Identification of I-mode with ion ITB in NBI-heated plasmas on the HL-2A tokamak

Improved energy confinement mode (I-mode) has been observed on the HL-2A tokamak. The I-mode features an edge transport barrier (ETB) in electron temperature and a low confinement mode like edge density. A weakly coherent mode (WCM) is observed in the edge region with the frequency of f∼60−160 kHz and the poloidal wavenumber of kθ∼0.5−2.5cm −1 . The maximum of WCM amplitude is located near the top of electron temperature pedestal. A critical value of E×B velocity shear for triggering the L–I transition has been found, and is much lower than that for triggering the L–H transition. Additionally, ion internal transport barrier (ITB) has been observed in the I-mode. The formation of ion ITB is due to the increase of E×B velocity shear, leading to the suppression of turbulence. Transport analysis further confirms the existence of electron ETB and ion ITB. The coexistence of electron ETB and ion ITB leads to an improved plasma confinement, which is comparable to that in the high confinement mode, suggesting that I-mode with ITB regimes could be an interesting operation scenario for future fusion devices.


Introduction
Future fusion devices, such as the International Thermonuclear Experimental Reactor (ITER), envisage the high confinement mode (H-mode) [1] as the baseline operation scenario [2]. The H-mode is achieved when the heating power exceeds a critical value [3]. It is characterized by the formation of a * Authors to whom any correspondence should be addressed.
Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. transport barrier or pedestal just inside the last closed flux surface. In the pedestal region, the heat and particle transports are strongly reduced. Therefore, the global energy confinement is significantly improved compared to the low confinement mode (L-mode). The steep edge pressure gradient of the H-mode can cause the magnetohydrodynamic instabilities called edge localized modes (ELMs) [4][5][6]. Large ELMs, such as Type-I ELMs, could transiently expel large amount of energy and particles onto the divertor targets. For fusion reactors such as ITER, this results in unacceptable heat loads on the divertor, causing severe erosion of the materials. Therefore, achieving ELM control is highly desirable for fusion research, with important implications for the operation of ITER [7]. ELM control has been extensively studied, and various techniques have been developed, including resonant magnetic perturbation [8,9], pellet injection [10,11], supersonic molecule beam injection [12][13][14], impurity seeding [15][16][17][18][19], lower hybrid current drive [20][21][22], and ion cyclotron resonance heating [23,24]. Alternatively, H-mode with small ELM regime or even ELM-free regime could be a possible candidate for the operation of ITER [25], such as the grassy ELM H-mode [26], type-II ELM H-mode [27], EDA H-mode [28], and QH-mode [29,30]. The improved energy confinement mode (I-mode), which shows high energy confinement comparable to H-mode, and particle confinement comparable to Lmode, is one of the promising operation regimes achieved in tokamaks [31][32][33][34][35]. The I-mode features an edge temperature transport barrier without a particle transport barrier. It is characterized by a steep temperature gradient comparable to the H-mode, while the density gradient remains similar to the Lmode [33]. Comparing to H-mode, I-mode can avoid the accumulation of impurities and Helium 'ash' due to the absence of an edge particle transport barrier, which is beneficial for fusion reactors. Moreover, it has been found that the I-mode pedestal is ideal peeling-ballooning stable [36,37], i.e. no ELMs are expected. Therefore, I-mode is being investigated as an alternative operation scenario for future fusion devices [38].
I-mode is often obtained in the 'unfavorable' configuration, where the ion B × ∇B drift is away from the active Xpoint. However, in C-Mod it has been found that the I-modes can also be accessed in the 'favorable' configuration [39]. The I-mode is usually accompanied by the appearance of a weakly coherent mode (WCM) in the pedestal region [33,35,40]. The WCM is thought to be responsible for the absence of edge particle transport barrier in the I-mode by regulating the particle flux. Recently, it has been shown on C-Mod and ASDEX Upgrade that there is a nonlinear coupling between the geodesic acoustic mode (GAM) and WCM, which explains the broad frequency structure of WCM [40,41]. On EAST, the I-mode is characterized by WCM and a radially localized edge temperature ring oscillation (ETRO) [42], while the GAM is not always observed in the I-mode [35]. Moreover, it has been found that the ETRO is caused by the alternating transitions between ion and electron turbulence [42].
This work reports the first observation of I-mode on the HL-2A tokamak. The paper is organized as follows. The identification of the I-mode is presented in section 2. Section 3 shows the formation of the ion internal transport barrier (ITB) in the I-mode. The threshold of power and velocity shear for L-mode to I-mode (L-I) transition are shown in section 4. Finally, the conclusions and discussions are given in section 5.

Observation ofTe pedestal
All experiments reported in this paper were performed on the HL-2A tokamak with the following conditions: the major radius R = 1.67 m, the minor radius a = 0.33 m, the plasma current I P = 140−160 kA, the toroidal magnetic field B T = 1.5−1.8 T, and the neutral beam injection (NBI) power P NBI = 0.8−1.2 MW. The plasma configuration is lower single null, where the ion B × ∇B drift towards the active X-point. Under these experimental conditions, sometimes plasmas with high energy confinement quality factor (H 98,y2 > 1) are observed, which are not H-mode. The waveform of such a typical discharge (#37028, red) and an H-mode discharge (#37012, blue) are shown in figure 1: (a) the NBI power and the plasma radiation power, (b) the central line-averaged electron density, (c) the edge electron temperature at r/a = 0.92 for discharge #37028, and at r/a = 0.90 for discharge #37012, (d) the electron temperature gradient at r/a = 0.92 for discharge #37028, and at r/a = 0.90 for discharge #37012, (e) the plasma stored energy, (f) the energy confinement quality factor (H 98,y2 ), (g) the divertor D α signal for discharge #37028, and (h) the divertor D α signal for discharge #37012, the spikes observed on the D α signal corresponds to the ELMs. The transition from the L-mode to the high confinement regimes are indicated by the vertical dashed line. In discharge #37028, the plasma stored energy is strongly increased after NBI injection, and the H 98,y2 is much larger than 1. It can be observed that the density remains basically unchanged, which is different from the H-mode discharge #37012. However, the edge electron temperature, and the electron temperature gradient are significantly increased. In this case, the increase in plasma stored energy is mainly due to the increase of electron temperature. It should be noted that the discharge # 37028 is not H-mode, no ELMs are observed from the D α signal. In fact, the high energy confinement regime in discharge #37028 is identified as I-mode plasma, as demonstrated later.
The electron temperature profiles of L-, I-, and H-mode in the edge region (r/a = 0.6−1.01) are shown in figure 2(a). The electron temperature is measured by a 32-channel electron cyclotron emission radiometer [43]. A steep electron temperature gradient is observed in the I-mode compared to the L-mode, forming a T e pedestal in the edge region. The density profile is measured by microwave reflectometry at the outer mid-plane with a time resolution of 10 µs [44]. As shown in figure 2(b), unlike the H-mode, there is no significant change in the edge density or density gradient in the I-mode. The density profile remains close to that in the L-mode. This is consistent with the features of I-mode, which exhibits an edge thermal transport barrier, while without accompanying particle transport barrier.

Features of WCM
The density fluctuations shown in figures 3(b) and (c) are measured by beam emission spectroscopy (BES). A BES system has been developed on the HL-2A tokamak to measure the plasma density fluctuations [45]. The system consists of 16 spatial channels, and is capable of measuring the density fluctuations in the region of r/a = 0.8−1.1. The radial position of the measured density fluctuation shown in figure 3(b) is at r/a = 0.92 for I-mode discharge #37028, which is close to the top of T e pedestal. In the I-mode phase, a significant increase in the amplitude of density fluctuation is observed in the frequency range of f ∼ 60−160 kHz. Figure 3(c) shows the density fluctuation at r/a = 0.92 for H-mode discharge #37012. Waveform of a typical discharge with high energy confinement quality factor (#37028, red) and an H-mode discharge (#37012, blue): (a) NBI power and plasma radiation power, (b) central line-averaged electron density, (c) edge electron temperature at r/a = 0.92 for discharge #37028, and at r/a = 0.90 for discharge #37012, (d) edge electron temperature gradient at r/a = 0.92 for discharge #37028, and at r/a = 0.90 for discharge #37012, (e) plasma stored energy, (f ) H 98,y2 factor, (g) divertor Dα signal for discharge #37028, and (h) divertor Dα signal for discharge #37012.
The density fluctuation is reduced in H-mode. The spectra of density fluctuation in the L-mode, I-mode and H-mode are shown in figure 3(d). Broad-band turbulence in the frequency range of f ∼ 60−160 kHz can be identified in the Imode phase, which is the signature of 'weakly coherent mode' (WCM). While in H-mode, the density fluctuation is decreased compared to the L-mode and I-mode. It should be noted that the spikes at around f ∼ 20 kHz are long lived mode (LLM), which is driven by plasma pressure gradient, and has the mode numbers of m/n = 1/1 [46,47]. Figure 3(e) shows the radial distribution of WCM amplitude. The WCM is mainly localized in the edge pedestal region, and the maximum of WCM amplitude is close to the top of pedestal. These results are consistent with previous observations on other devices [33,35,40].
The poloidal wavenumber of WCM is estimated from two BES channels in poloidal direction. Two-point correlation is used to determine the turbulence propagation direction and to estimate the wavenumber spectrogram S (k, f ), which is given as follows [48,49]: where M is the number of the realization divided from the fluctuations, S i 1 ( f ) and S i 2 ( f ) are the auto-power of the density fluctuations which have the poloidal separation of ∆x, the local wavenumber is deduced from k i ( f ) = ∆θ i 1,2 ( f ) /∆x, and θ i 1,2 ( f ) is the phase shift between two fluctuations in the frequency domain. Here, ∆k represents the resolution of wavenumber and is set to ∆k = 0.03 cm −1 . The indicator function is defined as  Figure 4 shows the poloidal wavenumber spectrogram S (k, f ) obtained from two separate poloidal channels of BES (∆x = 1 cm) at r/a = 0.92. Here, k θ > 0 indicates the turbulence propagates in the electron diamagnetic drift direction, and k θ < 0 indicates the turbulence propagates in the ion diamagnetic drift direction [45]. It can be observed that WCM is narrow in wavenumber space with k θ ∼ 0.5−2.5 cm −1 , and WCM propagates in the electron diamagnetic drift direction in the laboratory frame. This is similar to the WCM observed in C-Mod [41].
The spectra of derivative of phase fluctuation measured by Doppler reflectometry are shown in figure 5. Doppler reflectometry is dedicated to measure the turbulence velocity perpendicular to the magnetic field and the turbulence intensity [50,51]. The incident wave of the Doppler reflectometry is deliberately tilted in poloidal direction to create an angle θ 0 between the incident wave and the normal of its cut-off layer. According to the Bragg selection rule, the detected turbulence wavenumber at the cut-off layer is given by k ⊥ = 2k 0 sinθ 0 , where k 0 is the wavenumber of incident microwave in the vacuum [50,51]. The Doppler frequency shift caused by the rotation of turbulence can be given by f d = u ⊥ k ⊥ /2π , where u ⊥ is the turbulence velocity perpendicular to the magnetic field, k ⊥ is the measured perpendicular wavenumber. The u ⊥ is composed of E × B velocity and turbulence phase velocity υ ph , u ⊥ = V E×B + υ ph . The derivative of phase fluctuation of Doppler reflectometry can be given as [52] whereṼ E×B represents the fluctuation of E × B velocity,υ ph is the fluctuation of turbulence phase velocity, and dφ 0 /dt represents the density fluctuation at the cut-off layer [53].
In EAST, stationary I-mode is identified by WCM and ETRO, where ETRO is caused by the ion/electron turbulence transition [42]. WCM is measured through dφ 0 /dt, ETRO is measured throughυ ph , and GAM is measured throughṼ E×B  in the dφ /dt spectra [42]. On HL-2A, multi-channel Doppler reflectometry has been developed [54,55], which is dedicated to study turbulence physics such as the spatiotemporal characterization of zonal flows [56]. The spectra of derivative of phase fluctuation in figure 5 are measured by 44 GHz channel of Doppler reflectometry. The measured turbulence wavenumber is k ⊥ = 7 cm −1 , and the radial position of measurement is at r/a = 0.92. WCM and ETRO are not observed in the dφ /dt spectra, as shown in figure 5. These observations are quite different from the result of EAST [42]. As the ion turbulence does not exist, as shown in figure 4, there is no alternating transition between ion and electron turbulence. Therefore, it is not surprised that ETRO is not observed in the dφ /dt spectra. Besides, the no observation of WCM by Doppler reflectometry can be explained by the fact that the probed wavenumber of Doppler reflectometry (k ⊥ = 7 cm −1 ) is much larger than that of WCM (k θ ∼ 0.5−2.5 cm −1 ). Generally, I-mode is characterized by high confinement, edge electron temperature pedestal and WCM. The plasma discharge presented above is demonstrated as I-mode, since it shows all the characteristics of I-mode.

Observation of ion ITB in I-mode
Plasmas with ITB are also a desirable regime, mainly due to their enhancement of global fusion performance [57]. The formation of ITB has been well recognized by the suppression of turbulence through the magnetic shear or E × B shear [57,58]. On HL-2A, ion ITB can develop easily with the NBI heating [59]. The ion ITB has also been observed in the Imode plasmas on HL-2A. Figure 6 shows the waveform of an I-mode discharge with ion ITB. 1.1 MW NBI power is injected at t = 800 ms, as shown in figure 6(a). The L-I transition occurs at around t = 860 ms, as indicated by the vertical dashed line. After NBI injection, the electron temperature gradient (figure 6(b)) at the edge (r/a = 0.90) increases gradually, and then keep constant in the I-mode. The spectrogram of density fluctuation measured by BES in the edge region (r/a = 0.90) is shown in figure 6(c). It can be observed that WCM is excited in the I-mode. Figure 6(d) shows the E × B velocity shear |∂V E×B /∂r| at r/a = 0.90. The E × B velocity is derived by V E×B = E r × B/B 2 , where E r is the radial electric field, and B is the magnetic field. Here, E r is given by the radial force balance equation for ion species: where i indicates the ion species, P is the plasma pressure, Z is the ion charge number, n is the plasma density, V ϕ is the toroidal velocity, V θ is the poloidal velocity and B ϕ and B θ are the toroidal and poloidal magnetic fields, respectively. The ion temperature T i and toroidal velocity V ϕ are measured by charge exchange recombination spectroscopy [60]. The poloidal rotation velocity V θ is calculated from the neoclassical prediction [61]. It can be observed in figure 6(d) that the E × B velocity shear increases gradually from L-mode to Imode, and then reaches a saturation value around 80-90 kHz. This is consistent with the E r measurements in C-Mod [39], ASDEX-Upgrade [62], and EAST [35], where the E r well is deeper in the I-mode compared to the L-mode. These indicate that the formation of thermal transport barrier in the Imode is also likely due to the turbulence suppression by E × B velocity shear. Figure 6(e) shows evolution of ion temperature gradient in the plasma core (r/a = 0.4). The ion temperature gradient increases gradually after NBI injection, and then remains constant at around t = 890 ms, indicating the formation of internal ion temperature transport barrier. Figure 6(f ) shows the E × B velocity shear |∂V E×B /∂r| at r/a = 0.45, which is close to the foot of ion ITB. The turbulence spectrogram measured by Doppler reflectometry, and the turbulence intensity S k (integrated over f ∼ 0−600 kHz) are shown in figures 6(g) and (h), respectively. The radial position of measurement is at r/a = 0.45. During the formation of ion ITB, it can be observed that the E × B velocity shear is increased, while the turbulence intensity is decreased. These suggest that the increased E × B velocity shear suppresses the turbulence, leading to the formation of ion ITB. It should be noted that the ion ITB is formed after the L-I transition with a time delay of about 20-30 ms. This time delay can be explained by that the velocity shear reaches firstly the critical value for edge turbulence suppression, leading to the I-mode formation, then later reaches the critical value for core turbulence suppression, leading to the ion ITB formation. These indicate that the velocity shear plays a key role for both I-mode and ion ITB formations. However, these observations cannot definitely conclude that whether the ion ITB is coupled to the I-mode. The comparison of plasma profiles in the L-mode (blue) and I-mode with ion ITB (red) is shown in figure 7. In the I-mode, an edge transport barrier (ETB) can be observed in the electron temperature profile ( figure 7(a)). Besides, an ion ITB is observed in the core region, as shown in figure 7(b). A transport analysis has been performed in these two regimes by using ONETWO [63]. Figure 7(c) shows the thermal diffusivity of electrons χ e . In the ETB region, the χ e in the I-mode is significantly lower than that in the L-mode. The thermal diffusivity of ions χ i is shown in figure 7(d). In the ITB region, the χ i in the I-mode is decreased comparing to that in the Lmode. The transport analysis further confirms the existence of electron ETB and ion ITB. Figure 8 shows the H 98,y2 as a function of loss power P Loss for I-mode, H-mode, L-mode with ITB, and L-mode without ITB. The loss power is given as follows: where P oh is the ohmic heating power, and P aux is auxiliary heating, and W E is the plasma stored energy. It should be emphasized that the plasma stored energy W E is obtained by diamagnetic measurement [64], which includes both thermal energy and fast ion energy. It can be observed that the H 98,y2 of NBI-heated L-mode is around 20%-30% higher than that of electron cyclotron resonace heating (ECRH) L-mode. This difference is probably due to the contribution of fast ion energy in W E . Therefore, the H 98,y2 in NBI-heated plasmas is overestimated. These results are similar to the observations on EAST [65] and ASDEX-Upgrade [66], where H 98,y2 is estimated to be around 20% higher in the case of NBI heating. As shown in figure 8, the improvement of energy confinement from Lmode (NBI) to L-mode + ITB (NBI) is due to the ITB, and the increment of H 98,y2 due to ITB is about 0.3. The comparison between the H 98,y2 of discharges with I-mode + ITB (NBI) and L-mode + ITB (NBI) shows that the increment of H 98,y2 due to I-mode is about 0.2. Thus, both I-mode and ITB play key roles in the improvement of energy confinement, and the improvement factor H 98,y2 of the I-mode with ITB is comparable to that of H-mode. Recent results on EAST [67] have shown that the I-mode and the L-mode with electron ITB have similar H 98,y2 , which are higher than that of the L-mode. The super I-mode (i.e. I-mode + electron ITB) exhibits better energy confinement with a 50% higher than the standard I-mode, and has similar energy confinement improvement to the H-mode. These also suggest that both I-mode and electron ITB contribute to the improvement of energy confinement.

Threshold of power and velocity shear for L-I transition
The investigation on power threshold of I-mode and the physical mechanism for triggering I-mode are important issues in tokamaks. The power threshold of L-I transition has been studied in C-Mod [68], ASDEX-Upgrade [62], and EAST [69], in the unfavorable configuration, with ion B × ∇B drift away from the active X-point. It has been shown that the L-I transition power threshold depends weakly on B T , and the  power range for accessing I-mode increases with B T [62,68,69]. Moreover, I-mode obtained in a favorable configuration in C-Mod had narrow power ranges [39]. On HL-2A, the loss power versus plasma density at the L-H transition and L-I transition in favorable configuration are plotted as shown in figure 9. It can be seen that the dependence of L-H transition power threshold on plasma density is non-monotonic, which has been observed in several tokamaks [70][71][72]. Despite limited data for I-mode discharges it seems that the power threshold for the L-I transition is lower than that for the L-H transition. This is similar to that observed on EAST in unfavorable configuration [69]. Further experiments are required to better quantify the power threshold of L-I transition.
On HL-2A, it has been shown that the physical mechanism for triggering the H-mode is due to the turbulence suppression by the velocity shear, which is dominated by the ion pressure gradient term of E r [73]. A critical value of velocity shear for triggering the L-H transition has been found to be about ∼120 kHz, and is independent of the plasma density [73]. Figure 10 shows the critical value of the edge E × B velocity shear versus the line-averaged density for triggering the L-I (red dots) and L-H (blue diamonds) transitions. As shown in figure 10, the edge E × B velocity shear for triggering the L-I transition (∼80 kHz) is much lower than that for triggering the L-H transition (∼120 kHz). The I-mode to Hmode (I-H) transition has been observed in several tokamaks. On C-Mod and ASDEX-Upgrade, it has been shown that Imode pedestal relaxation events (PREs) often appear when the I-mode plasma transits to the H-mode plasmas [74]. On EAST, pedestal burst instabilities (PBIs) have been clearly identified during the I-H transition [75]. It has been shown that PBIs are triggered by the density gradient prompt increase prior to PBIs, and the prompt increase of density gradient can be considered as the precursor for controlling I-H transition. The I-H transition has not been observed on HL-2A. It can be explained by the following two reasons: firstly, the limitation of I-mode database, only three I-mode plasmas have been obtained; Secondly, due to the limitation of input power, the edge E × B velocity shear during all I-mode phases is always much below the critical value of the velocity shear for triggering the L-H transition, as shown in figures 6(d) and 10. Therefore, the I-H transition did not occur during these I-mode discharges. The study of the I-H transition will be an important research topic in the HL-2A tokamak in the near future.

Conclusions and discussions
The I-mode regime is observed for the first time on the HL-2A tokamak. The I-mode is obtained in NBI-heated plasmas with 'favorable' configuration. The edge electron temperature profile in I-mode shows a steep gradient, which is comparable to the H-mode, while the edge density remains L-mode like. The WCM is observed in the spectrogram of density fluctuation with a frequency range of f ∼ 60−160 kHz, and the poloidal wavenumber of WCM is k θ ∼ 0.5−2.5 cm −1 . The radial distribution of WCM amplitude is localized in the pedestal region. However, GAM and ETRO are not observed in the I-mode on HL-2A.
It has been found that on C-Mod [68], ASDEX-Upgrade [62] and EAST [69] that it is much easier to get the I-mode in the unfavorable configuration than in the favorable configuration, and almost all of the I modes in their database are in the unfavorable configuration. However, on C-Mod [39] and EAST [35], few I-mode plasmas in the favorable configuration were also obtained in a lower input power range. Up to now, the HL-2A tokamak has mainly operated in the favorable configuration, thus the I-mode plasma has not been observed in the unfavorable configuration at present. Future specific experiments will be dedicated to investigate the I-mode in the unfavorable configuration. Despite limited data for I-mode discharges it seems that the power threshold for the L-I transition is lower than that for the L-H transition. Besides, A critical value of E × B velocity shear for triggering the L-I transition (∼80 kHz) has been found, and is much lower than that for triggering the L-H transition. Therefore, the I-H transition did not occur during these I-mode discharges. The study of the I-H transition will be an important research topic in the HL-2A tokamak in the near future.
In addition, ion ITB has been observed in the I-mode with NBI heating. The formation of ion ITB is due to the increase of E × B velocity shear, leading to the suppression of turbulence. Transport analysis further confirms the existence of electron ETB (I-mode) and ion ITB. The plasma confinement is significantly improved in I-mode with ITB regime, which is comparable to that in H-mode, suggesting that the I-mode with ion ITB could be an interesting operation scenario for future fusion devices. Previous results on C-Mod [33], ASDEX-Upgrade [37], and EAST [35] show that there is not ITB in I-mode plasmas. However, the latest result on EAST has shown there is a regime with double transport barrier, combining the I-mode and the electron ITB, named as 'Super I-mode' [67]. I-mode discharges on HL-2A presented in this paper are always accompanied by the ion ITB. However, due to the limitation of database, it cannot be concluded whether the ion ITB is always present in I-mode plasmas, or whether the ion ITB is coupled to the I-mode. This question will be addressed in future experiments. 12105086. It is also partially supported within the framework of the cooperation between the French Commissariat`a l'Energie Atomique et aux Energies Alternatives (CEA) and the China National Nuclear Corporation (CNNC). The first author would like to appreciate the support of China Scholarship Council (CSC).