Cross-field transport in detached helium plasmas in Magnum-PSI

In this study, a reciprocating Langmuir probe was installed at the TS axial position. The reciprocation system was the same as that used in previous studies conducted on Pilot-PSI [15] and Magnum-PSI [16]. In a previous experiment conducted on Magnum-PSI [16], an ion-sensitive probe measurement was performed.

Figure 1(b) shows a schematic of the newly applied probe head with multiple electrodes. This probe head was formed of a 4 mm-diameter ceramic shaft and four 0.5 mm-diameter tungsten electrodes with an exposed length of 0.5 mm. Three of these electrodes were used for measuring the ion saturation current (I_s) and two floating potentials (V_f1, V_f2). The probe electrode for I_s was positioned at the upstream side and biased at −100 V. The other two electrodes for V_f1 and V_f2 were positioned perpendicularly to the magnetic field at a distance of d = 2 mm to measure the azimuthal electric field (E_θ), as described later. The floating potential at the midpoint connected to the I_s-measuring electrode along the magnetic field was deduced by V_f = (V_f1 + V_f2)/2. These signals were simultaneously acquired at a sampling frequency of 500 kHz by using isolated analog-to-digital converters (Yokogawa 720254, 16 bits).

During discharge, the probe head was moved from a radius of r_p = −50 mm to the radial center (r_p = 0) through compressed air (figure 1(a)). After a few seconds of measurement at r_p = 0, the probe head was extracted to minimize the damage caused to the probe materials by the steady-state plasma. The probe position was measured with a mark sensor by reading a barcode every 1 mm. The insertion and extraction speeds were ∼200–300 mm s⁻¹. This study only analyzed insertion and stationary phases (i.e. data during probe withdrawal were not included).

As shown in figure 1(c), at 351 mm upstream of the TS axial position, there was an electrically floating orifice plate, called the 'target skimmer.' Because the inner diameter of the target skimmer was 50 mm, the peripheral region at |r_p| > ∼25 mm at the TS axial position was not connected to the plasma source along the magnetic field.

A fast framing camera (Phantom V12, 12-bit grayscale) was used to capture a wide spatial region around the probe head. From the window opposite to the port where the probe system was mounted (figure 1(a)), a line-integrated visible light emission (I_em) perpendicular to the magnetic field was obtained without any optical filter. As shown in figure 1(a), r_c is defined as the distance from the plasma center in the direction perpendicular to the line of sight and magnetic field. In addition, z_c represents the axial displacement from the TS axial position along the magnetic field direction. The frame rate and exposure time were set to 97 073 fps and 3 μs, respectively, and the frame size and pixel resolution were 128 × 256 and ∼0.36 mm pixel⁻¹.

Figure 2 shows typical profiles of the mean values of I_em over a steady-state time period, ${\mu _{{\text{em}}}} \equiv \langle {I_{{\text{em}}}}\rangle$, in the recombination front, where $\langle \rangle$ indicates the average. The circular low-μ_em regions observed at the edge are outside the window outline. In figure 2(a), the probe head is fixed at the far periphery (r_p = −50 mm) and μ_em slightly decreases along the magnetic field with z_c increasing from upstream to downstream. In contrast, with the probe insertion (r_p = 0) in figure 2(b), the μ_em amplitude rapidly decreases at z_c ∼ 0 and downstream of this position. Because there is a plasma flow from the upstream, the disturbance to the plasma on the downstream side is strong. Additionally, because the probe diameter is not significantly smaller than the plasma-column diameter, the presence of the probe shaft creates a certain energy sink. Thus, the emission intensity in the upstream region is also slightly weakened. Furthermore, a local minimum of μ_em is found at (r_c, z_c) ∼ (−3, 0) mm in figure 2(b), which indicates the exact probe position when r_p = 0. Therefore, the most inward position of the Langmuir probe head is ∼3 mm distant from the plasma center in the negative r_c direction.

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Figure 2(c) shows μ_em under the lowest neutral pressure condition used in this study. The emission intensity is the background level, and we cannot analyze the I_em fluctuation in this case. As described later, because the electron temperature monotonically decreases with an increase in the neutral gas pressure, the emission intensity attributed to the ionization process is maximum under this low-pressure condition, despite the background-level emission. Therefore, most of the emission from recombining plasmas is attributed to the excited neutrals generated through the volume-recombination processes.

Magnum-PSI has a long target manipulator system, which can install various target shapes [17]. In this study, the target plate facing the main plasma was positioned 200 mm behind the TS axial position, as shown in figure 1(c). The shape of the target structure was not simple; it had five small target holders, whose detailed design is shown in [17]. The target was composed of a molybdenum sample mounted with a 64-mm-diameter hollow tantalum holder on a metal structure, which had a square surface with a side length of ∼64 mm. Considering the magnetic field geometry and spatial relationship, the measuring range of |r_p| < ∼45 mm at the TS axial position would connect to the target plate along the magnetic field, while the far periphery at |r_p| ∼50 mm would not connect to the target. In this study, the target plate was biased negatively at ∼−60 V and the total ion saturation current (I_tgt) over the target was measured using a current probe.

Figure 3(a) shows the neutral pressure dependences of line-emission intensities from highly excited states (He I: 2³P–7³D, 2³P–8³D, 2³P–9³D, 2³P–10³D, wavelength: 370.5, 363.4, 358.7, and 355.4 nm, respectively) at the TS axial position. Here, the line emissions are observed to be quite small in the lowest pressure case of P = 0.44 Pa, while they are high at P ∼ 1.8–3.9 Pa. At P = 4.7 Pa or more, the intensity decreases with increasing P. Therefore, recombining plasmas were generated except for that in the P = 0.44 Pa case. The recombination front, which is defined as the region where the electron-ion volume recombination strongly occurs [8, 9], exists near the TS axial position at P ∼ [2, 4] Pa and moves upstream at P > ∼4 Pa.

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Similarly, the I_tgt dependence on P is plotted in figure 3(b). By increasing P, I_tgt monotonically and rapidly decreases due to the plasma detachment. At P = 6.4 Pa, I_tgt becomes 25 times smaller than that at P = 0.44 Pa.

Figure 3(c) shows the n_e and T_e dependences on P measured with TS, which are averaged values around the plasma center (r_TS = [−2, 2] mm). Due to the small B, n_e is smaller than its typical range of Magnum-PSI. By increasing P, n_e increases from ∼4.3 × 10¹⁹ m⁻³ at P = 0.44 Pa to ∼7.7 × 10¹⁹ m⁻³ at P = 1.4 Pa, and then monotonically decreases, showing a rollover. In contrast, T_e suddenly decreases from ∼0.90 eV at P = 0.44 Pa to ∼0.34 eV at P = 1.4 Pa. Then, T_e monotonically decreases with increasing P and reaches ∼0.19 eV at P = 6.4 Pa.

Figure 4 shows the radial profiles of n_e and T_e measured with TS at P = 0.44, 1.4, 2.2, and 6.4 Pa. Most of the TS measurement range is within the target skimmer radius at |r_TS| ∼25 mm. Each profile has an axisymmetric profile, and the full width half maximum of each n_e profile is larger than 20 mm, which is larger than the typical width in Magnum-PSI because of the weak magnetic field [12]. At P = 0.44 Pa, n_e has a flat profile around the radial center, while T_e has a hollow profile at |r_TS| < ∼15 mm. In contrast, at higher P cases, n_e has Gaussian-like profiles and T_e values are flatter. Because T_e ≪ 1 eV except for P = 0.44 Pa, the electron-ion recombination process dominantly occurs, which reduces the plasma density and ion particle flux flowing into the target.

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To determine the neutral-pressure dependence of I_s measured with the Langmuir probe, its radial profile is contour-plotted along P, as shown in figure 5(a). Here, linear interpolation is performed between the discrete data points along P. The ion saturation current, which is proportional to the ion flux, is concentrated inside the target skimmer radius and decreases with increasing P at |r_p| < ∼25 mm. In contrast, focusing on the peripheral region behind the target skimmer, an increase and then a decrease in I_s with increasing P are observed with a peak at ∼2.5 Pa. As a result, the radial profile of I_s becomes broader (flatter) toward the periphery at P ∼ 2.5 Pa. This broadened profile is observed in the recombination front with high line-emission intensities (figure 3(a)), which is similar to the previous studies conducted on NAGDIS-II [7, 8]. Interestingly, the I_s radial profiles at P ∼ 1.4 and 1.8 Pa have a clear dip along r_p with a minimum at around |r_p| ∼ 35–40 mm.

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Figure 5(b) shows the logarithmic plot of the radial profiles of I_s at P = 0.44, 1.4, 2.2, and 6.4 Pa. Note that there would be some plasma disturbance at r_p ∼ 0, besides the fact that the r_p = 0 position is a few millimeters distant from the accurate plasma center, as mentioned in section 2.2. Therefore, the I_s peak observed at r_p < 0 in each case is attributable to the ion-flux reduction inside the plasma column by probe insertion. At P = 0.44 Pa, log₁₀(I_s) has a steep gradient at r_p ∼ −27 mm and is quite small in the periphery. At P = 1.4 Pa, the steep-gradient position shifts radially outward by ∼5 mm. Furthermore, I_s increases at r_p < ∼ −42 mm compared to the P = 0.44 Pa case. As a result, a dip with a small I_s is observed at r_p ∼ [−40, −32] mm. At P = 2.2 Pa, this dip disappears by further profile broadening. Under higher pressure conditions of P > 2.2 Pa, I_s decreases in the radial range.

Figure 6 shows the V_f profiles (a) as functions of r_p and P and (b) as a function of r_p at P = 0.44, 1.4, 2.2, and 6.4 Pa, where radially hollow profiles around the radial center can be observed. By using V_f and T_e, the plasma potential (V_p) can be calculated as V_p ∼ V_f + 3.7T_e under the assumption of T_e = T_i [8, 9], where T_i is the ion temperature. Figure 6(b) shows the radial profiles of V_p calculated with V_f and T_e, which are obtained by Langmuir probe and TS measurements, respectively. Here, T_e at r_p is assumed to be equal to that at r_TS. The V_p profiles are qualitatively similar to the V_f profiles, but higher due to the T_e component. Except for the lowest neutral pressure case, the T_e values are much lower than 1 eV (figure 4(b)). As a result, the V_p profiles are similar to the V_f profiles shifted up by ∼1 V in recombining plasma cases.

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The negatively biased cathode in the cascaded arc discharge makes the V_p radial profile of hollow shape, particularly in the ionizing plasma at P = 0.44 Pa. By promoting plasma detachment by increasing P, the V_p profile becomes shallower, which is similar to the axial V_p change in NAGDIS-II [8, 9, 18].

Figure 7 shows the power spectra of I_s as functions of frequency (f) and r_p at P = 0.44, 1.4, 2.2, and 6.4 Pa. In the ionizing plasma at P = 0.44 Pa, a large spectral peak is observed at f ∼ 30 kHz around r_p = [−18, −4] mm. By increasing P, this high-frequency component appears to weaken and shift to the low-frequency side. Furthermore, an additional frequency peak is observed around f = 6 kHz at the outer radial position in recombining plasmas (P ≥ 1.4 Pa). In the recombination front at P = 2.2 Pa, this component exists around r_p = [−25, −10] mm. Its peak frequency slightly increases with decreasing |r_p| within the range of f ∼ [3.5, 10] kHz, and apparently connects to the higher-frequency component at f > ∼10 kHz in the radially inner region. Moreover, strong f < ∼3.5 kHz components are confirmed around the radial center and in the periphery (|r_p| > ∼30 mm). Regarding the low-frequency component in the periphery, the appearing radial range in each P case simply corresponds to the region where the I_s value is high, as shown in figure 5.

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Below this subsection, detailed frequency characteristics at P = 2.2 Pa will be focused.

Figure 8(a) shows the power spectra of I_s at r_p = 0 and −50 mm, which correspond to the innermost and outermost positions, respectively, with a higher frequency resolution than that shown in figure 7(c). Additionally, the power spectra of V_f at r_p = 0 and −50 mm and I_tgt are plotted in figure 8(b). At f = 20, 40, 80, ... kHz, several sharp peaks are clearly observed for I_tgt, which are likely attributed to the discharge-power-supply noise in Magnum-PSI. These noise components with the same frequencies are also observed for I_s, particularly at r_p = −50 mm, but are not as outstanding as I_tgt. Furthermore, there is a strong peak at f ∼ 220 kHz, particularly in the power spectra of V_f, which may be due to some phenomenon because its amplitude becomes high inside the plasma; however, this fluctuation is beyond the scope of this paper. The power spectrum of I_s at r_p = −50 mm has a flat and inclined slope with a shoulder at f ∼ 4.5 kHz. Such a shoulder in the power spectrum is widely observed in the edge plasmas of several devices [19] when coherent structures such as blobs nonperiodically appear in a time series [20]. At r_p = 0, a shoulder or a little convex is observed at f ∼ 1.5 kHz. Furthermore, a small maximum is observed at f ∼ 20 kHz. The latter is connected to the high-frequency component observed in figure 7(c). In contrast, the power spectrum of I_tgt has a little convex at f ∼ 1.5 kHz, which is the same with the shoulder frequency of I_s at r_p = 0.

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Although the Langmuir probe is beneficial for measuring the local fluctuations, it might disturb the fluctuation characteristics, such as amplitude and frequency. To clarify the probe insertion effects on the fluctuation, I_em signals obtained by the fast framing camera were investigated. Because the probe structure is included in the line of sight at the exact TS axial position (figure 2(b)), the fluctuation characteristics of I_em in the vertically elongated rectangular pixels at z_c = −10 mm are investigated below.

Figure 9 shows the power spectra of I_em as functions of f and r_c without probe insertion (r_p = −50 mm) and with probe insertion (r_p = 0) at P = 2.2 Pa. It is confirmed that typical peak frequencies and spectral shapes are almost the same irrespective of whether or not the probe is inserted, although the fluctuation amplitude becomes weaker due to the probe insertion. The profile of the I_em power spectra resembles that of I_s in figure 7(c). The I_em power spectra at r_c = 0 with probe insertion is superimposed in figure 8(a). The spectral peaks of I_em at f ∼ [3.5, 10] kHz, which connect to the higher-frequency region, have no strong amplitude at r_c = 0 in figure 9. The small 20-kHz maximum observed in the I_s power spectrum at r_p = 0 is attributable to the slight deviation of the probe head from the radial center, as mentioned in section 2.2. In contrast, the low-frequency component at f < ∼3.5 kHz is strong at the radial center in both I_em and I_s power spectra. The same frequency component is also strong around |r_c| = 22 mm.

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Owing to the line-integral effect, odd and even modes along the azimuthal direction should become weak and strong, respectively, at r_c = 0 [21]. Therefore, strong fluctuation components at f> ∼3.5 kHz and f < ∼3.5 kHz have odd and even azimuthal mode numbers (m), respectively. The low-frequency component at the radial center has a small maximum at f ∼ 1.5 kHz. If this component is attributed to an even mode rotation with m = 2 or more, this rotation should occur at a radius of ∼22 mm or more, considering the line-integral effect [21]. Furthermore, the total ion flux flowing into the target plate, which covers a radius of 32 mm, is not sensitive to the rotation phenomenon (m ≥ 1) within its radius, owing to the integration effect in the azimuthal direction. However, as shown in figure 8, similar maxima at f ∼ 1.5 kHz are confirmed in the power spectra of the local fluctuation of I_s at r_p = 0 and I_tgt. Therefore, the mode number of the low-frequency component can be designated as m = 0.

By using the V_f and V_p radial profiles in figure 6, the E_r × B rotation frequency (f_θ) can be estimated, where E_r is the radial electric field. Because E_r = −dV_p/dr_p, the azimuthal rotation speed (v_θ) can be calculated by the V_p radial profile as v_θ = E_r/B = (−dV_p/dr_p)/B. Furthermore, if the contribution from the T_e gradient is negligible, v_θ ∼ (−dV_f/dr_p)/B. By using v_θ, f_θ = v_θ/2πr_p can be obtained as a function of r_p. Owing to the hollow potential profile, the E_r × B direction corresponds to the clockwise direction viewed from the source region, as shown in figure 1(a).

The estimated f_θ profiles from V_f and V_p are superimposed with black dashed lines and circles, respectively, in figure 7. Because of some disturbance and an inaccurate radial position, the estimated f_θ near the plasma center is not reliable. The f_θ values calculated from V_f and V_p are almost similar in all P cases. Therefore, the contribution of the T_e gradient is much smaller. At P = 0.44 Pa, f_θ is smaller than the spectral peak frequency of f ∼ 30 kHz around r_p = [−18, 4] mm. In contrast, f_θ shows good agreement with the spectral peak around f = 6 kHz at r_p ∼ [−25, −10] mm in the recombining states. A mode rotation with rotation frequency f_θ generates a fluctuation with the frequency of mf_θ at any fixed position. Therefore, this frequency match indicates that the mode number of the periodic fluctuation at f ∼ 6 kHz is m = 1.

In fusion devices, a typical nondiffusive edge plasma transport is called 'blobby plasma transport.' Inside a coherent plasma structure named a 'blob,' there is a poloidal (azimuthal) electric field (E_θ) generated by the gradient and curvature of the magnetic field, and the E_θ × B drift transports the blob radially outward [22, 23]. In the experimental studies of the blobby plasma transport, the cross-correlation between I_s and E_θ is often investigated because I_s and E_θ are proportional to n_e and the radial drift speed (v_r) as v_r = E_θ/B, respectively. Thus, a significant correlation between them indicates the existence of radial particle transport. By using three or more electrodes, as shown in figure 1(b), E_θ is estimated by a difference of two V_f values at poloidally (azimuthally) distant positions as ${E_{\rm{\theta }}} = - \left( {{V_{{\text{f}}1}} - {V_{{\text{f}}2}}} \right)/d$, assuming that T_e fluctuations at the V_f measuring electrodes are the same when a blob passes through the I_s measuring electrode. This study estimates E_θ by applying the same approach with V_f1 and V_f2. The E_θ sign is defined such that the E_θ × B drift direction points radially outward when E_θ is positive.

Figures 10(a)–(d) shows the cross-correlation functions between I_s and E_θ, C(I_s, E_θ), as functions of τ and r_p at P = 0.44, 1.4, 2.2, and 6.4 Pa, where τ is the time delay between two fluctuations. The cross-correlation function is defined by $C\left( {{I_{\rm{s}}},{\rm{}}{E_{\rm{\theta }}}} \right) \equiv \,\langle{{\tilde I}_{\rm{s}}}\left( t \right)\,{{\tilde E}_{\rm{\theta}} }\left( {t + \tau } \right)\rangle$. Before the calculation, a band-pass filter at f = [0.5, 200] kHz is applied to remove the low-frequency component due to the probe motion and high-frequency peak, which is particularly evident in V_f (figure 8(b)). At τ = 0, the C amplitude is proportional to the radial particle flux, under the assumption that ${\tilde I_{\text{s}}}$ corresponds to the density fluctuation. At r_p ∼ −18 mm, we can observe quasi-periodic repeating structures except for the P = 6.4 Pa case. At P = 0.44 Pa, ${\tilde I_{\text{s}}}$ and ${\tilde E_{\rm{\theta }}}$ are anti-phase with C < 0 at τ = 0, while ${\tilde I_{\text{s}}}$ and ${\tilde E_{\rm{\theta }}}$ are in-phase at P = 1.4 and 2.2 Pa. Thus, there are different instabilities in the ionizing and recombining states. The instability in the recombining state corresponds to the f ∼ 6 kHz component in figure 7 with m = 1. In contrast, at P = 6.4 Pa, only a positive correlation at τ ∼ 0 is found near the center of the plasma region. Outside the target skimmer radius in all pressure cases, there are no strong C values because of the small fluctuation amplitudes compared to the radial center.

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The amplitude of the correlation function is strongly affected by the fluctuation amplitudes of the two signals in addition to their similarity. Thus, the cross-correlation coefficient, which is defined by the normalized C as $R\left( {{I_{\rm{s}}},{E_{\rm{\theta}} }} \right) \equiv C\left( {{I_{\rm{s}}},{E_{\rm{\theta}} }} \right)/\langle{{\tilde I}_{\rm{s}}^2}\rangle^{0.5}\;\langle{{\tilde E}_{\rm{\theta}}^2}\rangle^{0.5}$, is calculated. Figures 10(e)–(h) shows the cross-correlation coefficients drawn with the same color scale. It is found that there is no strong R in the periphery of |r_p| > ∼ 30 mm at P = 0.44 Pa. In contrast, relatively strong correlation coefficients (R ∼ 0.4) are clearly observed at r_p ∼ [−40, −32] mm at P = 2.2 Pa and |r_p| > ∼ 30 mm at P = 6.4 Pa. The high-R structure in the former case (P = 2.2 Pa) seems to connect to the inner quasi-periodic structure (figures 10(c) and (g)), while the latter structure (P = 6.4 Pa) is separated from the inner structure (figures 10(d) and (h)). A positive correlation around τ ∼ 0 indicates the existence of radial transport due to the E_θ × B drift. At P = 2.2 Pa, the radial range with high-positive R corresponds to a region where I_s stops decreasing from the center and flattens (figure 5(b)). At |r_p| > ∼ 40 mm, a positive correlation exists but suddenly decreases (R ∼ 0.2). In contrast, at r_p ∼ −40 mm in the P = 1.4 Pa case, where the dip of the I_s profile is shown in figure 5, weak negative and positive correlation coefficients are observed at τ ∼ 0 and τ < 0, respectively (figure 10(f)). However, they are not reliable because of the low-I_s plasma, as discussed later.

To estimate the typical v_r, the conditional averaging (CA) technique is applied to the Langmuir probe signals at r_p = [−40, −32] mm, which is outside the target skimmer radius and equips a high correlation at P = 2.2 Pa and P = 6.4 Pa. CA has also often been used in blobby-plasma transport studies [19, 24]. Because in this experiment, the measurement position is changed with time, the moving-normalized I_s, ${I_{{\text{sn}}}} \equiv \left( {{I_{\text{s}}} - {\mu _{\text{m}}}} \right)/{\sigma _{\text{m}}}$, is used as a reference signal for CA, as in previous studies [7, 25]. Here, the moving-averaged mean and standard deviation are defined as ${\mu _{\text{m}}} = \langle{I_{\text{s}}}\rangle_{\text{m}}$ and ${\sigma _{\rm{m}}}\; = \;\langle{I_{\rm{s}}^2}\rangle_{\rm{m}}^{1/2}$, respectively, where ${\langle \rangle _{\text{m}}}$ indicates the average with a sliding window. The width of the sliding window is set to 40 ms in time, where a high-frequency component at $f \geq 25$ Hz becomes ∼0 in ${\mu _{\text{m}}}$. Before using the moving normalization, a low-pass filter at f = 19 kHz is applied to remove a non-negligible discharge-power-supply noise at f = 20 kHz and its harmonics, as described above. Furthermore, to restore the unit of the reference signal, $I_{\text{s}}^\prime \equiv \langle{\sigma _{\text{m}}}\rangle{I_{{\text{sn}}}}$ is defined. Similarly, $E_{\rm{\theta }}^\prime$ is calculated with a low-pass filter at f = 200 kHz.

Figure 11 shows the CA results of I_s', v_r', which is derived from the CA of E_θ', and I_s'v_r', which is roughly proportional to the radial particle flux. In this calculation, 110/41/46/41 time points are identified at P = 0.44/1.4/2.2/6.4 Pa, respectively, when I_sn exhibits positive spikes with peak amplitudes over 1.5. Then, I_s' and E_θ' signals around the detected time points are extracted and averaged in the same time domain along τ. In addition, because higher-frequency components exist at P = 0.44 Pa, the CA result with a low-pass filter at f = 50 kHz and a threshold value of 2.5 (111 time points) is additionally calculated and superimposed by the thin solid line.

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It is observed that I_s'v_r' at P = 2.2 Pa has the maximum amplitude, while I_s'v_r' in the ionizing state at P = 0.44 Pa is sufficiently small, which is independent of the frequency of the low-pass filter. At P = 2.2 Pa, a positive spike of I_s' with a duration of ∼0.2 ms accompanies a positive spike of v_r' with a similar time scale and a typical radial speed of 200–300 m s⁻¹. At P = 6.4 Pa, the I_s' peak appears later than the v_r' peak. This can be explained by the fact that the enhancement of the radial transport occurs near the recombination front, which is axially distant from the measurement position. The change in the plasma potential is transmitted in the parallel direction faster than that in plasma density, because the former and latter parallel speeds are determined by electrons and ions, respectively. Thus, the separated high-R structure in the periphery in figure 10(h) can be attributed to the localized radial plasma ejection and its parallel transport.

At P = 1.4 Pa, a negative v_r' with a longer time scale than I_s' spike is detected at τ > ∼ 0. As a result, I_s'v_r' becomes negative; however, the inward flux is not reliable. The longer-time-scale fluctuation in v_r' can be explained as follows. Under this condition, because I_s is quite small (figure 5), the plasma is very weak after the blob-like events pass the probe head. As an extreme condition, if there is no plasma, the time constant of the voltage change is determined by the resistance and capacitance in the probe circuit. Considering the input resistance of the analog-to-digital converter (1 MΩ) and the capacitance of the coaxial cable (∼1 nF per 10 m), the time constant becomes too long (>1 s with dozens of meters of the coaxial cable). Under this condition, if there is a difference in the time constants of two V_f measurement circuits, E_θ' and v_r' would have finite values after changing the probe voltage over a long time scale after the passing of the blob-like events. Outward transport is not confirmed at P = 1.4 Pa.

The above analyses indicate that an enhanced radial transport exists in the recombination front where the ion-flux profile broadening is observed, as in the previous study conducted on NAGDIS-II [8]. To investigate the dependence on the radial position, the CA analysis is also applied at r_p = [−22, −14] (94 time points) and [−30, −22] mm (63 time points) at P = 2.2 Pa, as shown in figure 12. The former and latter positions correspond to the region where the quasi-periodic fluctuation is clearly observed in figure 10(c) and the intermediate region between the former region and high-R region in figure 10(g), respectively. We can find a quasi-periodic I_s' fluctuation, positive v_r', and largest I_s'v_r' at r_p = [−22, −14] mm. By increasing |r_p|, the peak amplitude of I_s'v_r' decreases. In contrast, the v_r' amplitude becomes the highest at r_p = [−40, −32] mm. This might be because blob-like structures with large radial velocities are selectively transported to the periphery.

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Figure 13(a) shows a contour plot of ${\tilde I_{{\text{em}}}}$ at z_c = −10 mm as functions of t and r_c. In the drawn time period, there are several radially elongated structures beyond the target skimmer radius with positive ${\tilde I_{{\text{em}}}}$, which correspond to radial ejection events. Between r_c ∼ −15 and 15 mm, ${\tilde I_{{\text{em}}}}$ is anti-phase, agreeing with the above prediction that the mode number of the f ∼ [3.5, 10] kHz component at r_p ∼ [−25, −10] mm is m = 1. In addition, this fluctuation appears to be synchronized with the fluctuation around the radial center, whose mode number is m = 0.

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The horizontal slices of figure 13(a) at r_c = 0, −15, and −30 mm are shown in figures 13(b)–(d) as a function of t. The low-pass I_em at f < 3.5 kHz, I_emL, is also superimposed by green dashed lines in these figures. Here, f = 3.5 kHz lies roughly between the m = 1 rotation component and the m = 0 little maximum around the radial center; thus, I_emL reflects the m = 0 frequency component. The I_emL at r_c = 0 in figure 13(b) appears to have an anti-phase relationship with that at r_c = −30 mm in figure 13(d), while the I_emL amplitude at r_c ∼ −15 mm is small, as shown in figure 13(c).

Figures 13(e) and (f) shows the time series of I_s at r_p = −50 mm and I_tgt. Similar to I_emL, their low-frequency components, I_sL and I_tgtL, are overplotted by green dashed lines. The time series of I_s shows non-simple behavior, but I_sL seems to be correlated with I_emL at r_c = −30 mm with a time delay. In contrast, I_tgt and I_tgtL are quite similar to I_em and I_emL at r_c = 0, respectively.

Figure 13 shows the occurrence of several events within a short period of 2 ms. To clarify the spatiotemporal behaviors of the m = 0 and 1 modes over a longer period, a cross-correlation analysis is applied with the electrostatic signals at t = [2.3, 2.5] s under a steady-state condition.

First, the cross-correlation coefficient between I_s at r_p = −50 mm and I_em, $R\left( {{I_{\text{s}}},{\text{ }}{I_{{\text{em}}}}} \right)$, is investigated, as shown in figure 14. Here, a low-pass filter at f = 19 kHz is applied to I_s before the correlation analysis to remove the power-supply noise. The maximum correlation (R ∼ 0.4) is detected at r_c ∼ −28 mm when τ ∼ −0.3 ms, and this positive-correlation structure connects to the far peripheral region. This highest R position corresponds to the intermediate radial region (r_p = [−30, −22] mm) in the CA analysis result (figure 12), which is just outside the region where the quasi-periodic fluctuation is observed. This means that the plasma ejection originates from the enhanced quasi-periodic fluctuation with m = 1 and reaches the far edge region at r_p = −50 mm in ∼0.3 ms. At |r_c| > 30 mm, R in figure 14 decreases but an internal electric field, which drives the radial transport, is maintained, as shown in figure 12. In addition, a negative correlation is detected at r_c ∼ 0 when the maximum correlation is observed at τ ∼ −0.3 ms in figure 14.

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To understand in detail each mode relationship, the cross-correlation coefficient between I_tgt and I_emL, $R\left( {{I_{{\text{tgt}}}},{\text{ }}{I_{{\text{emL}}}}} \right)$, is investigated, as shown in figure 15(a). Here, a low-pass filter at f = 19 kHz is applied to I_tgt before the correlation analysis, in the same way as that in figure 14. A maximum correlation coefficient in $R\left( {{I_{{\text{tgt}}}},{\text{ }}{I_{{\text{emL}}}}} \right)$ is detected at r_c ∼ 0 when τ ∼ −0.04 ms (R ∼ −0.6). Thus, a decrease in I_emL around the radial center corresponds to the ion-flux reduction at the target with a time lag of tens of microseconds. In contrast, $R\left( {{I_{{\text{tgt}}}},{\text{ }}{I_{{\text{emL}}}}} \right)$ has negative peaks around |r_c| = 24 mm at the same τ, meaning that the I_emL radial profile becomes flatter when I_tgt decreases. In contrast, at τ ∼ −0.3 ms, correlations with opposite signs to those at τ ∼ 0 are confirmed. This indicates that the I_emL profile becomes steep before the profile flattening.

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To reveal the amplitude behavior of the m = 1 mode, the Hilbert transform is applied, which can extract the envelope component of the fluctuation, E, from the absolute value of the analytical signal [7, 26, 27]. First, a high-pass filter at f > 3.5 kHz is applied to I_em (I_emH), and then, its envelope, E(I_emH), is calculated. After that, a low-pass filter at f < 3.5 kHz is applied to the envelope, E(I_emH)_L. The low-pass envelope plus low-pass signal, I_emL + E(I_emH)_L, at each r_c is superimposed in figures 13(b)–(d) with a magenta dotted line. Similarly, I_sL + E(I_sH)_L and I_tgtL + E(I_tgtH)_L are overplotted in figures 13(e) and (f), respectively. In figure 13(c), we can observe that E(I_emH)_L detects the enhancement of the m = 1 mode, particularly at r_c = −15 mm.

Figure 15(b) shows the cross-correlation coefficient between I_tgt and E(I_emH)_L, $R\left( {{I_{{\text{tgt}}}},{\text{ }}E{{({I_{{\text{emH}}}})}_{\text{L}}}} \right)$, where a low-pass filter at f < 19 kHz is applied to I_tgt before the correlation analysis. Strong negative correlations in $R\left( {{I_{{\text{tgt}}}},{\text{ }}E{{({I_{{\text{emH}}}})}_{\text{L}}}} \right)$ are observed at |r_c| ∼ [10, 25] mm when τ ∼ −0.15 ms (R ∼ −0.6). Moreover, at τ ∼ −0.4 and 0.1 ms, positive correlations (R ∼ 0.4) are observed within the same radial range. This indicates that the m = 1 fluctuation becomes strong just before the I_tgt reduction and the m = 1 envelope amplitude oscillates quasi-periodically.

Because I_emL and E(I_emH)_L are shifted by approximately a quarter period of f ∼ 1.5 kHz from that in figures 15(a) and (b), a predator-prey-like relationship exists between the m = 0 and 1 modes. The analysis results can be interpreted as follows: before the I_tgt reduction at τ = 0, a weakening of the m = 1 mode occurs at τ ∼ −0.4 ms, and then, the I_emL profile sharpens at τ ∼ −0.3 ms. After that, the m = 1 mode strengthens at τ ∼ −0.15 ms and elongates toward the periphery, which leads to radial transport. At τ ∼ 0, owing to the radial plasma ejection from the plasma column, the I_emL profile becomes flatter, and the m = 1 mode weakens again at τ ∼ 0.1 ms. Although I_em is simply a line-integrated emission signal, considering the strong correlation between I_em and electrostatic signals, I_em reflects the motion of coherent structures. In addition, considering the phase relationship between changes in the m = 0 mode profile and the m = 1 mode intensity, the m = 1 mode can be directly or indirectly driven by the radial gradient of the plasma profile.

A strong relation between the m = 0 and 1 modes was also reported in previous experiments conducted on NAGDIS-II [7, 9] and a three-dimensional numerical simulation [28]. However, a clear quarter-period shift between the two modes and their quasi-periodicity is observed for the first time in this study.