An overview of the energetic electron induced instabilities with high-power ECRH on HL-2A

X.T. Ding; W. Chen; L.M. Yu; S.Y Chen; J.Q. Dong; X.Q. Ji; Z.B. Shi; Y. Zhou; Y.B. Dong; X.L. Huang; J.X. Li; Y.P. Zhang; X.Y. Song; X.M. Song; J. Zhou; J. Rao; J.Y. Cao; M. Huang; B.B. Feng; Z.Y. Cui; Y. Huang; Yi. Liu; L.W. Yan; Q.W. Yang; X.R. Duan; Y. Liu

doi:10.1088/0029-5515/53/4/043015

1. Introduction

Magnetohydrodynamic (MHD) instabilities driven by energetic particles including Alfvén eigenmodes (AEs) and energetic particle modes (EPMs), are of particular importance for future burning plasma devices, where energetic particles will be abundantly produced by high-power heating and fusion reactions [1–3]. The instabilities excited by fast ions have been widely investigated in different devices [4–8]. As we know, the drive for the instabilities depends on the energy of the particles rather than the mass, so that energetic electrons can also drive these unstable modes. Understanding the interaction between the energetic electrons and these modes can provide a contribution for burning plasma research, because their effect on the MHD modes can be used to simulate and analyse the alpha particles characterized by small dimensionless orbits, which are similar to the energetic electrons in a middle-sized tokamak plasma, as reported in [9]. The interaction of the energetic electrons with collective modes may play an important role in the plasma with high electron temperature and low collisionality in a fusion reactor. In fact, the precessional drift resonance was first described for fast electrons [10]. Theories for the interaction between energetic electrons and low-frequency modes have been proposed over the last few decades [9, 11]. The ideas have been proved by experiments in different devices. Fast electron driven toroidal Alfvén eigenmodes (TAEs) were first seen on Compass-D with electron cyclotron heating (ECH) only [12] and on Alcator C-mod with lower hybrid current drive (LHCD) [13] during the plasma current rising. With electron cyclotron resonance heating (ECRH) the EPM and acoustic-like modes were found on CHS [14] and HSX [15], respectively. Fishbone instability driven by fast electrons was observed with electron cyclotron current drive (ECCD) on DIII-D [16] first and then with ECRH on HL-1M [17]. Moreover, it was found that the addition of lower hybrid waves to ECRH significantly enhances the MHD excitation. This instability can also be destabilized by LHCD only on FTU [9, 18] and Tore Supra [19, 20]. Recently, a beta-induced Alfvén eigenmode (BAE) excited by energetic electrons has been found and identified in the experiments on the HL-2A tokamak [21]. Table 1 lists the previous experimental observations about the MHD instabilities driven by energetic electrons in different fusion devices.

Table 1. Instabilities driven by energetic-electrons in different fusion devices.

Device	Heating and power	Instability type	Mode character	Energy of EE	Reference
DIII-D	ECRH, ∼1.1 MW	Fishbone	m/n = 1/1, f ∼ 10 kHz	No measurement	[16]
Compass-D	ECRH, < 1.3 MW	TAE	m/n = 1/1?, f ∼ 300–500 kHz	10–100 keV	[12]
HL-1M	ECRH (∼0.25 MW) + LHW (∼0.16 MW)	Fishbone	m/n = 1/1, f ∼ 6–8 kHz	No measurement	[17]
FTU	LHW, <2.5 MW	Fishbone	m/n = 1/1,f ∼ 5–15 kHz	20–150 keV	[9, 18]
Tore-Supra	LHW, <3.0 MW	Fishbone	m/n = 1/1, 2/2, 3/3	20–80 keV	[19, 20]
			f ∼ 6–12 kHz, freq. jumps
C-Mod	LHW, <1.0 MW	TAE	n = 1–6, f ∼ 200–800 kHz	40–100 keV	[13]
HSX	ECRH, < 0.4 MW	Acoustic Like	m/n = 3/1, 5/1?, f ∼ 20–120 kHz	No measurement	[15]
CHS	ECRH, ∼0.1 MW	EPM	m/n = 2/1, f ∼ 50–100 kHz	No measurement	[14]
HL-2A	ECRH, 0.4–1.5 MW	Fishbone, BAE	m/n = 1/1, f ∼ 5–15 kHz	30–70 keV	[21, 26, 27]
			m/n = 3/1, f ∼ 10–25 kHz

With high-power heating, abundant experimental phenomena have been observed in low-density high electron temperature plasmas on HL-2A. A systematic analysis of all the phenomena would be very interesting to understand the interaction between the energetic electrons and the MHD modes. In this paper, an overview of the MHD instabilities induced by energetic electrons on HL-2A is given and the new experimental results during the high-power ECRH are presented. In section 2, the HL-2A tokamak and the high-power ECRH system are presented. The main experimental results are reported in section 3. In section 3, four different kinds of instabilities are reported in four subsections. Several new experimental results during the high-power ECRH, including the TAE induced by energetic electrons, the coexistence of multi-mode in the BAE frequency range, a new EPM-like mode driven by both ECRH and neutral beam injection (NBI) and fishbone frequency jump phenomena are described in detail. A summary is presented in the last section.

2. HL-2A tokamak and the high-power ECRH system

HL-2A is a medium-sized tokamak [22], with major radius R = 1.65 m and minor radius a = 0.4 m, which performs with a plasma current I_p = 100–350 kA, toroidal magnetic field B_t in the range 1–2.5 T and line-averaged electron density 〈n_e〉 = (0.4–4) × 10¹⁹ m⁻³. To investigate the energetic electron behaviours and their interaction with the collective modes, it is operated with low plasma density and high-power ECRH. In these discharges, the electron can be accelerated both by the ohmic electric field and ECRH. The fast electrons are of asymmetric velocity distributions in different cases: generally, trapped energetic electrons are dominant with high-power ECRH and passing electrons are dominant in the ohmic discharges. The high-power ECRH system was installed with six 68 GHz/500 kW gyrotrons. The maximum power is up to 2.4 MW, after taking off the transmission loss, but the injected power in low-density discharges is, in general, not over 1.8 MW. Both fundamental O-mode and second harmonic X-mode are adopted and injected to the plasma from the low-field side (LFS). The electron cyclotron wave (ECW) power can deposit at different radii both in the LFS and high-field side (HFS) through a change in the toroidal magnetic field. An NBI system with four ion sources (the maximum power up to 1.3 MW) was also operated in the experiments. The energy of the injected ions is about 40 keV.

In the HL-2A tokamak, there are about 30 diagnostics to provide the general plasma parameters, such as the electron temperature with electron cyclotron emission (ECE), the ion temperature with neutral particle analysis (NPA) and the electron density with an eight-channel HCN laser interferometer in the plasma core and microwave reflectometry at the plasma edge. The features of the collective modes are observed by Mirnov probes and soft x-ray (SXR) detector arrays. The magnetic fluctuations are measured by Mirnov probes, which are arranged around the wall of the device with 18 coils poloidally and 10 coils toroidally. Five SXR detector arrays, each having 20 channels, are used to measure the plasma fluctuations. The spatial and temporal resolutions are 2.5 cm and 10 µs, respectively. For a strong fluctuation, the position of the instability can be addressed with different channels of the SXR. A cadmium-telluride (CdTe) detector is used to monitor the hard x-ray (HXR) in the energy range 10–200 keV, which can be divided into six energy ranges. The non-thermal radiation measured by the ECE is also used to analyse the behaviours of the energetic electrons with very low density. In general, the non-thermal radiation of the ECE is more sensitive to the energetic electrons with high perpendicular velocity, which can be estimated from the downward relativistic frequency shift. The HXR emission is sensitive to the energetic electrons with high parallel velocity.

3. Experimental results

3.1. TAE during ECRH

High-frequency (200–350 kHz) instabilities were observed during high-power ECRH or NBI heating in the HL-2A tokamak. These high-frequency modes can be measured by the Mirnov pick-up coils on the wall. A typical discharge is shown in figure 1: (a) the plasma current and stored energy measured by the diamagnetic coil; (b) the line-averaged electron density detected by the HCN laser interferometer; (c) the ECE intensity with 79 and 94 GHz; (d) magnetic fluctuations measured by the Mirnov probes; (e) the heating power (ECRH with pink line and NBI with brown line); and (f) the frequency spectrum of the magnetic fluctuation during ECRH and (g) NBI from the top to the bottom.

**Figure 1.** (a) Plasma current and stored energy; (b) line-averaged electron density detected by the HCN laser interferometer; (c) ECE intensity with 79 and 94GHz; (d) magnetic fluctuations measured by the Mirnov probes; (e) heating power (ECRH with pink line and NBI with brown line); and (f) frequency spectrum of the magnetic fluctuation during ECRH and (g) NBI.
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In this discharge (B_T = 1.39 T, I_p = 150 kA), high-power ECRH of about 1.8 MW and NBI heating of about 500 kW were added in different time durations: ECRH from 400 to 620 ms, NBI from 620 to 1120 ms. The instability can be measured by Mirnov probes both in ECRH and NBI heating. It can be found that the frequency of the magnetic fluctuations increases during ECRH, as shown in figure 1(f). During ECRH, the density decreases because of the pump out effect. The density becomes high during NBI, which is also a fuelling method, and the frequency of the mode decreases with density increase. At the same time, the frequency is modulated by gas puffing: after the gas puffing the frequency decreases, and then increases up to the next puffing pulse indicating that the frequency is a function of the plasma density. A statistical analysis with different shots shows that the frequencies of the mode are proportional to the Alfvén velocity. As we know, the Alfvén velocity is proportional to $Bn_{\rm e}^{-1/2}$ , where B is the magnetic field and n_e is the plasma density. Figure 2 shows the statistical curves for frequency of the mode versus $Bn_{\rm e}^{-1/2}$ with magnetic field from 1.2 to 1.4 T and line-averaged electron density from 0.7 × 10¹³ to 2.3 × 10¹³ cm⁻³. In the figure, the red circles, blue squares and black diamonds represent the ECRH, NBI and ECRH+NBI cases, respectively. The curves clearly show that the frequencies of the mode are proportional to the Alfvén velocity, indicating that they are related to the Alfvén mode. The modes have relatively small amplitude, $\tilde{B}/B\sim 10^{-7}$ , so it is difficult to measure by SXR, because of high noise. Therefore, their locations and mode numbers cannot be determined.

**Figure 2.** Frequency of the mode versus $Bn_{\rm e}^{-1/2}$ with magnetic field from 1.2 to 1.4 T and line-averaged electron density from 0.7 × 10¹³ to 2.3 × 10¹³ cm⁻³. The red circles, blue squares and black diamonds represent the ECRH, NBI and ECRH +NBI cases, respectively.
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**Figure 2.** Frequency of the mode versus $Bn_{\rm e}^{-1/2}$ with magnetic field from 1.2 to 1.4 T and line-averaged electron density from 0.7 × 10¹³ to 2.3 × 10¹³ cm⁻³. The red circles, blue squares and black diamonds represent the ECRH, NBI and ECRH +NBI cases, respectively.
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The frequency of the TAE at different positions was estimated with the local density, safety factor and magnetic field from the following formula:

$\begin{equation} f_{{\rm TAE}} \cong V_{{\rm A}} /\left( {4\pi q_{{\rm TAE}} R} \right). \end{equation} \tag{ 1 }$

Here, V_A is the Alfvén velocity, q_TAE is the safety factor and R is the major radius. The local density can be obtained from microwave reflectomerty at the plasma edge and the eight-channel HCN laser interferometer at the plasma centre. The measurement of the q-profile is not available in HL-2A, so we estimate its profile with the tokamak simulation code (TSC) [23]. In the plasma core, q = 1 or 2, the density is about (1–3)×10¹⁹ m⁻³, then the frequency could be 180–330 kHz according to the above formula. The frequency is very close to the experimental results, as shown in figure 2. In fact, a neutral beam with 40 keV can be easily injected into the plasma centre in the discharges. The velocity of the injected deuterium ions with 40 keV is in the range V_A/3 < V < V_A in the plasma core. Therefore, TAE can be driven by the fast ions.

During ECRH, the electrons can be accelerated to fast electrons with very high energy. Figure 3 shows the ECE spectra at different times. The ECE spectrum before the ECRH (400 ms) is shown by the blue line with open circles. The ECE intensity is proportional to the electron temperature at this time. It is a typical temperature profile of the tokamak and the relation between the ECE frequency and the minor radius can be obtained with the formula $f_{\rm ECE}= 2{\it eB}_{0}R/m_{\rm e}(R-r)$ , here B₀ is the core toroidal magnetic field, R and r are the major and minor radii, respectively, and e and m_e are the electron charge and mass.

With ECRH, the spectrum becomes wide, which is expressed by the pink line with open squares in figure 3. This spectrum consists of two parts: the thermal radiation and the non-thermal radiation emitted by energetic electrons. We can see that the intensity of 77 GHz (the second harmonic of the ECE in the plasma core) increases slightly, indicating that the electron temperature also increases slightly, which can be identified by the stored energy measured by the diamagnetic coil. From figure 1, we can see that the stored energy decreases during ECRH, which is in agreement with the evolution of density. Some of the injected ECRH energy should be absorbed by energetic electrons. After taking off the thermal radiation before ECRH (subtracting the blue line from the pink line), we can obtain a spectrum with a peak of 91 GHz, which includes the non-thermal component (expressed by the green line with open triangles). The non-thermal component spectrum should be the relativistic shift-down frequency of the third harmonic of the ECE. The energy of the fast electrons can be estimated roughly from the following formula:

$\begin{equation} f=3f_{{\rm ce}} \bigg(1-\frac{v^{2}}{c^{2}}\bigg)^{1/2}=3f_{{\rm ce}} \bigg(1-\frac{T_{{\rm fast}} ({\rm keV})}{500}\bigg)^{1./2}. \end{equation} \tag{ 2 }$

Here, f_ce is the electron cyclotron frequency, c is the light velocity and T_fast is the average kinetic energy of the fast electrons. For energetic electrons at the plasma centre, the average kinetic energy can be up to 200keV, according to formula (2). The velocity of the fast electrons is much higher than the Alfvén velocity, but their precessional velocity is very close to the Alfvén velocity in the plasma core. Figure 4 shows the precessional frequency of the trapped electrons with different energies and with v_∥/v = 0.1, which is calculated from the formula [24]

$\begin{equation} \omega_{{\rm d}} =\frac{Eq}{eBR_{0} r}H(k,s)\{1+o(\varepsilon )\}. \end{equation} \tag{ 3 }$

Here, E is the energy of the electron, e is the charge of the electron, B is the intensity of the toroidal magnetic field, R₀ is the major radius, r is the minor radius, s is the magnetic shear, k is defined as $k=\sqrt {\frac{1+\varepsilon}{2\varepsilon}\cos \theta_{0}}$ and ε = r/R₀, θ₀ = arccos(ν_∥/ν) or cos θ₀ = ν_∥/ν, $H(k,s)=4s(k^{2}-1)-1+2(1+2s)\frac{E(k^{2})}{K(k^{2})}$ , ν_∥. and v are the parallel and total velocities of the energetic electrons. E(k²) and K(k²) are the second and the first complete elliptic integrals, respectively. In the calculation, a large pitch angle (v_∥/v = 0.1) is assumed, because of very strong ECRH. From figure 4, we can see that the precessional frequency of the fast electrons with about 100–200 keV at the plasma centre can be higher than 200 kHz and interact with the TAE.

**Figure 4.** Precessional frequency of the trapped electrons with different energies versus the minor radius with the toroidal magnetic field 1.39 T.
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The velocity of the fast ions with 40 keV during NBI is between V_A/3 and V_A and the precessional velocity of the trapped electrons during ECRH is also very close to the velocity. Comparing the ECRH cases with the NBI cases in figure 1, we can find that the energetic electrons produced by high-power ECRH can play the same role to drive the TAE in the same frequency range.

3.2. Lower frequency Alfvénic modes during ECRH

Lower frequency Alfvénic modes excited by energetic electrons were observed for the first time both in ohmic and ECRH plasmas in HL-2A [21]. The mode frequency is comparable to that of the continuum accumulation point of the lowest frequency gap induced by the shear Alfvén continuous spectrum due to the finite beta effect, and it is proportional to the Alfvén velocity with thermal ion-beta held constant. Therefore, the mode can be identified as a beta-induced Alfvén eigenmode (e-BAE). The experimental results show that the BAE is related not only to the population of the energetic electrons, but also to their energy and pitch angles. The results indicate that the barely circulating and deeply trapped electrons play an important role in the mode excitation.

A group of low-frequency modes was found in high-power ECRH plasmas with the following plasma parameters: I_p = 155–160 kA, B_t = 1.2–1.4 T and line-averaged electron density 〈n_e〉 < 1.4 × 10¹³ cm⁻³. These modes disappear in high-density discharges, indicating that the energetic electrons play an important role in exciting the modes. To observe the features of these modes at different heating powers, the ECRH power is increased step by step with a fixed toroidal magnetic field. The typical waveforms are shown in figure 5: (a) plasma current; (b) line-averaged electron density detected by the HCN laser interferometer; (c) electron temperature from ECE; (d) HXR in the energy range 10–20 keV; (e) magnetic fluctuations measured by the Mirnov probes; (f) ECRH power; (g) frequency spectrum of the magnetic fluctuation are plotted from the top to the bottom of the figure. The ECRH power values are 300 kW (520–670 ms), 600 kW (670–820 ms), 1.2 MW (820–980 ms) and 1.5 MW (980–1120 ms) at different heating stages. Since the toroidal magnetic field is 1.33 T in this shot, the ECRH power deposits at the minor radius of r = 15 cm in the LFS mainly.

From figure 5 we can see that the electron temperature measured by ECE increases with ECRH power and the electron density decreases. The HXR emitted by energetic electrons increases with the ECRH power dramatically. The evolution of the frequency spectrum of the magnetic fluctuation measured by the Mirnov probes is shown in figure 5(g). It can be found that the frequency spectra change obviously with increasing ECRH power. In the low-power ECRH plasma, a peak at about 22 kHz can be clearly seen in the frequency spectrum, which is identified as a e-BAE. The main characteristics of the e-BAE have been described in [21]. When the power is over about 600 kW, two peaks or three peaks appear and they broaden with the heating power. The spectrum becomes wide, and there are no obvious peaks when the power is high enough, generally higher than 1.5 MW. After ECRH switch-off, the spectrum comes back to the previous one with only one frequency peak. The signals of the edge channels of the SXR array show similar frequency spectra with the Mirnov probes. The peaks of the spectra disappear or are very weak in the centre channels, indicating that the modes are located outside of the plasma centre. The precise mode location is difficult to obtain, because the signal–noise ratio of the edge SXR is not high enough.

To obtain the detailed features of the modes in the high-power heating stages, the power density spectra and the toroidal and poloidal mode structures were analysed. Three clear frequency peaks at 12, 17 and 24 kHz, denoted by f₁, f₂ and f₃ in figure 6(a), are found in the power density spectra. Mode number analysis was carried out using a global fit of the phase of the Mirnov signal. The poloidal number m is measured using a set of seven Mirnov probes localized at the HFS and eleven probes localized at the LFS, and the toroidal number n is measured using a set of ten Mirnov probes localized at the LFS on the vessel [27]. Figures 6(b) and (c) show the singular value decomposition (SVD) analysis results of Mirnov signals in the 1.36 MW ECRH power discharge of shot 17929, where figure 6(b) gives the poloidal mode number m with different frequencies and figure 6(c) gives the toroidal mode number n with different frequencies. Therefore, the mode numbers of the three modes can be estimated to be m/n = 4/1, 5/2 and 2/1, respectively.

**Figure 6.** Analysis of the magnetic fluctuation measured by Mirnov probes in the high ECRH power discharge with 1.36 MW in shot 17929: (a) poloidal power density spectrum; (b) poloidal mode number m with different frequencies; (c) toroidal mode number n with different frequencies.
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The results of the spectral analysis with high ECRH power show that the modes overlap, and the spectrum broadens within 10–35 kHz. The bicoherence coefficient gives information on the degree of the phase coherence among three different frequency modes. The fact that the bicoherence coefficient is substantially higher than the statistical noise would indicate that there is a wave dynamical interaction in the system that couples the three modes non-linearly. To investigate the occurrence of the non-linear mechanism in the transition to the broadening fluctuation spectra we estimated the bicoherence coefficient of the magnetic fluctuations during the high-power ECRH, but no obvious mode coupling was found.

The parameter dependence of the mode frequencies was investigated by means of data statistical analysis. The statistical analysis shows that the frequencies of the three modes decrease with the plasma density. With the same density, the frequencies of the modes increase with the toroidal magnetic field. As we know, the Alfvén velocity is proportional to $Bn_{\rm e}^{-1/2}$ , where B is the magnetic field and n_e is the plasma density, so the frequencies increase with the Alfvén velocity, as shown in figure 7. This means the three magnetic fluctuations are related to the Alfvénic modes.

**Figure 7.** Statistical curves for frequency of the three modes versus $Bn_{\rm e}^{-1/2}$ with magnetic field from 1.2 to 1.4 T and line-averaged electron density from 0.3 × 10¹⁹ to 1.4 × 10¹⁹ m⁻³. f₁, f₂ and f₃ express the three peaks of the frequency in the spectra, respectively.
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According to the available theory about BAE, the frequency of the BAE is also related to the ion and electron temperatures, as shown in the formula [25] f_BAE ∼ (7/4 + T_e/T_i)^1/2 (T_i)^1/2. So it is important to investigate the relationship between the mode frequency and the plasma temperature. The measurement of the ion temperature in low-density discharges has some uncertainty, so a statistical analysis was carried out. We note that the electron temperature increase and the electron density decrease always occur together during the high-power ECRH, because the pump-out effect is very strong in low-density discharges. In fact, the statistical analysis shows that the electron temperature decreases with the electron density, as shown in figure 8. In the figure, the ion temperature measured by NPA is also shown. We can see that the ion temperature changes slightly in low-density ECRH plasmas. As we know, the electrons are heated by ECRH directly and the ions are heated through ion–electron collisions. The lower the collisionality, the weaker is the ion heating during the ECRH. According to the results of the statistical analysis, we can assume that the ion temperature remains almost constant in the low-density discharges. Therefore, the relationship between the mode frequency and (7/4 + T_e/T_i)^1/2 (T_i)^1/2 can be obtained by a statistical data analysis, as shown in figure 9. It can be found that the frequencies of the three modes have an increasing trend with (7/4 + T_e/T_i)^1/2 (T_i)^1/2. Then the frequency of the observed modes seems to be in agreement with this relation qualitatively.

**Figure 8.** The statistical analysis of the relationship between the plasma density and the electron/ion temperature.
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**Figure 9.** The statistical analysis of the relationship between the mode frequency and (7 T_i/4 = T_e)^1/2.
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The toroidal Alfvén frequency can be estimated by formula (1). The local density is obtained from microwave reflectomerty at the plasma edge and the eight-channel HCN laser interferometer at the plasma centre. We estimate the q-profile with the TSC. According to the q-profile, we obtained the positions of the q = 4, 3 and 2 surfaces, and then the local densities at the surfaces. The local frequency range of the TAE is from 196 to 347 kHz. Therefore, the frequencies of the three modes in figure 7 are about 10–15% of the toroidal Alfvén frequency, which is in the BAE frequency range.

3.3. EPM-like modes during NBI and ECRH

In the previous sections, instabilities with high frequency from 200 to 350 kHz and low frequency from 10 to 35 kHz were presented. Both of them are produced by the energetic electrons during high-power ECRH. In this section, another instability driven by ECRH and NBI together is shown. This is a new mode with frequency from 50 to 180 kHz, which is not in the TAE and BAE gaps. Figure 10 shows a typical discharge: (a) plasma current; (b) line-averaged electron density detected by the HCN laser interferometer; (c) ECE at the plasma edge; (d) magnetic fluctuations measured by the Mirnov probe; (e) NBI (pink line) and ECRH (brown line) power; (f) frequency spectrum of the magnetic fluctuation from the top to the bottom. It is very interesting to observe the evolution of the magnetic fluctuation during ECRH and NBI heating, as shown in figure 10. It should be noticed that the frequency spectrum of the magnetic fluctuation expands from 660 to 710 ms, in which both ECRH and NBI are switched on. The mode cannot be observed only with ECRH or NBI. A very clear mode can be observed from 669 to 697 ms. As shown in the spectrum, the frequency of the mode decreases from 100 kHz to about 60 kHz with the increasing of the plasma density. A few modes appear after 695 ms. These modes are also excited by both ECRH and NBI and have strong chirping down frequency features. The maximum frequency is about 180 kHz and these frequencies shift down within several milliseconds.

**Figure 10.** (a) Plasma current; (b) line-averaged electron density detected by the HCN laser interferometer; (c) ECE; (d) magnetic fluctuations measured by the Mirnov probe; (e) ECRH (brown line) and NBI (pink line) power; (f) frequency spectrum of the magnetic fluctuation.
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The modes can also be found from SXR. Figure 11 shows the evolution of the frequency spectra of the instability measured by both Mirnov probes and SXR detectors: (a) Mirnov signal; (b) centre SXR signal at r/a = 0.3; (c) SXR signal at r/a = 0.67. We can see from the figures that mode-induced fluctuations exist at the plasma centre and are absent at the edge, indicating that the mode is located inside of the 0.5 of the normalized minor radius. Because the frequency is higher and there are several modes existing at the same time, the mode number of the modes cannot be identified by both Mirnov probe and SXR.

To compare the mode frequency with TAE, the TAE frequency at the plasma centre was estimated. In this discharge, B_T = 1.3 T, the line-averaged electron density increases from 0.5 × 10¹⁹ to 1 × 10¹⁹ m⁻³. Therefore, the TAE frequency at the q = 1 or 2 surface is about 200 kHz, which is higher than the frequency of the observed modes.

Three important features of the unstable modes indicate that the modes may be EPMs. Firstly, the frequency of the modes is between the TAE and BAE, which means that the modes are not in the gap of the continuous spectral damping. Secondly, obvious frequency chirping appears within several tens of milliseconds or several milliseconds, which is different from the Alfvén eigenmodes shown in previous sections. Finally, the modes are driven by high-power heating. Generally, the total heating power is more than 2 MW to drive the modes, including about 1 MW of NBI power. In most of the low-density discharges on HL-2A, the NBI power is less than 1 MW and the ECRH power is less than 1.5 MW in HL-2A. Therefore, the modes are not observed only using NBI or ECRH, indicating that a low heating power is not enough to overcome the strong damping. In fact, the ECRH power is close to 1.8 MW sometimes, but the modes are not observed only with ECRH. It is possible that the contribution of the NBI and ECRH might be different to excite the modes, because the power absorbed by energetic particles from both heating methods is different. It may explain why the modes always occur with NBI and ECRH together. This experiment also indicates that the EPM could be excited by both energetic ions and energetic electrons. In future experiments, it will be interesting to try to excite the modes only with ECRH.

3.4. E-fishbone mode during ECRH

The fishbone mode was experimentally observed during ECRH on HL-2A [26, 27]. The energy distribution of the electrons is measured by the HXR detector (CdTe) with the pulse height analysis. Experiments show that energetic electrons play an important role in driving the mode. The e-fishbone can be excited during off-axis ECRH deposited on both the HFS and the LFS. In order to identify the e-fishbone mode, the resonance condition of the wave–particle was investigated. On comparing with experimental results, the calculation analyses show that the mode frequency is close to the precession frequency of the barely trapped electrons or barely circulating electrons when the magnetic shear is very weak or negative. The frequency spectra of the SXR show that the frequency of the fluctuations is about 5 kHz at the low ECRH power and increases to about 8 kHz when the power increases to 1.2 MW. With increasing of the ECRH power, the frequency shows some new phenomena with up- and down-chirping behaviours, and sometimes also with V-font-style sweeping. The chirping mode during ECRH was also identified as the fishbone instability induced by energetic electrons in the previous investigation in the device [26, 27].

Periodic mode frequency jumps were detected by an SXR array for the first time during large-power ECRH on HL-2A. The frequency jump phenomena were observed during LHCD in Tore Supra [19] and the distributions of the energetic electrons were obtained by the multi-channel HXR. The theories have indicated that fishbone instabilities can be driven by both passing particles and trapped particles. With ECRH, trapped particles are dominant. It will be very interesting to compare with the e-fishbone features during LHCD, in which passing particles are dominant. And it is also very important to study the confinement of the energetic particles.

To observe the e-fishbone behaviours during the different ECRH powers, the ECRH power is added step by step from 300 KW to 1.2 MW in shot 17892. The typical waveforms are shown in figure 12: (a) plasma current (red line), line-averaged electron density detected by the HCN laser interferometer (blue line) and ECRH power (black line); (b) electron temperature from ECE (green line) and SXR intensity of one channel (pink line); (c) HXR in the energy range 10–20 keV; (d) the frequency spectrum of the SXR fluctuation from the top to the bottom. ECE and HXR emitted by the energetic electrons increase significantly when the ECRH power is higher than 0.6 MW. The frequency jump can be observed, when the ECRH power increases to about 0.9 MW and the difference between the low and high frequencies increases with ECRH power. The frequency jumps between 8 and 14 kHz within about 25 ms periodically, when the power is 1.2 MW, as shown in figure 12(d).

**Figure 12.** (a) Plasma current (red line), line-averaged electron density detected by the HCN laser interferometer (blue line) and ECRH power (black line); (b) electron temperature from ECE (green line) and SXR intensity of one channel (pink line); (c) HXR in the energy range 10–20 keV; (d) frequency spectrum of the SXR fluctuation.
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The poloidal mode number can be obtained by the tomography of two SXR arrays. The results show that the modes are located at d ∼ 12 cm and the poloidal mode numbers are m = 1 or 2, as shown in figure 13. We estimate the q-profile with the TSC. The q = 1 radius can also be estimated by the sawtooth inversion radius. It can be observed that the sawteeth reversal appears near d = 7.3 cm to d = 12.0 cm during ECRH. That means the q = 1 surface locates between 7.3 and 12.0 cm of the minor radius, which is in agreement with the q-profile from code TSC. That means the mode changes between m/n = 1/1 and m/n = 2/2.

**Figure 13.** Evidence of the changes of poloidal wave number obtained by the results of the tomography of two SXR arrays.
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A statistical relationship between the frequency of the e-fishbone and the ECRH power was obtained, as shown in figure 14, with plasma current from 155 to 160 kA, line-averaged electron density from 0.2 × 10¹³ to 0.5 × 10¹³ cm⁻³, and toroidal magnetic field from 1.2 to 1.22 T. It is found that the jump amplitude of the e-fishbone increases with the ECRH power. In the figure, the blue circles represent the frequency value of the low-frequency branch, and the red diamonds represent the frequency value of the high-frequency branch during various ECRH power steps.

Figure 15 shows the evolutions of the HXR emission from the plasma centre with different energy ranges. The HXR outside of the 0.5 of the normalized minor radius is very weak. It is very clear that the HXR emission from the plasma centre is stronger than that from the plasma edge. The HXR intensity increases with the ECRH power. When the ECRH power is about 1.2 MW, the electrons with 30–40 keV are increased significantly.

4. Summary

With high-power ECRH, abundant new phenomena related to energetic particle physics were observed in the HL-2A tokamak. These unstable modes were proved to be excited by energetic electrons induced by high-power ECRH or together with the energetic ions injected by the NBI system.

High-frequency (200–350 kHz) instabilities are observed during the high-power ECRH or NBI heating in the HL-2A tokamak. The frequencies of the modes are proportional to the Alfvén velocity and the modes are very close to the toroidal Alfvén eigenmode in the plasma core. The experiments show that the energetic electrons produced by high-power ECRH can play the same role as the energetic ions in driving the TAE in the plasma core.

The multi-mode coexistence phenomena occur in the BAE frequency range from 10 to 35 kHz during the high-power ECRH. The modes are located outside the r = 20 cm flux surface in the radial direction. When the power increases to about 0.6 MW, two or three modes are clearly observed in the spectra. The mode numbers of the three modes are estimated to be m/n = 2/1, 5/2 and 4/1. The frequencies of the modes increase with the Alfvén frequency, but are much lower than it. The relationship between the mode frequency and (7/4 + T_e/T_i)^1/2 (T_i)^1/2 is obtained by a statistical data analysis. It is found that the frequencies of the three modes have an increasing trend with (7/4 + T_e/T_i)^1/2 (T_i)^1/2. The frequency spectra broaden and overlap with each other, when the ECRH power is high enough. No clear non-linear coupling between the modes is observed in the high-power ECRH plasma.

A group of new modes with frequencies from 50 to 180 kHz is observed with high-power ECRH and NBI heating together and identified as EPM-like modes. The frequency of the modes is between the TAE and BAE. Obvious frequency chirping appears within several milliseconds or several tens of milliseconds, which is different from the Alfvén eigenmodes. The modes are not observed using NBI or ECRH only, indicating that the NBI heating power lower than 1 MW is not enough to overcome the strong continuous spectrum damping. This experiment indicates that the EPM could be excited by both energetic ions and energetic electrons.

A frequency jump of the e-fishbone mode is observed when the ECRH power increases to about 0.9 MW, and the difference between the low and high frequencies increases with the ECRH power. The frequency jumps between 8 and 14 kHz within about 25 ms periodically when the power is 1.2 MW. The modes are located inside the q = 1 surface and the mode numbers change between m/n = 1/1 and m/n = 2/2.

Acknowledgments

The authors would like to thank the HL-2A Team for tokamak device operation and technical assistance. The authors would also like to thank Professor L. Chen, Dr F. Zonca, Dr Z.H. Lin and Dr G.Y. Fu for helpful discussions and assistance with physical analysis. This work is supported by the NNSF of China under Grant No 11005035 and by the ITER-CN under Grant No 2013GB104001 and No 2013GB106004.

An overview of the energetic electron induced instabilities with high-power ECRH on HL-2A

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Abstract

1. Introduction

2. HL-2A tokamak and the high-power ECRH system