Investigation of energetic ion losses induced by long-lived saturated internal mode with energetic particle diagnostics in the HL-2A tokamak

Several sets of energetic particle diagnostics, including a set of neutron flux monitoring systems, a solid-state neutral particle analyzer and a fast ion loss probe (FILP), have been used to investigate the energetic ion losses induced by the long-lived saturated internal mode (LLM) in the HL-2A tokamak. Clear experimental evidence for different levels of energetic ion losses induced by LLM, sawtooth and minor disruption has been observed. A numerical calculation for the evolution of neutron emissions was carried out with the FBURN code, and it shows that the neutron emission drop rate linearly increases with the LLM amplitude and no threshold perturbation amplitude exists, illustrating that the loss mechanism for LLM induced energetic ion loss is dominantly convective. In addition, measurement results of the FILP demonstrate that LLM tends to expel energetic ions with relatively low energy ( E<27 keV) and high pitch angle ( θ>60∘ ), and can suppress the prompt loss of energetic ions with high energy and low pitch angle to a certain degree. Furthermore, the physical process for LLM induced energetic ion loss can be explained by orbit calculations, which show that LLM induced lost energetic ions will transport from center to peripheral region first, and then get lost out of plasma. The experimental observations are successfully reproduced by calculations using the ORBIT code combined with both the NUBEAM code and the MARS-K code. The paper clearly describes the whole physical process of LLM induced energetic ion loss for the first time in the HL-2A tokamak.


Introduction
One of the essential preconditions for achieving self-sustained D-T burning plasma is to confine the energetic ions in fusion plasma long enough to heat the fuel ions [1]. Among the energetic fusion ions in D-T burning plasma, fusion born α particles are of particular interest because they play a vital role in plasma ignition. Actually, energetic ions via auxiliary heating are also important in D-D fusion plasma and allow us to study energetic particle interactions [2]. Hence, it is the inexorable requirement of fusion reactors to achieve excellent confinement quality for energetic ions. Energetic ion losses deteriorate the confinement quality, leading to the reduction of neutral beam injection (NBI) current drive and heating efficiency [3], which is not conducive to the enhancement of the energy gain factor. Furthermore, intense and localized energetic ion loss may damage the plasma facing components, and then cause impurity pollution to the plasma [4]. A small fraction of energetic ion loss in large magnetic fusion devices including ITER might be intolerable [5]. Understanding the behavior of energetic ion loss in fusion plasma is therefore still a crucial issue for fusion research.
Numerous efforts have been made to study the energetic ion loss induced by different magnetohydrodynamic (MHD) instabilities, like toroidal Alfvén eigenmodes (TAEs) [6,7], energetic particle modes [8,9], fishbones [10,11], sawteeth [12] and tearing mode [13]. Investigations of long-lived saturated internal modes (LLMs) observed on many fusion devices [14][15][16][17] demonstrate that LLM can eject energetic ions from the plasma core region. The LLM induced energetic ion losses have been observed in MAST with a neutron emission profile monitor [18] and a fast ion loss detector [19]. However, the physical mechanism and process for energetic ion loss induced by LLM are still not sufficiently clear. It should be noted that LLM is a key MHD instability that plays an important role in the advanced scenarios for ITER operation [20], because sustained elevated central safety factor q can be achieved from the action of LLM [21]. Among the advanced scenarios, the hybrid scenario is believed to be a potentially interesting operation scenario for future fusion devices, and many devices such as MAST [14], JET [22], JT-60U [23], DIII-D [24], ASDEX-U [25], EAST [26] and HL-2A [27] have carried out experiments based on the hybrid scenario. Thus, it is of great scientific importance and practical value to investigate the behavior of energetic ion loss induced by LLM.
The present work aims to investigate the physical mechanism and process of energetic ion loss induced by LLM. The experimental setups are described in section 2, in which energetic particle diagnostics including neutron flux measurement (NFM) systems, neutral particle analyzer (NPA) and fast ion loss probe (FILP) are introduced. The experimental results are shown in section 3. Physical mechanism and process analyses are depicted in sections 4 and 5, respectively. Finally, conclusions are drawn in section 6.

Experimental setups
The HL-2A tokamak [28] is a medium-size conventional tokamak with a closed divertor. It has a major radius of 1.65 m, and a minor radius of 0.4 m. The plasma current I p ranges from 150 to 430 kA, and its orientation is counterclockwise from the top view of HL-2A. The toroidal magnetic field along the magnetic axis B t , which is mainly created with sixteen toroidal magnetic field coils, ranges from 1.3 to 2.7 T, and is oriented to be clockwise from the top view of HL-2A. The divertor of HL-2A, which is characterized with two closed divertor chambers, enables that it can be operated in either of singlenull (SN) and double-null divertor configurations theoretically. However, only lower SN divertor configuration is considered in the present paper.
The NBI system on HL-2A consists of two neutral beam lines, and each beam line is equipped with four positive ion sources. Both beam lines share the same parameters. Each beam line has a maximum injection power of 2 MW. The neutral beam particles have three energy components, i.e. full injection energy E, E/2, and E/3. Its full injection energy E has a typical value of 40 keV. The neutral beam is injected into the plasma tangentially with a tangency radius of 1.4 m and an angle of 32 • with respect to the plasma current along the magnetic axis (see figure 1(a)). Three kind of energetic particle diagnostics are used to study the behavior of energetic ion loss induced by MHD instabilities, i.e. NFM systems, NPA and FILP. The layout of the energetic particle diagnostics is shown in figure 1(a).
There are two different NFM systems: the one is the ZnS detector, and the other is the 235 U fission chamber. The ZnS detector is a newly developed NFM system with an optimum temporal resolution of 1 µs [29,30]. It is ∼5 m away from the center of HL-2A. The ZnS detector is sensitive to fast neutrons (E > 0.7 MeV) rather than slow neutrons and γ/X rays. The 235 U fission chamber is a conventional NFM system with a temporal resolution of 1 ms, and it is sensitive to thermal neutrons rather than fast neutrons and γ/X rays. It is ∼11 m away from the center of HL-2A. Since the fission chamber was calibrated with a 252 Cf neutron source, it can be used as a neutron yield measurement system [31].
The NPA system in the present paper is a kind of solidstate NPA [32]. It is located at the low field side in the vacuum chamber and about 15 cm lower than the middle plane. It is equipped with a collimator facing toward the high field side through the plasma core region (see figure 1(b)). An AXUV Figure 1. Layout of the NBI system and the energetic particle diagnostics in the planform of HL-2A (a). Plasma current Ip is oriented to be counterclockwise, while toroidal magnetic field Bt to be clockwise. Poloidal view of the NPA system and its sightline, as well as the location of the FILP (b). silicon photodiode coated with a 100 nm thick tungsten film makes the NPA suitable for measurements of neutral particles with energy over 26 keV generated in the plasma core region. Its sampling rate is 1 MHz. However, the NPA system in the present paper does not have an energy resolution.
The FILP [33] is located at the low field side on the middle plane in the vacuum chamber. Its detector head is ∼3 cm away from the last closed magnetic flux surface of the HL-2A plasma (see figure 1(b)). The FILP is used to detect the Larmor radius ρ i of the lost energetic ion as well as its pitch angle θ, from which the energy E i can be derived: and v are respectively the mass of the lost ion, the local magnetic field at the FILP head, the electrical charge of the lost ion, its velocity parallel to the local magnetic field, and its velocity. The FILP has a temporal resolution of 2 ms.

Experimental results
LLM is observed frequently in the HL-2A plasma during NBI with sufficiently high injection power. Figure 2 shows the time traces of some main parameters of an NBI plasma with strong LLMs in which some sawteeth are inserted. An NBI pulse with ∼0.5 MW in total is injected into the HL-2A plasma from 900 to 1900 ms. The typical value of the plasma current I p , the central line-averaged electron density n e and the central electron temperature T e is about 160 kA, 1.8 × 10 19 m −3 , and 2.2 keV, respectively. The sampling rates of n e and T e are respectively 1 MHz and 30 Hz. A minor disruption occurs at 978 ms, and it has a significant effect on I p , n e and T e . It can be seen from figures 2(c) and (d) that, after the minor disruption, the first LLM appears at ∼1100 ms and vanishes at ∼1220 ms, and then several LLMs appears during 1300 ms and 1900 ms together with several sawteeth. This shot makes it possible to investigate the energetic ion losses induced by LLM and sawtooth. In order to characterize the LLM, Bayesian based soft x-ray (SXR) tomography reconstruction [34] for the mode structure has been carried out. The mode structure of LLM at about 1111 ms is shown in figure 3. Both m/n = 1/1 mode and m/n = 2/2 mode exist simultaneously in the plasma core region, characterizing the existence of LLM [14]. The m/n = 1/1 mode with a frequency of ∼10 kHz and the m/n = 2/2 mode with a frequency of ∼20 kHz can also be observed in the frequency spectrogram of the SXR signal shown in figure 2(d). The normalized minor radius r/a of the q ∼1 surface is estimated to be ∼0.25.  Since neutral particles exist densely in the plasma peripheral region, energetic ions lost from the plasma core region are likely to become energetic neutral particles via chargeexchange recombination interactions in the plasma peripheral region. Hence, it is possible to study the energetic ion losses in the plasma core region with the NPA system [35,36]. Figure 4 represents the flux of neutral particles with energy over 26 keV as well as its frequency spectrogram. It can be found that there exist several kinds of MHD instabilities, including mainly minor disruption, LLM and sawtooth. The neutral particle flux responds to minor disruption, LLM and sawtooth, reflecting that all the three MHD instabilities can induce the energetic ion losses.
The emission rate of fusion neutrons is positively associated with the confinement property of the energetic ion population, i.e. the energetic ion loss can lead to the decrease in neutron yield. To investigate the energetic ion loss behavior, neutron diagnostics can play an important role. The LLM induced energetic ion losses have been observed in different fusion devices indeed by using neutron diagnostics [18,21]. Figure 5 shows the temporal evolution of neutron emissions measured with both the 235 U fission chamber and the ZnS detector.
Both curves respectively measured with the 235 U fission chamber and the ZnS detector have the same variation trend, and the deviation between the two curves may attribute to different detection positions (see figure 1). The minor disruption at 978 ms cause a sudden drop in neutron emission. After the minor disruption, a long-lived mode appears. It can be found that the LLM during 1090 ms and 1210 ms induces a slight drop first and then a slight increase in neutron emission, and the drop gets more prominent when sawtooth occurs during 1300 ms and 1900 ms. The slight increase in neutron emission during 1150 ms and 1300 ms might benefit from the reduction in magnetic perturbation amplitude. A prominent continuous decrease in neutron emission is observed during LLM phase inserted with several sawtooth crashes, which was also observed in JET [37].
Since the decrease in neutron emissions may be caused not only by the energetic ion loss but also by the decline in main parameters of the bulk plasma, it is necessary to introduce a precise calculation for the evolution of neutron emissions, which will be described in detail in the next section.
Lost energetic ions can be directly detected by FILPs which have been developed in many fusion devices [38][39][40][41]. The energetic ion losses induced by various MHD instabilities have been observed in the HL-2A tokamak by using a FILP [42]. Figure 6 presents the energetic ion losses induced by LLM and/or sawtooth in terms of distribution map measured with the FILP. An NBI pulse with ∼1 MW in total is injected into the HL-2A plasma during the entire period of the figure. Both LLM and sawtooth can be observed from the SXR signal and its frequency spectrogram.
Four distribution maps in figure 6 depict the energetic ion losses related to prompt loss only (t 1 and t 4 ), both LLM induced and prompt loss (t 2 ), and both sawtooth induced and prompt loss (t 3 ), respectively. Notably, all the distribution maps during the LLM phase are similar to each other. Lost ions are mainly concentrated in three zones in each distribution map, i.e. zone α, β, and γ. Zone α is the region with relatively high energy (E ∼ 40 keV) and low pitch angle (θ ∼ 57 • ), zone β is the region with relatively low energy (E ∼ 20 keV) and high pitch angle (θ ∼ 63 • ), and zone γ is the region with relatively low energy (E ∼ 20 keV) and highest pitch angle (θ ∼ 75 • ). It can be found that the prompt loss of beam ions, which are distributed in zone α and β, dominates the energetic ion loss during NBI. In addition, energetic ion losses respectively induced by LLM and sawtooth are also observed. The spots for prompt loss at t 1 and t 4 have almost the same brightness and area, while the spots for LLM induced loss at t 2 and sawtooth induced loss at t 3 have higher brightness and larger area especially in the region of relatively low energy and high pitch angle (see zone β and γ). It illustrates that both LLM and sawtooth tend to expel energetic ions with relatively low energy and high pitch angle rather than other cases which are usually caused by other central MHD, such as TAE [43,44], NTM [45] and TM [42]. For example, TAE is likely to eject energetic ions with relatively high energy (40 keV< E < 180 keV) and low pitch angle (θ < 45 • ) in LHD [44], and NTM to eject those with comparable energy and relatively low pitch angle (θ ∼ 40 • ) in ASDEX Upgrade [45], compared with beam ions. Our result further verifies the simulation result that sawtooth crashes may provide a mechanism to expel energetic ions with relatively low energy and could be used for He ash removal [46].

Physical mechanism for energetic ion loss
Mechanisms for energetic ion loss induced by MHD instabilities can be classified into three categories, characteristics of which are listed as follows [43,[47][48][49]. The dominant loss mechanism of the first category is convection. It has no threshold perturbation amplitude and does not induce thermal ion loss, and the loss quantity is proportional to the amplitude of MHD modes. The second category is dominantly diffusion. It has a threshold amplitude and the loss quantity varies quadratic with the amplitude of MHD modes. The last category is mainly stochastic process. It has higher perturbation amplitudes than the second category, and energetic ion losses as magnetic field and ion orbits become stochastic. The last category can induce thermal ion losses.

Neutron emission calculation
To analyze the physical mechanism for energetic ion loss induced by LLM, it is required to find out the relationship between the energetic ion loss rate and the perturbation amplitude of magnetic field. A neutron emission analysis code called FBURN [50] is used to perform a precise calculation for the evolution of neutron emissions. The required input parameters are listed below.
Electron density profile: It is measured with the far-infrared laser interferometer [51]. Electron temperature profile: It is measured with the multipoint vertical-Thomson scattering diagnostic [52]. Ion temperature profile: It is measured with the charge exchange recombination spectroscopy [53]. Ion density profile: The profile of deuteron density is obtained from the equation n D = ( Z eff −ZC 1−ZC )n e , where Z eff is the effective plasma charge, Z C the atomic number of carbon and n e the electron density. Effective plasma charge: The effective plasma charge measured with the visible bremsstrahlung diagnostic [54] show that Z eff ∼ 2.5 before the minor disruption and Z eff ∼ 4 after the plasma recovered from the minor disruption. Neutral beam deposition profile: The neutral beam deposition profile is calculated using the same method as the neutral beam model of the Simulation of Spectra code [55]. Figure 7 shows the calculated neutral beam deposition profile for shot #39020 with a total NBI power of 0.5 MW. The proportion of the three energy components of neutral beam particles, i.e. E, E/2, and E/3, is 0.44, 0.39, and 0.17, respectively. The neutral beam deposition profile is peaked at the plasma center, which implies that most neutral beam particles are deposited in the plasma core region.
With the input parameters described above, the FBURN code can calculate the neutron emission profiles, as shown in figure 8. Neutron emission profiles are peaked at the center  as expected, illustrating that fusion reactions mainly occur in the plasma core region. Both LLM and sawtooth occur in the region around q ∼ 1 surface (ρ ∼ 0.25). It can be found that the neutron emission profiles are much distinct from each other in the plasma core region with normalized radius ρ ⩽ 0.4, while they are almost indistinguishable in the peripheral region with normalized radius ρ > 0.4. It indicates that the energetic ion loss in the MHD active phase mainly occurs within the normalized radius of 0.4.

Analysis for loss mechanism
The neutron emission evolution curves both measured with neutron diagnostics and calculated with the FBURN code are compared in figure 9. The calculated neutron yield agrees well with the measurement before 1100 ms, which illustrates that the calculation results are sufficiently accurate. The agreement between calculation and measurement for the minor disruption is due to that FBURN has considered the prominent thermal ion losses induced by the minor disruption at 978 ms. In addition, the deviations between the calculation curve and the experimental curves during LLM and/or sawtooth can be observed after 1100 ms. The FBURN calculation has considered the prompt loss of beam ions without any MHD activities by setting the diffusion coefficient of energetic ions to be 0.2 m 2 s −1 , which is estimated from neutron emission measurements during MHD quiescent phase. Among its input parameters described above, only the calculated neutral beam deposition profile has a correlation with energetic ions, while other input parameters are associated with the bulk plasma. It  should be noted that the anomalous energetic ion loss induced by MHD instabilities is not included. Hence, the deviation between the experimental curves and the calculation curve during LLM and/or sawtooth illustrates that energetic ion loss happens in the period. Comparison between the experimental and calculated neutron emission evolution curves shows that, the LLM during 1090 ms and 1210 ms induces a ∼15% reduction in neutron emission, and both the LLMs and sawteeth during 1300 ms and 1900 ms induces more than ∼30% reduction in neutron emission. Figure 10 shows the dependence of the drop rate of total neutron emission rate on LLM amplitude measured by a magnetic probe located on the internal surface of the vacuum vessel. The drop rate of total neutron emission rate linearly increases with the perturbation amplitude, i.e. the energetic ion loss rate has a positive linear relation on the perturbation amplitude. In addition, it can be found from the positive intercept of the fitting line (the red solid line) that no threshold perturbation amplitude exists in the relation. Both characteristics indicate that the dominant loss mechanism for LLM induced energetic ion loss is convection, which is also the dominant loss mechanism of TAE induced energetic ion loss [43,47,56]. The relation between energetic ion loss rate and perturbation amplitude is verified by calculations, which will be discussed in section 5.2.

Analysis for energetic ion loss process
Since the energetic ion loss rate is proportional to the light output of the scintillator of the FILP head, the energetic ion loss rate induced by LLM and sawtooth can be estimated from the statistical analyses of the distribution maps in figure 6. Energetic ion loss distribution functions of light output vs. energy and pitch angle are shown in figure 11. Prompt loss is the average of energetic ion loss at t 1 and t 4 . LLM induced loss and sawtooth induced loss are respectively evaluated as the increment of energetic ion loss at t 2 and t 3 from the prompt loss. The LLM induced energetic ion loss is estimated to be 13% of the prompt loss, and the sawtooth induced energetic ion loss is estimated to be 75% of the prompt loss. However, the estimated sawtooth induced loss herein may contain partial or total LLM induced loss. Hence, the estimation value of sawtooth induced energetic ion loss is revised to be 62%-75% of the prompt loss. Since the time scale of LLM is much larger than sawtooth, the energetic ion loss induced by LLM is a mild process that has a much smaller loss rate than prompt loss, while the energetic ion loss induced by sawtooth is a drastic process compared with that induced by LLM. According to the neutron signal, less than 10% neutron yield reduction is observed during the sawtooth crash.  Figure 11(a) shows that LLM induced energetic ion losses concentrate in zone β and γ, and those induced by sawtooth cover a much wider energy range. It indicates that energetic ion losses induced by LLM have relatively low energy (E < 27 keV) compared with the prompt loss. Figure 11(b) shows that both LLM induced and sawtooth induced energetic ion losses concentrate in zone β and γ, i.e. energetic ion losses induced by LLM have relatively high pitch angles (θ > 60 • ) compared with the prompt loss. Negative light output for the LLM induced loss curve appears during an energy range 37 keV < E < 55 keV and a pitch angle range 56 • < θ < 60 • (in zone α). It means that the energetic ion losses in zone α during LLM phase are less than the prompt loss, i.e. part of the prompt loss with high energy and low pitch angle is suppressed by LLM, so that the redistribution of energetic ions occurs with the presence of LLM. It is reported that Alfven instability induced redistribution of energetic ions can reduce the central magnetic shear leading to a reversed shear in a tokamak [57]. It indicates that the redistribution of energetic ions may produce a certain influence to the current redistribution, and even the formation and sustainment of flat or weakly reversed q profiles which are worth studying in the advanced scenarios for ITER operation [21]. Further, it can be speculated that LLM induced energetic ion loss might be related to some observation of internal transport barrier formation during central MHD such as LLM or fishbone, in which poloidal flow is enhanced [58].
The orbits of energetic ions in a magnetic field can be calculated with the following equation, m i where m i is the mass of energetic ion, e i the charge of energetic ion, ⃗ v the velocity of energetic ion, ⃗ B the magnetic field strength which can be obtained from the equilibrium reconstructed by the EFIT codes [59] combined with the Faraday rotation angle from polarimeter, as well as the constraint of central qvalue during sawtooth [60]. The calculated poloidal projections of the lost energetic deuteron ion orbits, which are calculated backward in time from the FILP head, are drawn in figure 12.
Three main components in the distribution maps in figure 6 have been considered in the calculation. For the first component (zone α: E = 40 keV, θ = 57 • ), both trapped and passing particle orbits are observed, and the trapped particle orbits pass through the plasma core region. For the second component (zone β: E = 20 keV, θ = 63 • ) and the third component (zone γ: E = 20 keV, θ = 75 • ), only trapped particle orbits are observed, and all the trapped particle orbits pass through the peripheral region. The first component has a brighter spot because it corresponds to the maximum energy and therefore dominates according to figure 7. Additional magnetic perturbation is introduced to induce anomalous energetic ion losses when MHD instabilities are exited. Since LLM is excited around q ∼ 1 surface [37] which is shown by the yellow dash circles in figure 12, the energetic ions in the plasma core region are expected to be expelled to the peripheral region via convection as shown by the white arrows in figure 12. For the first component (see figure 12(a)), the lost energetic ions expelled from the plasma core to the peripheral region on the low field side (see the white arrows) have no chance to encounter lost particle orbits. On the contrary, the lost energetic ions expelled from the plasma core to the peripheral region on the low field side (see the white arrows) for the second component (see figure 12(b)) are likely to encounter lost particle orbits and be recorded by the FILP system. It explains why LLM tends to expel energetic ions with relatively low energy and high pitch angle. Please note that the loss orbits of the third component are located at the plasma edge. It illustrates that the energetic ions during LLM instabilities transport from the plasma core region to the peripheral region first, and then being scattered into the loss orbit, which is the same as the energetic ion transport behavior during TAE instabilities [61].
Notably, there exists another possible explanation for the reduced brightness of the main spot during LLM activity. In figure 12(a), both trapped orbits have banana tips located on the high-field side, i.e. their pitch angles are close to precession reversal ω D = 0. Banana guiding centers of such particles can be trapped by LLM and experience wide (few cm) super-banana oscillations [62]. Such super-banana particles will cross the last closed flux surface well outside the midplane, i.e. these loss ions cannot be detected by FILP. In this instance, the conclusion that LLM tends to expel energetic ions with relatively low energy should be relaxed. In order to confirm which explanation is more reasonable, theoretical calculations for LLM induced energetic ion loss is therefore necessary.

Theoretical calculations for LLM induced energetic ion loss
To reproduce the experimental observations for LLM induced energetic ion losses, theoretical calculations are carried out.  figure 13(b)). It can be interpreted as due to the slowing down process of energetic ions in plasma. In order to calculate the distribution map of lost energetic ions with the ORBIT code [64], the perturbation displacement structure of LLM mode should be input the calculation as a necessary parameter. Figure 14(a) presents the perturbation displacement structure of the LLM mode calculated with the MARS-K code [65]. It can be found that m = 1 mode has a prominent perturbation displacement, while m = 2 and 3 modes have rather smaller displacements, which can also be seen in figure 2. The perturbation displacement shown by the green curve in figure 14(a) corresponds to the 2/1 mode, while the second harmonic in figure 2 is the 2/2 mode. However, since the ratio of the 2/2 and 1/1 components is sufficiently small which is estimated to be ∼1% according to figure 3, the discrepancy between calculation and experiment has very limited impact on subsequent ORBIT calculations. Since magnetic probes are located on the vacuum vessel, they cannot measure the absolute mode amplitude of core-localized mode. Herein, we just set the mode amplitude of LLM to be 65 Gs, which is about two times the measured value in figure 10. The factor of 2 is used in the ORBIT simulation here because the mode amplitude of core-localized mode is much higher than the measured value with the edge magnetic probes. Beside the perturbation displacement structure of LLM mode calculated with MARS-K, the ORBIT calculations take the energetic ion distribution calculated with NUBEAM as an input parameter. It should be noted that, unlike the distribution maps of lost ions measured with the FILP, the lost energetic ion in the ORBIT calculations is defined as the energetic ion whose guiding-center can cross the last closed flux surface in 5 ms. The distribution map of lost energetic ions in the pitch-angle vs. energy plane calculated with the ORBIT code is depicted in figure 14(b). The ORBIT calculation here has simulated 500 thousand particle markers. Figure 14(b) shows that lost energetic ions with relatively low energy (E < 20 keV) and high pitch angle (θ ∼ 62 • ) are more likely to be expelled during LLM mode. Conversely, lost energetic ions with relatively high energy (E > 20 keV) and low pitch angle (θ < 60 • ) are negligible. Hence, the calculation results are in qualitative agreement with the measurement results, i.e. the experimental observations that LLM tends to expel energetic ions with relatively low energy and high pitch angle are reproduced by the theoretical calculations.
In addition, the dependence of the energetic ion loss rate on the magnetic perturbation amplitude caused by LLM can be obtained from calculations with the ORBIT code, as shown in figure 15. The ORBIT calculations here have simulated 70 thousand particle markers for each magnetic perturbation amplitude. Figure 15 shows that the energetic ion loss rate increases with the magnetic perturbation amplitude linearly, and the intercept of the fitting line (the red solid line) is about Figure 15. Dependence of energetic ion loss rate on magnetic perturbation amplitude caused by LLM. The energetic ion loss rate increases with the magnetic perturbation amplitude linearly, and no threshold perturbation amplitude for energetic ion loss exists.
1.5%, indicating that no threshold perturbation amplitude exists for LLM induced energetic ion losses. The calculation result has the same linear relation as the experimental result shown in figure 10 which shows that the mechanism for LLM induced energetic ion loss is dominantly convective. However, there is a quite large difference (∼5 times) between the measured drop of the neutron rate during LLM and the fast ion loss rate calculated by the ORBIT code. There are mainly two aspects of factors for causing the difference. One is that the redistribution of energetic ions is also a significant effect in LLM active plasma in addition to ion loss, which has also been observed in the spherical-torus device [21]. Hence, the measured drop of the neutron rate includes the contribution of the redistribution of energetic ions. The other is that the ORBIT calculations take the NUBEAM calculation results, which considered the moderated energetic ions, as an input parameter. Notably, the initial beam-born ions suffering prompt loss was not considered in the NUBEAM calculation results. Thus, the fast ion loss rate calculated by the ORBIT code is underestimated, since the ORBIT calculations did not consider the prompt loss of initial beam-born ions.

Summary
Energetic ion losses induced by LLM have been measured and investigated in the HL-2A tokamak by means of energetic particle diagnostics, including the NFM systems, the solidstate NPA and the FILP. Measurements show that LLM, sawtooth and minor disruption can lead to varying degrees of energetic ion losses.
Neutron emission calculation has been performed by using the FBURN code with input parameters without considering MHD induced energetic ion losses. Calculated neutron emission profiles show that the energetic ion losses in the MHD active phase mainly occur within the normalized radius of 0.4. The deviation between the neutron emission evolution curves obtained from calculation and experiment illustrates that energetic ion losses are induced by LLM and/or sawtooth. Dependence of the drop rate of total neutron emission rate on LLM amplitude shows that the energetic ion loss rate linearly increases with perturbation amplitude and no threshold amplitude exists in the relation which is verified by the later calculation with the ORBIT code. Hence, the loss mechanism for LLM induced energetic ion loss is dominantly convective.
It is observed with the FILP system that the energetic ion loss induced by LLM is a mild process that has an ion loss rate of 13% of that of the prompt loss. On the one hand, LLM tends to expel energetic ions with relatively low energy (E < 27 keV) and high pitch angle (θ > 60 • ) rather than other cases. On the other hand, LLM can partially suppress the prompt loss of energetic ions with high energy and low pitch angle, indicating that the redistribution of energetic ions and even plasma current may occur with the presence of LLM. The orbit calculations for energetic ions in a magnetic field not only satisfactorily explain the physical process of energetic ion loss induced by LLM, but also show that the lost energetic ions will transport from the plasma center to the peripheral region first, and then get lost out of plasma. In addition, the experimental observations for LLM induced energetic ion losses are also reproduced by theoretical calculations.