β-induced Alfvén eigenmodes and fishbone driven by energetic electrons in EAST electron heating dominant plasmas

β-induced Alfvén eigenmodes (e-BAE) and fishbone (e-fishbone) driven by the energetic electrons have been identified on the experimental advanced superconducting tokamak in electron cyclotron resonance heating (ECRH), low hybrid wave (LHW) together with neutral beam injection plasma and in pure radio frequency heating plasma, respectively. The e-BAE is predominantly located near the pedestal region, and its frequency typically displays a chirping characteristic. The frequency is notably associated with the count of energetic electrons with energy between 30 keV and 80 keV driven by LHW and undergoes three distinct phases. A direct correlation is established between the frequency of e-BAE and the global parameters, including electron temperature, Alfvén velocity and βp . The e-fishbone emerges in the core and becomes noticeable shortly after ECRH initiation, in an electron heated dominant and core confinement enhanced discharge. Experimental analyses suggest that the e-fishbone ties closely with both the population and energy distribution of energetic electrons. These observations can provide valuable insights into the behavior of energetic electrons, which play a crucial role in the formation and sustainability of transport barriers within hybrid plasma, both in the internal and pedestal regions.

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.

Introduction
In magnetic fusion devices, one central issue is the confinement of charged fusion fuel components and energetic particles (EPs) to achieve self-sustaining ignition conditions, controlled nuclear fusion reactions, and high-power outputs [1].EPs comprise not just the supra-thermal ions and electrons generated by external heating, but also charged deuteriumtritium (D-T) fusion products, predominantly α particles in burning plasmas [2,3].While fusion reactions necessitate collisions between these energetic fuel ions, the energetic ions produced by mechanisms like neutral beam injection (NBI), ion cyclotron resonance frequency (ICRF), etc. Do not directly heat these fuel ions.Instead, energetic electrons play a pivotal role in energy transfer as well as ensuring plasma electrical neutrality and stability [4].Additionally, energetic electrons can also contribute to the formation of internal transport barrier and play a role in maintaining the edge transport barrier, which is associated with the high-confinement mode (H-mode) of plasma operation [5].Consequently, the study of energetic electrons is critical to the development and performance of burning plasma devices such as the international thermonuclear experimental reactor and the demonstration power station (DEMO) [2,6].
The generation of large population of EPs in plasma on one hand can enhance the plasma heating and current drive, contributing to the steady-state operation of tokamak [7][8][9], but on the other hand it can induce Alfvénic and acoustic-type magnetohydrodynamics instabilities, deteriorating plasma performance [7,10,11].In future burning plasmas, energetic ions produced by fusion reactions risk significant losses, potentially surpassing collision-induced losses, due to resonance with Alfvén eigenmodes (AEs) [2,[12][13][14].The destabilization mechanism of AEs is one form of inverse Landau damping, which results from wave-particle interactions involving either energetic ions or electrons [15].
Over past decades, various energetic-ion driven AEs, including reversed shear Alfvén eigenmodes [16], toroidal Alfvén eigenmodes [17], β-induced Alfvén eigenmodes (BAEs) [18] and β-induced Alfvén acoustic eigenmodes [19], have been extensively observed in currently-operating tokamaks.Yet, Alfvénic instabilities closely tied to energeticelectron remain scarcely reported.In 1999, the new mechanism that internal kink instabilities induced by barely trapped supra-thermal electrons was first discovered and investigated in off-axis ECRH plasma on DIII-D tokamak [20].Subsequent findings in 2001 on HL-1M tokamak identified a strong m = 1 mode excited by energetic-electron in pure RF heating plasma [21].With the progression of experiment and theory, energetic-electron induced BAE (e-BAE) was observed and reported in the Ohmic and ECRH heating plasma on HL-2A [22][23][24], suggesting the dependence of e-BAE on the population, energy and pitch angle of energetic-electron.The fishbone-like instabilities driven by supra-thermal electrons were also obtained in EAST heavy impurity ohmic plasma in 2013 [25].This so-called fishbone-like instability is named just based on its frequency traits, its further validation is stuck on the absence of energetic-electron velocity distribution information due to diagnostic limitations.
During EAST 2019 and 2021 summer campaigns, energetic-electron driven fishbone instability in plasma core and BAE in pedestal were observed, respectively.And fortunately, the upgraded energetic-electron related diagnostics at that time enabled detailed analysis.This paper is structured as follows: section 2 outlines the experimental setup and diagnostics used.Section 3 and section 4 delve into the energeticelectron driven e-BAE and e-fishbone on EAST, respectively.A summary and outlook are presented in section 5.

Experiments setup and diagnostics used
EAST, a medium-sized tokamak with a major radius R = 1.85 m and a minor radius a = 0.45 m, is fully superconducting tokamak and oriented towards steady-state operation.The e-BAE discharges (#84902 and #84903) detailed in this work are performed in the upper single null divertor configuration with plasma current I p ≈ 0.4 MA in the anti-clockwise direction from the top-view, toroidal magnetic field B t ≈ 2.4 T in the clockwise direction, and plasma line-averaged density N e ≈ 3.6 × 10 19 m −3 .For plasma heating, LHW [26,27], ECRH [28][29][30] and NBI [31,32] are all utilized.The e-fishbone discharge (#98326) is carried out in the lower single null configuration.It is heated by pure RF, using both LHW and ECRH.This plasma has a plasma current I p ≈ 0.5 MA and toroidal magnetic field B t ≈ 2.4 T, both in the anti-clockwise direction.The line-averaged density is slightly lower at N e ≈ 2 × 10 19 m −3 for this discharge.
For measurements in this study, the line-averaged density N e is determined using the far-infrared hydrogen cyanide interferometer system [33].The modes fluctuation and identification are mainly measured by Mirnov probes [34] and soft x-ray (SXR) [35], the layout of EAST Mirnov probes in the poloidal cross-section can be found in [36].Given the hard x-ray (HXR) [37] energy spectrum system detected by cadmium telluride (CdTe) can facilitate the analysis of fast electron behavior, two 20-channel independent CdTe detectors have been equipped on equatorial port A on EAST since 2021.This enhancement broadens our capacity to investigate fast electron behavior, as well as the deposition and driving effects of LHW.

Experimental observations and mode identification
The e-BAE has been identified in EAST H-mode plasmas.Its features primarily frequencies are demonstrated by the magnetic pickup probes.Initially undergoing a typical downward chirping phase as fishbone characteristics [38], the e-BAE frequency then exhibits two further evolutionary phases.In figure 1(b), 1.6 MW LHW and 0.8 MW ECRH were turned on at the beginning of discharge #84902, while 1.5 MW NBI was introduced at approximately t = 3.4 s.The enlargement as the frequency's downward chirp, from around 40 kHz to  31 kHz, during the absence of NBI is detailed in figure 1(c).Figure 1(d) captures the third phase that the frequency chirping ups and downs between 30 kHz and 40 kHz repeatedly in the presence of NBI.After activating the NBI, a noticeable rise in magnetic perturbation amplitude is evident from figure 1(a).
Due to the complexity of the second phase, it will be demonstrated and discussed separately here.From the spectrum of the second phase displayed in figure 2(a), it can be roughly concluded that there are two modes.The frequency of the stronger mode chirps from 30 kHz up to 43 kHz, while the frequency of the other mode ups and downs between 20 kHz and 30 kHz periodically.The frequency of the second phase seems to integrate characteristics from the preceding and succeeding phases, suggesting its role as a transitional stage.
Consistency is observed between the spectra from the Mirnov probes and the Doppler backscatter (DBS) [39] system diagnostics, illustrated in figure 3. The evolutions of toroidal mode number n = 1 and the mode frequencies are obtained by the toroidal Mirnov probes and are shown in figure 3(a).The approach for calculating n refers to [40]. Figure 3(b) shows the election density perturbation spectrum from the e-BAE frequency's initial phase, detected by the DBS edge channel, which indicates that the mode origination is at the pedestal top of H-mode.

Evidence of energetic electron driven by LHW
The HXR energy spectrum system equipped on EAST measures bremsstrahlung HXR energy ranging from 20 keV to 200 keV, which contains upper and lower two arrays (each array comprising 20 channels) with a time resolution of 2 millisecond and covers the entire poloidal cross-section.Its capabilities are essential for studying fast electrons behavior and LHW deposition.Figure 4 shows the time traces of energy spectra, specifically focusing on energies between 30 keV and  80 keV, for all the channels in the lower array.Channel 13 passes through the core of plasma, while channel 6 and channel 18 capture HXR emissions around the pedestal region.The confinement of fast electrons with energy from 30 keV to 80 keV is enhanced after L-mode to H-mode transition not only in the core region, but also in the edge pedestal region.Given the fact that the fast electron with ECRH has a dominate energy less than 50 keV, and this value could be up to 100 keV with LHW instead, while the NBI dominates heating ions, the observation in figure 4 illustrates that NBI does not play a significant role in e-BAE excitation.In addition, the fast electrons generated by on-axis ECRH were located at the core region.Since the e-BAE is highly relative to the fast electrons near pedestal and with energy over 50 keV, it can be concluded that the counts near pedestal (the location of e-BAE) predominantly originate from LHW.
A comprehensive comparison between the evolution of HXR photon counts (ranging from 30 keV to 80 keV) in the pedestal region and the e-BAE frequency is illustrated in figure 5.A strong correlation emerges between these HXR photon counts and the e-BAE frequency.Another supportive observation is the slight precedence of the evolution of HXR photon counts over the frequency changes, reinforcing the hypothesis that LHW-generated energetic electrons are indeed responsible for the mode excitation.

Mode characteristics: frequency statistical analysis and competition with ELMs
In this section, we statistically analyze the dependence of the e-BAE frequency on key global parameters, including electron temperature, electron density and β p .This analysis is motivated by the evident relationships these parameters exhibit, as  depicted in figure 6.Our investigation reveals no discernible correlation between the e-BAE frequency and the safety factor at the 95% normalized toroidal magnetic flux surface denoted by q 95 [41].As such, we have opted not to delve further into this aspect.
Drawing from data across discharges #84902 and #84903 during the flat-top phase of plasma current, our statistical findings are consolidated in figure 7. Specifically, figure 7(a) demonstrates how e-BAE frequency varies with electron temperature under different heating methods.With pure RF heating, the frequency is directly proportional to the electron temperature.However, when RF is combined with NBI heating, the proportional relationship is seemingly disrupted by the data marked with the green shaded region.This is due to the frequency of e-BAE is less sensitive to the plasma temperature than plasma beta and density, and the temperature operation regime near pedestal is narrow.Figure 7(b) gives the frequency with respect to N e −1/2 , here N e represents electron density, and N e is in an exponential relationship with the Alfven velocity v A , expressed as N e −1/2 ∝ v A .The statistical results indicate that the e-BAE frequency mirrors trends in the Alfvén velocity v A .This observation is consistent with findings from other devices, including HL-2A [22,42].Figure 7(c) shows a clear positive correlation between the e-BAE frequency and β p .These statistical results are generally reasonable, but the global parameters here are limited in scope.Therefore, further experiments and studies are needed to provide more robust conclusions.
Figure 8 shows the interplay between ELMs and e-BAE activities.In figure 8(a), the light blue shading marks the ELMs phases, while magenta highlights ELM-free intervals.Notably, the e-BAE frequency chirping down is predominantly seen in ELM-free segments, suggesting a potential interplay or competition between ELMs and e-BAE.The increasing α Balmer emission line of deuterium signal (D α ) appears to be inversely related to the e-BAE frequency, raising intriguing questions about the role of energetic electrons in the modulation or suppression of ELMs.

Experimental observations
The fishbone instability was first discovered in NBI injected plasmas on PDX in 1983 [43].Aptly named for the magnetic perturbations it caused, which resembled fishbones, this energetic-ion driven internal kink mode was called ionfishbone.In 1999, the energetic-electron driven fishbone termed the e-fishbone was observed in off-axis electron cyclotron current drive plasma on DIII-D tokamak [20].Since then, observations of both electron and ion driven fishbones have been commonly reported across numerous magnetic fusion devices [44][45][46].
During EAST 2021summer campaign, the e-fishbone was identified in plasmas exclusively heated by pure RF. Figure 9 illustrates the main parameters traces of this electron heated dominant e-fishbone discharge.As delineated in figure 9(b), the 2.45G LHW initiates with a power of 0.8 MW around t = 1 s, followed by the 4.6G LHW at 2 MW near t = 2 s.The 0.45 MW ECRH is then activated at roughly t = 2.5 s.Concurrently, with the LHW and ECRH in operation, the plasma stored energy increases.In contrast, from t = 3.5 s to t = 4.5 s, there is a notable reduction in electron density, attributable to the cut off of gas-puffing, as depicted in figure 9(c).
Both the core SXR original intensity and emission spectra, presented in figure 10, reveal the presence of two branches of fishbones.The first fishbone branch appears immediately after the ECRH activation, disappears with the decrease of plasma density around t = 3.85 s, which is a consequence of the turn off of gas-puffing.The other branch of fishbone gets triggered at around t = 7 s and disappears again less than a second later.The plasma stored energy decreases slightly during the shutdown phase of gas-puff, while it is relatively steady in the presence of fishbone, as shown in figure 9(c).Figure 11 shows the detailed time traces of both the fishbone perturbation, frequency and HXR flux.It is evident that the e-fishbone cycle, i.e. the time interval of two adjacent fishbone bursts is about 2 milliseconds.The maximum perturbation induced by fishbone is about 5% and its frequency does not chirp down as that of typical ion-fishbone.This is not surprising as e-fishbone frequencies on other devices such as C-Mod and HL-2A also do not always have the chirping down feather [47,48].Furthermore, it is evident that the increase in core HXR flux leads the increase in fishbone amplitude, as shown in figure 11(c).Figure 12 shows the 2D distribution of the SXR emissivity and perturbation at t = 7.24478 s and t = 7.24486 s as marked by blue cycles in figure 11(a).The structure of m = 1 mode can be clearly seen in the perturbed temperature distribution, with m representing the poloidal mode number.To glean insights into the destabilization mechanics of the fishbone, the fast electron behavior close to the moments of fishbone emergence and vanishing is pursued.

Evidence of e-fishbone driven by ECRH-generated energetic electrons
Figure 13 displays typical HXR photons counts for pure ECRH, pure LHW, and combined ECRH and LHW heating plasmas in both H-mode and low confinement mode (Lmode) discharges on EAST.It is evident that both ECRH and LHW can drive electrons with energies ranging from 25 keV to 53 keV and typically located at plasma core and edge, respectively.Meanwhile, LHW alone can drive electrons with energies from 53 keV up to around 130 keV.Additionally, plasma density considerably affects the ECRH-driven electrons within the 25 keV to 63 keV energy range.As illustrated in figure 13(b), by halving the plasma density, the counts of HXR photons can be increased up to two times for the pure ECRH heating case.For the other two heating plasmas, the    maximum electron energy can be extended from 112 keV to 141 keV.
Figure 14 shows the HXR photons counts with energies between 30 keV and 50 keV, corresponding closely to the moments of fishbone appearance and disappearance.As presented in figure 14(a), the turn on of ECRH at approximately t = 2.5 s leads to an uptick in the fast electron population with energies between 30 keV and 50 keV, coinciding with the onset of fishbone instability.The population of fast electrons with energies ranging from 30 keV to 50 keV begin to reduce after t = 3.5 s and then the fishbone disappears at about t = 3.85 s.The behavior of the second fishbone branch mirrors this trend: an increase in the fast electrons' population heralds the onset of fishbone instability, while a decrease signals the termination of fishbone.This consistent pattern suggests that ECRH-induced electrons, particularly those with energies between 30 keV and 50 keV in plasma core, are chiefly responsible for triggering the fishbone instability.
During the interval from t = 3.5 s to t = 4.5 s, the gaspuffing was shut off, leading to a reduction in the counts of electrons within the 30 keV and 50 keV energy range.Given the sensitivity of the line-averaged electron density to both LHW accessibility and current drive efficiency, and considering the synergy effects of LHW and ECRH, it is probable that the declining electron density instigated the disappearance of the fishbone.

Summary and outlook
In this work, we explore the dynamics of energetic electron-driven modes, specifically e-BAE and e-fishbone, observed in H-mode plasmas heated by the combination of ECRH&LHW&NBI and ECRH&LHW on EAST tokamak.
For e-BAE, our findings reveal the following characteristics: (a) e-BAE is predominantly located in the pedestal region and is primarily triggered by energetic electrons produced through LHW; (b) the evolution of e-BAE frequency exhibits three distinct developmental phases; (c) our statistical analyses establish a direct correlation between e-BAE frequency and key global parameters such as electron temperature, Alfvén velocity, and β p ; (d) the dependence of e-BAE frequency on electron temperature is less pronounced in the presence of NBI, attributed to the less sensitive of the frequency to the plasma temperature and the narrow temperature operation regime near the pedestal; (e) notably, e-BAE demonstrates incompatibility with ELMs.Both EAST and HL-2A exhibit shared trends, with e-BAE commonly associated with the pedestal region and displaying similar frequency dependencies.
In pure RF heating plasmas, two branches of e-fishbone were activated by on-axis ECRH.The e-fishbone characteristics are summarized as follows: (a) the initial branch was promptly excited post ECRH activation and later disappeared, correlating with a decline in energetic electrons due to the cessation of gas-puffing, and the behavior of the second fishbone branch follows this established trend; (b) this consistent pattern emphasizes the significance of ECRH-induced electrons, particularly in the 30 keV-50 keV energy range, in initiating e-fishbone instability; (c) unlike typical ion-fishbones, the e-fishbone frequency does not chirp down.This is not unexpected, as e-fishbone frequencies on other devices, such as C-Mod and HL-2A, also do not always show the chirping down feather.
Importantly, the locations of e-BAE and e-fishbone align consistently with power deposition.With a higher electron density, the LHW deposited in the pedestal region and induced e-BAE, suppressing ELMs.In the case of e-fishbone, the deduce of electron density caused by the stop of gas-puffing resulted in the disappearance of e-fishbone.This correlation underscores the sensitivity of line-averaged electron density to LHW accessibility, current drive efficiency, and the synergy effects of LHW and ECRH, necessitating further investigation.Understanding energetic electron behavior is crucial for controlling and optimizing transport barriers within a tokamak, which in turn is essential for achieving and maintaining the conditions necessary for efficient nuclear fusion.Moreover, the nonlinear interactions of energetic electron-driven e-BAE and e-fishbones with plasma turbulence, occasionally leading to improved confinement through turbulence stabilization or profile stiffness.Hence, nonlinear effects induced by these energetic electrons instabilities also merit thorough investigation.

Figure 1 .
Figure 1.Time traces of discharge #84902: (a) magnetic perturbation detected by Mirnov probes, (b) LHW (in purple), ECRH (in blue) and NBI (in black) power along with the magnetic perturbation spectrum, (c) and (d) detailed view of the frequency evolution during the first and third phases of the e-BAE.

Figure 2 .
Figure 2. The second evolution phase of the frequency of e-BAE.

Figure 3 .
Figure 3.The spectra of (a) toroidal Mirnov probes and (b) edge (ρ ∼ 0.9, with ρ representing the square root of the normalized toroidal flux) signal of DBS.

Figure 4 .
Figure 4. Energy spectra depicted through HXR photon counts (ranging from 30 keV to 80 keV) for all channels in the lower array.

Figure 5 .
Figure 5. Comparative evolutions of (a) counts of HXR photons with energy from 30 keV to 80 keV near pedestal area and (b) the e-BAE frequency.

Figure 9 .
Figure 9.Time traces for discharge #98326: (a) plasma current, (b) ECRH and LHW power, and (c) electron density (in black) and plasma stored energy (in red).

Figure 10 .
Figure 10.(a)Intensity of core SXR, (b) and (c) detailed view of the intensity of core SXR, (d) and (e) detailed view of the spectra for two branches of fishbones.

Figure 11 .
Figure 11.Time traces of the (a) relatively perturbation, (b) frequency for the second branch of fishbone, (c) fishbone amplitude and core HXR flux.

Figure 13 .
Figure 13.HXR photon counts versus energy of fast electrons for different heating plasmas in EAST: (a) H-mode and (b) L-mode discharges.

Figure 14 .
Figure 14.HXR photons counts in the 30 keV to 50 keV energy range during the intervals: (a) t = 2.5 s to t = 4.5 s, (b) t = 6.85 s to t = 7.05 s and (c) t = 7.5 s to t = 7.7 s.