Observation of electrostatic fluctuations driven by runaway electrons in EAST disruptions

Electrostatic fluctuations driven by runaway electrons (REs) have been observed following a thermal quench during Experimental Advanced Superconducting Tokamak–intended disruptions, which are triggered by massive gas injection. Electrostatic fluctuations are clearly detected using several radiation-related diagnostics and in two distinct frequency bands: 10–20 kHz and 30–40 kHz. The appearances of fluctuations are directly correlated with REs. Fluctuations observed during argon injection and neon injection have significantly different evolution with time, whereas no fluctuations can be found with helium injection. The measured frequency scales with different amounts of injected gases finally tend to be saturated. A clear phase difference is detected, and a mode structure of (m, n) = (1, 0) is identified in the soft x-ray detector array. Here, m and n are the poloidal and toroidal mode numbers, respectively. The geodesic acoustic mode proposed as a candidate instability is further discussed, and the barely trapped/passing electrons can contribute to drive the mode. Fluctuations are also correlated with significant RE loss, which supports the possibility of kinetic instability for RE mitigation in a tokamak reactor.


Introduction
Runaway electrons (REs) generated during disruptions may incur destructive damages to the first wall because of the localized loss for future large-current tokamaks [1,2]. The interplay between RE generation and loss determines whether a RE plateau could be formed. Thus, the avoidance of RE generation and the dissipation of RE current have attracted intensive focus in a variety of research works, and are considered essential in the exploration of potential mitigation methods for ITER [3,4].
So far, experimental results have demonstrated that REs can be suppressed by bremsstrahlung radiation [5], synchrotron radiation [6], magnetic field ripples [7], and orbit drifting [8]; moreover, RE loss due to magnetic field fluctuations is one of the major concerns. For example, resonant magnetic perturbations can be externally applied to increase the RE radial transport and lead to resultant RE loss [9]. Kink instabilities at low safety factor in the post-disruption RE beam can cause significant RE loss on a timescale similar to the mode growth [10]. Kinetic instabilities are also considered as a potential method to dissipate REs [11]. The two mechanisms correlated with the RE loss produced by kinetic instability [12,13] areas follows: first, inducing local magnetic perturbations and therefore increasing the radial transport; second, wave-particle interactions with the enhanced pitch-angle scattering of REs contributes to reducing the toroidal runaway current and inducing significant synchrotron damping of RE energy.
REs as energetic particles can frequently drive instabilities via wave-particle resonances, and the free energy is provided by the non-monotonic feature in the RE energy distribution function [14]. Studies concerning RE-driven instabilities may enhance our understanding of RE loss due to magnetic perturbations and support further investigation on RE mitigation. Rapid frequency chirping instabilities driven by REs have been observed in the DIII-D tokamak [15], wherein the frequency chirps by 0.3-02.4 MHz linearly as the toroidal magnetic field increases, indicating that it could be related to Alfvenic fluctuations. These relatively low-frequency instabilities also lead to intermittent RE loss. High-frequency whistle waves excited by multi-MeV REs have also been observed in DIII-D [16], and the activity is correlated with the RE intensity (as measured by hard x-ray [HXR] emission level) and the number of REs, opening a new direction for controlling REs. The highenergy tail of the RE distribution function can drive kinetic instabilities [17] in a massive injection of argon experiments, and the instabilities eventually contribute to the RE loss during the current quench (CQ), which finally suppresses the RE plateau formation. Moreover, abnormal RE loss due to kinetic instabilities has been recently observed during the RE plateau phase in the Experimental Advanced Superconducting Tokamak (EAST) with unintended disruptions [18].
In this work, experimental observation of electrostatic fluctuations driven by REs, as well as resultant RE loss events, during EAST intended disruptions triggered by massive gas injection (MGI) will be reported.

Experimental setup
REs and RE-related electrostatic fluctuations have been observed during disruption mitigation experiments on the EAST tokamak. Experiments are conducted in the upper single null divertor configuration, and the key parameters are presented as follows: major radius R = 1.85 m, minor radius a = 0.45 m, toroidal magnetic field B t = 2.5 T, and plasma current I p = 400 kA. Diagnostics illustrated in figure 1 can capture the REs behaviors and characteristics of fluctuations. Four horizontal absolute extreme ultraviolet (AXUV) detectors [19] in port P measure the line-integrated radiation power covering the entire plasma, and another two sets of vertical AXUV detectors are located at the toroidal neighbor port together providing toroidal phase differences. Three sets of soft x-ray (SXR) arrays [20] are shown in figure 1(b), which share a similar layout as AXUV(P). The CdTe and BGO HXR detectors [21,22] help measure HXRs with energies ranging from 30 to 300 keV and 0.34 to 6.13 MeV, respectively named HXR and RA. Note that HXR detectors are placed inside the vacuum vessel and directly facing plasma; therefore, the HXR system measures the bremsstrahlung produced by collisions between confined REs with bulk ions and also deconfined REs hitting the limiter/vessel wall; however, RA can detect only HXRs generated because the REs are deconfined and collide with the walls because its detectors are installed outside the tokamak. In addition, an MGI valve is installed just below the midplane and applied to inject noble gases to trigger disruptions.
Three typical waveforms of disruption mitigation experiments, distinguished by the species of injected impurity gases, are illustrated in figure 2, where the same number of gases is applied. Disruptions were triggered several milliseconds after massive impurity injection. During the thermal quench (TQ), cold impurities radiate away the thermal energy, and a continuous increase in AXUV after the injection of noble gas also confirms intense radiation. The sharp drop in the electron cyclotron emission (ECE) signal indicates a decrease in the plasma temperature; the post-disruption temperature is ∼10 V as evaluated in a previous work [23]. Simultaneously energetic electron populations produced by lower hybrid waves before disruption decrease as HR drops. Afterward, the cold plasma further generates a large amount of REs at the onset of the CQ phase, which is indicated by the subsequent intense burst in HXR signals with both CdTe and BGO detectors when REs finally lose to the wall. As the divertor configuration is confirmed to be unfavorable to the formation of RE plateau [24], no RE plateaus are found in these cases due to the RE loss from intense radiation or strong magnetic perturbations. Figure 2 also reveals that more REs are generated during CQ with argon injection than that with neon, which is apparently evidenced by higher peaks in HR and RA signals when RE is finally lost. In contrast, for helium cases, HXR emission approaches nearly 0, indicating that no obvious REs are generated. Overall, the highest Z impurity argon effectively increases the RE population, whereas neon is less effective and  helium is the least effective. The result that the high-Q impurity is more favorable for RE generation has also been confirmed in JET [25]. Finally, REs generated during disruption can excite fluctuations observed at the onset of CQ, as shown in section 3. The difference in evolution of RE populations between the two types of gases may lead to distinguished characteristics of fluctuations. At the beginning of CQ, the fluctuations have been clearly recognized in the signals of HXR, SXR, and AXUV, but not in Mirnov coils, indicating that they should be electrostatic fluctuations. Besides, the corresponding density fluctuations have been detected using the polarimeter-interferometer system in the order of δn e ∼ 5 × 10 16 m −3 , and the background density should be up to 1 × 10 20 m −3 . Noting that fluctuations can be only apparently found with argon and neon injection but not with helium injection, consistent with the negligible HXR during CQ with helium injection, suggesting that these fluctuations are driven by REs.
Time traces of the amplitude of AXUV fluctuations and frequency are shown in figure 4, wherein a clear frequency jump is presented. Moreover, the frequency jump can even  occur several times in a single discharge, as shown in figure 4. Accompanied by the frequency jump, a significant increase in the amplitude of fluctuations is also detected. Furthermore, the frequency jump further corresponds to the amount of RE loss, which is evidenced by a single peak with a larger amplitude in SXR signals; subsequently, fluctuations of higher frequency are found to be accompanied by larger amplitude in both SXR and HXR signals. One possibility related to this phenomenon is attributed to a strong magnetic perturbation with a structure of (m, n) = (2, 1) which is frequently observed in EAST disruptions and causes numerous REs to be lost to the wall. This instability has been identified as tearing mode [26]. Importantly, the tearing mode can appear without the observation of electrostatic fluctuations, suggesting that fluctuations are not driven by the tearing mode [27].
With neon injection, two separate branches of the fluctuations are clearly observed. The low-frequency branch with a frequency of 10-15 kHz is first observed, and another branch with a higher frequency of 30-40 kHz is observed successively, both of which only last for about ∼1 ms. The time interval of ∼2 ms exists between these two branches. Moreover, the low-and high-frequency branches here are found experimentally to be similar to the frequencies before and after the frequency jump occurs in the argon injection case, shown in figure 5. Note that the error bar in frequency is determined to cover the whole frequency range with strong fluctuation intensity, as illustrated in figure 4(b). Unlike the argon injection cases, the intensity of the low-frequency branch is higher than that of the high-frequency branch with neon injection. In addition, the duration of the high-frequency branch in argon cases is apparently longer, whereas the duration of the lowfrequency branch is almost the same in both argon and neon injection cases. These differences in the wave pattern are speculated to be caused by more REs generated by argon injection.
All discharges with the appearance of electrostatic fluctuations have been analyzed to figure out the correlation between frequency and amounts of injected gases. The dataset contains 16 argon cases and 8 neon cases. Figure 5 illustrates that with argon injection, the frequencies of both the low-and highfrequency branches are mapped to increase with the amounts of injected gases and finally tend to be constant as adequate gases are injected. A similar trend can be found for the time duration of the fluctuations in argon injection cases. The results can be understood that during MGI experiments, more REs is generated due to more impurities and resultant colder plasma, and eventually contribute to the positive correlation, whereas the excess of a certain value of injected gases will not produce more REs; therefore, the RE population finally must be saturated and so does the frequency. However, no obvious trend is found for the high-frequency branch with neon injection. For the low-frequency branch, there is a slight decrease in the fluctuation frequency with more gas injection. Dash lines in figure 5 also indicate a threshold for injected gases over which fluctuations can be observed, with exact values being 3400 Pa·l for argon and 12 000 Pa·l for neon. This threshold further suggests that adequate numbers of RE are essential for the fluctuation excitation.
In figure 2(b), apparent RE losses have been confirmed according to periodic fluctuations in HXR signals. Moreover, RE losses are found to be correlated with the frequency of fluctuations. The RE loss is represented by the amplitude of the HXR fluctuations and has been shown to be a function of frequency, as shown in figure 6. RE losses are positively correlated with the frequency of fluctuations in each discharge. The possible mechanism with respect to RE loss due to electrostatic fluctuations will be discussed later.
A clear phase difference is detected in the signals of the poloidal AXUV and SXR arrays, but not in the HXR arrays. To identify the precise structure of fluctuations, the singular value decomposition (SVD) method is applied to analyze the perturbation structure [28] based on the SXR arrays, which cover the whole plasma ( figure 1(b)). The poloidal structure of the fluctuations is clearly figured out by the spatial components of the SVD technique in figure 7(a), wherein the horizontal axis representing the amplitude of fluctuations and 0 represents no fluctuations, the vertical axis representing the height in space. The evolution of the last closed flux surface is also accompanied. The results reveal that the poloidal mode number of the fluctuation is 1 (m = 1), which is consistent with the opposite phase difference in figure 7(c) with locations of the two channels noted in figure 2(b). The SXR and HXR signals presented here also illustrate that these electrostatic fluctuations are periodic. The maximum and minimum amplitude of fluctuations occur at the edge of the plasma in figure 7(a) and further indicate that the fluctuations mainly appear in the edge region of the main plasma. The fluctuations as n = 0 mode has also been identified because no phase difference can be detected in either toroidally located SXR or AXUV arrays. As a result, the mode numbers (m, n) = (1, 0) can eventually be obtained. Besides, figure 7 also presents the appearance of a tearing mode with poloidal mode number m = 2; and reverse phase in toroidal symmetry located in Mirnov coils in figure 7(b) indicates toroidal mode number n = 1. Finally, the instability with (m, n) = (2, 1) can be clearly identified, which has been specifically described in an earlier study [24] and can be commonly triggered by EAST disruptions.

Discussion
Fluctuations observed at the beginning of CQ exhibit no corresponding periodic magnetic fluctuations, indicating that it should be an electrostatic mode. Furthermore, weak electron density fluctuations and the mode structure of (m, n = 1, 0) are also identified, which are the characteristics typical for geodesic acoustic mode (GAM). As a result, the possibilities of GAM and RE-driven EGAM are proposed as follows, and barely trapped/passing REs with relatively low characteristic frequency can contribute to excite these modes [29].
The GAM is considered as a candidate instability of the low-frequency fluctuations, because the dominant axisymmetric electric potential fluctuations have not been confirmed because of the limits of the corresponding diagnostics during disruptions. A simple estimate focusing on the low-frequency fluctuations is shown in figure 8. The local GAM frequency [30] is theoretically presented as f = (7/4 + T e /T i ) 1/2 (2T i /m i ) 1/2 /2πR, in which T e and T i are electron and ion temperatures, respectively. T e = T i is assumed in this estimation, m i is the average mass of ions based on the densities of different ion species, and R is the major radius. Assimilation rates of 10% for argon gases are considered [31]. Figure 8 illustrates the calculated local GAM frequency by scanning of electron temperature and number of injected argon gases ranging from 10 to 20 kHz, which is consistent with the experimentally observed low-frequency fluctuations. Note that the GAM frequency is shown to decrease with the more gases injected and the resultant higher m i , which is consistent with the slight decrease observed in the lowfrequency branch of neon cases ( figure 5(c)), however, is contrary to experimental observations in the argon cases. Factors leading to the difference between these two species of gas injections are currently uncertain because of the lack of essential diagnostics, and more attention is needed in our future work.
Moreover, for the high-frequency branches of which the frequency is almost twice the local GAM frequency, their characteristics can be satisfactorily captured by the energeticparticle-driven GAM (EGAM) theory [32] and the experimental results in large helical device (LHD) [33]. The EGAM is excited by the resonant interaction of energetic particles (EP) with the GAM, with the frequency ω G ∼ V i /R 0 [34,35]. Here, V i is the velocity of ions and R 0 is the major radii. In LHD experiments with very low plasma density, high plasma temperature and high EP birth energy, the EGAM frequency can reach twice of the local GAM frequency [33], and the observations were interpreted by a new mechanism [32] of high-frequency EGAM excitation by a not fully slowed down energetic particle beam due to the low collisionality as a result of the low density discharge with very high plasma temperature, with the free energy from both the velocity space anisotropy and the positive slope in distribution function. Thus, EGAM can also be excited by REs, with the free energy coming from the non-monotonic energy distribution function of REs. Note that, due to the large parallel velocity of REs, it is expected that EGAM cannot be driven by well passing or deeply trapped electrons, whose transit/bounce frequencies are too high to be resonant with the local GAM frequency. However, the barely trapped/passing electrons induced by the high collisionality and enhanced pitch-angle scattering [36] during MGI could contribute to excite the mode, due to their relatively low transit/bounce frequencies, as discussed extensively for the case of toroidal Alfven eigenmode excitation in a previous study [29]. The collisionality between REs and partially ionized high-Z impurities also plays an important role in pitchangle scattering of REs into barely trapped/circulating REs by partial screening effect [37]. These barely trapped/circulating REs with much lower bounce/transit frequency are crucial for the resonance with the low frequency GAM.
Similar arguments can be applied to the present observations of RE-driven EGAM in that the high-frequency fluctuations are found to be twice the frequency of the lowfrequency branch, which is speculated to be local GAM. Note that because the theoretical explanation for LHD ignores the helicity and assumes a large aspect ratio, consistent with the experimental observation in the center of device, it can be validly extrapolated to the tokamak. Furthermore, the positive gradient is noted to be indispensable for EGAM excitation as mentioned in a previous study [32]. It is interesting to note that the positive gradient in the EP distribution function in the LHD experiment is formed by the low collisionality, whereas the high collisionality during the MGI here is crucial for the formation of the positive gradient in the RE distribution function, by dissipating the lower energy part of the RE distribution. One potential mechanism for forming the nonmonotonic RE distribution is that the effect of the wave diffusion in momentum space can hinder REs from going to higher energy, resulting in a positive gradient in the RE distribution function [38]. In addition, the sudden loss of lowenergy REs by MHD instabilities can also cause this positive gradient, a possible mechanism may be attributed to the inward radial drift of high-energy REs and resultant better confinement [39].
In addition to the energy space gradient, the spatial gradient of REs can also lead to the excitation of EGAM, considering that the Dreicer generation is sensitive to temperature and parallel electric field; moreover, injected high-Z impurities have been demonstrated to substantially enhance the inward convection transport of trapped REs due to strong Ware pinch [36]. Eventually, the transport of trapped REs from edge to the core makes it possible for the appearance of spatial gradients to excite these modes.
As a final remark, the transit/bounce resonance with EGAM [35], will further pitch-angle scatter REs across the trappedpassing boundary into un-confined barely trapped particle, leading to RE loss corresponding to fluctuations in figure 2(b). This mechanism is expected to be effective, as the resonant REs are already localized near the trapped-passing boundary due to the low frequency feature of GAM/EGAM. On the other hand, the modes may lead to energy and spatial diffusion, which can further move the REs out of the tokamak core. These processes will provide a new channel for RE mitigation via spontaneously excited kinetic instabilities.

Summary
In summary, RE-driven electrostatic fluctuations have been observed in EAST disruptions triggered by MGI. Fluctuations are only detected with argon and neon injection, but not with helium injection, suggesting that the fluctuations are driven by REs. Two typical evolutions of fluctuations are found with the injected of different species of gases. With argon injection, a mode starts with a frequency of 10-20 kHz and suddenly jumps to a high frequency of 30-40 kHz and lasts for a total of up to 5 ms. Their frequencies are found to increase with the amounts of injected gases and finally tend to be saturated. With neon injection, two separate branches with first low frequency of 10-15 kHz and later high frequency of 30-40 kHz are found, both of which can last only 1 ms. REs loss has also been confirmed in HXR signals and is found proportional to the mode frequency. Mode structures with mode numbers (m, n) = (1, 0) are clearly identified based on the SXR emission together with the SVD technique, indicating that fluctuations appear at the plasma edge.
GAMs are proposed as candidate instability due to similar features to experimental observations, while the highfrequency branch at twice the local GAM frequency can be explained by EGAM. Barely trapped/passing REs can be satisfactory for exciting the mode. However, further studies are required to provide definite conclusions. As a final remark, the key motivation for studying RE-driven fluctuations is to understand the dynamics of instabilities and corresponding RE loss events, supporting further research works to provide possible methods to mitigate REs during disruptions in future large-device tokamaks.