Multipoint measurements employing a microwave interferometer and a Langmuir probe in the detached linear plasma

Multipoint measurements were carried out by employing a microwave interferometer (MI) and a Langmuir probe (LP) in steady-state detached plasmas in the linear plasma device NAGDIS-II to reveal the structure of fluctuations along the magnetic field. We changed the LP position along the magnetic field while the MI was fixed at an upstream position. In addition, a fast framing camera was used to identify an azimuthal mode number, and the predominant mode number was identified as m = 1. By analyzing correlations between signals observed by the LP and the MI, it was found that a time delay of 10–20 kHz fluctuations gradually decreased toward the downstream direction. The results indicate a decrease in the rotation velocity in the E × B direction, and suggest that the 10–20 kHz fluctuation forms a spiral shape.Multipoint measurements were carried out by employing a microwave interferometer (MI) and a Langmuir probe (LP) in steady-state detached plasmas in the linear plasma device NAGDIS-II to reveal the structure of fluctuations along the magnetic field. We changed the LP position along the magnetic field while the MI was fixed at an upstream position. In addition, a fast framing camera was used to identify an azimuthal mode number, and the predominant mode number was identified as m = 1. By analyzing correlations between signals observed by the LP and the MI, it was found that a time delay of 10–20 kHz fluctuations gradually decreased toward the downstream direction. The results indicate a decrease in the rotation velocity in the E × B direction, and suggest that the 10–20 kHz fluctuation forms a spiral shape.


I. INTRODUCTION
In magnetic confinement fusion reactors such as ITER and DEMO, it is necessary to minimize the damage to the plasma-facing components caused by the plasma flowing out from the core region. In the divertor configuration, in order to accomplish this, the particle flux and the heat flux are led to the divertor region. However, unless countermeasures are adopted, the divertor target will be exposed to a thermal load of several tens of MW/m 2 , which greatly exceeds the allowable thermal load of the materials. Therefore, reduction of the heat load to the divertor target is important for the implementation of nuclear fusion reactors.
As a method for reducing the thermal load of the divertor region, detached plasma is effective. 1 In this method, by increasing the neutral gas pressure, the plasma is neutralized in front of the divertor target by the plasma recombination process. At this time, in addition to the heat flux, the particle flux to the divertor target decreases, and then the thermal load decreases greatly. 2 The simulation of detached plasma still experiences difficulties in reducing the ion particle flux to the same degree as the actual experimental. 3 This may possibly be due to the fact that, in addition to the volume recombination, the plasmas are transported in the cross-field direction. When the divertor was detached, a flattening of an electron density profile in the scrape-off layer happened and was explained as an increase in the cross-field transport. 4,5 Furthermore, around the detached plasmas in several toroidal devices [6][7][8] and linear devices, 9,10 enhanced cross-field transports were observed. However, the phenomenon is insufficiently understood, and detailed investigations are needed to improve the accuracy of the simulation.
In the linear device NAGDIS-II, in the vicinity of the recombination front where strong gradients of plasma parameters existed, large electron density fluctuation and an axially local increase in radial plasma ejection have been ARTICLE scitation.org/journal/adv observed. 11,12 A fast framing camera measurement, which captured line-of-sight signals along the magnetic field, clarified that the ejected plasma transported in the periphery forms a spiraling structure rotating in the E × B drift direction. 13 Further, the dominant azimuthal mode numbers are identified as m = 1 and 2. From past research, however, the phase relationship of the plasma structure along the magnetic field has not yet been clarified. Therefore, we investigated the phase relationship of fluctuations along the magnetic field in this study. We carried out multipoint measurements employing a microwave interferometer (MI) 14 and a Langmuir probe (LP) in the steady-state detached plasma, and changed the measurement position of the LP at equal intervals in the direction of the magnetic field. Correlation analysis was applied to the ion saturation current (I sat ) fluctuation obtained at each point and the line-integral electron density (n el ) fluctuation of the MI. In order to identify the azimuthal mode number m, correlation analysis was also applied to the emission intensity signal observed from the side of the vessel with the fast framing camera. Consequently, a time delay in the fluctuation between two distant locations was found. Moreover, we discussed fluctuation behaviors along the magnetic field in the detached plasma.
In the following section, the experimental setup in NAGDIS-II will be explained. Analyses and the results will be shown in Sec. III. A discussion of the results and concluding remarks will be given in Sec. IV and V, respectively.

II. EXPERIMENTAL DEVICES AND MEASUREMENTS
The parameter measurement was conducted in the linear plasma device NAGDIS-II, which can generate a cylindrical steady-state helium plasma by a DC discharge. 15 As shown in figure 1(a), NAGDIS-II has a cylindrical vacuum chamber with a length of ∼2.5 m including the discharge region and the test region. The radius of the test region is 90 mm. A detach plasma is easily produced by increasing the neutral gas pressure around the end target in this device. The  Table I. We investigated the structure of fluctuation along the magnetic field by employing the MI and the LP. The two measurements simultaneously sampled plasma properties at a sampling frequency of 1 MHz.
The 70.15 GHz MI obtained the upstream n el fluctuation without disturbances. As shown in figure 1(a), the MI was fixed at z = 0 mm (660 mm upstream from the end target). The microwave passed through the plasma column at y = 20 mm from the plasma center in the −x direction. Strong emission from near the recombination front was further upstream from the position of the MI, according to spectrometry. The electromagnetic wave was the O wave, and the cut-off frequency, n c , was 6.1 × 10 19 m −3 , and is given by the following formula: (1) Its spatial resolution was a few centimeters in the radial direction.
We employed the LP to measure I sat at downstream positions along the z direction. The ion saturation current and electron density, n e , have the following relationship: where T e is the electron temperature. The LP enables twodimensional measurement by insertion with the robot cylinder and rotation of the insertion rod, as shown in figure 1(b). Therefore, the LP can move in both directions, i.e., parallel and perpendicular to the magnetic field. In this study, the position of the LP was changed at intervals of 25 mm in the z direction within the range z =10-635 mm. The radial distance was fixed as 20 mm in the x direction. We also applied the fast framing camera to identify an azimuthal mode number (m). The fast framing camera with a resolution of 8×640 was fixed at z = 330 mm. The frame rate was 87000 fps, the sampling period was ∼11.5 µs, and the shutter speed was 9 µs. Figures 2(a) and (b), respectively, show a time series of fluctuations (solid line) and 10-20 kHz components (dashed line) in n el and I sat when the LP was fixed at z = 10 mm. The two signals were measured at the same time, and it was confirmed that there was a phase difference between them. The fluctuation level in theñ el appeared to be higher, because it included all fluctuations along the line of sight.

A. Frequency characteristics
In this section, the frequency characteristics of the fluctuations are investigated with Fourier analysis. Figure 3(a) exhibits the power spectral densities (PSDs) of n el and I sat fluctuations. It can be confirmed that there are spectral peaks between 10 and 20 kHz in both PSDs. It is likely that the 10-20 kHz fluctuation corresponds to azimuthal rotation, as will be discussed in Sec. III C. There is also a strong fluctuation in the low-frequency band (<4 kHz) in n el , because it included some of the center fluctuation due to the spatial resolution of the MI. Figures 3(b) and (c) show a spectrogram and the statistical moments of I sat as a function of the distance between the MI and the LP in the z direction, respectively. The peak between 10 and 20 kHz gradually decreases toward the downstream direction because of the detachment.

B. Correlation between two distant locations
Correlation analysis is widely used in the fusion plasmas and is a powerful tool for identifying a spatial-temporal behaviour. 16,17 In this section, we investigate the correlation between n el and I sat fluctuations by focusing on the 10-20 kHz frequency components. Thus, before the correlation analysis, a bandpass filter with a range of 10-20 kHz was applied to  these signals. The cross-correlation coefficient between the two signals a(t) and b(t) is defined by The results of R(n el , I sat ) at every position of the LP along the magnetic field are summarized in figure 4. It can be noticed that there is a temporal periodicity, and the peak magnitudes of R(n el , I sat ) decrease toward the downstream direction. In addition, the drawn patterns fall downward to the right as illustrated by the dashed line. The intercept is ∼15 µs and the slope is ∼-0.04 µs/mm, which corresponds to a phase speed of 25 km/s.

C. Mode number identification
To identify an azimuthal mode number of the 10-20 kHz frequency components, we applied the correlation analysis to images of the visible light emission captured by the fast framing camera. We first averaged the emission intensity in the axial direction and obtained a 292-sized data array with 10 5 time frames. Before applying the correlation analysis, we extracted the 10-20 kHz frequency components by using a bandpass filter. Figure 5(a) shows a plot of the standard deviation of the 10-20 kHz frequency components of the emission intensity versus the y direction, E y . In figure 5(a), peaks appear at y = ±10 mm. Figure 5(b) shows R(E 10 mm , E y ), which is the correlation coefficients between E 10 mm and E y . The auto-correlation coefficients are expressed by the dashed line. R(E 10 mm , E y ) was low around y = 0 mm, because the captured emission intensity was the line-integrated data in the x direction and canceled by the high-intensity and low-intensity components. It is confirmed that there are periodicities around ±10 mm, which have an anti-phase relationship.

IV. DISCUSSION
Because the fluctuation rotated with m = 1 in the E × B direction, i.e., in the counterclockwise direction in figure 1(b), the time delay between n el and I sat can transform into a phase difference. For example the phase difference became ∼90 • the LP was at z = 10 mm, which coincided with the positional relation in the MI and the LP, because the time delay was ∼15 µs and the rotation period T ∼60 µs.
The rotation velocity, v rot , was estimated to be ∼2.1 km/s by using the relation v rot = 2πmr/T, where r is the radius. On the other hand, the ion sound speed, C s , was estimated to be in the range 2.2-2.7 km/s by using the electron temperature measured by the double-probe method at x = 20 mm. Because the Mach number, M c , in detached plasmas was ∼0.4 in NAGDIS-II, 18 the parallel flow v = M c C s was comparable to or less than v rot . In Sec. III B, the phase speed was estimated at 25 km/s, which is much greater than v and v rot . We interpret the determination of the phase speed below.
One possible reason for the above phase speed estimation result is that an instability generating the plasma ejection has an azimuthal phase shift along z. However, from past research, 11,19 the ejecting region would be localized in the z direction around the recombination front, which was further upstream from the measuring position in this study.
In such a case, the phase shift shown in figure 4 could be explained as follows. Figure 6 illustrates the time traces of azimuthal positions of the two types of ejected plasmas. One does not move along z after the ejection (A in figure 6). The other moves along z with a parallel speed of v (B in figure 6). Due to the radial electric field, they rotate in the azimuthal direction by the action of the E × B drift. If the E × B drift speed were constant along z, the phase difference between them would always become zero in the azimuthal direction, as illustrated in figure 6(a). However, the E × B drift speed would not be constant in the detached plasmas. Because T e decreases along the magnetic field toward the end target because of the detachment, the magnitude of the space potential, |V s |, could become small. The space potential at each position is calculated by V f + 3.7T e where V f is a floating potential. Radial distributions of V s at several z positions are shown in figure 7. Its gradient in the range 10-20 mm in the radial direction surely becomes smaller as the increment in z direction. Thus, the E × B rotation speed becomes small with increasing z, as illustrated in figure 6(b). In this case, a phase delay would occurs that coincides with figure 4. As a result, the fluctuation component would form a spiral shape that rotates in the E × B direction.

V. CONCLUSION
In order to clarify the structure of the fluctuation along the magnetic field, we have conducted multipoint measurements with a microwave interferometer and Langmuir probe in NAGDIS-II. Applying spectral and correlation analysis techniques, we found that the 10-20 kHz fluctuation propagated toward the downstream direction with a time delay while rotating azimuthally with mode number m = 1. The time delay decreased linearly with increasing distance between the microwave interferometer and the LP along the magnetic field. A possible reason for this is that the rotation velocity in the E × B direction gradually decreased with axial distance because of the decrease in the temperature. Further, the results suggest that the 10-20 kHz fluctuation forms a spiral shape rotating in the E × B direction.
Because the measurements in this study were performed further downstream from the recombination front, it would be interesting to employ the recombination front from upstream to downstream. We are planning to investigate fluctuation behaviors in detail in the vicinity of a recombination front with this system in the near future.