Identification of core ion cyclotron instabilities on HL-2A tokamak

Instabilities in multiplies of ion cyclotron frequency range are identified and termed as core ion cyclotron emission (ICE) in recent HL-2A neutral beam injection heated experiments. Characteristics of the core ICE are presented, including frequency dependence and harmonics features. The detected frequencies are found to agree well with the multiplies of the deuterium cyclotron frequency around the magnetic axis. Additionally, the core ICE exhibits a predominantly compressional property. Observations of distinct spectrum features and individual excitation of each harmonic have demonstrated that the core ICE harmonics are independent multiple modes. Notably, the variation of plasma current is a necessary condition for exciting the 4th harmonic ICE individually. The results suggest that the drive mechanism of core ICE varies between the different frequency ranges.


Introduction
Electromagnetic instabilities in multiples of ion cyclotron frequency range ( f ci = qB/(2πm i ), where q is the ion charge, B is the local magnetic field and m i is the mass of the ion), termed ion cyclotron emission (ICE), have been attached great importance in magnetically controlled fusion plasmas [1]. * Authors to whom any correspondence should be addressed.
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. Assessment of ICE for diagnosing lost and barely confined fast ions [2,3] is a critical topic in the International Tokamak Physics Activity Energetic Particle (EP) physics topical group.
The experimental results of ICE were first observed to be excited by fast ions in TFR tokamak [4] and PDX magnetic mirror [5], whose frequency peaked at multiples of the ion cyclotron frequency. In JET [6][7][8][9] and TFTR [10,11] deuterium and tritium (D-T) experimental results, ICE excited by alpha particles was investigated. Importantly, a strong linear correlation between ICE intensity and neutron emission rate was discovered in JET D-T experiments. Through comparing the detected frequency and f ci , the ICE was located around the outer edge midplane of the plasma and was believed to be excited by deeply trapped alpha particles reaching the plasma edge. Subsequently, a significant amount of research has been conducted on ICE in tokamaks, including JT-60U [12][13][14][15], KSTAR [16][17][18], TUMAN-3M [19,20], ASDEX-U [21][22][23][24][25], EAST [26], START [27], MAST [28], JET [29] NSTX/NSTX-U [30,31] and DIII-D [32][33][34][35], stellarators, including W7-AS [36] and LHD [37][38][39][40], and field reversed configuration C-2U device [41,42]. ICE is located around both the edge and the core of the plasma, and is destabilized by EP from D-T and D-D fusion reaction, neutral beam injection (NBI), and plasma heating in the ion cyclotron range of frequencies. Fast ions confined at the plasma core are likely to excite the core ICE. A brief summary of the experimental results of core ICE is displayed in the table 1 in the discussion section.
Based on the experimental and theoretical results presented above, it is believed that the ICE spectrum contains detailed information about the contributions of EP driving across the velocity space. It is crucial to diagnose the EP population in a fusion reactor as it plays a significant role in enhancing reactor performance [60][61][62]. The method for diagnosing EP through measuring ICE is noninvasive and applicable to fusion reactor environments.
In addition to the EP diagnostic applications, ICE may also provide a means of achieving 'alpha-channelling', which means the direct channeling of alpha-particle energy to thermal ions through wave-particle interaction [63]. Experimental findings in C-2U plasmas have demonstrated that the ion cyclotron wave effectively couples with fuel ions, creating a high-energy tail on sub-collisional timescales that dramatically enhances the fusion rate [42]. A similar waveparticle resonance of ion cyclotron wave has been observed in solar-terrestrial plasmas, leading to energy transfer proceeds of ion energization [64]. Simulation results also demonstrated the 'alpha channelling' scenario of the fast Alfvén wave [65]. Therefore, the study of ICE is significant for ITER and future D-T burning fusion reactors. More experiments need to be conducted to study the physical properties of ICE and improve the theoretical models.
In this paper, we focus on the recent results of core ICE on the HL-2A tokamak. Section 2 introduces the experimental setup, including HL-2A tokamak, NBI system, ICE B-dot probes, and other related diagnostics. Section 3 presents the identification of the core ICE driven by fast ions, including the frequency dependence and polarization of ICE. Section 4 describes the feature of ICE harmonics, which would be shown to exist as independent modes at multiple frequencies. Section 5 would discuss and summarize the comparison of experimental results from HL-2A in this work with those from other devices.
The NBI system [69] consists of two independent beamlines, both beamlines are co-injected into the HL-2A tokamak tangentially with an injection angle of 58.1 • (the angle between the NBI beamline and major radius). The beam power P NBI into the plasma is, P NBI = η injection × P extraction , where P extraction = ∑ i =1:4 V × I, is the total electric power of ion beams, and i denotes the sequence number of the ion source, V and I are the values of beam voltage and current respectively. η injection is the injection efficiency which depends on the neutralization efficiency, beam drift loss et al. The maximum ratio of NBI power to ion beam power η injection can exceed 50%, which depends on multi-factors such as the acceleration voltage of ion beams and the gas pressure in the ion source discharge chamber. The typical maximum port-through power of the two NBI beamlines is about 1.5 MW and the energy of the beam ions (deuterium) can be accelerated up to about 50 keV.
The ICE B-dot probes are mounted on the low field side (LFS) of the HL-2A NO port (at φ ≈ 45 • near NBI 1#), shown in figure 1(a) [70]. Three B-dot probes have been installed and the specific location is illustrated in figure 1(b). Two of them are aligned perpendicular to the toroidal field direction illustrated in figures 1(d) and (e), which aims to be sensitive to the compressional waves. Another B-dot probe in figure 1(c) is aligned parallel to the toroidal field direction, which aims to be sensitive to the shear waves. The probe in figures 1(c) and (d) are the single-turn loop made of copper with the Teflon insulating sleeve. The probe has a loop area of ∼40 cm 2 . A stainless steel (316L) frame is designed to hold and protect the probe. And the probe in figure 1(e) is a single-turn circle loop made of stainless-steel coaxial line with diameter of 5 cm i.e. loop area of ∼20 cm 2 . The radio frequency signals are sampled with a fast analog-to-digital converter digitizer (NI PXIe-5172). The line-averaged electron density is measured with a four-channel formic acid (HCOOH) laser interferometer [71]. The ion temperature and toroidal rotation are detected by charge exchange recombination spectroscopy (CXRS) [72].  The amplitude of the magnetic perturbations in the toroidal and poloidal directions are compared in figure 3. The blue line represents the amplitude of toroidal magnetic perturbations (A δBϕ = 20 × log10(δB ϕ )). In the same way, the red line stands for the amplitude of poloidal magnetic perturbations (A δBθ ). The A δBϕ is much larger than A δBθ for the three modes, which suggests that the measured modes are compressional waves.
The f cD depends on the magnetic field and charge-to-mass ratio. In figure 4, the location of the magnetic axis gradually approaches the LFS before disruption from 1725 ms to 1750 ms. Figures 4(a) and (b) show the charge coupled device (CCD) camera images at 1725 ms and 1750 ms respectively. The position of the magnetic axis is closer to the high field side at 1725 ms and moves to the LFS at 1750 ms. Figures 4(c) and (d) display the poloidal magnetic topology calculated by equilibrium fitting code (EFIT) [73]. At 1725 ms, the magnetic   frequencies of the coherent modes mainly rely on the magnetic field, consisting of multiples of ion cyclotron frequency. Figure 5 displays the relation of three ranges of measured frequencies versus the magnetic field at the magnetic axis for several shots represented by the markers. The lines denote the calculated multiply of f cD . The measured frequencies of the three ranges fit well with calculated frequencies among different shots with changing toroidal magnetic fields. The mode whose frequency fits the fundamental f cD could not be observed in almost all shots. Figure 6 illustrates the comparison between the f cD that varies with R and the measured frequency in two shots. Figure 6(a) shows a time slice of the frequency spectrum of shot #38224, representing the amplitude of the instabilities. The observed frequencies are compared with the f cD in figure 6(b), in which the red line represents the second harmonic of f cD . The experimental frequencies of the three instabilities match the harmonics of f cD at R ≈ 1.71 m, which is around the magnetic axis marked by the green dashed line in the poloidal magnetic topology reconstructed by EFIT in figure 6(c). Figure 6(d) shows the intensity of the instabilities of shot #38226. In this experiment, two modes are excited which are the most common observations in HL-2A. Their frequencies are equal to the double and four times f cD at R = 1.72 m, which is also around the magnetic axis shown in the poloidal magnetic topology in figure 6( f ).
From the results described above, the frequencies of observed modes agree with the double, triple, and four times f cD around the magnetic axis, mainly depending on the toroidal magnetic field. We could conclude that the coherent magnetic instabilities are core ICE excited by fast ions introduced by NBI in HL-2A. Therefore, we would call the modes as 2nd, 3rd, and 4th ICE in the following content. The strongest mode is the 2nd ICE, while the 1st ICE could not be detected in almost all shots.

Independent multiple modes of ICE
This section presents the features of ICE harmonics observed under different experiments, including the excitation of the 2nd, 3rd, and 4th ICE in a single shot, as well as individual excitations of each ICE harmonic. Figure 7 shows the detailed spectrum of the 2nd, 3rd, and 4th ICE for shot #38735. The time of existence and frequency features are different in three frequency ranges. The spectrum of the 4th ICE is illustrated in figure 7(a), in which the frequency evolution displays bursting characteristics. Around 1058 ms and 1072 ms, the frequency increases about 300 kHz rapidly in 0.5 ms. At about 1065 ms marked by a yellow ellipse, only the 4th ICE exists. The 3rd ICE around 29.1 MHz in figure 7(b) shows a quasi-coherent feature. At 1064 ms, only the 3rd ICE is visible marked by the yellow ellipse. The 2nd ICE whose frequency is around 19.25 MHz in figure 7(c) is more coherent. From 1060 ms to 1067 ms, the 2nd ICE is absent, while the 3rd and 4th ICE are excited. At 1078 ms, only the 2nd ICE is exist marked by the yellow ellipse. It is clear that the modes are excited at different times and the frequency features vary between the different harmonics.
In addition to the existence of 2nd, 3rd, and 4th ICE in a single shot, individual excitation is also observed in HL-2A. Figure 8(a) shows a time slice of the frequency spectrum of shot #37991. Only 2nd ICE is excited, which is a common experimental result in HL-2A. In this experiment, the magnetic  Figure 8(c) illustrates the frequency spectrum in the 2nd ICE frequency range that around 18.6 MHz. In this experiment, with the accompanied sawtooth oscillation in the core region, the disappearance of ICE can be seen in figure 8(c), which may be due to the fast ion loss caused by sawtooth crash. Signals from two toroidally arranged Bdot probes are used to calculate the toroidal mode number of ICE. Figure 8(d) shows the color-coded spectrum of the core ICE, in which the dominant mode number is n ≈ −12, indicating that the 2nd ICE in this shot propagates in the counter-I p direction. Figure 9 shows a typical result of individual excitation of the 3rd ICE of shot #39246. In figure 9(a), the time slice of the frequency spectrum of shot #37991 represents that only the 3rd ICE is excited. In this experiment, the magnetic field B t is 1.35 T. Plasma current I p is about 160 kA as shown in figure 9(b) red line. The power of NBI is 0.55 MW plotted by the blue line. It should be mentioned that the individual excitation of the 3rd ICE is relatively rare in HL-2A experiments. As there have been no significant changes in the experimental parameters and conditions, the reason for exciting 3rd ICE alone is currently unclear. Figure 9(c) illustrates the frequency spectrum in the 3rd ICE frequency range. There was no accompanying sawtooth in the experiment, while the 3rd ICE is damped sometimes. Figure 9(d) shows the color-coded spectrum of the core ICE, in which the dominant mode number is n ≈ 11, indicating that the 3rd ICE in this shot propagates in the co-I p direction.    Power of NBI is 0.58 MW plotted by the blue line. The plasma current I p is raising from about 115 kA-130 kA as shown in figure 10(b) red line. It is found that the variation of plasma current is a necessary condition for exciting the 4th ICE alone. Figure 10(d) shows the color-coded spectrum of the core ICE, in which the dominant toroidal mode number is n ≈ −10.
From the results above, although the frequencies of the modes match the multiples of core ICE frequency, the modes are independent of each other. The excitation mechanism may involve different phase space distributions of fast ions, which will be studied in our future work. Table 1 summarized the experiments of core ICE in different devices destabilized by fusion-born products and fast ions introduced through NBI. In JT-60U [12], AUG [21,25], and EAST [26] tokamaks, the core ICE are excited by fusion-born ions, which are the proton (H + ), and tritium (T + ) produced by the D-D reaction:

Discussion and summary
In these experiments, the velocity of energetic H + and T + are super Alfvénic. The ICE is located around the plasma core. The 1st and 2nd T-ICE are observed in EAST, while in other results, the 1st T-ICE (around 10 MHz) and 1st H-ICE (around 40 MHz) are studied. Core ICE driven by fast ions introduced by NBI in TUMAN-3M [20], AUG [22,23], EAST [26], NSTX/NSTX-U [30,31], DIII-D [34,35], and HL-2A tokamaks are also summarized. The velocities of fast ions are lower than the Alfvén velocities. In NSTX-U, the location of ICE is near the internal transport barrier. In other devices, the ICE is all around the plasma core. Low integer harmonics are observed with co-I p NBI in these devices. With near tangential counter-I p NBI, higher-order harmonics are detected in DIII-D results.
In this work, magnetic instabilities around multiples of f ci are identified as core ICE in HL-2A tokamak. The core ICE is excited during the duration of NBI. The detected frequencies of ICE are found to agree with the second, third, and fourth harmonics of core f cD around the magnetic axis. The magnetic perturbations amplitude in the toroidal and poloidal detections are compared. The amplitude of toroidal perturbations is about 30 dB larger than that of the poloidal direction, which implies that the core ICE may belong to the compressional wave.
The independent multiple modes of ICE are easily recognizable in one shot when three frequency ranges of ICE are excited. The existent time and frequency features are different for the three modes. The individual excitation of only one frequency range of ICE is also observed. The excitation of the 2nd ICE alone is the common result in HL-2A. The 4th ICE is excited alone only when the plasma current is changing. The propagating direction and toroidal mode number are analyzed. For the 2nd ICE, the dominant mode number is n ≈ −12, indicating that the propagation direction of the wave is in the counter-I p direction. It should be mentioned that independent multiple modes are core ICE, while edge ICE shows different results and will be studied in our future work. We conjecture that the excitation mechanisms of different ICE modes are distinct and may involve different regions of the fast ion phase space or possibly different fast ion species.
The 2nd and 4th ICE consistently exhibit the highest amplitude which is similar to the DIII-D co-I p results [34]. The frequencies of these two modes coincide with the proton fundamental cyclotron frequency and its second harmonic. Potential excitation sources arise from two key areas: the fast ions accelerated by NBI, and the energetic protons generated through D-D fusion reactions. Since ICE at the 3rd deuterium harmonic is frequently excited in HL-2A experiments, albeit more weakly that the 2nd and 4th harmonics, it is clear that at some of the ICE reported in this paper is driven by fast D + ions. However, the possibility of fusion protons cannot be completely ruled out. As fusion protons, which are produced in the plasmas as a result of beam-thermal and beam-beam D-D fusion reactions, are largely poorly confined due to their large Larmor radii and orbit widths relative to the minor radius of HL-2A. It is possible that some of these fusion protons, particularly those in deeply passing orbits, could be confined long enough to trigger core ICE. If part of the fusion proton is confined, high anisotropy is expected as a result of first orbit losses, and this anisotropy could potentially act as one of the instability drivers. Therefore, further comparison between experimental results and theoretical simulations is needed. In our following research, we will prioritize the simulation work to investigate the underlying excitation mechanism, specifically by comparing the growth rate of different ICE modes under various conditions. With a deeper understanding of the correlation between the detailed ICE spectrum and fast ion distribution, the possibility and accuracy of using ICE for EP diagnostics in ITER and future fusion reactors could be significantly improved.