Introduction

Density control plays an important role in achieving practical fusion energy, since plasma density is inversely proportional to the electricity cost generated by nuclear fusion power plants1 and the square of plasma density is proportional to fusion power (\({{P}_{\text{fus}}\propto n}^{2}\))2. The main methods (e.g. pellet injection3, gas puffing4 and neutral beam injection) are difficult to directly intervene in the core plasma density5,6. Understanding the self-organized mechanism of particle confinement is essential to control the plasma core density.

Turbulence driven by free energy from density or temperature gradients are responsible for anomalous particle transport in fusion devices7. Simulations show that trapped electron modes (TEM) and ion temperature gradient (ITG) mode turbulence can dominate the direction of particle pinch, which impacts particle transport and changes plasma density8,9,10,11. Recent research suggests that for flat density profiles, the destabilization of the TEM driven by electron temperature gradient (∇Te-TEM) and ITG turbulence can lead to inward particle flux, while for steep density profiles, the TEM driven by density gradient (∇n-TEM) or coexisting ITG and TEM turbulence are dominant, resulting in outward particle diffusion12. Plasma peaking density profiles are obtained in Alcator C-Mod tokamak when the outward flux generated by the ∇n-TEM turbulence is balanced with the inward flux induced by the Ware pinch13. Due to the limitations of the plasma core (\(\uprho <0.4\)) TEM turbulence measurement methods, many theories and simulation results regarding TEM turbulence have not been validated, the understanding of the effects of TEM turbulence on particle transport and plasma density is still insufficient. The primary experimental challenge in plasma core turbulence measurement is the difficulty of simultaneously characterizing different turbulence scales and their nonlinear interactions14. Collective Thomson scattering (CTS) can measure turbulence fluctuations in the core plasma, and CTS diagnostics have been used on several tokamaks, including Tore Supra15, NSTX16, KSTAR17. Investigating TEM turbulence in the plasma core and its effects on particle transport is critical to regulate the plasma core density.

Plasma flows can regulate TEM turbulence, and the interaction between plasma flow and TEM turbulence is a self-organized behaviour18,19,20,21,22. Residual Reynolds stress is usually generated by the asymmetry in the turbulence spectrum and the nonlinear dynamics of turbulence, which can drive mean flow / zonal flow23,24,25. Sheared \(E\times B\) flow can suppress turbulence by influencing turbulence amplitude, radial correlation and phase correlation of turbulence eddies26,27,28,29. Recent simulation results show that with the increase in \(E\times B\) shearing, the inward particle pinch becomes more pronounced, resulting in a strong effect on particle transport30. Investigating the interaction between TEM turbulence and plasma flow is helpful to further understand the improvement mechanism of particle confinement and expand the methods for increasing the plasma core density.

Previous experimental results on the EAST tokamak have shown that the plasma density peaking factor can be modulated by affecting electron-scale turbulence31. This paper focuses on the spontaneous evolution of density peaking factor in TEM turbulence-dominated H-mode plasma discharge. This paper is organized as follows: The experimental set-up and experimental conditions are introduced in section “Experimental set-up and conditions”. Section “Spontaneous evolution of density peaking factor and TEM turbulence” investigates the connection between TEM turbulence and the density peaking factor. The positive feedback mechanism for particle confinement improvement is analysed in section “Positive feedback mechanism for particle confinement improvement”. The effect of the positive feedback mechanism on the formation of density Internal transport barriers (ne-ITBs) is studied in section “The formation of ne-ITBs and positive feedback mechanism”. Section “Discussion” discusses the effect of TEM turbulence intensity gradient on poloidal \(E\times B\) rotation velocity. Finally, all the results are summarized in section “Summary”.

Experimental set-up and conditions

EAST is a non-circular cross-section superconducting tokamak, and the basic parameters are as follows: major radius (R) is 1.85 m, minor radius (r) is 0.45 m, toroidal magnetic field \({B}_{T}<3\text{ T},\) plasma current \({I}_{p}<1\text{ MA}.\) EAST is equipped with various auxiliary heating including electron cyclotron resonance heating (ECRH), ion cyclotron resonance heating (ICRH), lower hybrid wave (LHW) and neutral beam injection (NBI).

The poloidal CO2 laser collective scattering diagnostic system in the EAST tokamak is established based on the principle of collective scattering14, which can simultaneously measure multi-scale turbulence (\(1<{k}_{\theta }{\rho }_{s}<5,\) where \({k}_{\theta }\) is poloidal wavenumber, \({\rho }_{s}\) is the ion sound gyroradius) in the core (\(\uprho \approx 0-0.4\)) and outer (\(\uprho \approx 0.4-0.8\)) regions32,33. Figure 1 displays the optical design of this collective scattering diagnostic

Fig. 1
figure 1

The optical design of the CO2 laser diagnostic inside the EAST tokamak.

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system inside the EAST tokamak, the initial CO2 laser beam is split by the beam splitter into one probe beam and four local oscillator beams (LO). The probe beam overlaps with LO1, LO2 in region A of plane γ and overlaps with LO3, LO4 in region B of the poloidal plane β separately. Based on the calculation in reference34, we have designed the angle between the plane β and γ as α = 5°, achieving the turbulence measurement of the region A (outer region, \(\uprho \approx 0.4-0.8\)) and the region B (core region, \(\uprho \approx 0-0.4\)). By adjusting the angle between the probe beam and the LO beam in detecting region (A, B), the turbulence information at \({\text{k}}\,{ = }\,{10}\,{ - }\,{\text{30cm}}^{{ - 1}}\) in the corresponding region can be measured34. Finally, the scattered beams from regions A and B mix with their respective LO beams in the HgCdTe detector. The wavenumber resolution Δk of this collective scattering diagnostic system is approximately 2 cm−1.

In addition, the measured turbulence frequency can be used to calculate the plasma poloidal rotation velocity:

$${\omega }_{k}^{*}={\omega }_{k}+{\omega }_{E\times B}={v}_{\theta }{k}_{\theta },$$
(1)

where \({\omega }_{k}^{*}\) is the turbulence frequency measured by this system, \({\omega }_{k}\) is the turbulence frequency and \({\omega }_{E\times B}\) is decided by \(E\times B\) rotation35,36. Generally, the turbulence frequency \({\omega }_{k}\) is much smaller than the \({\omega }_{E\times B}\), i.e., \({\omega }_{k}\ll {\omega }_{E\times B}{=k}_{\theta }{v}_{E\times B}\) 36,37, so the \({v}_{E\times B}\) can be simply calculated as follows:

$${v}_{E\times B}\approx {v}_{\theta }={\omega }_{k}^{*}/{k}_{\theta }.$$
(2)

Note that the measurement of turbulence by this diagnostic system is regional, so the calculation of poloidal rotation velocity is an average value in the measurement region.

Figure 2 shows the plasma parameters in shot 75261: the plasma current is 600 kA, \({B}_{T}\approx 2.7 T\), poloidal beta \({\beta }_{P} \sim 0.7\). The collisionality in the region of interest (\(\uprho \approx 0-0.4\)) is relatively low (\({v}_{eff}=0.1{n}_{e}{Z}_{eff}R/{T}_{ek}^{2}<5\), where \({n}_{e}\) is the electron density in 1019 m−3, \({Z}_{eff}\) is the effective ion charge, \(R\) is the major radius in m and \({T}_{ek}\) is the electron temperature in keV38). This discharge is completed by two auxiliary heating methods including LHW and NBI, and the heating power remains stable, as illustrated in Fig. 2(g) and 2(h). The NBI1 and NBI2 are co-injection and counter-injection, respectively. The stored energy, plasma density, core electron temperature, core ion temperature and extreme ultraviolet (XUV) radiation signal are displayed in Fig. 2(a), 2(b), 2(c), 2(d) and 2(e), respectively. As illustrated in Fig. 2(f), the plasma transits from L-mode to H-mode when the Dα signal drops at \({\text{t}}\approx 3.14\text{ s}\). The stored energy, plasma density, the core electron temperature and the core ion temperature increase. Then, the stored energy decreases slightly after 3.2 s. The core electron temperature and core ion temperature decrease gradually during the subsequent evolution of the H-mode, the plasma density and plasma radiation power continues to increase. The increase in plasma density and plasma radiation level with the constant auxiliary

Fig. 2
figure 2

Plasma discharge parameters in shot 75261: (a) stored energy, (b) line-averaged electron density, (c) core electron temperature, (d) core ion temperature, (e) XUV signal (f) Dα signal, (g) LHW heating, (h) NBI injection.

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heating power may be responsible for the reduction in the core electron temperature and core ion temperature.

Figure 3(a) displays electron temperature (Te) profiles measured by the Thomson scattering (TS) system39, while Fig. 3(b) displays the ion temperature (Ti) profiles measured by the X-ray imaging crystal spectrometers (XCS) system40 and the q profiles. Both the electron and ion temperatures gradually decrease during the period of 3.3–3.7s, with slight changes in q profiles during this process. The plasma density (ne) profiles measured by the polarimeter-interferometer (POINT) diagnostic system41 is shown in Fig. 3(c). In the H-mode, the edge density transport barrier is formed, and the plasma density continues to increase in the subsequent evolution of the H-mode (seen in Fig. 2(b)). Figure 3(d) displays the effective diffusion coefficient and the neoclassical diffusion coefficient of electron density computed by the ONETWO code42. The effective particle diffusivity \({D}_{\text{eff}}\) is calculated by inverting the Eq. 43:

$$\nabla \bullet \left({D}_{\text{eff}} \nabla {n}_{\text{e}}\right)+S=0$$
(3)

where \(S\) represents the particle source. Here the effects of the possible Ware pinch and the convection terms have been included in \({D}_{\text{eff}}\). As for plasma core region, \(S\) predominantly comes from the NBI fueling, which is also calculated with NUBEAM. It is clearly found that the electron density effective diffusion coefficient is strongly reduced during the time interval from 3.3 s to 3.7 s, particularly in plasma core. Improvements of particle confinement can be inferred from the development of density pedestals and the increase in plasma density44,45. The gradual decrease of electron density effective diffusion coefficient implies that particle

Fig. 3
figure 3

(a) Electron temperature profiles, (b) ion temperature profiles (solid line) and q profiles (dotted line), (c) plasma density profiles and (d) electron density effective diffusion coefficient computed by the ONETWO code in the H-mode of shot 75261.

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transport is suppressed. These results suggest that the particle confinement is continuously improved during the evolution of the H-mode.

Spontaneous evolution of density peaking factor and TEM turbulence

In the EAST discharge shot 75261, the turbulence at \({k}_{\theta }=12 {\text{cm}}^{-1}\) in both core and outer regions was measured simultaneously with the poloidal CO2 laser collective scattering diagnostic system. In this discharge, the spatial length (\({k}_{\theta }{\rho }_{s}\)) for turbulence at \({k}_{\theta }=12 {\text{cm}}^{-1}\) in the core and outer region is \({k}_{\theta }{\rho }_{s} \sim 1.5-2.1\) and \({k}_{\theta }{\rho }_{s}\sim 1.0-1.5\), which is close to the feature length of TEM turbulence (\(0.5\le {k}_{\theta }{\rho }_{s}\le 2\)). Figure 4(a) shows the temporal evolution of density peaking factor (\(\frac{\langle {n}_{e}(\uprho \approx 0)\rangle }{\langle {n}_{e}(\uprho \approx 0.5)\rangle }\)), which is defined as the ratio of the integrated density in two vertical locations measured by the POINT system. The turbulence amplitude (the normalized value of the integrated intensity of the turbulence spectrum relative to the local density, denoted as \(\frac{{S}_{k}}{{n}_{e}}\), is a widely used method for representing density fluctuations46,47) at \({k}_{\theta }=12 {\text{cm}}^{-1}\) and the poloidal rotation velocity in different regions are illustrated in Fig. 4(b) and 4(c), respectively. Figure 4(d) displays the turbulence power spectral density (PSD) at \({k}_{\theta }=12 {\text{cm}}^{-1}\) in the core region.

Fig. 4
figure 4

Measurements for the EAST discharge 75261: (a) the density peaking factor, (b) the turbulence amplitude at \({k}_{\theta }=12 {\text{cm}}^{-1}\) , (c) mean poloidal rotation velocity and (d) the turbulence power spectral density at \({k}_{\theta }=12 {\text{cm}}^{-1}\) in the core region measured by CO2 laser collective scattering diagnostic.

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The density peaking factor increases gradually during the period of 3.3–3.7 s. The turbulence amplitude at \({k}_{\theta }=12 {\text{cm}}^{-1}\) weakens in both core and outer regions, while the mean poloidal rotation velocity increases gradually. Additionally, in the H-mode discharge, the turbulence spectrum at \({k}_{\theta }=12 {\text{cm}}^{-1}\) shows a broadband mode in the frequency range of \(f\sim 500-2000\) kHz, which is similar to the broadband mode characteristic of density gradient-driven TEM turbulence as described in reference 48. Note that the increase in the density peaking factor during the H-mode lasts for 400 ms, indicating continuous improvement of particle confinement in the long-time period. Density peaking and confinement improvement in the plasma core were also observed in the JT-60 tokamak with pellet injection49 and the JET tokamak with pellet-enhanced performance modes50, while the understanding of plasma confinement improvement mechanism is insufficient51. It is interesting to explore the mechanism behind the spontaneous evolution of particle confinement improvement in the long-time period.

The Trapped-Gyro–Landau-Fluid (TGLF) model is a simplified model for turbulence transport, which aims to offer a fast and accurate approximation of linearly unstable eigenmodes for drift-wave instabilities (ITG, TEMs, and ETG)52,53. TGLF has refined the capabilities initially established by its predecessor, the GLF23model. Compared to its predecessor GLF23, the enhanced TGLF model is more accurate and extended with comprehensive physics (dynamic electrons, deuterium and carbon ions electron–ion collisions, shaped Miller geometry, and electromagnetic finite beta physics) and has been used to perform linear stability analysis of DIII-D discharges successfully54. Figure 5(a) and 5(b) display the k spectrum of the linear growth rate and frequency of the most unstable modes calculated by TGLF at \({\text{t}}=3.70\text{ s}\) for shot 75261, respectively. The normalized growth rate and the normalized frequency are respectively \({\gamma }{\prime}=\gamma (a/{c}_{s})\) and \({\omega }{\prime}=\omega (a/{c}_{s})\), where \(a\) represents the minor radius of the last closed flux surface, \({c}_{s}=\sqrt{{T}_{\text{e}}/{m}_{\text{i}}}\) represents the ion sound speed, \({\rho }_{s}={c}_{s}/{\Omega }_{s}\) and \({\Omega }_{s}=eB/{m}_{\text{i}}c\) represents the ion-gyro frequency. Linear analysis shows that the low-k (\({k}_{\theta }{\rho }_{s}\)< 0.5) and high-k (\({k}_{\theta }{\rho }_{s}\)> 2) mode instabilities are suppressed at the position \(\uprho \approx 0.18\), and the TEM modes dominate in the medium-k (0.5 < \({k}_{\theta }{\rho }_{s}\)< 2) region, which dominates particle transport in the core region. The shaded part in Fig. 5 represents the spatial scale of turbulence at \({k}_{\theta }=12 {\text{cm}}^{-1}\) (\({k}_{\theta }{\rho }_{s}\sim 1.5-2.1\)) in the core region (\(\uprho \approx 0-0.4\)) measured in this experiment, which has an overlapping region with the dominated turbulence mode at \(\uprho \approx 0.18\), as calculated by TGLF. These findings suggest that the turbulence at \({k}_{\theta }=12 {\text{cm}}^{-1}\) (\({k}_{\theta }{\rho }_{s}\sim 1.5-2.1\)) reflects the characteristics of TEM turbulence, which is also the dominant turbulence mode in the core region during the evolution of H-mode. Note that the TEM turbulence measured in this experiment exhibits a smaller spatial scale (\({k}_{\theta }{\rho }_{s}\sim 1.5-2.1\)) and higher frequency (\(f\sim 500-2000\) kHz) compared to dissipative TEM (DTEM) turbulence observed in EAST Tokamak, where the frequency is usually less than 100 kHz55 and the spatial scale range is \(0.06<{k}_{\theta }{\rho }_{s}<0.1\) 56. Therefore, the broadband turbulence at \({k}_{\theta }=12 {\text{cm}}^{-1}\) in this experiment is classified as collisionless TEM (CTEM).

Fig. 5
figure 5

Comparison of (a) growth rate and (b) frequency spectrum at the position of \(\uprho \approx 0.18\) at \({\text{t}}=3.70\text{ s}\) for shot 75261 from TGLF. Note that the shaded region represents the spatial scale range of turbulence at \({k}_{\theta }=12 {\text{cm}}^{-1}\) (\({k}_{\theta }{\rho }_{s}\sim 1.5-2.1\)) in the core region (\(\uprho \approx 0-0.4\)) as measured in the experiment, the positive frequency corresponds to the electron diamagnetic drift direction.

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The connection between plasma density peaking factor and TEM turbulence amplitude in the core and outer region is statistically analysed with similar plasma parameter conditions during the evolution of the H-mode, as illustrated in Fig. 6(a) and 6(b). The initial turbulence amplitude within the selected time period in different shots is normalized to 1 (i.e. divided by the turbulence amplitude at the initial moment) to demonstrate the connection between the plasma density peaking factor and the turbulence amplitude. In these five discharges, the plasma density peaking factor increases gradually while the turbulence amplitude at \({k}_{\theta }=12 {\text{cm}}^{-1}\) decreases. The negative correlation connection between the plasma density peaking factor and the TEM turbulence amplitude suggests that the suppression of TEM turbulence contributes to the increase in density peaking factor. In the Alcator C-Mod tokamak, the outward flux generated by the ∇n-TEM turbulence is balanced by the inward flux induced by the Ware pinch, leading to a peaked central plasma density profile13. In addition, NBI fueling57 and Ware pinch58 further contribute to the increase in the density peaking factor. Thus, the density peaking factor increases when TEM turbulence is suppressed.

Fig. 6
figure 6

Statistical relationship between plasma density peaking factor and the \({k}_{\theta }=12 {\text{cm}}^{-1}\) turbulence amplitude in the (a) core and (b) outer regions during the evolution of the H-mode. The selected time periods are 3.3–3.7 s for shot 75260 and shot 75261, the selected time period is 3.8–4.2 s for shot 75271, the selected time period is 4.3–4.7 s for shot 75287 and shot 75290 with a time interval of 50 ms.

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Positive feedback mechanism for particle confinement improvement

During the evolution of H-mode, the statistical results of the TEM turbulence amplitude and the \(E\times B\) flow in the core and outer regions are displayed in Fig. 7(a) and 7(b), respectively. In these five discharges, the turbulence amplitude at \({k}_{\theta }=12 {\text{cm}}^{-1}\) reduces as the \(E\times B\) rotation velocity increases, and the \(E\times B\) rotation velocity is negatively correlated with the turbulence amplitude at \({k}_{\theta }=12 {\text{cm}}^{-1}\). These observations are consistent with previous studies59,60, which suggest that when the \(E\times B\) shearing rate exceeds the maximum linear growth rate (γmax) of the dominant instability, this instability is suppressed and the corresponding transport level will decrease. This implies that the suppression of TEM turbulence is caused by the \(E\times B\) flow, thereby improving particle confinement in the H-mode. Since the poloidal rotation velocity provided by the CO2 laser collective scattering diagnostic system is a relative value, it is difficult to calculate the \(E\times B\) shearing rate in the study.

Fig. 7
figure 7

Statistical relationship between the \({k}_{\theta }=12 {\text{cm}}^{-1}\) turbulence amplitude and the mean poloidal \(E\times B\) rotation velocity in the (a) core and (b) outer regions during the evolution of the H-mode.

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It is critical to take pressure and pressure gradients into account during the investigation of plasma equilibrium poloidal flow. Based on the plasma discharge parameters in shot 75261 H-mode, the plasma pressure gradient profile is calculated using the ONETWO code, as illustrated in Fig. 8(a). During the spontaneous evolution of H-mode, plasma pressure gradient increases significantly in the core region, while it changes slightly in the outer region. Furthermore, in the initial stage of the H-mode evolution (t = 3.3s), the higher pressure gradient is observed in the plasma core region. The neutral beam injection can increase plasma density by fueling effect57, and it also contributes to plasma heating61. The increase in core density, core electron temperature and core ion temperature during the NBI1 injection period (t = 3.10–3.20s, as seen in Fig. 2) may contribute to the increased pressure gradient in the initial stage of H-mode evolution.

Fig. 8
figure 8

(a) Plasma pressure gradient profile calculated by ONETWO code, the connection between the mean poloidal \(E\times B\) rotation velocity and the average pressure gradient in the (b) core and (c) outer regions for shot 75261.

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To further investigate the variations in plasma pressure gradient and the plasma poloidal rotation, the connection between the average pressure gradient and the \(E\times B\) rotation velocity in different regions were displayed in Fig. 8(b) and 8(c). Note that the plasma poloidal rotation velocity obtained by this collective scattering diagnostic system is the average value of the measurement region, the average pressure gradient in the corresponding region is calculated based on Fig. 8(a). In the core region, the average plasma pressure gradient increases gradually and shows a positive correlation with the \(E\times B\) rotation velocity, while this positive correlation is not found in the outer region. According to the radial force balance equation, the plasma pressure gradient is proportional to the radial electric field, particularly in conditions with higher pressure gradient62,63. The increase of the plasma pressure gradient can strengthen the radial electric field and further promote the generation of the \(E\times B\) flow. Therefore, the strengthening in plasma pressure gradient in the core region with higher pressure gradient may be responsible for the gradual increase of the core region \(E\times B\) rotation velocity in the H-mode. As for the plasma outer region where the pressure gradient is lower, the average plasma pressure gradient shows no correlation with the \(E\times B\) rotation velocity, which implies that the plasma pressure gradient is not the dominant factor driving the increase in \(E\times B\) rotation velocity in the outer region with lower pressure gradient.

The interaction between \(E\times B\) flow and TEM turbulence is studied in different pressure gradient scenarios. In the plasma core region with higher pressure gradient and lower collisionality (\({v}_{eff}<5\)), the suppression of TEM turbulence caused by the \(E\times B\) flow reduces anomalous particle transport and increase the plasma pressure gradient, which contributes to the increase in the \(E\times B\) flow, and the increased \(E\times B\) flow could further suppress the TEM turbulence. This positive feedback process may be the reason for the continuous improvement of particle confinement during the evolution of H-mode, which supports the feedback mechanism proposed in reference51 that the suppression of turbulence and transport by \(E\times B\) flow can increase the plasma pressure gradient, and the increase of pressure gradient will further increase the \(E\times B\) flow. Furthermore, the simulation in reference12 indicates that ∇n-TEM turbulence is dominant in steep density profile, resulting in outward particle diffusion. The phenomenon that increased plasma density and improved particle confinement caused by the TEM turbulence suppression in the TEM turbulence-dominated plasma core region supports this simulation. As for the outer region with lower pressure gradient, the change in the plasma pressure gradient cannot explain the increase in poloidal \(E\times B\) flow perfectly.

The formation of ne-ITBs and positive feedback mechanism

The continuous improvement of plasma particle confinement during the spontaneous evolution of H-mode in shot 75261 could be explained by a positive feedback mechanism among poloidal \(E\times B\) flow, TEM turbulence, and plasma pressure gradient. However, the ne-ITB did not form in this process. To explore the connection between ITB formation and this positive feedback mechanism in the spontaneous evolution of H-mode, we focus on the experiment with higher auxiliary heating power for further examination. The comparisons of plasma discharge parameters between shots 74803 and 75261 as presented in Table 1. For shot 74803, the total power of LHW and NBI is 3.8 MW, higher than shot 75261, while the plasma current, density and poloidal beta are 0.5 MA, \({n}_{e}\approx 2.7\times {10}^{19}{m}^{-3}\) and 0.6, slightly lower than shot 75261. Figure 9(a) and 9(b) display the evolutions of plasma density at different vertical locations (Z = 0 cm is the plasma center) and plasma density gradient for shot 74803 from t = 3.7 to 4.0 s, respectively. During this time interval, the electron density near the plasma center (Z = 0 cm) steadily increases, while it changes slightly at the edge. With the significant increase of the density gradient in the plasma core at around t≈3.79 s, a ne-

Table 1 Comparisons of parameters for plasma discharges for shot 74803 and 75261.
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Fig. 9
figure 9

Time evolutions of (a) line-averaged density (PointN1 to PointN6) and (b) density gradient contour, (c) the electron plasma electron temperature and (d) ion temperature profiles (solid line) and q profile (dotted line) for shot 74803.

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ITB forms. Figure 9(c) and 9(d) show the electron plasma electron temperature and ion temperature profiles before and after the formation of ne-ITB. For shot 74803, there is no significant increase in the plasma core electron temperature and ion temperature before and after the formation of ne-ITB, indicating that only ne-ITB are formed in this experiment. In addition, it can be seen that the rational surface (q = 3) present at the foot (ρ≈0.3) of ne-ITB in Fig. 9(d).

The change of poloidal \(E\times B\) flow, TEM turbulence, and plasma pressure gradient during the process of the ne-ITB formation are analysed. Figure 10(a) shows the temporal evolution of turbulence amplitude at \({k}_{\theta }=12 {\text{cm}}^{-1}\) (black) and the mean poloidal rotation velocity (red) in the core region (\(\uprho \approx 0-0.4\)) from t = 3.70 to 3.85 s. The turbulence amplitude at \({k}_{\theta }=12 {\text{cm}}^{-1}\) (\({k}_{\theta }{\rho }_{s}\sim 1.4-1.8\)) reduces and the poloidal rotation velocity increases gradually. In addition, the mean poloidal rotation velocity is approximately designated as \(\overline{v }\)≈ 427 m/s when the ne-ITB forms at around t ≈ 3.79 s, which may represent the \(E\times B\) flow threshold for ne-ITB formation in this experiment. The plasma core effective electron density diffusion coefficient drops to closely the neoclassical level in this process, as shown in Fig. 10(b). In Fig. 10(c), the plasma core pressure gradient increases gradually from t = 3.70 to 3.85 s, which is positively correlated with the core poloidal rotation velocity (seen in Fig. 10(a)). These results indicate that this positive feedback mechanism involving \(E\times B\) flow, TEM turbulence, and pressure gradient significantly contributes to the formation of ne-ITB during the spontaneous evolution of H-mode.

Fig. 10
figure 10

(a) The turbulence amplitude at \({k}_{\theta }=12 {\text{cm}}^{-1}\) (black) and mean poloidal rotation velocity (red) in the core region (\(\uprho \approx 0-0.4\)), (b) electron density effective diffusion coefficient and (c) plasma pressure gradient profile for shot 74803.

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An attempt of ITB power threshold identification for weak or reversed-shear plasmas by the ITB Database Group and the ITPA Topical Group on Transport and Internal Barrier Physics resulted in a scaling law of ITB formation power threshold, as below64:

$${P}_{\text{Th}}^{\text{ITB}}=3.14{n}_{19}^{0.9}{\text{a}}^{2.13}{\text{k}}_{95}^{1.34}{\left(0.2+{\delta }_{95}\right)}^{-0.15}{\text{B}}_{\text{t}}^{0.23}.$$
(4)

In this expression, \({\text{k}}_{95}\) and \({\updelta }_{95}\) are, respectively, the elongation and triangularity of the plasma cross-section at 95% of the volume averaged flux surface, and the units are 1019 m−3 for ne and T for Bt. Recent work of Professor Gao indicates that this scaling law of ITB formation power threshold is applicable to the EAST tokamak65. According to Eq. (4), we calculated ITB power threshold for two discharges in this paper. As for shot 75,261, the parameters are \({\delta }_{95}=0.27\),\({k}_{95}=1.48\),\({B}_{\text{t}}=2.47 \text{T}\) and \({\text{n}}_{\text{e}}=3.3\times {10}^{19} {\text{m}}^{-3}\). The power threshold is approximately 3.9 MW, while the total heating power of this shot is 2.4 MW, which is below than the required threshold for ITB formation. As for shot 74803, the parameters are \({\delta }_{95}=0.31\),\({k}_{95}=1.60\),\({B}_{\text{t}}=2.47 \text{T}\) and \({\text{n}}_{\text{e}}=2.7\times {10}^{19} {\text{m}}^{-3}\). The power threshold is approximately 3.64 MW, while the total heating power of this shot is 3.8 MW, which exceeds the ITB formation power threshold, These results suggest that when the heating power is below the power threshold, the positive feedback mechanism leads to a spontaneous increase in ne but no ne-ITB formation; while when the heating power exceeds the threshold, the positive feedback mechanism triggers a spontaneous increase in ne and the ne-ITB formation.

Discussion

As for the plasma outer region (\(\uprho \approx 0.4-0.8\)) with lower pressure gradient, the average plasma pressure gradient shows no correlation with the \(E\times B\) rotation velocity (seen in Fig. 8(c)), plasma pressure gradient is not the dominant factor driving the increase in \(E\times B\) rotation velocity in this region. Experimental results on the DIII-D tokamak demonstrated that the \(E\times B\) rotation velocity measurements only in the steep gradient region of ITB cases are consistent with the neoclassical theory66. For the disagreement of poloidal rotation between neoclassical predictions and measurements, turbulence may provide significant poloidal rotation drive66,67. Turbulence Reynolds stress68 is the usual mechanism for driving plasma poloidal rotation, and it may affect the \(E\times B\) flow.

The radial divergence of turbulence spectrum can generate Reynolds stress gradient, playing a critical role in poloidal rotation23,31. According to the quasi-linear theory of turbulence-driven rotation, early results suggest that the wave energy density flow divergence is essential to drive the mean poloidal rotation, and the Reynolds stress is positively correlated with the wave energy density flux gradient in the radial direction23. Recent research from poloidal rotation and electron-scale turbulence in EAST tokamak shows that the contribution of Reynolds stress to poloidal rotation velocity could be broadly characterized by the electron-scale turbulence intensity ratio at different radial locations (i.e. turbulence intensity radial gradient) when the magnetic topology is unchanged31:

$${V}_{\theta }\propto \sum_{n=1}^{n}{\alpha }_{{k}_{n}}f\left({S}_{gradient,{k}_{n}}\right)=\sum_{n=1}^{n}{\alpha }_{{k}_{n}}\frac{k{\left({2\omega }_{k}\right)}^{-1}}{{L}_{n}{m}_{i}{n}_{0}}\frac{{\nabla S}_{k,r}}{\nabla r} ,$$
(5)

where \({\alpha }_{{k}_{n}}\) represents the wavenumber coefficient of serial number n. \(\sum \left|{\alpha }_{{k}_{n}}\right|=1\), \({k}_{n}\) is the turbulence wavenumber corresponding to serial number n. \(f\left({S}_{gradient,k}\right)\) is the turbulence intensity radial gradient, which can be calculated by \(f\left({S}_{gradient,k}\right)=\frac{k{\left({2\omega }_{k}\right)}^{-1}}{{L}_{n}{m}_{i}{n}_{0}}\frac{{\nabla S}_{k,r}}{\nabla r}\), where \({L}_{n}=-{\left(\frac{\partial \text{In}n}{\partial r}\right)}^{-1}\), \({m}_{\text{i}}\) represents the ionic mass, \({n}_{0}\) represents the plasma density, \({S}_{k,r}\) represents the drift turbulence energy density flux. Based on Eq. (5), the turbulence intensity gradient at \({k}_{\theta }=12 {\text{cm}}^{-1}\) is calculated in the discharge of shot 75261. The connection between the outer region \(E\times B\) rotation velocity and the \({k}_{\theta }=12 {\text{cm}}^{-1}\) turbulence intensity radial gradient \(\sum {\alpha }_{k}f\left({S}_{gradient,k}\right)\) is displayed in Fig. 11. It can be seen that the turbulence intensity radial gradient at \({k}_{\theta }=12 {\text{cm}}^{-1}\) increases gradually during the evolution of H-mode. There is a positive correlation connection between the outer region poloidal rotation velocity and the turbulence intensity radial gradient at \({k}_{\theta }=12 {\text{cm}}^{-1}\), which implies that the strengthening of TEM turbulence intensity radial gradient contributes to the gradual increase of the outer region poloidal \(E\times B\) flow in the H-mode, and it is consistent with the results in reference31. This finding suggests that the Reynolds stress may contribute to the increase in poloidal \(E\times B\) flow in the outer region with lower pressure gradient.

Fig. 11
figure 11

Statistical relationship between outer region poloidal \(E\times B\) rotation velocity and the \({k}_{\theta }=12 {\text{cm}}^{-1}\) turbulence intensity gradient \(\sum {\alpha }_{k}f\left({S}_{gradient,k}\right)\) during the evolution of H-mode.

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Summary

In the EAST discharge experiments, we investigate the spontaneous evolution of particle confinement in TEM turbulence-dominated H-mode plasma.

The relationship between broadband turbulence (\(f\sim 500-2000\) kHz) and particle confinement is experimentally reported for the first time. During the evolution of H-mode, with the effect of the positive feedback mechanisms involving \(E\times B\) flow, TEM turbulence, and pressure gradient, the plasma density peaking factor continuously increases. In the plasma core region (\(\uprho \approx 0-0.4\)) with higher pressure gradient and lower collisionality (\({v}_{eff}<5\)), the effect of \(E\times B\) flow suppresses TEM turbulence and reduces the particle transport, which increases plasma pressure gradient, while the strengthening of the pressure gradient further enhances the poloidal \(E\times B\) flow, the positive feedback mechanism finally leads to a scenario where particle confinement improves continuously. Additionally, this positive feedback mechanism could induce the ne-ITBs formation with higher heating power. In the plasma outer region (\(\uprho \approx 0.4-0.8\)) with lower pressure gradient, the positive correlation connection between the \(E\times B\) rotation velocity and TEM turbulence intensity radial gradient suggests that the Reynolds stress may contribute to the increase in poloidal \(E\times B\) flow.

Triggering the positive feedback mechanisms involving \(E\times B\) flow, TEM turbulence, and pressure gradient in the H-mode is important to obtain better particle confinement, which is helpful for plasma density control and ITB formation. Note that the plasma radiation levels rise (seen in Fig. 2(e)) with the plasma density continues increase in the evolution of H-mode, which ultimately limits the continuous improvement of the particle confinement. Exploring appropriate methods to reduce plasma radiation levels and increase plasma temperature is the most urgent issue for better understanding and utilizing the positive feedback mechanism, requiring more work in the future.