Various edge low-frequency fluctuations during transition to a detached divertor in Experimental Advanced Superconducting Tokamak

Various edge low-frequency fluctuations with distinct characteristics exist in different detached divertor states. Three edge low-frequency fluctuations ( f< 10 kHz), namely low-frequency quasi-coherent fluctuation (LFCF), low-frequency broadband frequency fluctuation (LFBF), and low-n X-point mode (LNXM) on Experimental Advanced Superconducting Tokamak (EAST), are systematically assessed. The basic features of these fluctuations, such as spectral width, location, mode number, propagating direction, and particle transport capacities, are examined. LFCF occurs when the inner strike point is energy detached or nearly energy detached with Tet,inner∼ 8–15 eV ( Tet,inner is the electron temperature of the inner strike point), and a large electron temperature gap between the inner and outer strike points $?> with ΔTet> 25 eV ( ΔTet is the electron temperature gap between the inner and outer strike points) is essential for the occurrence of LFCF. By contrast, LFBF occurs when the inner strike point is energy detached with Tet,inner< 8 eV, while the outer strike point is nearly energy detached or attached. The ΔTet of LFBF is generally lower than that of LFCF, which is < 25 eV. LNXM is related only to the radiative divertor with impurity seeding and considered to be excited by the geodesic acoustic mode proposed in earlier work (Sun 2021 Nucl. Fusion 61 014002; Diallo 2020 28th IAEA Fusion Energy Conf.), or the coupling of impurity radiation condensation instability and drift waves proposed in a previous work (Ye 2021 Nucl. Fusion 61 116032). In addition, the possible physical mechanisms of LFBF and LFCF are proposed, with LFBF being the purely growing rippling mode and LFCF being the mode formed by the coupling of the rippling mode to the drift waves. Related research may be beneficial to better clarify the various low-frequency fluctuations that occur during different divertor states.


Introduction
A major challenge for future fusion reactors, such as the International Thermonuclear Experimental Reactor (ITER), is to avoid damaging erosion on the divertor material due to massive transient and steady-state heat/particle fluxes [1,2]. Divertor detachment operation [3], which is characterized by low heat/particle fluxes toward targets, is a highly promising method for achieving tolerable steady-state heat/particle fluxes to divertor targets [4][5][6]. Over the past few decades, extensive experiments have been performed on divertor detachment on mainstream tokamak devices, such as Doublet III D-shaped cross section (DIII-D) [6][7][8][9], Axially Symmetric Divertor Experiment Upgrade (AUG) [10,11], Compact Assembly (COMPASS) [12], Joint European Torus (JET) [13][14][15], and Experimental Advanced Superconducting Tokamak (EAST) [16,17]. Of note, in these devices, some low-frequency fluctuations are typically observed in the edge region during the detached state, and the properties of these fluctuations tend to differ considerably.
In DIII-D, low-frequency quasi-coherent fluctuation (LFCF), which occurs at approximately 3 kHz, appears when the inner strike point nearly detaches, but the outer strike point remains attached. Subsequently, with detachment of the outer strike point, LFCF fades. Similarly, low-frequency broadband fluctuation (LFBF), which occurs at approximately 5 kHz, has been detected in AUG [10] and COMPASS [12] when the inner strike point is detached and the outer strike point remains attached. As the outer strike point detaches, LFBF disappears. Both LFCF and LFBF occur at frequencies less than 10 kHz and are strongly associated with detachment. Additionally, both LFCF and LFBF are considered as current convective instability (CCI) [18][19][20]; however, they differ substantially in terms of some basic features, including spectral width and toroidal and poloidal structures. The spectral width of LFCF is approximately 1 kHz, whereas that of LFBF is about 3 kHz. The ratio of LFCF spectral width ∆f to its frequency f is about 30%, whereas that for LFBF is about 60%. In addition, LFCF is strongly localized in the inner target region and associated with the finite toroidal mode number n = 1, whereas LFBF is toroidally symmetric (n = 0) and not localized in the poloidal space. Furthermore, in DIII-D, LFCF occurs when the inner strike point nearly detaches (T et,inner ∼ 10 eV, where T et,inner is the electron temperature of the inner strike point). In AUG, LFBF occurs when the inner strike point is pronounced detached (T et,inner < 5 eV).
For the first time, we observed the aforementioned two modes at the same discharge with ramping up of bulk plasma density in EAST. In addition to LFCF and LFBF, a lown X-point mode (LNXM) has been observed with the low-Z impurity (such as deuterated methane (CD 4 ) and boron) seeding experiment in EAST [21,22]. The mode is closely related to the impurity concentration. In the present study, three low-frequency modes are distinguished and classified comprehensively in EAST. Additionally, the parameter space and physical mechanism of the three modes are assessed.
Detachment is typically defined by the loss of heat flux and particle flux along the field lines from upstream down to the target [3,23]. In recent years, to better understand the evolution of the detachment process, particle detachment with rollover of particle flux [3] and energy detachment with T et < 10 eV [3,[24][25][26] are introduced. In this work, the three modes are more closely related to the temperature, and we pay more attention to the change of temperature; therefore, energy detachment with T et < 10 eV is applied to describe the detachment process.
This paper is organized into five sections. Section 2 provides a brief introduction of the experimental setup in EAST. The detailed experimental observations on the characteristics and transitions of the modes are presented in section 3. A theoretical model of the nature of LFCF and LFBF is given in section 4. Finally, section 5 concludes with a discussion and summary.

Experimental setup
EAST is a fully superconducting tokamak with major and minor radii of R 0 = 1.88 m and a = 0.45 m, respectively, aimed at demonstrating high-power long-pulse operation. The designed plasma current I p is up to 1 MA, and the toroidal magnetic field B t is up to 3.5 T. A flexible poloidal field is designed for achieving lower single null, double null, and upper single null (USN) during a long-pulse discharge. Moreover, EAST has been equipped in ITER-like global plasma electronic heating systems, including lower hybrid wave (LHW) heating [27], electron cyclotron resonance heating (ECRH) [28], ion cyclotron resonance heating (ICRH) [29], and neutral beam injecting (NBI) heating [30]. The sum of P LHW , P ECRH , P ICRH , and P NBI represents the total source power P total , which is up to 8 MW in the present study.
In this study, LFCF, LFBF, and LNXM are assessed under USN divertor configurations with favorable B t (B × ∇B ↑) during the plasma current flattop phase. Figure 1 displays the key diagnostics used in this study. The radiation power was measured using 64-channel absolute extreme ultraviolet (AXUV) arrays [31], and the D α emission intensity was measured by a filter-scope spectral diagnosis [32]. The magnetic fluctuations were measured by fast Mirnov coils mounted on the first wall [33]. The electron temperatures on the divertor target plates were measured by the divertor triple Langmuir probe (Div-LP, 26 sets) [34]. Notably, the electron temperature measured by the divertor triple Langmuir probe is typically higher than that measured by the single and double Langmuir probes [35]. The impurity line emission intensity was measured using the extreme ultraviolet spectrometers [36].  Figure 2 displays a typical H-mode discharge, including the evolution of LFCF and LNXM with CD 4 seeding from the upper divertor near the outer strike point. The plasma with I p ∼ 450 kA, B t ∼ 2.4 T, and q 95 ∼ 5.8 is heated by a total source power of about 2-8 MW. The plasma stored energy W MHD is about 150-230 kJ, and the normalized density f GW is about 0.45-0.68. The plasma current ramps up to its flattop phase, the L-H transition occurs at about 2.1 s in this shot, and the temperature of the inner strike point reaches its peak value. The plasma density is increasing at 2.1-2.5 s caused by the L-H transition. Due to the increase of the heating power at 2.5 s (ECRH is added at 2.5 s), the confinement and plasma density increase at 2.5-2.7 s. At 2.7-2.8 s, the fueling rate of D 2 in the outer midplane, as shown by the blue line in figure 2(a), is decreasing, and the plasma density decreases as well. The gas puffing of D 2 is turned off at 2.8 s; subsequently, J s of the outer and inner strike points decreases at 2.95 and 3 s, respectively. At 3 s, the electron temperature of the inner strike point is roughly constant, as low as about 10 eV, suggesting that the inner strike point is nearly energy detached. However, the outer target is attached with a high strike point temperature (T et,outer ) of about 55 eV at 3-4.5 s, as displayed in figure 2(d). LFCF occurs and grows gradually with a frequency of approximately 3 kHz when the inner strike point is nearly energy detached and the outer strike point temperature remains at a high level, Figure 2. Evolution of (a) carbon 6+ line emission intensity (black), D 2 (blue), and CD 4 (magenta) gas valve voltage; (b) central-line-averaged electron density normalized by Greenwald density; (c) plasma stored energy (black) and total source heating power (magenta); (d) target electron temperature near the inner (blue) and outer (red) strike points measured by the Div-LP; (e) ion saturation current density near the inner (blue) and outer (red) strike points measured by Div-LP; and ( f ) power spectra measured by AXUV (channel 57). as illustrated in figure 2(f ). At around 4 s, the LFCF amplitude enhances significantly, and two harmonics with frequencies of 7 and 10 kHz occur. Another low-frequency mode (∼1.5 kHz) that appears at 4 s is the core magnetohydrodynamic (MHD) instability. At 4.6 s, the electron temperature near the outer strike point decreases significantly (T et,outer drops from 55 to 26 eV) due to CD 4 seeding, and the inner strike point temperature decreases slightly (T et,inner drops from 10 to 8 eV). The large temperature gap between the inner and outer strike points disappears (∆T et drops from 45 eV to only 18 eV), and LFCF disappears immediately at t = 4.6 s. Despite the increase in the heating power at 5 s, the impurity concentration increases rapidly due to continuous CD 4 seeding. Therefore, the target temperature does not rise with the increase in heating power, but it decreases gradually with the increase in the impurity concentration. With the continuous accumulation of impurities and the decrease in the electron temperature of the outer strike point, another low-frequency mode named LNXM with a frequency of approximately 5.5 kHz appears at 6.2 s. Numerous experiments and simulation studies of LNXM have been conducted on EAST. LNXM triggered by real-time boron power injection was first reported by Sun et al [21], who claimed that LNXM is a geodesic acoustic mode (GAM)-like mode caused by the poloidal charge asymmetry [37]. This mode can be triggered by CD 4 (or other low-Z impurities) seeding, as reported by Ye et al [22], who revealed that the mode is closely related to the impurity concentration and the local electron temperature. Furthermore, they speculated that the coupling of radiation condensation instability and drift wave is the driving mechanism of LNXM. Figure 3 shows a typical discharge, including LFCF and LFBF evolution through the ramping up of bulk plasma density. The basic plasma parameters I p , B t , q 95 , and P total are 450 kA, 2.45 T, 6.3, and 5 MW, respectively. Similarly, LFCF (∼1.3 kHz) and its harmonic (∼2.6 kHz) appear when the inner strike point is nearly energy detached with T et,inner ∼ 10 eV, and the outer strike point temperature remains at a high level (T et,outer ∼ 50 eV). After 3 s, LFCF and its harmonics weaken gradually and finally disappear at 3.5 s. As the plasma density f GW ramps up to 0.5 at t = 5.2 s, the temperature of the inner strike point drops to less than 5 eV, and the outer strike point is nearly energy detached with T et,outer ∼ 12 eV, as shown in figure 3(c). LFBF appears at a frequency of about 4.2 kHz, as shown in figure 3(e). The ratio of LFBF spectral width ∆f (3 kHz) to its frequency f is about 70%, which is significantly higher than that of LFCF (∼25%). Finally, as the plasma density f GW ramps up to 0.68 at t = 7.8 s, the stored energy and the temperature of the outer strike point decrease, and LFBF disappears.

LFCF and LFBF.
The aforementioned modes are in the similar frequency space, that is, at the frequency lower than 10 kHz. Therefore, the location, mode number, propagating direction, and influence on particle flux in the divertor target of these modes should be studied to obtain a superior distinction.

Location difference.
The poloidal location of the three modes can be obtained by comparing their magnetic fluctuation amplitude at poloidally distributed Mirnov coils shown by the red circles in figure 4(a). The relative amplitudes of the modes from the Mirnov coils are estimated as follows: where f lower to f upper represent the frequency bandwidth of the three modes, S a ( f ) represents the auto-power spectra during the mode excitation period, and S base a ( f ) represents the baseline level of the modes. Finally, the mode amplitudes calculated with different poloidally distributed Mirnov coils are normalized as follows: As shown in figure 4(b), the magnetic fluctuation amplitude of LFCF peaks at channel 5, which is located near the upper inner strike point. Moreover, this phenomenon is confirmed by Div-LP and D α diagnostics. The spikes of LFCF can be detected only by Div-LP near the inner strike point and D α emission channel passing through the inner strike point, but they do not exist in the upper outer divertor or other core diagnostics. Therefore, LFCF is highly localized to the inner strike point, which is similar to LFCF observed in DIII-D [9]. Unlike LFCF, the magnetic fluctuations of LFBF can be observed in the whole poloidal space, as shown in figure 4(c), which is consistent with those of LFBF observed in COMPASS [12]. Of note, the LFBF amplitude of channel 17 around the lower inner target is significantly larger than that of the other channels, as shown in figure 4(c). This phenomenon could be related to the large gap of the effective ion charge between the inner and outer divertors under a graphite lower divertor, which is discussed in section 5. LNXM can be clearly observed by 57-59 channels of AXUV in EAST shot #93373, which is near the X-point. To better exhibit the poloidal distribution of LNXM, we illustrate shot #91660 in the same round of CD 4 injection experiments with more CD 4 injection and thus stronger LNXM, as shown in figures 4(d) and 5(c). Figure 4(d) shows that the magnetic fluctuation amplitude of LNXM peaks at channel 8 (near the upper X-point), and the amplitude of LNXM at other channels is relatively low. This trend differs from that of LFBF. Figure 5 shows the mode number of the three modes calculated by the Mirnov coils. The toroidal mode number is shown in the left column, indicating that both LFCF and LNXM exhibit finite low toroidal mode number characteristics (n = 1 and 0 ⩽ n ⩽ 1, respectively). The toroidal structure of LFCF in EAST is consistent with that in DIII-D [9]. By contrast, the toroidal mode number of LFBF is 0, as shown in figure 5(b), consistent with that of LFBF in COMPASS [12]. The right column shows only the poloidal mode number of LFBF. This is because LFCF is highly localized in the poloidal direction, making it difficult to judge its propagation direction at present. The poloidal mode number m of LFBF obtained with the poloidally distributed Mirnov coils is −2, as shown in figure 5(d). The negative value of m suggests that LFBF propagates in a counterclockwise direction. Figure 5(e) depicts the poloidal magnetic perturbations calculated by a narrow filter with 3.78-3.8 kHz, which further reveals that LFBF propagates in the counterclockwise direction, as shown by the red dashed arrow in figure 5(e). The toroidal magnetic field of this shot is in the counterclockwise direction in the top view, indicating that LFBF propagates in the ion diamagnetic direction (IDD). Unlike LFBF, LNXM propagates in the electron diamagnetic direction (EDD), as demonstrated in [22].

3.2.3.
Influence of the three modes on particle flux in the divertor target. As shown in figure 6(a), LFCF with a basic frequency of about 3 kHz can be observed in the power spectrum of floating potential V f of the inner strike point, and a spike of about 3 kHz can also be seen from the ion saturation current density J s , as shown by the black line in figure 6(b). The spikes disappear as the LFCF vanishes, as shown in figure 6(c), suggesting that the spikes shown in J s are associated with LFCFs. To isolate the LFCF spikes in 4.4-4.5 s, we first determine all values of LFCF spike J s,spike and the corresponding time point t spike of each spike, as shown by the red circles in figure 6(b), and then find the baseline value J s,baseline in the time window: [t spike − 1/2f LFCF , t spike + 1/2f LFCF ], shown by the blue boxes in figure 6(b). Therefore, the averaged J s,spike corresponds to the fluctuation resulting from the LFCF, and the averaged J s,baseline corresponds to the background J s . The poloidal distributions of J s,spike (red) and J s,baseline (blue) are calculated, as shown in figure 6(c). The J s,spike in the scrape-off-layer (SOL) region about 6 cm from the strike point is two times higher than the J s,baseline , implying that the mode could result in an enhancement of the particle flux near the inner strike point. Note that the J s profile exhibits a double-peak structure, with a second peak nearly 8 cm away from the inner strike point, which is consistent with that of the double-peak structure that is likely to be seen in the inner divertor target with favorable B t direction in EAST [38].
For the LFBF transport, it is difficult to extract the LFBF spikes like LFCF for two reasons: (a) the frequency of LFBF is not constant due to the wide spectrum characteristics of LFBF.  (b) LFCF exists in inter or no edge localized mode (ELM) phase, while LFBF can usually coexist with high-frequency ELMs, which will make it more different to extract LFBF spikes. Therefore, another method is used here to study the LFBF transport, i.e. the transport of LFBF can be studied from divertor particle deposition. The influence of LFBF on the particle flux in the divertor target can be studied from the divertor particle deposition. The particle flux deposited in the divertor targets can be calculated from the following equation: Figure 7. Evolution of (a) plasma stored energy (black) and plasma βp (blue), (b) central-line-averaged electron density normalized by Greenwald density (black) and the global recycling coefficient (blue), (c) target electron temperature near the inner (blue) and outer (red) strike points measured by Div-LP, (d) auto-power spectra of radiation power fluctuations measured by AXUV (channel 57), and (e) total particle deposition on divertor plates (black) and its averaged value (red). (f ) Statistics of normalized total flux on the divertor target plates vs the LFBF amplitude.
where l is the poloidal coordinate along the divertor plate, R div is the major radius of the divertor probe, J s (R div ,l) is the ion saturation current density, θ is the angle between the magnetic field and the divertor target plane, and e is the elementary charge. The total particle flux deposited in divertor targets can then be evaluated by the following equation: where Γ t,UI , Γ t,UO , Γ t,LI , and Γ t,LO are particle flux deposited at the target of upper inner, upper outer, lower inner, and lower outer, respectively. To eliminate the influence of confinement and plasma density on target particle flux, shot #79362 without significant change of confinement (as shown by the black and blue line in figure 7(a)) and density (as shown by the black line in figure 7(b)) is shown to illustrate the influence of LFBF on particle flux deposited in the divertor target. As shown in figure 7, LFBF appears when T et,inner is below 10 eV and T et,outer is about 12-15 eV in 2.7-5.5 s. The LFBF amplitude has increased at 3.9 s, which may be caused by the increase of temperature gap (T et,inner decreases and T et,outer increases) between the inner and outer targets, and the temperature change of the inner and outer targets may be caused by the slight movement of the strike point. However, it is puzzling that the LFBF amplitude changes from strong to weak in 2.75-3.8 s. There should be other driving or damping terms, such as effective ion charge Z eff gradient, parallel current, and parallel thermal conductivity (which will be introduced in section 4), to change the mode amplitude, while currently there are no relevant diagnostics to measure these parameters near the upper divertor in EAST. The black line in figure 7(e) shows the total particle flux deposited in the divertor target, clearly exhibiting that the baseline (red line) of Γ total increases with the presence of LFBF. Of note, the baseline defined here is the averaged value of the total particle flux J s,total in 3-6.3 s, which is different from the J s,baseline mentioned earlier. (J s,baseline represents the averaged value of the inner particle flux J s,inner that filters out the LFCF spikes in 4.4-4.5 s.) There are two possible mechanisms for the increase in the total particle flux: increase in global recycling level and the parallel transport of LFBF. As shown by the blue line in figure 7(b), the global recycling coefficient R global [39] that we calculated by using the global particle balance model has a very slight increase, about 2% in 3-5 s (from 0.78 to 0.80), which is lower than the increase in the total particle flux, about 39% (from 1.14 to 1.58 × 10 24 s −1 ). In quantitative terms, the increase in recycling level does not seem to fully explain the rise in total particle flux; therefore, the transport of LFBF may also contribute to the increase in particle flux. Figure 7(f ) shows statistics of total particle flux normalized by the central-line-averaged electron density vs the mode amplitude measured by the AXUV (channel 57) over 12 shots. These shots are chosen from the same day with similar discharge parameters. It can be seen that the total particle flux appears to increase with the mode amplitude, which implies that the LFBF transport has a certain contribution to the increase in total flux deposited in the divertor target. As for the Ne injection at 5.5 s, T et,inner increases to about 11 eV, T et,outer decreases to about 8 eV, and LFBF disappears. For LNXM, a proportional relationship exists between the total flux of the upper outer target and the mode amplitude, as demonstrated in [22], suggesting that LNXM can enhance the particle flux of the divertor target. In addition, LNXM also produces net transport and drives particles out from the core into the boundary to prevent impurity accumulation, as shown in [21], which led the authors to consider that LNXM can drive some particle transport near the X-point. 3.2.4. Parameter space of the three modes. As evidenced by the aforementioned typical discharges, the evolution of these modes appears to be closely related to the electron temperature in the divertor region. To further explore the temperature space of these modes, about 50 shots are counted as the database to statistically analyze the parameter space of the three modes. The plasma parameters in the datasets include different plasma currents (I p : 400-500 kA; q 95 : 4.7-6.5), different absorbed heating power schemes (absorbed power: 0.7-4.2 MW), different plasma configurations (USN, upper triangularity: 0.47-0.58; elongation: 1.57-1.66), and different plasma confinement states (L-and H-modes). As shown in figure 8(a), the inner strike point temperature space of LFBF (blue circles) is the lowest, and the appropriate range is T et,inner ⩽ 8 eV, which is the typical electron temperature range of energy detachment (T et,inner ⩽ 10 eV) in EAST [25,26]. By contrast, LNXM (green circles) can be excited at a high electron temperature of the inner strike point T et,inner ∼ 15 eV, suggesting that the energy detached inner target (T et,inner < 10 eV) is not essential for the generation of LNXM. For LFCF (red circles), the temperature ranges of both the inner and outer strike points are higher than those Parameter space of f GW and P total,abs for LFCF, LFBF, and LNXM in different confinement states (L-and H-mode). P total,abs is the absorbed auxiliary heating power.
for LFBF, which are T et,inner ∼ 8-15 eV and T et,outer ⩾ 35 eV, respectively. Further exploration reveals that an obvious proportional relationship exists between the LFCF amplitude and the temperature gap between the inner and outer strike points, as shown in figure 8(b). This characteristic is unique to LFCF and not observed in the other two modes. Figure 9 shows the dependence of the three modes on density and the absorbed auxiliary heating power. The present study distinguishes the difference between the three modes in L-and H-modes. In L-mode, the density limit for the appearance of LFCF is f GW ⩽ 0.4, as shown by the yellow circle, whereas that in H-mode is f GW ⩽ 0.55, as shown by the blue circle. For LFBF identified by the triangle, the required density is higher than that for LFCF under similar heating power level, irrespective of the L-or H-mode. This result is consistent with the lower electron temperature space of LFBF, as shown in figure 8. LNXM appears at high heating absorbed power due to the fact that LNXM can be observed only in the H-mode [22], and it exists in a wide range of f GW , that is, 0.45 ⩽ f GW ⩽ 0.8.

Theoretical model of LFCF and LFBF
Both LFCF in DIII-D and LFBF in COMPASS and AUG are considered to be CCI [18][19][20], which is also called the 'rippling mode' [40][41][42]. The linear growth rate of the rippling mode can be expressed as: [42]. Here, j ∥ is the parallel current; η ′ is the resistivity gradient; k ⊥ and k ∥ are the perpendicular and parallel wave numbers, respectively; B is the magnetic field; and κ ∥ is the parallel thermal conductivity. According to the growth rate expression of the rippling mode, this mode can be driven by the resistivity gradient that arises from the temperature or effective ion charge Z eff gradient in the edge of the tokamak plasma. This mode can couple to the drift wave because of the cross-field electron temperature gradient [40,43]. According to the theoretical model developed in [42], as the electron temperature increases, the unstable mode transitions from the purely growing rippling mode to the drift-rippling mode and finally to the dissipative drift mode. At a sufficiently low temperature, the purely growing rippling mode can be obtained by neglecting parallel pressure, and the purely growing rippling mode predicted by the theoretical model corresponds to LFBF experimentally. At a higher temperature, the drift-rippling mode can be obtained by introducing pressure perturbation. The drift-rippling mode corresponds to LFCF at higher temperature. At even higher temperature, the parallel thermal conduction becomes critical, and the rippling mode evolves into the temperature gradientmodified dissipative drift mode.
The numerical study reveals that the LFBF and LFCF parameter space can be divided by the normalized collisionality Here, the plasma density near the detached divertor target is measured by the Div-LP, which is slightly lower than the upstream separatrix density that is measured by microwave reflectometry [45]. As shown in figures 10(a) and (b), before the ion flux density rolls over, the electron density of the inner strike point measured by Div-LP is about 1.7 × 10 19 m −3 , as shown by the blue box in figure 10(b) at 3 s, which is about three times higher than that of the upstream separatrix (about 0.55 × 10 19 m −3 at the high-field side) measured by microwave reflectometry. After the ion flux density rolls over, the electron density near the inner strike point is about 1 × 10 19 m −3 , as shown by the red circle in figure 10(b), and the upstream separatrix density is about 1.25 × 10 19 m −3 . The decrease in electron density near the inner strike point may be caused by the decrease in ion flux density after the particle detachment. The peak particle flux is away from the strike point and moves to the far SOL after particle detachment [46], and the high-density region also moves to the far SOL. The numerical simulation results are shown in figure 11. When the electron temperature of the inner strike point T et,inner is lower than 4 eV, the corresponding normalized parallel current is in 3 * , which is in the unstable region of LFBF. However, when T et,inner is greater than 4 eV and lower than 8 eV, that is, 4 eV< T et,inner < 8 eV, the corresponding normalized parallel current is in the range C −1 * < J * < C − 3 4 * , which is in the unstable region of LFCF.
The electron temperature range of LFBF observed in the experiment, shown in figure 8, is T et,inner < 8 eV, and the electron temperature range of LFCF is slightly higher than that of LFBF, that is, 8 eV < T et,inner < 15 eV. The temperature range of LFCF predicted by the model is also higher than that of LFBF, which is qualitatively consistent with the experimental results. Nevertheless, quantitatively, the electron temperature ranges of LFBF and LFCF predicted by the model are not completely consistent with the experimental results. The inconsistency may be attributed to the inaccurate triple Langmuir probe measurement. Existing studies have revealed that the electron temperature measured by the divertor triple Langmuir probe is typically about a factor of 2 higher than that measured by the single and double Langmuir probes [35]. Therefore, the inner strike point temperature ranges of LFBF and LFCF may be T et,inner < 4 eV and 4 eV < T et,inner < 7.5 eV, respectively, indicating that the temperature spaces of LFCF and LFBF predicted by the model are in agreement with experimental statistics. This is also the first time to verify the correctness of this model in an experiment. Therefore, this model was developed in [42], and the novelty here is its validation with experimental data. Notably, this model does not include the physical mechanism of LNXM. Previous studies have indicated that LNXM may be the GAM [21,37] or the coupling of radiation condensation instability and drift wave [22].

Discussion and summary
As mentioned in section 3.2, the LFBF amplitude around the lower inner target is significantly larger than that around the other poloidal channels, and this phenomenon is widely observed under the lower carbon divertor (upper tungsten divertor). However, under the upgraded lower tungsten divertor with a new geometry [47], as shown in figure 12(d), the phenomenon was not observed. The significant difference in the poloidal distribution of LFBF may be attributed to the difference in the effective ion charge gradient between the inner and outer divertors under different divertor materials and geometries. Figure 12(a) shows that the CIII emission intensity passing through the outer divertor is stronger than  that passing through the inner divertor under the lower carbon divertor. At t = 5.2 s, LFBF appears (shown in figure 3(e)) as the CIII emission intensity passing through the outer divertor increases significantly. The strong in-out asymmetry of carbon impurities may result in the large ion effective ion charge gradient between the inner and outer divertors in the lower divertor areas, which remarkably increases the growth rate of the rippling mode. Therefore, an extremely strong LFBF amplitude exists near the lower inner target under the lower carbon divertor. The CIII emission exhibits considerable inout asymmetry under the lower carbon divertor, in addition to other impurities, such as lithium and oxygen, suggesting that the strong in-out asymmetry of impurities may not only be attributed to the different divertor materials but also to the different divertor geometries. However, after upgrading the full tungsten divertor with the new geometry in 2021 for EAST, the difference in CIII emission between the inner and outer divertors becomes almost negligible, as shown in figure 12(c), and the poloidal difference in the LFBF amplitude no longer exists, as shown in figure 13(b).
In summary, three edge low-frequency fluctuations, namely LFCF, LFBF, and LNXM, related to divertor detachment are observed in EAST. The present study is the first to systematically assess these three modes in the same tokamak device. Table 1 shows the main characteristics of these modes. The key findings are summarized as follows: Electromagnetic Electromagnetic Electromagnetic Influence on the particle flux in the divertor target Enhance the particle flux near the inner strike point Enhance the total particle flux in the divertor target Enhance the particle flux in the divertor target caused by the strong particle transport Driving mechanism Coupling of rippling mode and drift wave Purely growing rippling mode GAM/coupling of radiation condensation instability and drift wave (a) LFCF with the toroidal mode number n = 1 can be observed in L-and H-mode plasmas through impurity seeding or ramping up of plasma density. LFCF occurs with a low electron temperature near the inner strike point and a large temperature gap between the inner and outer strike points. LFCF, along with its harmonics, is localized in the inner target region, which can enhance the particle flux of the inner target. These observations of LFCF in EAST are consistent with the quasi-coherent fluctuation reported on DIII-D. The mechanism of LFCF is considered to be the coupling of the rippling mode to drift wave, and it is excited only under relatively low electron temperature conditions (8 eV < T et,inner < 15 eV). (b) LFBF with the toroidal mode number n = 0 and the poloidal mode number m = 2 can be observed in L-and Hmode plasmas in EAST. LFBF exists in the whole poloidal direction, and the mode propagates in the IDD. The total particle flux in the divertor target can be enhanced by LFBF. LFBF occurs when the inner strike point is detached and the outer strike point is nearly energy detached or attached, which is consistent with the observation in COMPASS and AUG. LFBF is the purely growing rippling mode and is excited only under sufficiently low electron temperature conditions (T et,inner < 8 eV). (c) LNXM with the toroidal mode number n ⩽ 1 can be observed only in the H-mode plasma with impurity seeding experiments in EAST. This mode, with strong particle transport capabilities, occurs when the impurity concentration exceeds the threshold and is manifested by the oscillations of a radiation front near the X-point. LNXM is considered to be the GAM-relevant mode proposed by Sun et al and Diallo et al [21,37], whereas Ye et al [22] considered it as the coupling of radiative condensation instability and drift wave.