Matrix effect suppressing in the element analysis of soils by laser-induced breakdown spectroscopy with acoustic correction

1.   Introduction

The high confinement mode (H-mode) has been observed in different types of magnetic confinement fusion devices since it was first discovered in ASDEX device in 1982 [1]. In H-mode operation, the plasma confinement performance is significantly improved compared with the low confinement mode (L-mode) performance. In H-mode, it is commonly observed that the plasma pressure in the pedestal region undergoes quasi-periodic collapse and subsequent reconstruction, a phenomenon referred to as edge localized mode (ELM) [2]. The eruption of ELM will cause the collapse of the boundary transport barrier and cause large amounts of particles and energy fluxes onto the plasma-facing components (PFCs) and the target plates of the divertor. The instantaneously increased heat load poses a significant threat to the safety and life of the material. Therefore, research focused on ELM physics and the development of effective control methods for ELMs is a current area of interest in tokamak research [3–6].

In order to study ELM properties, a variety of diagnostics have been successfully applied on several tokamaks, such as MAST [7], ASDEX Upgrade [8, 9], DIII-D [10], KSTAR [11, 12] and JET [13]. The development of diagnostic technology has led to the creation of vacuum ultraviolet (VUV) telescope diagnostic for edge plasma studies, initially implemented on the Large Helical Device (LHD) [14]. In recent years, a high-speed vacuum ultraviolet imaging (VUVI) diagnostic system has been developed on EAST. The system selectively measures impurity radiation with a center wavelength of 13.5 nm. Under the existing H-mode discharge conditions, the radiation mainly comes from pedestal region [15]. The signals generated by the VUVI system are highly responsive to fluctuations in both electron density and impurity density. Utilizing this diagnostic, successful observation of filament structures produced by ELM bursts during H-mode discharge on EAST was achieved, and a number of experimental results were derived using this diagnostic [16–19].

In this paper, analyses of the one-dimensional (1D) and two-dimensional (2D) signals of the filaments captured by the high-speed VUVI system during type-I ELMs are presented. Section 2 introduces the basic experimental conditions on EAST and related diagnostics to analyzing. Sections 3 and 4 show characteristics of type-I ELM filamentary structures and the temporal characteristics of ELMs, respectively. The results and summary are described in section 5.

2.   Experimental setup

EAST is a fully superconducting tokomak with major radius ${R}_{0}$ = 1.85 m and minor radius $a$ = 0.45 m. In 2018 experiments, it was outfitted with an ITER-like tungsten upper divertor and a graphite lower divertor, respectively [20]. Experimental data obtained in ELMy H-mode discharges are selected for analysis, which are mainly heated by neutral beam injection (NBI) [21] and lower hybrid wave (LHW) [22] in an upper single null (USN) configuration. There are several important diagnostics for analysis in this work, including the VUVI system, the fast sweeping microwave reflectometry (Refl.) [23], the divertor Langmuir probe diagnostic system (DivLP) [24], the Thomson scattering diagnostic system (TS) [25], the multichannel far-infrared laser-based POlarimeter-INTerferometer (POINT) diagnostic system [26], and the tangential X-ray crystal spectrometer (TXCS) [27]. Figure 1 shows the poloidal view of the key diagnostics.

Figure  1.  A poloidal view of the vital diagnostics for analysis on EAST, which include the vacuum ultraviolet imaging (VUVI) diagnostic system, the fast sweeping microwave reflectometry (Relf.), the divertor Langmuir probe (DivLP) diagnostic system in the upper outer divertor, the Thomson scattering (TS) diagnostic system and the 11-channel POlarimeter-INTferometer (POINT).

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Refl. is used to measure the edge electron density profile with a temporal resolution of 50 $\mathrm{\mu }\mathrm{s}$. It is positioned 3 cm above the midplane in the low field side (LFS). The time history of the ion saturation current is supplied by the DivLP system. TS diagnostic system is used to measure the electron temperature (${T}_{\mathrm{e}}$) and density (${n}_{\mathrm{e}}$) profile. The 11 horizontal POINT channels are uniformly distributed from the midplane to the edge plasma region. It has been developed for current density and electron density measurements on EAST. The principle of TXCS is to collect the spectra emitted by ions in the plasma, from which information about ion temperature (${T}_{\mathrm{i}}$) and rotation velocity (${V}_{\mathrm{t}}$) can be calculated.

The ELM induced filamentary structures are obtained from the imaging data measured by the high-speed VUV imaging system. The key optics of the VUVI system consists of three parts: an inverse Schwarzschild telescope, a microchannel plate (MCP) detector and a high-speed CMOS camera. Its plasma-facing telescope is comprised of Mo/Si multilayer mirrors, which selectively detect plasma emission at a wavelength of 13.5 nm. It mainly contributed from carbon, which is one of the inherent impurities in EAST, specifically the n = 4→2 line emission [15]. Figure 2 shows the time history of basic plasma parameters of a typical H-mode discharge with a USN configuration obtained on EAST. In figures 2(a)–(e), the plasma current, line-averaged electron density, plasma stored energy, heating power and line emission intensity of ${\mathrm{D}}_{{\text{α}}}$ are shown, respectively. As shown in figure 2(f), at t = 14.1 s, ${T}_{\mathrm{e}}$, ${T}_{\mathrm{i}}$ and ${n}_{\mathrm{e}}$ are measured using TS, TXCS and POINT, respectively. The density distribution of ${\mathrm{C}}^{5+}$ is calculated using 1D impurity transport model. From the result, the peak of C VI line emission occurs in the pedestal region. Therefore, VUVI can be used to study plasma information in the pedestal region by measuring C VI line emission. Figure 3 shows the system placed in horizontal D-port of the EAST tokamak and inclined at an angle of 22.5° relative to the centerline of the D-port. The center of the detector is located at 250 mm above the midplane. Therefore, all these results are obtained under the assumption that the ELMs are confined to a narrow layer in the plasma, as the filament structures are extracted from line-integrated imaging data. During the experiment, the system generally runs at a framing rate of 20000 frames per second with a frame size of 512×320 pixels.

Figure  2.  Typical plasma waveforms in H-mode discharge on EAST: (a) plasma current ($I\mathrm{_p}$), (b) line-averaged density (${n}_{\mathrm{e}}$), (c) plasma stored energy (${W}_{\mathrm{m}\mathrm{h}\mathrm{d}}$), (d) auxiliary heating power, (e) ${\mathrm{D}}_{{\text{α}}}$ intensity, (f) the density, temperature and ${\mathrm{C}}^{5+}$ profiles at 14.1 s.

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Figure  3.  Top view of schematic layout of the VUVI system at D-port in EAST tokamak.

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3.   Characteristics of type-I ELM filamentary structures and transport

3.1   Parallel transport during ELMs

During the ELM crash, particles are ejected from the pedestal and arrive at the divertor target by parallel transport after they enter the SOL region. The time delay derived from the same ELM caused perturbations measured by the VUV camera at the outer-midplane and the ion saturation current at the outer divertor can show the characteristics on the parallel transport under different plasma conditions. As mentioned in the previous section, perturbations captured by the VUV imaging system are mainly contributed from the pedestal region. The database consists of 132 single ELM events within three H-mode shots that are used for time delay analysis, in which the divertor is not influenced by gas puffing. Figure 4 shows the plasma waveforms of a typical type-I ELMy H-mode discharge on EAST, which is one of the experimental shots. The plasma current, line-averaged electron density, plasma stored energy, heating power, line emission intensity of ${\mathrm{D}}_{{\text{α}}}$, ion saturation current, edge radiation intensity and VUVI intensity are presented from (a) to (h), respectively. In these discharges, the plasma current is about 0.45 MA, and the toroidal magnetic field is about −1.6 T. Negative magnetic field means the magnetic field is in the clockwise direction from a top view. The total heating power ranges from 2.2 MW to 4.2 MW. As the NBI is increased to 2.7 MW step-by-step, the ELM frequency increases from 95 Hz to 140 Hz as well, indicating a typical feature of type-I ELM.

Figure  4.  Typical plasma waveforms in type-I ELMy H-mode discharge on EAST: (a) plasma current, (b) line-averaged electron density, (c) plasma stored energy, (d) heating powers from NBI and LHW, (e) ${\mathrm{D}}_{{\text{α}}}$ intensity, (f) ion saturation current, (g) core radiation intensity, (h) VUVI intensity.

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The cross-correlation function is a mathematical tool utilized to quantify the degree of dependence between two sets of signals, proving particularly valuable for estimating signal delays. Its maximum value corresponds to the optimal time lag between signals, providing the time delay between two signals. In order to determine the time required for the transport of particles and heat fluxes from the midplane to the divertor target plate, we employ the time difference in the response between the VUVI signals and the ion saturation current signals measured by DivLP. on the divertor target plate. Given the similarity in signals induced by the common source of ELM, these two signals exhibit resemblance. As the systems collect and process discrete signals, we utilize discrete cross-correlation functions for data processing. Assuming the ion saturation current signal is represented as ${x}_{1}\left(t\right)$ and the VUVI signal as ${x}_{2}\left(t\right)$, the discrete cross-correlation function takes the form of equation (1),

where m represents the discrete time shift between the VUVI signal and the ion saturation current signal, M denotes the number of sampling points, and n indicates discrete data time points. When ${R}_{{x}_{1}{x}_{2}}$ reaches its maximum value, the two signals exhibit maximum similarity, and the discrete time shift m at this point corresponds to the transport time difference.

In this work, the singular value decomposition (SVD) method is employed to extract the filament structures from the imaging data [17]. Extracting the zeroth-order temporal component of filamentary structures from imaging data reveals the temporal evolution of the equilibrium component. Figure 5 illustrates the zeroth-order temporal component (open triangles) obtained by performing SVD of VUVI image data captured during an entire ELM burst within a time window of approximately 3 ms, and the ion saturation current (open cycles). Cross-correlation of the two signals is performed within each window to compute the relative delay of signals for an individual ELM burst.

Figure  5.  The VUVI and ion saturation current signals within a time window of ~ 3 ms.

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To investigate the power dependence, two heating power steps of NBI at 0.9 MW and 2.7 MW were selected, as shaded in orange in figure 4. The time delay is calculated and plotted in figure 6. Considering the particles ejected into the SOL due to the ELMs is proportional to the ELM size, the peak intensity of ion saturation current measured at the divertor is employed as an approximate of the ELM size, i.e. the higher the peak intensity of the ion saturation current, the larger the ELMs. The results indicate that, ELM size is larger under a higher heating power, and the particles expelled into the SOL region during high-size ELMs experience a faster parallel transport compared to ELMs with a smaller size. This phenomenon arises from the broader mode structures associated with ELMs with larger size, leading to the emission of plasma located closer to the core. The closer to the core of the plasma, the higher the plasma temperature. Consequently, the transport speed in the parallel direction increases. The black dashed line represents the estimated ion parallel convective transport time ${\tau }_{\parallel }$. The value of ${\tau }_{\parallel }$ is given by ${\tau }_{\parallel }={L}_{\parallel }/{C}_{\mathrm{s}}$ with the connection length ${L}_{\parallel }=2{\text{π}} qR$, between the outer midplane and the upper divertor outer target plate. ${C}_{\mathrm{s}}=\sqrt{({T}_{\mathrm{e}}^{\mathrm{p}\mathrm{e}\mathrm{d}}+{T}_{\mathrm{i}}^{\mathrm{p}\mathrm{e}\mathrm{d}})/{m}_{\mathrm{i}}}$ is the sound speed calculated for equal electron and ion pedestal temperatures, and ${m}_{\mathrm{i}}$ is the mass of ion. The value of ${T}_{\mathrm{e}}^{\mathrm{p}\mathrm{e}\mathrm{d}}$ is measured in the pedestal region during a discharge similar to one of the shots, where the electron temperature is approximately 300 eV. Under low-power conditions, data points are higher than the parallel transport time ${\tau }_{\parallel }$. Under high-power conditions, when the ELM amplitude is relatively large, the experimental results show transport times close to the parallel transport time. Additionally, the scattering of ion saturation current results at high power may be attributed to local effect of the divertor. As seen in figure 4, with increasing power, edge radiation also increases, potentially leading to increased impurity sputtering in the divertor region and thus decreasing the temperature and enhancing the recycling.

Figure  6.  Time delay between ELM signals measured by the VUV imaging system (at the midplane) and the DivLP (at the divertor) are plotted versus peak ion saturation current (i.e. ELM size).

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3.2   ELM mode structure derived from the VUV imaging data

ELM induced filamentary structures can be captured by the high-speed VUVI system in ELMy H-mode experiment. Figure 7(a) displays the extracted filament structures from the VUV imaging data. The color bar represents the amplitude of fluctuation and the stripes in the figure shows adjacent filamentary structures. Due to the limited field of view of the VUVI system on EAST, only a 256×256 pixels image is shown in this case. As previously stated, the angle between the primary optical axis of the system and the centerline of the D-port is 22.5°, so the x-axis represents the quasi-toroidal direction and the y-axis represents the poloidal direction. The black dotted lines in the figure represent the center of the filament structures, which are derived following the method discussed in reference [16]. The toroidal separation ($\Delta \varphi$) of the adjacent filaments in the toroidal direction can be determined by considering the pitch angle of the adjacent filaments. Then, the toroidal mode number $n\equiv 2{\text{π}} /\Delta \varphi$ can be estimated from the image.

Figure  7.  (a) An ELM induced fluctuation image taken by VUVI system. Black dotted lines are the center of the filament structures. White solid line is the position for toroidal asymmetry research. (b) Density profile measured at the moment preceding the ELM crash, i.e. the last measurement before an ELM crash indicating by the rise of ${\mathrm{D}}_{{{\text{α}}}}$ signal, and one fitting profile where pedestal height and top are marked.

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To investigate the pedestal height dependence of the ELM mode structure, the electron density profile measured by the Refl. at the moment preceding the ELM crash is used. It is fitted by the modified hyperbolic tangent (MTanh) function in the real space, and the density pedestal height (${n}_{\mathrm{e},\mathrm{p}\mathrm{e}\mathrm{d}}$) is indicated in the figure 7(b). It should be noted that the VUVI measurement is line integrated, which limits the accuracy of determining the spatial position of the image. However, it is assumed that the position of the filament depicted in figure 7(a) is located at the top of the density pedestal.

Figure 8 shows the dependency of estimated dominant toroidal mode number of ELMs on the pedestal height. The database comprised 24 similar H-mode plasma discharges, with pedestal densities ranging from $2.4\times {10}^{19}$ to $3.3\times {10}^{19}\;{\mathrm{m}}^{-3}$. In this analysis, the plasma current is about 0.45 MA, and the toroidal magnetic field is about −1.6 T. Due to constant toroidal magnetic field but with different plasma current values, the data is divided into two subsets: high ${q}_{95}$ and low ${q}_{95}$. The total heating power is about 3 MW, which are mainly contributed by NBI and LHW. Due to the variation in toroidal mode numbers during the eruption of ELMs, image selection was positioned at the moment just before the peak of the VUVI signal to ensure relative consistency in the selected mode at that instant. It is found that the toroidal mode ranges from 6 to 40, approximately. The ELMs are smaller and have a higher toroidal mode number at a higher density in discharges with both low and high ${q}_{95}$ values. Under high-density conditions, the most unstable toroidal mode numbers typically increase with density and collisionality, making the unstable modes more similar to ballooning modes. The toroidal mode number of the most unstable mode increases with the decrease in edge bootstrap current density. Additionally, simulation results incorporating nonlinear physical mechanisms indicate that E×B and diamagnetic drift suppress the growth rate of high-mode numbers, stabilizing the ballooning modes within a certain range [28]. Conversely, under low-density conditions, the inhibitory effect of collisions on bootstrap current diminishes, enhancing the edge bootstrap current [29].

Figure  8.  The dependence of the toroidal mode number on the edge density pedestal.

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3.3   Toroidal asymmetry observed in ELM crash

The evolution of ELMs undergoes a transition from linear to non-linear, leading to a chain of events. Upon entering the non-linear phase, the possibility of toroidal asymmetry arises. Studies on this phenomenon have been conducted on ASDEX-U [30] and DIII-D [31]. The eruption phenomenon of ELMs as a macroscopic instability can be observed in VUVI. Two images clearly show a set of temporal variation of signal intensity associated with the ELM event. Since the VUVI is placed semi-tangentially on EAST, the x-axis direction of the image is approximately in the toroidal direction of the device in real space and the y-axis is approximately in the poloidal direction, respectively. A column image is selected with the same location as white solid line of $x=200$ as shown in figure 7(a) for comparison in different ELMs. The time evolution of the extracted column images from the position within the same ELM cycle is obtained, and the grayscale values have been normalized, as depicted in figure 9. The two images depict the temporal evolution of the intensity at the same toroidal position during one ELM burst under one shot. The white solid line represents the 1D perturbation signal from VUVI. The major parameters of shot #80766 are ${I}_{\mathrm{p}}\sim0.4\;\mathrm{M}\mathrm{A}$, ${B}_{\mathrm{T}}\sim 1.58\;\mathrm{T}$, ${n}_{\mathrm{e}}\sim 3.0\times 10^{19}\;{\mathrm{m}}^{-3}$, ${q}_{95}\sim 4.3$, ${P}_{\mathrm{a}\mathrm{b}\mathrm{s}}\sim 4.0\;\mathrm{M}\mathrm{W}$.

Figure  9.  (a) The temporal evolution of the image and the 1D signal at a specific toroidal position during an ELM crash are presented, with the two peak points of the signal highlighted by red circles. (b) During another time interval of ELM crash, a single peak time point is marked by a red circle.

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In figure 9(a), two red circles indicate the presence of two peaks in the 1D signal, and correspondingly, disturbances appear twice in the images. It can be observed that the toroidal perturbation caused by ELM exhibits non-uniformity over time. Strong disturbance is only evident during the peak phase of the signal, indicating that specific toroidal position experiences relatively strong perturbation as the ELM moves outward. This corresponds to the separation of a single filamentary structure at that particular position, and possible secondary instabilities driving the radial breakup. However, in figure 9(b), the overall evolution of the signal over time exhibits a uniform change, with only one peak observed in the signal. The toroidal distribution induced by the ELM appears more uniform. This corresponds to the approximately uniform separation of multiple filamentary structures in the toroidal direction [31].

3.4   Effect of RMP on filament structures

As one of the most effective techniques to controlling ELM, RMP mitigation and suppression has been successfully achieved in multiple tokamak devices [32–34]. An in-vessel RMP system with 2×8 coils has been installed in EAST in 2014. Each coil has 4 turns, and the maximum coil current capability is 4 kA (or 16 kAt) [35]. This system can generate RMPs with toroidal mode number up to n = 4, which will be used for ELM control in ITER. The RMP spectrum can be adjusted by changing upper-lower coil phasing i.e. the toroidal phase difference between the upper and lower coils current [33].

In the ELM control experiments with RMP, the influence of RMP on filamentary structures is successfully observed using the VUVI system. ELM mitigation is investigated by scanning the phase difference between the upper and lower coils, denoted as ${\Delta \varPhi }_{\mathrm{U}\mathrm{L}}$. Figure 10 illustrates the process of RMP-induced ELM mitigation. In the shot #78730, the coil rotation frequency is f = 1 Hz with a toroidal mode number n = 2, and this rotation persisted for two cycles. Before RMP application, there are two heating power steps by NBI. With the increase in NBI power, the ELM frequency of ELMs increases, which is a typical characteristic of type-I ELM. Around 3.4 s, the ELM frequency reaches 80 Hz. Upon introducing RMP, the amplitudes of the VUVI and ${\mathrm{D}}_ {\text{α}}$ signals decreased, and the frequency increased, reaching up to 500 Hz around ${\Delta \varPhi }_{\mathrm{U}\mathrm{L}}$ ≈ 270°. The transition of ELMs occurs from type-I to type-III.

Figure  10.  Plasma waveforms before and after the introduction of RMP. (a) Plasma current, (b) line-averaged density, (c) plasma stored energy, (d) auxiliary heating power, (e) ​${\mathrm{D}}_ {\text{α}}$ radiation signal, (f) VUVI signal and RMP coil current, (g) ELM frequency and RMP coil phase.

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In order to illustrate the effect of RMP on the width of the filamentary structure, we initially specify the method of selecting the width in the image. A specific column of data along the y-axis is selected, as indicated by the vertical white dashed line in figure 11(a). Gaussian fitting is employed to process the peak portion, where the resulting full width at half maximum (FWHM) represents ${\omega }_{\mathrm{F},\mathrm{i}}$. The pitch angle θ represents the inclination between the central line of the filament and the x-axis, which has been demonstrated to align well with local magnetic field line [17]. Finally, the poloidal width of the filamentary structure is defined as ${\omega }_{\mathrm{w}\mathrm{i}\mathrm{d}\mathrm{t}\mathrm{h}}\;= {\omega }_{\mathrm{F},\mathrm{i}}\times \mathrm{c}\mathrm{o}\mathrm{s}\theta$ [16]. Figure 11(b) shows the response of filament width on the scanning phase difference ${\Delta \varPhi }_{\mathrm{U}\mathrm{L}}$ of RMPs. The time range of the extracted filament width in the figure spans from 3.5 s to 5.5 s. With the periodic variation of ${\Delta \varPhi }_{\mathrm{U}\mathrm{L}}$, the dimensions of filamentary structures also exhibit systematic changes, indicating that the phase difference between the upper and lower coils affects the width of ELM filamentary structures. Here, we can divide the figure into three sections: when ${\Delta \varPhi }_{\mathrm{U}\mathrm{L}}$ is in the range of 0°–135°, the width of filamentary structures increases and reaches its maximum around 135°. This corresponds to the time intervals of t $\in$ [4.2, 4.5] s and t $\in$ [5.2, 5.5] s in figure 10(g), where the ELM frequency is at its minimum value. When ${\Delta \varPhi }_{\mathrm{U}\mathrm{L}}$ is in the range of 135°–270°, the width of filamentary structures decreases and reaches its minimum value around 270°. This corresponds to the time intervals of t $\in$ [3.8, 4.2] s and t $\in$ [4.8, 5.2] s, where ELM mitigation is strongest around 3.8 s and 4.8 s, exhibiting the highest frequency, most pronounced density pump out, and the lowest stored energy. Finally, when ${\Delta \varPhi }_{\mathrm{U}\mathrm{L}}$ is in the range of 270°–360°, the width continues to increase, corresponding to time intervals t $\in$ [3.5, 3.8] s and t $\in$ [4.5, 4.8] s, during which the ELM frequency decreases with the increasing phase difference.

Figure  11.  (a) Image of filamentary structure obtained through VUVI diagnostics. ${\omega }_{\mathrm{F},\mathrm{i}}$ is the peak full width at half maximum obtained through Gaussian fitting on the column vector. The pitch angle θ represents the inclination between the central line of the filament and the x-axis. ${\omega }_{\mathrm{w}\mathrm{i}\mathrm{d}\mathrm{t}\mathrm{h}}$ denotes the approximate poloidal width of the filament. (b) The impact of coil phase difference on the width of filamentary structures.

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4.   The temporal characteristics of ELMs

Filamentary structures, as large-scale formations along magnetic field lines, significantly impact the stability of device operation through the transport of heat and energy both along and across the open magnetic field lines to the divertor target plate and the first wall. Investigating the temporal evolution of ELM bursts is crucial for comprehending the transport processes in the SOL and estimating material constraints and lifetimes of plasma-facing components. For this purpose, we analyze the rise and decay times of the ELMs incoming to the pedestal and SOL region. The dataset comprises 147 single ELM events within 4 similar H-mode plasma discharges, where the plasma shape is single null configuration. The major parameters are ${I}_{\mathrm{p}}\sim0.5\;\mathrm{M}\mathrm{A}$, ${B}_{\mathrm{T}}= 1.58\;\mathrm{T}$, ${n}_{\mathrm{e}}\sim 3.3{\times 10}^{19}\;{\mathrm{m}}^{-3}$, ${q}_{95}\sim 4$ with NBI and LHW heating. Figure 12 shows the temporal evolution of a type-I ELM burst as one of the four shots, which is extracted from the zero-order component of the temporal component (also known as Chronos) obtained by SVD of the VUVI 2D signal to dimensionality reduction of the image. The energy deposition on the divertor can be calculated by the following equation:

Figure  12.  Typical temporal evolution of a single ELM burst obtained from VUVI. The solid black line is the interpolated signal obtained from the zeroth-order component of the temporal component by performing SVD of VUVI data.

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where E is the total energy reaching the divertor, τ is the characteristic decay time and ${q}_{\mathrm{B}\mathrm{G}}$ is the background heat flux. This formula in [36] based on the vacuum free-stream model (FSM) to fit the temporal evolution of the power deposition on the divertor target plate measured by IR camera during ELM bursts is used in devices such as ASDEX-U [36], JET [37], and others. However, there is no suitable model for fitting the signals obtained from VUVI data. Therefore, we employed interpolation fitting to process the data, represented by the black solid line in the figure 12. The temporal evolution of ELMs is divided into two phases: the rise phase (${\tau }_{\mathrm{r}\mathrm{i}\mathrm{s}\mathrm{e}}$) is defined as the period from 10% below the peak value to the peak after the signal rises, and the decay phase (${\tau }_{\mathrm{d}\mathrm{e}\mathrm{c}\mathrm{a}\mathrm{y}}$) is defined as the time interval from the peak time to the time at which the signal decays to 1/e of its maximum value.

The relationship between the temporal characteristics ${\tau }_{\mathrm{r}\mathrm{i}\mathrm{s}\mathrm{e}}$ and ${\tau }_{\mathrm{d}\mathrm{e}\mathrm{c}\mathrm{a}\mathrm{y}}$ of ELMs is depicted in figure 13. The rise and decay times are approximately within the range of 100–300 μs, and the fitting results indicate a negative correlation trend between ${\tau }_{\mathrm{d}\mathrm{e}\mathrm{c}\mathrm{a}\mathrm{y}}$ and ${\tau }_{\mathrm{r}\mathrm{i}\mathrm{s}\mathrm{e}}$. This result differs from observations derived from measurements in the divertor region on other devices, where the decay time is typically 1.5–4 times longer than the corresponding rise time [38, 39]. Time durations (${\tau }_{\mathrm{r}\mathrm{i}\mathrm{s}\mathrm{e}}$ and ${\tau }_{\mathrm{d}\mathrm{e}\mathrm{c}\mathrm{a}\mathrm{y}}$) on other devices are the same as this work defined. The observed discrepancy may stem from the fact that VUVI is line-integrated measurement at the pedestal region, while it is mainly measured locally at the divertor region by IR camera in other devices. As the perturbation happens at the pedestal region and transports radially to the SOL region, it will contribute to the rise in the VUVI measurement. Therefore, the rise time in the VUVI data may be greater than the decay time.

Figure  13.  Comparison of the decay time to the rise time of the temporal characteristics during type-I ELMs and the result of linear fitting.

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Simultaneously, we investigated the relationship between relative energy loss during ELM bursts and decay time. Firstly, the specific calculation process for the energy loss ${\mathrm{\Delta }W}_{\mathrm{E}\mathrm{L}\mathrm{M}}$ due to ELM is illustrated in figures 14(a) and (b). For each individual ELM, the energy loss (${\mathrm{\Delta }W}_{\mathrm{E}\mathrm{L}\mathrm{M}}\left(i\right)$) induced by an ELM burst is calculated from the ${W}_{\mathrm{M}\mathrm{H}\mathrm{D}}$. For the calculation of ${\mathrm{\Delta }W}_{\mathrm{E}\mathrm{L}\mathrm{M}}$ [40], the time of the $i\mathrm{th}$ ELM burst is defined as $t\left(i\right)$, and the time when ${\mathrm{D}}_{\mathrm{\alpha }}$ decreases to ${1/\mathrm{e}}^{3}$ of the peak value for the $i\mathrm{th}$ ELM is defined as ${t}_{\mathrm{e}\mathrm{n}\mathrm{d}}\left(i\right)$. Due to the $i\mathrm{th}$ ELM, the energy loss ($\mathrm{\Delta }{W}_{\mathrm{E}\mathrm{L}\mathrm{M}}\left(i\right)$) is calculated as the difference between the maximum value and the value of ${W}_{\mathrm{M}\mathrm{H}\mathrm{D}}$ at ${t}_{\mathrm{e}\mathrm{n}\mathrm{d}}\left(i\right)$ in a small time interval around the $i\mathrm{th}$ ELM event, i.e. ${\mathrm{\Delta }W}_{\mathrm{E}\mathrm{L}\mathrm{M}}\left(i\right)={W}_{\mathrm{m}\mathrm{a}\mathrm{x}}\left(i\right)-{W}_{\mathrm{e}\mathrm{n}\mathrm{d}}\left(i\right)$. Therefore, the relative energy loss of the $i\mathrm{th}$ ELM is denoted as ${\mathrm{\Delta }W}_{\mathrm{E}\mathrm{L}\mathrm{M}}\left(i\right)/{W}_{\mathrm{m}\mathrm{a}\mathrm{x}}\left(i\right)$ (${W}_{\mathrm{m}\mathrm{a}\mathrm{x}}$ is also as the total pre-ELM plasma energy ${W}_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}$). The relationship between the relative energy loss during ELM bursts and the decay time of VUVI is illustrated in figure 15. This suggests that the factor influencing the magnitude of ELM energy loss may be the energy expulsion during the decay phase rather than the rise phase time. As mentioned in the preceding section 3.1, the VUVI measurement location is at the midplane, while the IR camera measures the position of the divertor plates. During the ELM crash, particles are expelled from the pedestal, entering the SOL region, and subsequently transported parallelly to reach the divertor target. Therefore, we speculate that the ${\tau }_{\mathrm{d}\mathrm{e}\mathrm{c}\mathrm{a}\mathrm{y}}$ in VUVI may be correlated with the ${\tau }_{\mathrm{r}\mathrm{i}\mathrm{s}\mathrm{e}}$ in IR camera. The temporal evolution of power deposition on the divertor induced by ELMs was studied using IR on JET [41]. The material temperature on divertor target plate of JET reached a peak during the ${\tau }_{\mathrm{r}\mathrm{i}\mathrm{s}\mathrm{e}}$ of power flux, indicating the significant role of ${\tau }_{\mathrm{r}\mathrm{i}\mathrm{s}\mathrm{e}}$ in temperature increase of material on the divertor. This indicates that the results in figure 15 exhibit similarities to the findings from JET.

Figure  14.  The definition of energy loss in one ELM cycle. The evolution of the ${\mathrm{D}}_{ {\text{α}} }$ signal (a) and plasma stored energy (b).

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Figure  15.  The relative ELM energy loss ${\mathrm{\Delta }W}_{\mathrm{E}\mathrm{L}\mathrm{M}}/{W}_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}$ with respect to the decay characteristic time ${\tau }_{\mathrm{d}\mathrm{e}\mathrm{c}\mathrm{a}\mathrm{y}}$.

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5.   Summary and prospect

The process of ELM crash can be clearly observed through the VUVI system on EAST. The experimental results indicate that transport time at low heating power generally tends to be slower than high heating power. At higher heating power, the amplitude of ELMs is more likely to be influenced by local effect in the divertor region, and ELMs with larger amplitudes eject particles into the SOL region faster than those with smaller amplitudes through ion parallel transport. By combining the filament structure images obtained from the VUVI system with pedestal density profiles obtained from density profile reflectometry, an estimate of the toroidal mode number can be determined. The results indicate that the toroidal mode number is proportional to the edge density pedestal, but limitations in the field of view of the VUVI system prevent the display of complete filament structures under low toroidal modes. As a macroscopic instability, ELMs exhibit asymmetry in their toroidal eruption. A pronounced toroidal asymmetry was evident, with variations in duration and intensity at the same toroidal position. The response of ELMs to RMP is also confirmed by the VUVI measurement. By scanning the phase difference in the current of the upper and lower coils of the RMP, the periodic variation in the width of filamentary structures validates the effectiveness of RMP control over ELMs. Employing a high temporal resolution camera has facilitated the collection of statistical data on the rise and decay times. The findings reveal that both time intervals fall within the range of 100‒300 μs, exhibiting a negative correlation trend. Moreover, the energy loss during ELMs is positively correlated with ${\tau }_{\mathrm{d}\mathrm{e}\mathrm{c}\mathrm{a}\mathrm{y}}$. Future work will involve establishing a suitable model based on the ELM burst signals captured by VUVI, and further understanding of these results by using simulations with BOUT++ code [42] will be performed.