Observation of fast electron redistribution during saturated kink mode in high βp H-mode discharge with central heating in EAST tokamak

In the EAST tokamak, we have developed an internal transport barrier (ITB) high-confinement mode (H-mode) scenario characterized by dominant electron heating and centrally peaked electron temperature profiles, facilitated primarily through the combustion of lower hybrid current drive and electron cyclotron radio heating (ECRH). Hard x-ray diagnostics reveal a marked increase in the population of fast electrons with energy from 30 keV to 80 keV, concurrent with augmented ECRH power during H-mode plasma operations. This surge in fast electron population precedes the formation of the electron temperature ITB (Te-ITB). Within the Te-ITB H-mode discharge, a mild and long-lived m/n = 1/1 mode (where m and n denote the toroidal and poloidal mode numbers, respectively) emerges proximal to the ITB region. This mode precipitates a redistribution of fast electrons, contributing to an increase in the safety factor near the magnetic axis and thereby promoting the stability of the Te-ITB. Furthermore, we explore the influence of fast electrons on plasma pressure and examine the effects of the profile of fast electrons on the central Te. Strategies to maintain the m/n = 1/1 mode at a moderate amplitude are also discussed, highlighting their significance in the sustained management of Te-ITB.

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Introduction
In the quest for viable commercial fusion energy, advanced scenarios featuring weak or reversed magnetic shear in the internal transport barrier (ITB) region have garnered attention due to their high bootstrap current fraction [1].This study concentrates on the formation and long-sustention of ITB in EAST discharges with lower hybrid wave (LHW) and electron cyclotron radio heating (ECRH).Characterized by dominant electron heating and minimal torque input, these discharges closely mimic the conditions anticipated in future reactors [2,3].Recent experiments in the AUG tokamak have illustrated that the presence of fast particles can induce robust, axisymmetric E × B flows, playing a pivotal role in ITB formation [4].However, the stability of ITB is a critical concern.A continuous growth of the m/n = 1/1 mode can lead to the collapse of ITB, especially when the minimum safety factor, q min , approaches to unity [5,6].Furthermore, three-dimensional nonlinear magnetohydrodynamic (MHD) simulations within tokamak geometry suggest that an increase in β p might mitigate the saturation amplitude of such infernal-type m/n = 1/1 modes [7].This insight could be crucial for maintaining ITB stability and offers a potential pathway for optimizing operational parameters in fusion devices.
The phenomenon of flux pumping, induced by the helical m/n = 1/1 mode, has been instrumental in elucidating the atypical current broadening observed in hybrid advanced scenarios, as evidenced by both experimental [8,9] and theoretical [10,11] investigations.In plasma environments dominated by LH and EC heating, the emergence of the helical m/n = 1/1 mode is known to precipitate a redistribution of fast electrons within the core region.This redistribution, in turn, gives rise to a localized negative current in the vicinity of the magnetic axis [12].In the EAST tokamak, a similar occurrence of negative current has been observed.Intriguingly, this phenomenon is attributed to the action of small-scale electron turbulence, especially prevalent in discharges characterized by high electron beta β pe [13].
In this study, we observe the formation of a electron temperature ITB (Te-ITB) following the transition from low confinement mode (L-mode) to high-confinement mode (H-mode) transition.This phenomenon appears to be intricately connected to a sudden surge in the population of fast electrons.Subsequent to the establishment of Te-ITB, a m/n = 1/1 helical mode is destabilized, exhibiting a relative electron temperature T e,11 /T e0 of approximately 10% and a relative electron density N e,11 /N e0 of about 1%.This mode is not only persistent but also plays a pivotal role in redistributing fast electrons, thereby contributing to the flattening of the central safety factor and the prolonged sustenance of Te-ITB.
The structure of the paper is as follows: section 2 provides a concise overview of the EAST high β p scenario, emphasizing the characteristics of Te-ITB.Sections 3 and 4 delve into the dynamics and evolution of the m/n = 1/1 mode and fast electrons, respectively, presenting the core findings of our research.In section 5, we discuss the strategies for controlling the m/n = 1/1 mode.Finally, section 6 offers a comprehensive summary of our study, encapsulating the significant insights and implications.
2. EAST high β p discharges: m/n = 1/1 mode within the ITB region EAST, a medium-sized, fully superconducting tokamak designed for steady-state operation, boasts a major radius (R) of 1.85 m and a minor radius (a) of 0.45 m.The EAST team has recently focused on advancing electron-dominant heating scenarios in L-mode [13], improved mode [14] and Hmode [15,16].A recurring feature in these electron-heating dominant discharges is the formation of Te-ITB [13], typically with its foot around ρ ∼ 0.25, where ρ represents the square root of the normalized toroidal flux ρ = ϕ /ϕ max (with ϕ max being the total toroidal flux).In the Te-ITB region, the internal kink mode with a poloidal/toroidal mode number of m/n = 1/1, along with its harmonic modes, is a common occurrence, often coinciding with the condition where the minimum safety factor, q min approximates unity.The safety factor profile is reconstructed using the EFIT code, complemented and constrained by measurements from the polarimeter-interferometer system [17,18].
Figure 1 presents a typical Te-ITB H-mode discharge, characterized by a power input of 2 MW LHW and 1.2 MW ECRH.The discharge maintains a fully non-inductive plasma current, evidenced by a loop voltage (V loop ) of approximately zero during the stable H-mode phase post t ∼ 4.5 s.Subsequently, at t = 5.8 s, an additional 0.4 MW of ICRF was introduced, which did not notably alter the V loop .This experiment was conducted in the upper single null divertor configuration.The parameters included a counter-clockwise plasma current I p of around 0.3 MA (viewed from the top), a clockwise toroidal magnetic field B t of about 2.5 T, a line-integrated density N e0 of 4 × 10 19 m −3 , and a plasma elongation κ of approximately 1.674.The plasma inductance was high at l i = 1.2, with an edge safety factor q 95 of 9.5 and a poloidal normalized beta β p reaching up to 2.5.A detailed view within the figure reveals the emergence of the m/n = 1/1 mode and its harmonic m/n = 2/2 counterpart as the electron temperature gradient at R = 1.95 m (around ρ ∼ 0.2) surpasses a critical threshold.The mode's amplitude increase coincides with a decrease in frequency.Approximately 150 ms post-emergence, the m/n = 1/1 kink mode attains saturation in both amplitude and frequency, with the latter (∼5 kHz) significantly exceeding the plasma's rotation at the Te-ITB region and closely matching the electron diamagnetic drift frequency at q min .Notably, the input of IC power, since a modest 0.4 MW, does not significantly influence the amplitude or frequency of the mode.
Both ECE and soft x-ray (SXR) diagnostics have been employed to examine the spatial structure and dynamics of the internal kink mode.Figure 2 demonstrates that this mode predominantly resides within the R = 1.98 m region, peaking in amplitude at R = 1.95 m.The perturbation in electron temperature δT e induced by this mode constitutes approximately 10% of the equilibrium temperature.Notably, the mode's structural intensity diminishes sharply beyond the q = 1 surface (around R ∼ 1.98 m), exhibiting characteristics typical of an ideal kink mode.In comparison, density perturbations are relatively minor, amounting to about 1.5% of the equilibrium density.The SXR perturbations of the m/n = 1/1 mode in figure 2(c) not only corroborates the mode's spatial positioning but also suggests a predominant m = 1 mode structure.As depicted in figure 3, both the m/n = 1/1 mode and its harmonic m/n = 2/2 are confined within the q = 1 surface, sharing the same spatial domain.The δT e attributable to the m = 2 harmonic is merely one-tenth of that caused by the m = 1 mode.Characteristically, both the m = 1 and m = 2 modes align with the ideal kink mode and do not exhibit any discernible phase inversion at the resonant surface.
Figure 4 depicts a detailed account of the temporal progression of plasma confinement and the electron temperature gradient R/L Te emerges subsequent to the transition from L-mode to H-mode, closely trailing the steep rise of R/L Te at the q = 1 magnetic flux surface.As the m/n = 1/1 mode experiences nonlinear growth, R/L Te diminishes at q = 1 and escalates at q = 1.5 surface.Upon entering a steady state, the m/n = 1/1 mode drives R/L Te to a minimal value at q = 1 surface and saturates it at q = 1.5 surface.Notably, the density gradient peaks at q = 1.5 surface, diverging from the characteristics typical of Te-ITB.Following the m/n = 1/1 mode's saturation, a subsequent peak in Te aligns with the peak of the density gradient.In this particular discharge, the absence of Ti-ITB can be attributed to the exclusive use of ECRH and LHW without neutral beam injection.A sharp escalation of R/L Te at q = 1 surface, subsequent to an additional increase in ECRH power, signifies the onset of Te-ITB.The forthcoming section will elaborate on the intricacies of ITB formation and the initiation of the m/n = 1/1 mode.The safety factor q and current profiles have been reconstructed by kinetic-EFIT [19].As depicted in figure 5 for discharge #123867 featuring Te-ITB, the q profile exhibits a flat characteristic within the core region, with q min approximating unity at ρ ∼ 0.25.This flatness in the core's q profile and the proximity of q min to unity may contribute to the emergence of the m/n = 2/2 harmonics mode, potentially due to the presence of weak magnetic shear in this region [1,20,21].

Fast electron dynamics throughout the Te-ITB formation process
Recent advancements in both simulation and experimental research have revealed that the generation of ITBs may be instigated by fast particles through the induction of zonal flows during multi-scale interactions [4].This finding has inspired us to delve into the role of fast electron dynamics in the formation of Te-ITB, especially considering the combined LHW and ECRH heating mechanism utilized in EAST.Moreover, it is noteworthy that fast electrons can potentially drive internal kink modes, either through resonant or nonresonant mechanisms [22][23][24], or alternatively, contribute to the stabilization of such modes [25,26].
Figure 6 provides a direct observation of the hard x-ray (HXR) spectrogram aligning with the frequency evolution of the m/n = 1/1 mode, as measured by SXR diagnostics.The HXR emissions, originating from fast electrons with energies ranging from 30 keV to 80 keV, display a phase discrepancy when compared to SXR emissions as shown in figure 6(a).This phase difference suggests that the fast electrons are being modulated by the m/n = 1/1 mode.To further explore the interplay between the m/n = 1/1 mode and these fast electrons, we have charted the temporal progression of fast electron counts alongside the amplitude of MHD modes in figure 7.
Figure 7 elucidates the sequential events following the transition from L-mode to H-mode (t1).Initially, there's a gradual improvement in the confinement of fast electrons within the 30 keV to 80 keV energy range.Approximately 0.55 s post-transition, a sharp rise in the population of fast electrons occurs, coinciding with the formation of Te-ITB.The onset of the m/n = 1/1 mode (t3) trails the Te-ITB formation by about 30 ms.Notably, the transition from L-mode to H-mode (t1) is attributed to ECRH input, while the sudden increase in fast electron population and the subsequent Te-ITB formation (t2) correlate with an additional surge in ECRH power, as indicated in figure 1(c).The amplification of the m/n = 1/1 mode leads to a slight reduction in the fast electron count, yet the population recuperates once the mode reaches a saturation level (t ∼ 6.5 s).This sequence underscores the pivotal role of increased fast electron counts, driven by combined ECRH and LHW heating, in fostering Te-ITB.It is crucial to acknowledge that the destabilization of the m/n = 1/1 mode is linked to the amplified R/L Te gradient, stemming from the surge in fast electron population, as detailed in figure 1(d).
The amplification of the m/n = 1/1 mode significantly alters the distribution of fast electrons.In EAST, the HXR diagnostic boasts a temporal resolution of approximately 10 ms in the energy spectrum, enabling a detailed analysis of the fast electron dynamics throughout the protracted growth phase of the m/n = 1/1 mode, spanning from t = 5 s to t = 6.5 s.The experimental findings are illustrated in figure 8.During the growth phase of the m/n = 1/1 mode, the evolution of the HXR spectrum reveals an interesting pattern: the population of fast electrons with energies below 55 keV tends to increase, whereas electrons with energies exceeding 55 keV show a decrease.This redistribution is a direct consequence of the influence exerted by the m/n = 1/1 mode.The surge in lower energy fast electrons within the core region contributes to a reduction in the non-inductive current induced by LHW near the magnetic axis.This phenomenon bears a resemblance to magnetic flux-pumping induced by saturated MHD modes, which leads to alterations in the q profile within the core [10].Notably, the flattening of the q profile in the core is conducive to the sustained presence of Te-ITB [14].

Influence of fast electrons profile on T e0
Figure 1(d) illustrates that the m/n = 1/1 mode becomes destabilized when the local R/L Te surpasses a critical threshold.Intuitively, with increased on-axis heating via ECRH, a higher central peak in T e0 is expected.Additionally, the distribution of fast electrons emerges as another crucial factor influencing the central peak of T e .For a comparative analysis, discharge #122275, which undergoes LHW and ECRH combated heating and with on-axis peaking fast electron profile, is juxtaposed with discharge #123867 at t = 7 s, with a broaden off-axis peaking fast electron profile.As depicted in figure 9, simulation outputs generated by the CQL3D code [27] forecast a density of fast electrons (with energy exceeding 25 keV) reaching up to 2% for discharge #122275, and 1.3% for discharge #123867.Notably, in discharge #122275, these fast electrons are projected to contribute to approximately 6% of the total plasma pressure, underscoring their significant role in shaping the central peak.
Figure 10 captures the evolution of fast electrons within the 30 keV to 80 keV energy range, as measured by the HXR diagnostics, for discharges #122275 and #123867.Notably, discharge #122275 exhibits a higher population of fast electrons    compared to discharge #123867, attributable to the higher ECRH power input (2 MW in #122275 vs. 1.2 MW in #123867).However, a more significant observation is the shift in the fast electron profile to an off-axis peak configuration, marking a pivotal change in electron distribution dynamics.
Fast electrons, generated through and ECRH, typically form an on-axis peak, resulting in an elevated central electemperature T e0 .Conversely, off-axis peak of fast electron profile is associated with a reduction in T e0 , as depicted in figure 11.Specifically, discharge #122275 exhibits an onaxis peak in the fast electron profile, correlating with a higher The evolution of the HXR spectrum from the initiation to the saturation of the m/n = 1/1 mode.This phase is marked by a notable increase in the intensity of HXR emissions within the 30 keV to 50 keV range, coupled with a decrease in emissions above 50 keV.The redistribution in the fast electron spectrum inherently paves the way for the generation of a negative current in the plasma center.T e0 of approximately 8 keV.In contrast, when the fast electron distribution shifts to an off-axis peak configuration, the maximum T e0 observed drops to below 6 keV.

Saturation mechanism of the m/n = 1/1 mode
The establishment of Te-ITB significantly enhances plasma confinement.In central electron-dominated heating scenario, fast electrons can trigger the formation of ITB.However, an increase in core confinement may precipitate the destabilization of the m/n = 1/1 infernal type mode.It is imperative to mitigate the continuous growth of the m/n = 1/1 mode for two primary reasons.First, the robust presence of the m/n = 1/1 mode could potentially incite tearing modes due to the forced magnetic reconnection process [2].And second, too strong m/n = 1/1 mode can led to a significant expulsion of fast electrons (energy < 50 keV), resulting in a reduction in T e0 and overall plasma stored energy, as illustrated in figure 12.
Figure 12 demonstrates the proliferation of super-fast electrons (energy > 100 keV) and the concurrent depletion of fast electrons (energy < 50 keV).The modulation of fast electrons within the 30 keV to 50 keV range impacts T e0 and the plasma stored energy Wmhd by 25% and 7%, respectively.Milder m/n = 1/1 modes with higher frequencies and smaller amplitudes are better to confine fast electrons (energy < 50 keV).Frequency chirping in these m/n = 1/1 modes can reach up to 80%, primarily due to variations in local diamagnetic drift velocity [2].The generation of super-fast electrons has the capability to drive non-inductive current and alter V loop , with a maximal V loop shift recorded at approximately 20 mV at t = 24.8s.The contribution of fast electrons to plasma pressure aligns with the predictions made by CQL3D, as delineated in figure 9.In conclusion, strong m/n = 1/1 modes exert a profound influence on plasma current and pressure.Therefore, understanding the saturation mechanism of these modes is crucial for the control and optimization of plasma behavior.
The nonlinear MHD model referenced in [7] indicates that the amplitude of the mode could diminish in conditions of high β p due to magnetic flux pumping.Additionally, a high β p can contribute to an increased Shafranov shift, further stabilizing infernal-type modes.It is important to note that the elongation  of plasma is relatively static, as it influences the coupling of RF power along with numerous other factors during long pulse operations.Consequently, for a fixed q 95 , operating at a high β p and thereby altering the local magnetic shear appears to be a viable strategy for controlling the m/n = 1/1 infernal mode.
Statistical analysis of typical EAST discharges reveals that the amplitude of the m/n = 1/1 mode diminishes with an increase in β p and a decrease in l i , as depicted in figure 13.The findings presented in figure 13 suggest that the m/n = 1/1 infernal mode may not pose a significant challenge to high β operations in future devices, reinforcing the potential for controlled management of these modes.
Figure 14 provides a visual analysis of the control mechanisms for the m/n = 1/1 mode in the context of tokamak operations.The dashed lines depicted in figure 14 indicate that a larger frequency of the m/n = 1/1 mode corresponds to a smaller amplitude, which is associated with a higher lower hybrid current drive (LHCD) power and an increased population of fast electrons with energy from 30 keV to 80 keV.This increase in fast electron density is likely a direct consequence of the enhanced LHCD power, which energizes the electrons to higher velocities.Therefore, the finding illustrates a significant interaction between LHCD power input, the dynamics of the m/n = 1/1 mode, and the resultant energy distribution of fast electrons within the plasma.

Summary
In the EAST tokamak, a scenario characterized by centrally peaked Te and Te-ITB has been successfully developed, utilizing purely electron heating mechanisms facilitated by LHW and ECRH.This study reveals that the elevated temperatures at the magnetic axis and the formation of Te-ITB are primarily attributed to the enhancement of fast electrons, with energies below 50 keV, following the transition from L-mode to H-mode.A reduced temperature gradient ∇T e will be possibly caused by a phenomenon ascribed to the off-axis peak distribution of fast electrons.The augmentation of fast electrons during H-mode is instrumental in triggering Te-ITB.Furthermore, a long-lived m/n = 1/1 mode is conductive to the maintenance of Te-ITB by facilitating the redistribution of fast electrons.
Simulations using the CQL3D code indicate that fast electrons contribute approximately 6% to the total plasma pressure.These electrons are implicated in the destabilization of the m/n = 1/1 mode through a non-resonant effect.Conversely, the observed stabilization of the m/n = 1/1 infernal type mode under high β p conditions is linked to changes in magnetic surface curvature, accompanied by a significant Shafranov displacement.
The existence of a Te-ITB in the EAST tokamak is closely linked to the behavior of fast electrons.Non-resonant interactions of these electrons with the mode, where their interaction does not match the natural frequency of the mode, can either dampen or excite it.Damping occurs when fast electrons transfer energy away from the mode, reducing its amplitude, which is generally favorable for Te-ITB stability.Excitation happens when energy is transferred to the mode, increasing its amplitude and potentially disrupting the Te-ITB.The assumptions underlying these effects include a broad energy distribution of fast electrons affecting the mode, the sensitivity of the mode's frequency to electron interactions, and the plasma conditions supporting such interactions.Modulating LHW and ECRH power can thus influence the Te-ITB by altering fast electron behavior and, consequently, the dynamics of the m/n = 1/1 mode.
The nuanced interplay between the non-resonant damping or excitation effects of fast electrons on the infernal m/n = 1/1 mode merits further exploration.Future research will leverage numerical tools such as the M3D-C1 + K code [28] and other computational models [29] to delve deeper into these complex dynamics.

Figure 1 .
Figure 1.Temporal evolution of a saturated internal kink mode in EAST high βp ∼ 2.5 electron central heating H-mode discharge: (a) plasma current Ip, (b) loop voltage and plasma density, (c) LHCD, ECRH, and ICRF power, (d) electron temperature gradient at R = 1.95 m near q = 1 magnetic flux surface, measured by the multi-channel electron cyclotron emission (ECE) diagnostic (in black) and the amplitude of internal kink mode within the frequency range of f ∈ [4 20] kHz (in red), and (e) frequency spectrogram of the saturated internal kink mode.

Figure 2 .
Figure 2. Spatial characteristics of the saturated kink mode: (a) time-space contour of ECE perturbation: illustrates the concentrated presence of the mode near R = 1.95 m, (b) perturbation amplitudes: the temperature perturbation amplitude induced by the mode is around 10%, (c) time-space contour of SXR perturbation: showcases an m = 1 mode perturbation structure.

Figure 4 .
Figure 4. Temporal dynamics and spatial profiles in plasma confinement, temperature and density gradients: (a) evolution of energy confinement time, demarcated by three vertical dashed lines indicating the transition from L-mode to H-mode, the onset of the m/n = 1/1 mode, and the mode's subsequent saturation, (b) time-space domain contour plot of R/L Te , highlighting an observed rise in R/L Te at the q = 1.5 surface preceding the saturation of the m/n = 1/1 mode, (c) time-space domain contour plot of ∇ne in time-space domain, pinpointing the apex of ∇ne near the q = 1.5 magnetic flux surface.

Figure 5 .
Figure 5.Typical (a) q and (b) current profile in Te-ITB H-mode discharges with high plasma inductance (l i = 1.2).

Figure 6 .
Figure 6.Dynamics of fast electrons in the m/n = 1/1 mode process: (a) the m/n = 1/1 mode amplitude alongside the intensity of HXR emissions in the 30 keV to 80 keV energy range, (b) HXR spectrogram, and (c) SXR spectrogram.

Figure 7 .
Figure 7.The evolution of HXR emissions with energy from 30 keV to 80 keV and the m/n = 1/1 mode amplitude.The m/n = 1/1 mode emerges subsequent to the establishment of Te-ITB.

Figure 8 .
Figure 8.The evolution of the HXR spectrum from the initiation to the saturation of the m/n = 1/1 mode.This phase is marked by a notable increase in the intensity of HXR emissions within the 30 keV to 50 keV range, coupled with a decrease in emissions above 50 keV.The redistribution in the fast electron spectrum inherently paves the way for the generation of a negative current in the plasma center.

Figure 9 .
Figure 9. Simulation results from CQL3D code: (a) fast electron density profile and (b) fast electron pressure profile with energy above 25 keV.

Figure 10 .
Figure 10.Time-space contour of HXR emissions (30 keV to 80 keV) for scenarios: (a) on-axis peaking, (b) off-axis peaking.A distinct enhancement in the fast electron population correlated with the m/n = 1/1 mode in discharges of #122275 and #123867.Notably, an off-axis peak in HXR emissions within the 30 keV to 80 keV range is observed in discharge #123867.

Figure 11 .
Figure 11.Characteristic Te profiles under different fast electron profiles: on-axis peak (in red), and a broaden off-axis peak (in blue) .

Figure 13 .
Figure 13.Variation in the saturated amplitude of the m/n = 1/1 mode as function of (a) βp and (b) l i .

Figure 14 .
Figure 14.The m/n = 1/1 mode amplitude control via fast electron energy phase space modulation by lower hybrid current driven (LHCD): (a) the change of fast electron energy spectrum and amplitude of the m/n = 1/1 mode, (b) spectrogram of the m/n = 1/1 mode frequency and the power of LHCD.