Dynamic response of recombining detached plasma to electron beam injection Open Access

Plasma detachment is regarded as a plausible method to reduce heat load on the divertor plate in fusion devices.¹ The key processes governing plasma detachment are the atomic and molecular processes in the plasma, and volume recombination processes, which are triggered when the plasma temperature drops sufficiently low (⁠ $≪2–3$ eV).² Without detachment, the heat load will well exceed the value that is able to be handled on the divertor in future fusion devices including ITER.³ The divertor plate is also subjected to transient heat and particle loads accompanied by edge localized modes (ELMs).⁴ The amplitude of the steady state heat load is expected to be up to 10–20 MW/m^2,5 while the transient heat load will be orders of magnitude larger than that of the steady state one. For example in ITER, the transient heat load with a duration of $∼$1 ms is expected to exceed 10 MJ/m² for $Q=10$ discharge,⁶ which corresponds to 10 GW/m². Therefore, it is of importance to study the dynamic response of detached plasma to pulsed heat loads caused from ELMs.

Experimental characteristics of detachment have been studied in ELMy H-mode experiments in JET tokamak.⁷ A positive spike of the ion saturation current was observed during the ELM heat pulse accompanying phase, while a negative spike was found in the D_α line emission signal. This was likely caused by the fact that the recombination component of line emission was reduced by ELMs, where the electron temperature became higher than that before the heat pulse arrival. This phenomenon is called “negative (or inverse) ELMs” and has been observed not only in JET but also in other devices such as DIII-D⁸ and ASDEX-Upgrade.⁹ 

In linear divertor simulators, taking advantage of their flexibility and experimental reproducibility, the detailed dynamic response of the detached plasma to the heat pulse was investigated. In the linear plasma device NAGDIS-II, a whistler wave excitation antenna with a frequency of 13.56 MHz was installed, and the response to heat pulse was observed.¹⁰ At the time when the antenna was turned on, high-energy electrons were injected into the detached plasma and the target ion particle flux increased. The Balmer series emissions had negative peaks, as in the negative ELMs, and also showed different time responses at low and high excitation levels. In the linear plasma device DT-ALPHA, an ion beam was superimposed on the generated detached plasma¹¹ to simulate an ion component in ELM pulses; the rate of volume recombination reaction was reduced by 20%–30% with the influx of energetic ions. Another method is the generation of pulsed high-energy plasma by instantaneously increasing the discharge power, which was performed in NAGDIS-II¹² and Magnum-PSI.¹³ Although the pulsed plasma superposition is similar to a realistic environment, such experiments show complicated time responses of parameters: the former and the latter show that fast electrons in pulsed plasma and recycling particles at the target plate play important roles in changing the dynamic behavior, respectively.

Because the pulsed plasma due to ELMs consists of hot electrons and hot ions, it is ideally desirable to study interactions between detached plasma and high-energy pulsed plasma, but this makes the interpretation of observed phenomena difficult. Therefore, this study will focus on the interaction with hot electrons, the importance of which has been pointed out in the studies described above.

In this study, a plasma-heated electron beam source that can control the beam energy is applied to the detached plasma in the linear device NAGDIS-II, and the dynamic response is investigated by measuring emission signals with high temporal resolution. The physical processes behind the dynamic signal variations are then interpreted using a collisional radiative (CR) model, which is applicable to two electron temperature components. Section II describes the experimental setup including the electron beam source and the measurement system. In Sec. III, we show how the line emission changes in response to electron beam injection, and the possible mechanism about the changes is explained in Sec. IV. Finally, the conclusions are given in Sec. V.

Interaction between detached plasma and electron beam was investigated by using the linear plasma device NAGDIS-II.¹⁴  Figure 1(a) shows a schematic of the experimental setup. Steady-state helium (He) plasma was generated by DC arc discharge with a heated LaB₆ cathode. The magnetic field was formed by solenoid coils, and the strength, B, was 0.2 T. Along the linear magnetic field, the generated cylindrical plasma with a typical diameter of $∼$ 20 mm was introduced into the divertor test region, and it finally terminates at the end target plate made of tungsten. The end plate with a diameter of 70 mm was negatively biased (−100 V) to measure the total ion flux. By increasing the neutral pressure, which was measured near the end plate, with gas puffing, the current to the end plate, $Iend$⁠, monotonically decreases, as shown in Fig. 1(b), due to the enhancement of volume recombination processes. Figure 1(c) shows a typical emission spectrum obtained in detached He plasma. Several line emissions due to excited He neutrals were measured with high temporal resolution with respect to the electron beam injection, as described later.

A tungsten (W) disk electrode was used as the electron beam source as in the previous study,¹⁵ in which the space charge effect was investigated. The size of the W electrode was 2 mm in diameter and 0.5 mm in thickness, which was inserted into a plasma column to be heated. The normal direction of the W plane was aligned with the magnetic field. During the experiment, alternating positive and negative bias was applied to the W electrode relative to the plasma potential, $Vp$⁠. When the W electrode was positively biased, it was heated by electron bombardment and the current from the plasma (⁠ $IW<0$⁠). When negatively biased after sufficient heating, thermal electrons were emitted (⁠ $IW>0$⁠) and accelerated by the potential difference between $Vp$ and the W electrode potential, $VW$⁠. As a result, a pulsed electron beam with electron beam energy of $Eb=Vp−VW$ was realized. Detailed values of the applied bias will be described later.

The W electrode was attached to a sample insertion rod via a tantalum (Ta) wire (0.5 mm diameter). The Ta wire was covered with an alumina tube (1.5 mm) to be electrically isolated from plasma and to prevent deformation of the Ta wire due to the Lorentz force. The distance from the target plate to the W electrode was 660 mm [see Fig. 1(a)].

In this study, plasma emission was measured using a photomultiplier tube (PMT). Emission from the plasma $∼$ 165 mm in front of the target was focused onto a fiber by a lens, transferred to a Czerny–Turner-type spectrometer with a focal length of 0.75 m, and detected by a PMT (Hamamatsu Photonics, R3896). The PMT signals were then passed through a low-noise current preamplifier (Stanford Research Systems, SR570) and measured as voltages on an oscilloscope (Yokogawa, DL850E). A relative sensitivity calibration was performed using a standard light source.

The time evolution of line emission intensities from states with different principal quantum numbers was measured. The line emission intensity from the principal quantum number p is represented as $Sp$⁠. In this work, the intensities at wavelengths of 587.6, 447.1, 402.6, 382.0, and 370.5 nm, corresponding to transitions from the $33$ D, $43$ D, $53$ D, $63$ D, and $73$ D states to the $23$ P state, respectively, were used for $Sp$⁠. As described in Sec. III A, the electron temperature of the plasma at the OES position is basically be less than a few electron volt. Therefore, the dielectronic recombination is not dominant¹⁶ and one of the two electrons of a helium neutral particle is considered to be in the ground state.

Both the sampling frequencies of $Sp$ and $Iend$ were 1 MHz. To reduce the noise of $Sp$⁠, 128 electron beam injection events were accumulated and then averaged in each measurement condition.

Pulsed electron beam was injected into a detached plasma generated at $Pn∼22$ mTorr [see Fig. 1(b)]. The electron temperature $Te$ and electron density $ne$ without the electron beam at the OES measurement position were measured as $Te∼0.5$ eV and $ne∼7×1017$ m⁻³ by using the laser Thomson scattering system.^17,18 Under this parameter, the three-body recombination process is dominant.¹⁶ At the W electrode position, $Te∼1.6$ eV and $ne∼2.5×1018$ m⁻³ were evaluated from the current–voltage (⁠ $IW$– $VW$⁠) characteristic without the W electrode heating. At there, the recombination coefficient is not so high and ionizing plasma component can be larger. Therefore, the recombination front, where the volume recombination processes were most enhanced, was located between the OES measurement position and the W electrode.

Figure 2 shows the time evolution of $VW$ and $IW$ with different beam energies. The voltage of the same waveform with square shape was repeatedly applied in a 50 ms time cycle. During the heating phase, $VW$ was set to 10 V and $IW∼−0.56$ A for 48 ms before a pulse, as shown in Fig. 2. When the electron beam was emitted, $VW$ was set to $−40,−50,−60$⁠, or $−70$ V for 2 ms per one pulse (from $t=0$ s in Fig. 2). Given that the plasma potential $Vp$ was $−13$ V, the electron beam energy $Eb$ was calculated to be 27, 37, 47, or 57 eV. During the beam injection (electron emission) period, ions can also enter the W electrode, i.e., the ion current was contained in $IW$⁠. Without the electron beam generation, the ion saturation current (⁠ $Is$⁠) flowing into the W electrode was measured as $∼$ 0.15 A. Therefore, the electron beam current was $∼$1 A [see Fig. 2(b)], which corresponds to 10  $×$ 10²³ m⁻² s⁻¹ in terms of electron beam flux near the W electrode. Immediately after stopping the electron beam, it is noticed that $Iw$ swung to a significantly negative value for a short time (⁠ $IW∼−1.5$ A at $t=2$ s). This is thought to be due to the return of electrons emitted just before from the W electrode.

We would like to emphasize that the advantage of this technique is that the time with a constant electron beam is clear, unlike the method that increases the discharge power instantaneously.¹² This allows a detailed discussion of the time response of the detached plasma with high temporal resolution.

Since the ion flux flowing into the end plate is reduced by the volume recombination processes, $Iend$ can be used as an indicator of plasma detachment. Figure 3(a) shows the time evolution of $Iend$ in response to electron beam injection at different electron energies $Eb$⁠. At the start time of the electron beam injection (⁠ $t∼0$ s), $Iend$ increases rapidly, as shown in the magnified view in Fig. 3(b). It then increases slowly, and decreases sharply at $t=2$ ms, when the electron beam injection ends. After that, $Iend$ decreases slowly and returns to its original value at $t∼4$ ms. Although the general shape of the time evolution of $Iend$ is similar with different $Eb$⁠, the higher the electron beam energy, the larger the amplitude change in $Iend$⁠. At $Eb=37$ eV, $Iend$ increases to 1.5 times the initial value at $t=0.05$ ms and then saturates at double the value. At $Eb=57$ eV, $Iend$ increases to double the value at $t=0.05$ ms and then becomes triple at $t=2$ ms. As mentioned above, since the volume recombination reducing the ion flux was dominant before the beam injection, it is likely that the electron beam prevents the volume recombination, especially when $Eb$ is high.

When the electron temperature is significantly low, the heat flux is mainly attributed to the surface recombination component, which is proportional to the ion particle flux. Obtained results suggest that the electron beam injection could increase the heat load by a factor of three at the highest $Eb$ case, although it should be noted that the initial heat load in this experiment is significantly reduced due to the plasma detachment.

In the previous study in Magnum-PSI,¹³ it is reported that the recycling neutrals can affect the plasma when $λn−i<λn−n$⁠, where $λn−i$ and $λn−n$ are the mean free paths of neutral–ion and neutral–neutral collisions, respectively. In this study, considering the neutral pressure and the ion-accelerating voltage at the sheath, $λn−n$ is smaller than 0.1 m, which is much smaller than $λn−i$⁠. Furthermore, the amount of neutral particle flux recycled from the end plate is not large due to the volume recombination, and the majority of neutral particles are supplied externally from the downstream region of the device. Therefore, recycling neutrals would not significantly affect the detached plasma formation.

Figure 4(a) shows the time evolution of line emission intensities $Sp$ from $p=3$⁠, 4, 5, 6, and 7 for the highest electron energy case with $Eb=57$ eV. It can be seen that $Sp$ is significantly changed by the electron beam injection. Immediate changes at the start and end of the beam and gradual changes during the beam can be seen. Enlarged views of $S3$ and $S5$ at the time periods near the start and end are shown in Figs. 4(b) and 4(c), respectively.

The time variations can be divided into the following seven phases with six typical time points (A, B, C, D, E, and F):

• Phase (i) (⁠ $t<0$ ms, before A): steady state phase.

• Phase (ii) (⁠ $0<t<0.01$ ms, A–B): $S3$ increases significantly, while $S4$⁠, $S5$⁠, $S6$⁠, and $S7$ do not change that much. In this phase, $Iend$ rapidly increases (Fig. 3).

• Phase (iii) (⁠ $0.01<t<0.1$ ms, B–C): all $Sp$ values (⁠ $p=3–7$⁠) decrease.

• Phase (iv) (⁠ $0.1<t<2$ ms, C–D): all $Sp$ values (⁠ $p=3–7$⁠) gradually increase.

• Phase (v) (⁠ $2<t<2.02$ ms, D–E): $S3$ decreases significantly, while $S4$⁠, $S5$⁠, $S6$⁠, and $S7$ do not change.

• Phase (vi) (⁠ $2.02<t<2.04$ ms, E–F): all $Sp$ values (⁠ $p=3–7$⁠) increase.

• Phase (vii) (2.04 ms $<t$⁠, after F): all $Sp$ values (⁠ $p=3–7$⁠) gradually decrease and return to the original values.

Figures 5(a)–5(c) shows the time evolution of $S3$⁠, $S4$⁠, and $S5$⁠, respectively, at different $Eb$ of 27, 37, 47, and 57 eV. Among the three emission intensities, the energy dependence is most pronounced in $S3$ in Fig. 5(a). Compared to the value before the beam injection [phase (i)], $S3$ during the beam injection [phase (ii–iv)] increases with increasing $Eb$ when $Eb=47$ and 57 eV, while it does not increase so much when $Eb=27$ and 37 eV. At $Eb=57$ eV, $S3$ is increased by about three times by beam injection. For $S4$ [Fig. 5(b)] and $S5$ [Fig. 5(c)], the variations during the decreasing phases (iii–iv) and increasing phases (vi–vii) become greater with increasing $Eb$⁠. When $Eb=27$ eV, $S3$⁠, $S4$⁠, and $S5$ show similar temporal changes, suggesting that the difference between low- and high-excited state emissions seen with high $Eb$ would be originated from the excitation by the high-energy electron beam.

In Sec. III, it was confirmed that electron beam injection has a significant effect on $Iend$ and $Sp$ with high $Eb$⁠. Considering the continuity equation, an increase in target ion flux with the beam implies an increase in ionization and/or a decrease in volume recombination processes. Such an atomic process would be affected directly by the electron beam and indirectly by the parameter change of bulk plasma. Here, a CR model¹⁹ is used to understand the qualitative time response of $Sp$⁠. It is noted that the emission intensity is proportional to the population density at the upper excited state. In the following, the population densities at excited states 3³D (⁠ $p=3$⁠) and 5³D (⁠ $p=5$⁠) are denoted as $n3$ and $n5$⁠, respectively, by adding the quantum number p as a subscript. Therefore, the qualitative change in $np$ is the same as that of $Sp$⁠.

In the CR model, the population density can be calculated by providing the ground state atomic density, $Te$⁠, and $ne$⁠, assuming that the ion density is the same as $ne$⁠. In the experiment, $Sp$ includes the effect of line integrals, but this is ignored in the CR model calculation in this section. Therefore, no quantitative comparisons will be made. Further, transport of metastable atoms (⁠ $21$S and $23$S states) with long lifetime are also ignored. Moreover, in the background plasma parameter (⁠ $Te∼0.5$ eV and $ne∼7×1017$ m⁻³), the lifetimes of $21$S and $23$S states are 1.9 and 19  $μ$ s, respectively. The latter lifetime is similar to the time scales of the short-term variations in phases (ii) (v), and (vi), causing quantitative differences between the OES results and the CR model. Additionally, because the electron beam energy (⁠ $Eb=57$ eV) is higher than the second ionization energy (54.4 eV) and the excitation energy of He⁺ (e.g., 40.8 eV from the ground state to 2p state), He²⁺ and excited He⁺ could be generated near the electron beam source. However, these cross sections are much smaller than those of elastic collision, ionization, and excitation of He neutral, and this shortens the mean free path of the electron beam, as described later. Therefore, the effect of He²⁺ and excited He⁺ on the emission signals at the OES position is thought to be limited in the qualitative discussion. In addition, although the radiation trapping should be important in detached plasmas,²⁰ this is ignored to simplify the physics and for only the qualitative discussion.

Figure 6 shows $Te$ dependence of $n3$ (3³D state) and $n5$ (5³D state) with $ne=7×1017$ m⁻³ and $Pn=22$ mTorr, which are the parameters without the electron beam injection. Here, the neutral gas temperature was assumed to be 300 K. Ionization and recombination components of the population densities, which are represented by dashed and dotted lines, become dominant at high and low $Te$ ranges, respectively. In this figure, the intersection of the dashed line and the dotted line, indicating that the ionizing and the recombining components are equal, is slightly lower (0.1–0.2 eV) for the blue curve (⁠ $p=3$⁠) compared to the red curve (⁠ $p=5$⁠). Since $p=3$ state has a lower energy than that of $p=5$⁠, the $Te$ at which the magnitude relationship between the ionization and recombination components swaps is lower for $p=3$⁠.

Before the electron beam injection, where $Te=0.5$ eV, both $np$ value at $p=3$ (3³D) and $p=5$ (5³D) are dominated by the recombination component. Hypothetically, we will attempt to explain phase (ii–iii) in the experiment using this diagram with its dependence on the single effective $Te$⁠. In phase (ii) (from A to B), $S3$ increases while $S5$ is not so changed in Fig. 4(b). This variation can be explained if the effective $Te$ rapidly increases from 0.5 to 1.4 eV, where the values of $S5$ are almost the same, due to the electron beam injection. Next to that, in phase (iii) (from B to C), both $S3$ and $S5$ are found to decrease. For both decreases to occur, $Te$ and/or $ne$ must decrease. However, for $Te$⁠, it is unnatural to decrease immediately after its increase by the electron beam. Further, $ne$ would not be reduced, because an increase in ionization and a decrease in recombination should have occurred due to the electron beam injection. As an interim conclusion, phase (ii–iii) cannot be explained by a single electron temperature diagram.

Next, instead of a single electron temperature, consider the existence of an electron beam component in addition to a bulk component. Between the electron beam source and the OES position with a distance of 495 mm, the electrons collide with neutral particles. The total cross section $σ$ (elastic collision, ionization, and excitation) for an electron to helium atoms is $∼$ 2  $×10−20$ m⁻² at $Eb=27$ eV and $∼$ 1  $×10−20$ m⁻² at $Eb=57$ eV.²¹ At $Pn=22$ mTorr, the mean free path is calculated as 71–141 mm. This is much shorter than the distance between the beam source and the OES position, and thus the electron beam is considered to be thermalized to some extent before reaching the OES position.

In the following, therefore, an interpretation will be performed based on calculations with two temperature components with the high-temperature one (⁠ $Teh$ and $neh$⁠) derived from the electron beam and the low-temperature one (⁠ $Tel$ and $nel$⁠) of bulk plasma. This treatment in the CR code is described in the  Appendix. Since the electron beam flux is nearly constant in Fig. 2, the parameters of the high-temperature component are assumed to be constant, while the bulk plasma parameters are assumed to vary with time during the electron beam injection. Here, it is noted that the temperature relaxation time between the bulk and the beam electrons calculated by the electron-electron collision time²² is less than 5  $μ$s at the region between the W electrode and the OES position. Therefore, the temperature of the bulk electrons can change on such a timescale.

Figure 7 shows the calculation results of (a) and (b) $n3$ and (c) and (d) $n5$ considering two temperature components as functions of bulk plasma parameters of $Tel$ and $nel$⁠. In Figs. 7(a) and 7(c), there is no high-energy component due to the electron beam for phases (i, v, vi, and vii); i.e., the calculation is done with single temperature component. On the other hand, a constant-parameter high-energy component is contained for phases (ii, iii, and iv) in Figs. 7(b) and 7(d). As the high-temperature plasma parameter due to the electron beam, $neh$ is set to be 0.3% of $nel$ before the beam injection, similar to the previous work where the high-energy component was considered.¹² The electron temperature attributed to the beam, $Teh$⁠, is set to 2 eV. This is because, if $Teh$ is too low, the effect of electron beam will not be visible, and if it is too high, the effect of parameter changes of the bulk plasma will not be seen. In other words, the ionizing and recombining plasma components for low-excited state neutrals are of the same order during the electron beam injection. In the parameter range of Fig. 7, $n3$ increases by adding the beam component, as shown in Figs. 7(a) and 7(b). In contrast, the difference is not clear for $n5$ in Figs. 7(c) and 7(d), because highly excited state neutrals have less increase due to the excitation from the ground state than low-excited state, as in Fig. 6, and the re-ionization of excited atoms can easily occur at higher excited state, as described later.

In phase (ii) (A–B) and phase (v) (D–E), only $S3$ changed rapidly after the start and end of electron beam injection in Fig. 4. These changes are easily seen in Fig. 8, which shows $n3$ and $n5$ as a function of the point {A, B, C, …, F, A}. Circles and crosses indicate the cases without and with high-temperature component, respectively, and the dashed line bridging circles and crosses is the one connecting the arrows in Fig. 7. These changes would be attributed to the addition or subtraction of the high-temperature component with a small parameter change of the bulk plasma. This corresponds to the movement from point A in Figs. 7(a) and 7(c) to point B in Figs. 7(b) and 7(d) in phase (ii), and from point D in Figs. 7(b) and 7(d) to point E in Figs. 7(a) and 7(b) in phase (v). Next, in phase (iii) (B–C) and phase (vi) (E–F), all $Sp$ values decrease and increase, respectively. Such qualitative changes can be explained by the slight increase in $Tel$ in Figs. 7(b) and 7(d) and decrease in Figs. 7(a) and 7(c). Here, $Tel$ at point C is set to 0.7 eV so that a certain degree of decrease in $n3$ can be found in phase (iii). After that, in phase (iv) (C–D) and phase (vii) (F–A), all $Sp$ values increase and decrease, respectively, with longer timescale than the preceding phases. Given that particle transport is slower than heat transport and that the target particle flux is changing in phase with $Sp$⁠, $nel$ would be increasing or decreasing in these phases. Here, $nel$ at point D is tentatively set to 1.3 times higher than that at point C, because $Iend$⁠, which is proportional to the electron density, increased by a similar degree in phase (iv). Qualitative changes of $S3$ and $S5$ in Fig. 4 are found to be reproduced in Fig. 8; e.g., in phases (ii) and (v), distinct $np$ increase and decrease are seen only for $p=3$⁠, respectively.

The differences seen between low- and high-excited states are attributed to the different sensitivity of the ionization and recombination components to the electron temperature (see Fig. 6). In phase (ii), the increase in $S3$ is larger because lower-excited state neutrals are generated more by the excitation due to the electron beam. In phase (iii), the increase in bulk plasma temperature makes volume recombination more difficult to occur, and the competition between the decreased recombination component and the increased excitation results in greater decrease in $np$ of higher excited state.

Regarding the ion flux flowing into the end plate, $Iend$ mainly increases in phases (iii) and (iv), and the change in the short time (⁠ $∼$ 0.01 ms) of phase (ii) is not large (see Fig. 3). Therefore, the increase in $Iend$ could be mainly attributed to an increase in bulk electron temperature, which makes volume recombination less likely, and an increase in bulk electron density.

The above interpretation for the reason why $S3$ and $Sp$ at $p=4,5,6,7$ changed differently in the successive phases (ii)–(iii) is based on the electron beam injection and the change in bulk electron temperature $Tel$⁠. In addition to this, there is a possibility that only the re-ionization of excited atoms has such an effect; i.e., due to the different sensitivity of ionization from the excited state, $np$ at high p can be reduced except for $n3$ by only adding the high-temperature electrons without changing $Tel$⁠. In the case where the re-ionization occurs, $Iend$ would increase.

Figure 9 shows the dependency of $np$ on $Teh$ at different $neh$ from 0% to 100% of $nel$ at $p=3,5$⁠, and 7. In this figure, $Tel$ and $nel$ are set by the parameters without the beam injection. When $Teh<∼$ 0.5 eV (although this temperature is not high), recombination increases, while excitation from the ground state increases when $Teh>∼$ 2 eV. As a result, all $np$ values increase at these $Teh$ ranges compared to when $neh=0$ (before the electron beam injection). At the intermediate temperature range around $Teh∼1.2$ eV, $n3$ and $n5$ increase monotonically with increasing $neh$⁠, while $n7$ decreases by about 3% when $neh=0.1nel$ and then increases. The decrease in $n7$ under the low $neh$ condition is attributed to the re-ionization of excited atoms, while there is no decrease in $n5$⁠. Therefore, re-ionization contributes to the difference in changes between low- and high-excited atoms, but it alone was unable to reproduce qualitative changes with the given bulk plasma parameters in this study.

In order to investigate the dynamic response of recombining detached plasma to hot electrons by ELMs, an electron beam source made of tungsten (W) electrode was installed in the linear plasma device NAGDIS-II. By applying a square wave bias, the W electrode in the helium plasma column was heated with positive bias and then thermal electrons were accelerated with negative bias to a beam energy of $Eb$⁠. Pulsed electron beams with different $Eb$ were injected into the detached helium plasma. When $Eb$ was high, ion particle flux at the target plate was doubled in less than 0.1 ms and was tripled in 2 ms during the beam injection.

To understand the atomic processes, emission intensities from five excited states from the quantum numbers of $p=3,4,5,6$⁠, and 7 were measured using the photomultiplier tube with high temporal resolution. As a result, different time variations were observed between low (⁠ $p=3$⁠) and high (⁠ $n≥4$⁠) excited states immediately after the start and end of the electron beam injection. These differences are more pronounced when $Eb$ is high, indicating that they originated from the excitation due to the electron beam.

Qualitative changes in emission intensities were interpreted using the collisional radiative (CR) code applicable to two electron temperature components, one for the low-temperature bulk plasma and the other for the high-temperature component attributed to the electron beam. The rapid increase or decrease observed only for low-excited state would be due to the change in the ionizing plasma component caused by the electron beam, while in-phase variations of all excited states would be due to the change in the recombining plasma component of the bulk plasma. The increase in ion particle flux to the target appears to be caused by the decrease in volume recombination due to the increase in bulk electron temperature and the increase in bulk electron density. In addition, re-ionization of excited atoms contributes somewhat to the change in population density in the highly excited state and the ion particle flux.

Although qualitative changes of emission intensities can be reproduced by introducing a high-temperature plasma in addition to the bulk plasma into the CR code, quantitative agreement has not been obtained. This would be due to several processes that are ignored (line-integral effect, metastable atom, radiation trapping, etc.) and/or the fact that the beam-induced component is given by the thermal component in the calculation. For more detailed investigation and comparison with the CR code calculation, plasma parameter measurements with high temporal resolution are required; e.g., high temporal resolution Thomson scattering measurement is desired.²³ Furthermore, because the density of the high-temperature component indicated by the CR code calculation is significantly small, precise measurements with the high S/N ratio by averaging a number of signals are required. In order to compare with the high-temporal resolution measurement, the application of the CR code that does not assume a steady state is necessary for the interpretation of the short-team variations. In the future, it is also important to focus on changes in the distribution along magnetic field lines, such as how the ionization/recombination front position moves against the ELM heat load.

This work was supported by JSPS KAKENHI (20H00138, 21KK0048, 22H01203, 22K18701, and 24H00201), NIFS Collaboration Research program (NIFS22KIPP002, NIFS23KUGM176, and NIFS23HDAF011), and Research Foundation for the Electrotechnology of Chubu, and NINS program of Promoting Research by Networking among Institutions (01411702).

The authors have no conflicts to disclose.

Hirohiko Tanaka: Formal analysis (equal); Funding acquisition (equal); Methodology (equal); Software (equal); Visualization (equal); Writing – original draft (equal). Shin Kajita: Methodology (equal); Supervision (equal); Validation (equal); Writing – review & editing (equal). Hideki Kaizawa: Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Validation (equal); Visualization (equal); Writing – original draft (equal). Noriyasu Ohno: Methodology (equal); Project administration (equal); Resources (equal); Supervision (equal); Writing – review & editing (supporting).

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Thus, $W$ is the function of $Te$ and $ne$⁠. Here, $imax$ is the highest excitation level considered within the code.

In the CR code, various rate coefficients such as C and S are first calculated with $Te$ etc. Then, by substituting Eq. (1) into Eq. (A3) and solving the determinant with $W(Te,ne)$⁠, the population coefficients are obtained. After that, by using the obtained $R0$ and $R1$ in addition to $n(1)$⁠, the population density, which is proportional to the emission intensity, at each excited state can be calculated.