stability point. The resulting fishbone mode depends not only on the injected power but also on the radial deposition location of ECRH, and the instability can be completely suppressed when the injected ECRH power exceeds certain threshold. Analysis by the fishbone dispersion relation, including the resistive effect, suggests that the magnetic Reynolds number plays a key role in the mode stabilization—it weakens the mode growth-rate and enhances the critical energetic–ion beta without changing the energetic–ion population. This ion fishbone stabilization mechanism can be important for future devices such as ITER, which has significant ECRH capability.

The temporal-spatial structures of plasma flows and turbulence around tearing mode islands are presented. The experiments were performed using Langmuir probe arrays in the edge plasmas of J-TEXT tokamak. The correlation analyses clearly show that the flows have similar structures of m/n = 3/1 as the magnetic island does (m and n are the poloidal and toroidal mode numbers, respectively). The sign of the potential fluctuations for the flows inverses and the powers significantly reduce at q = 3 surface. Approaching to the last closed flux surface for the magnetic islands, the radially elongated flow structure forms. The flows are concentrated near separatrix and show quadrupole structures. The turbulence is concentrated near X-point and partly trapped inside the magnetic islands.

Multi-scale interactions have been observed recently in the HL-2A core NBI plasmas, including the synchronous coupling between kink mode and tearing mode, nonlinear couplings of TAE/BAE and TM near surface, AITG/KBM/BAE and kink mode near surface, and between kink mode and high-frequency turbulence. Experimental results suggest that several couplings can exist simultaneously, Alfvenic fluctuations have an important contribution to the high-frequency turbulence spectra, and the couplings reveal the electromagnetic character. Multi-scale interactions via the nonlinear modulation process maybe enhance plasma transport and trigger sawtooth-crash onset.

This paper reports the main recent results of the RFX-mod fusion science activity. The RFX-mod device is characterized by a unique flexibility in terms of accessible magnetic configurations. Axisymmetric and helically shaped reversed-field pinch equilibria have been studied, along with tokamak plasmas in a wide range of q(a) regimes (spanning from 4 down to 1.2 values). The full range of magnetic configurations in between the two, the so-called ultra-low q ones, has been explored, with the aim of studying specific physical issues common to all equilibria, such as, for example, the density limit phenomenon. The powerful RFX-mod feedback control system has been exploited for MHD control, which allowed us to extend the range of experimental parameters, as well as to induce specific magnetic perturbations for the study of 3D effects. In particular, transport, edge and isotope effects in 3D equilibria have been investigated, along with runaway mitigations through induced magnetic perturbations. The first transitions to an improved confinement scenario in circular and D-shaped tokamak plasmas have been obtained thanks to an active modification of the edge electric field through a polarized electrode. The experiments are supported by intense modeling with 3D MHD, gyrokinetic, guiding center and transport codes. Proposed modifications to the RFX-mod device, which will enable further contributions to the solution of key issues in the roadmap to ITER and DEMO, are also briefly presented. © 2017 IAEA, Vienna.

The ion temperature gradient (ITG) modes in transport barriers (TBs) of tokamak plasmas are numerically studied with a code solving gyrokinetic integral eigenvalue equations in toroidal configurations. It is found that multiple ITG modes with conventional and unconventional ballooning mode structures can be excited simultaneously in TBs with steep gradients of ion temperature and density. The characteristics of the modes, including the dependence of the mode frequencies, growth rate and structure on plasma parameters, are systematically investigated. Unconventional modes with large mode-number (where denotes a certain parity and peak number in ballooning space) dominate in the large region (), while the conventional mode with dominates in the medium region (), and unconventional modes with small mode-number dominate in the small region (). Thus, the spectra of these conventional and unconventional modes at steep gradients are qualitatively different from those of the conventional ITG modes at small or medium gradients, in which the growth rate of the only ITG mode with reaches maximum at the medium value . Through scanning ion temperature gradient and density gradient separately, it is proven that the synergetic effect of and , rather than alone, drives the unconventional ITG modes in TBs. Moreover, it is found that the critical value of for driving the unconventional ITG modes with large l number increases with increasing . In addition, the effects of magnetic shear on conventional and unconventional ITG modes in the high confinement regime (H-mode) are analyzed in detail, and compared with equivalent effects on conventional modes in the low and intermediate gradient regimes (L- and I- modes). Finally, the effects of the poloidal wave number and gradients of ion temperature and density on radial transport are analyzed based on quasi-linear mixing length estimations.

Strong resonant and non-resonant internal kink modes (abbreviated as RKs and NRKs, respectively), which are also called resonant and non-resonant fishbones, are observed on HL-2A tokamak with high-power ECRH + ECCD− (or ECRH) and ECRH + ECCD+, respectively. ('Resonant' derives from the existence of q = 1 surface (the resonant surface), and 'non-resonant' originates from the absence of q = 1 surface (). ECCD+ and ECCD− mean the driving direction of energetic electrons is the same and opposite to plasma current, respectively.) RK has features of periodic strong bursting amplitude and rapid chirping-down frequency, but NRK usually has the saturated amplitude, slow changed or constant frequency and long-lasting time. The NRK excited by energetic electrons is found for the first time. The reversed q-profiles are formed, and q min decreases during plasma current ramp-up. The value of q min is slightly smaller and a bit bigger than unity for RK and NRK conditions, respectively. The internal kink mode (IKM) structures of RKs and NRKs are confirmed by the ECEI system. Although there are different current drive directions of ECCD for excitation of RK and NRK, they all propagate in electron diamagnetic directions in poloidal. The radial mode structures, frequency and growth rate for IKMs are obtained by solving the dispersion relationship. The NRK is stable when q min is larger than a certain value, and with the decreasing q min the frequency drops, but the growth rate almost keeps constant when . This result is in agreement with experimental observation. Studying IKMs excited by energetic electrons can provide important experimental experiences for ITER, because the NRKs may be excited by high-power non-inductive drive of ECCD or ECRH in the operation of hybrid scenarios.

Transitions between low (L-mode) and intermediate (I-phase) confinement regimes triggered by sawteeth are investigated using multiple Langmuir probe arrays in the edge plasmas of the HL-2A tokamak. The I-phase is characterized by limit-cycle oscillations (LCOs). Repeated L-I-L transitions induced by sawtooth heat pulses are also observed. Statistical analyses show that the delay time of the L-I transition relative to sawtooth crashes is less than ∼1 ms. The intensity of turbulence bursts in the I-phase is stronger than those observed in L-mode plasmas. Measurements are consistent with zonal flow reducing turbulence intensity in the frequency band ∼20-100 kHz, while the LCO turbulence of frequency higher than 100 kHz has more power than that in the L-mode. The analyses of time-resolved power transfers between turbulence and zonal flows suggest that power transfers exist between turbulence and zonal flows. The direction of the power transfers is from turbulence into geodesic acoustic modes in ohmic plasmas. © 2013 IAEA, Vienna.

Edge localized mode (ELM) is successfully mitigated by helium and deuterium supersonic molecular beam injections (SMBIs) on HL-2A. During the ELM mitigation by SMBIs, gradients of ion temperature (T i) and electron density are softened in the pedestal. It has been observed that the averaged gradient of the T i decreases around 44% and the well depth of radial electric field (E r) is reduced by the SMBI during ELM mitigation. Furthermore, at least 20% decrements of T i have to be attained to achieve a noticeable increase (decrease) of the ELM frequency (amplitude). In addition, the duration of ELM mitigation with helium SMBI is much longer than that with deuterium, likely due to the higher level of recycling neutral gas compared to that of deuterium; in the case of ELM mitigation by helium SMBI, the recovery duration of the density gradient is much shorter (10–20 ms) than that of T i (up to 40 ms or longer), indicating the importance of the T i in the ELM mitigation by SMBI. Finally, it has been observed that the T i is reduced before the beginning of the ELM mitigation, suggesting that the mechanism of the ELM mitigation by SMBI is closely related to the cooling effect.

Ion internal transport barriers (iITBs) are first observed in neutral beam injection (NBI) heated plasmas at the HL-2A tokamak. The position of the barrier foot, in the stationary state, coincides with the q = 1 surface within its uncertainty of measurement. iITBs can develop more easily at the beginning of NBI heating. Also, iITBs are unstable for the sawtooth plasma. Simulations reveal that the thermal diffusivity of ions (χ i) inside the barrier can be as low as the neoclassical level. It is observed that the flow shear in the stationary iITB state reaches the level required for suppressing the ion temperature gradient mode instability, which indicates the important role of flow shear in sustaining the iITB.

This paper summarizes the main achievements of the RFX fusion science program in the period between the 2008 and 2010 IAEA Fusion Energy Conferences. RFX-mod is the largest reversed field pinch in the world, equipped with a system of 192 coils for active control of MHD stability. The discovery and understanding of helical states with electron internal transport barriers and core electron temperature >1.5 keV significantly advances the perspectives of the configuration. Optimized experiments with plasma current up to 1.8 MA have been realized, confirming positive scaling. The first evidence of edge transport barriers is presented. Progress has been made also in the control of first-wall properties and of density profiles, with initial first-wall lithization experiments. Micro-turbulence mechanisms such as ion temperature gradient and micro-tearing are discussed in the framework of understanding gradient-driven transport in low magnetic chaos helical regimes. Both tearing mode and resistive wall mode active control have been optimized and experimental data have been used to benchmark numerical codes. The RFX programme also provides important results for the fusion community and in particular for tokamaks and stellarators on feedback control of MHD stability and on three-dimensional physics. On the latter topic, the result of the application of stellarator codes to describe three-dimensional reversed field pinch physics will be presented. © 2011 IAEA, Vienna.

Ion temperature gradient (ITG) driven modes in the presence of impurity ions are studied in reversed-field pinch plasmas by solving the gyrokinetic integral eigenmode equation. Detailed numerical studies for single and multiple impurity ion species indicate that the ITG modes are enhanced by impurity effects and the stability threshold values become higher than that in pure hydrogen plasmas when density gradients of the impurity ions are opposite to that of electrons and main ions. In addition, a mode is driven unstable by impurity ions no matter how low the main ion temperature gradient is when the destabilizing effect of the impurity ions is strong enough. These results resemble the effects of impurities in tokamak plasmas. Analysis of the typical RFX-mod experiments is performed and the results show that the ITG and impurity driven modes may be linearly unstable in the edge region of the plasmas when the observed radial profiles of the impurity ions are considered.

In a fusion experiment based on the single-turn tokamak concept, the plasma is surrounded by a massive conducting structure composed of several layers of material with different resistivities. This conducting shell is located near the plasma edge and is magnetically coupled to the plasma column. The plasma magnetohydrodynamic (MHD) equilibrium is studied by neglecting the effect of structural induced currents. Eddy current effects are then analyzed. Poloidal uniformization of the poloidal field magnet current distribution required for plasma equilibrium is demonstrated. The possibility of continuous-limiter discharges in a single-turn tokamak configuration is pointed out. The significance of these results for the operation of a high-current tokamak experiment is discussed. >

The characteristics of beta-induced Alfven eigenmode (BAE) at L–I–H transitions have been investigated in the HL-2A experiments for the first time. It is found that a BAE of fBAE ~ 13.6 kHz coexists with the limit cycle oscillations of fLCO ~ 2.6 kHz and both disappear after the I–H transition in the discharges with L–I–H transitions. It is also found that the ambient turbulence is modulated by the radial electric field at the BAE frequency and that the level of density fluctuation gradually drops in L–I–H transitions, but it remains invariant in L–I–L ones. These results suggest a possible correlation between the BAE and the L–I–H transitions. The sudden disappearance of the BAE in L–I and I–H transitions has the similar effect of sawtooth crashes on triggering L–I–H transitions in the HL-2 A tokamak.

The first comprehensive measurements of plasma flows and fluctuations nearby static magnetic islands driven by resonant magnetic perturbations are presented. These experiments were performed using multiple Langmuir probe arrays on the edge plasmas of the J-TEXT tokamak. Controlled variations of the island size and location are explored. This study aims to understand the interaction between turbulence and magnetic islands, and to elucidate magnetic island effects on edge turbulence and flow intensity profiles, edge electric fields, and thus confinement regime transitions. Turbulence and low frequency flows (LFFs) all drop inside the magnetic island, but increase at its boundary, as island width increases. The geodesic acoustic mode is damped in most of the edge area with magnetic islands. The sign of the radial electric field changes from negative to positive within the islands. The gradient of turbulent stresses vanishes at the island center, and becomes steeper at the boundaries of the islands. The particle transport induced by the turbulence is reduced inside the magnetic islands. The magnetic island effects on flows and turbulence can lead to an increase in LFFs and enhance Reynolds stresses near the last closed flux surface (LCFS). A stronger radial electric field layer can be formed near the LCFS when magnetic islands are present. The results suggest that magnetic islands can be used as a tool to enhance edge turbulence and flows, edge electric fields, and thus to trigger confinement regime transitions.

The dynamics of low?intermediate?high confinement transitions was studied using a four-step Langmuir probe in the HL-2A edge plasma. Two types (dubbed type-Y and type-J) of limit cycle oscillations (LCOs) with opposite temporal ordering between the radial electric field and turbulence were first observed. In type-Y, the turbulence grows first, followed by the localized electric field. In contrast, the electric field leads turbulence in type-J. In addition, the Reynolds stress gradient is found not enough to drive the LCO flow and the three-wave nonlinear coupling is weak there. The continuously increasing amplitude of magnetic fluctuations and the significant correlation between the magnetic fluctuation and the electron pressure gradient indicate an important role of diamagnetic drifts in the L?H transition. Mode numbers of magnetic fluctuations in the LCO frequency are identified to be m/n?=?1/0.

A generalized dispersion relation for fishbone instability is obtained by considering Gaussian distributions of spatial density and pitch angle of energetic electrons (EEs). The fishbone modes excited by trapped EEs are analysed in detail based on the HL-2A tokamak electron cyclotron resonant heating (ECRH) experiment. Numerical results show that the calculated time evolution of the mode real frequency is in reasonable agreement with the observations in ECRH experiment. Density gradient of the EEs plays an important role in excitation of the modes via resonant interaction between the modes and EEs. The modes are excited at the positions of maximum EE density gradient. The frequency of the mode in the case of on-axis heating is higher than that in the case of off-axis heating. The background plasma tends to prohibit excitation of the fishbone instabilities. The numerical results show that there is a cut-off background plasma density (or background plasma-β) for the fishbone instabilities. In addition, the toroidal magnetic field Bt has to be higher than a critical value in order to excite the mode, and the real frequency of the modes decreases with increasing Bt.

Two groups of frequency sweeping modes are observed and interpreted in the HL-2 A plasmas with qmin ~ 1. The tokamak simulation code calculations indicate the presence of a reversed shear q-profile during the existence of these modes. The mode frequencies lie in between TAE and BAE frequencies, i.e. ωBAE 1 and nqmin − m > 0, and another group of modes characterized by up-sweeping frequency with qmin drop, owing to qmin < 1 and nqmin − m < 0 before sawtooth crash. The kinetic Alfven eigenmode code analysis supports that the down-sweeping modes are kinetic reverse shear Alfven eigenmodes (KRSAEs), and the up-sweeping modes are RSAEs, which exist in the ideal or kinetic MHD limit. In addition, the down- and up-sweeping RSAEs both have fast nonlinear frequency behaviour in the process of slow frequency sweeping, i.e. producing pitch-fork phenomena. These studies provide valuable constraint conditions for the q-profile measurements.

The drift instabilities in the toroidal reversed field pinch (RFP) plasmas are numerically studied with gyrokinetic integral eigenmode equations, by taking into account the trapped electrons (TEs) and full ion kinetic effects. Both the collisionless and collisional plasmas are investigated. Two topics are addressed: the TE effects on the ion temperature gradient driven mode, and the instability of the trapped electron mode (TEM). A comparison with a circular tokamak configuration has been made. Although the TEs generally play a similar role in RFPs as they do in tokamaks, their effects become significant in RFPs only when very steep density/temperature profiles exist. Indeed, the instability of the TEM in RFP plasmas requires a much steeper density/temperature gradient and has a much narrower kθρs spectrum than in tokamak plasmas.

We report recent experimental results from HL-2A and KSTAR on ELM mitigation by supersonic molecular beam injection (SMBI). Cold particle deposition within the pedestal by SMBI is verified in both machines. The signatures of ELM mitigation by SMBI are an ELM frequency increase and ELM amplitude decrease. These persist for an SMBI influence time τI. Here, τI is the time for the SMBI influenced pedestal profile to refill. An increase in fELMSMBI/fELM0 and a decrease in the energy loss per ELM ΔWELM were achieved in both machines. Physical insight was gleaned from studies of density and vΦ (toroidal rotation velocity) evolution, particle flux and turbulence spectra, divertor heat load. The characteristic gradients of the pedestal density soften and a change in vΦ was observed during a τI time. The spectra of the edge particle flux Γ ∼ 〈ṽrñe〉 and density fluctuation with and without SMBI were measured in HL-2A and in KSTAR, respectively. A clear phenomenon observed is the decrease in divertor heat load during the τI time in HL-2A. Similar results are the profiles of saturation current density Jsat with and without SMBI in KSTAR. We note that τI/τp (particle confinement time) is close to ∼1, although there is a large difference in individual τI between the two machines. This suggests that τI is strongly related to particle-transport events. Experiments and analysis of a simple phenomenological model support the important conclusion that ELM mitigation by SMBI results from an increase in higher frequency fluctuations and transport events in the pedestal. © 2014 IAEA, Vienna.

This paper reports the highlights of the RFX-mod fusion science programme since the last 2010 IAEA Fusion Energy Conference. The RFX-mod fusion science programme focused on two main goals: exploring the fusion potential of the reversed field pinch (RFP) magnetic configuration and contributing to the solution of key science and technology problems in the roadmap to ITER. Active control of several plasma parameters has been a key tool in this endeavour. New upgrades on the system for active control of magnetohydrodynamic (MHD) stability are underway and will be presented in this paper. Unique among the existing fusion devices, RFX-mod has been operated both as an RFP and as a tokamak. The latter operation has allowed the exploration of edge safety factor q edge < 2 with active control of MHD stability and studies concerning basic energy and flow transport mechanisms. Strong interaction has continued with the stellarator community in particular on the physics of helical states and on three-dimensional codes. © 2013 IAEA, Vienna.

In our previous letter, the geodesic acoustic mode (GAM) induced by energetic particles (EGAMs) was reported in low density ohmic plasma on HL-2A (Chen et al 2013 Phys. Lett. A 377 387). We extend the experimental results of the EGAM mode in this paper. During strong tearing modes (TMs), the beta-induced Alfv?n eigenmodes (BAEs) and EGAM-induced density fluctuations are firstly measured by microwave Doppler reflectometers with different work frequencies. As predicted by theory, the measurements of magnetic probes and Doppler reflectometers suggest the EGAM magnetic oscillations have poloidal/toroidal mode numbers of m/n?=?2/0, and are localized in the core with a broad radial structure. The mode frequency is less than that of the conventional GAM (i.e. fEGAM/fGAM?1), and is constant in the radial direction. Our experimental results suggest that a density limit exists for the excitation of the EGAM in the ohmic plasma, and the density limit is improved with electron cyclotron resonance heating + neutral beam injection heating on HL-2A. The auto and cross squared bicoherences of magnetic and density fluctuations indicate that intense nonlinear interactions exist among EGAM, BAEs and strong TMs. These new observations will help us to understand the underlying physics mechanism for the excitation of fluctuations in the sub-Alfv?n frequency range.

The generation mechanisms of three-dimensional large-scale coherent structures (LSCSs) along magnetic field lines in the edge plasmas of the HL-2A tokamak are investigated using 10-tip poloidal and 8-tip radial probe arrays toroidally separated by 2100 mm. The LSCSs with radial and poloidal sizes of about (20–30)ρs (hybrid Larmor radius) ~10–15 mm and a finite parallel wave vector are experimentally observed with high spatial and temporal resolutions. The turbulence energy from 30 to 60 kHz is found to contribute significantly to the growth of the turbulent eddies of the broad spectrum. The latter gradually increase, following an increase in turbulence energy at 30–60 kHz, and then break up into LSCSs with dipolar floating potential fluctuations at the inner side of the last closed flux surface (LCFS), where the Reynolds stress driven E × B flow is strong, the flow shearing rate has a maximum and the time scale is close to the LSCS generation time. The LSCSs are then disconnected by the E × B flow shear, move across the LCFS and enter into the scrape-off layer. The back-reaction of the LSCS on turbulence is also observed and may result in LSCS intermittent behaviours. Thus, the increasing turbulent energy and the spontaneous E × B flow shear are identified to be responsible for the generation of LSCSs, which is in agreement with the theoretical prediction and provides unambiguous experimental evidence for the LSCS generation mechanism in tokamak edge plasmas. The correlation between the sheared flow and Reynolds stress is demonstrated. The evidence for the back-reaction of LSCS on turbulence is also presented.