In future fusion reactors, detached divertor is employed to reduce heat flux entering the divertor plate by cooling and neutralizing the plasma in the scrape-off layer (SOL). As a result, the dominant atomic process along the magnetic field line transitions from ionization to recombination. Numerical simulations have shown that the electron temperature Te decreases monotonically, and the electron density ne exhibits a rollover behavior along the field line [1]. The location where volumetric recombination occurs most actively is referred to as the recombination front. As well as the location, the scale length of this front is critical for its control.
In many linear plasma devices, measurements of Te and ne are performed at fixed points by systematically varying the neutral gas pressure p in the vacuum chamber [2, 3]. Measurements at downstream and upstream ports have suggested a decrease in temperature and/or density along the field line [4]. However, direct measurements of the gradient scale length were difficult due to restriction of measurement port accessibility. We developed a local two-point measurement probe called a forked probe to evaluate the scale lengths of electron temperature and density. This paper presents initial results of the forked probe, which suggest that the electron temperature gradient becomes steep near the pressure at which the density peaks.
The experiment was conducted in the electron cyclotron resonance (ECR) linear plasma device NUMBER [5], which consists of a cylindrical vacuum chamber with its axis defined as the z-axis. Helium plasma was produced between the microwave injection window at z = 0 m and an endplate at z = 1.98 m. Although the magnetic field B in downstream test region varies with time, this study focuses on the range B = 0.1–0.3 T. Feeding additional helium gas into the downstream region, we obtained volumetric recombining plasma as previously reported [6].
We developed a forked probe, and its conceptual diagram is illustrated in Fig. 1. It has electrostatic probes capable of simultaneous measurements at two points with a spatial resolution of Δz = 40 mm apart. The upstream and downstream electrodes are referred to as UE and DE, respectively. Using the single-probe method, we evaluate Te and ne. We also evaluate the inverse scale length of Te and ne gradients along the field line: 1/LTe is defined as
Fig. 1.
Schematic diagram of the forked probe (left) and a corresponding photograph (right) taken from below, showing the actual probe configuration.
|
1
L
T
e
=
1
T
¯
e
T
e
,
DE
−
T
e
,
UE
Δ
z
,
| (1) |
where T¯e represents the average temperature between UE and DE. 1/Lne is also defined using a similar equation. The forked probe was positioned at z = 1.66 m, and the pressure dependence of these parameters was measured.
Figure 2 shows the measured pressure dependence of Te, ne, 1/LTe, and 1/Lne. As neutral pressure increases, Te decreases monotonically. At pressures p ≥ 1.4 Pa, Te measurements by the single-probe method may be overestimated [7]. Consequently, since ne is derived from the probe current using Te, it may be underestimated in the same pressure region. For ne, a rollover (referred to as a ne-p rollover) is observed, where ne increases up to 7 × 1017 m−3 at p = 0.8 Pa and then monotonically decreases.
.
Figures 2(c) and (d) present 1/LTe and 1/Lne with third-order polynomial fits, denoted as gTe(p) and gne(p). Negative values of the inverse scale lengths in Figs. 2(c) and (d) correspond to decreasing temperature and/or density in a downstream direction. The inverse scale lengths for both temperature and density are on the order of 1 m throughout the experimental pressure range. The spatial temperature gradient exhibits distinct behavior across different pressure regimes. In the low-pressure regime p ≤ 0.7 Pa, the Te decreases toward downstream but moderately, where the scale length of the temperature gradient is about |LTe| ∼ 1 m, comparable to device scale. In the high-pressure regime p > 0.7 Pa, a steep temperature gradient is observed at the probe position, where the scale length reaches |LTe| ≃ 0.3 m, much shorter than the device scale. The average temperature in the steep temperature gradient is Te < 3 eV, lower than in the low-pressure region, as shown in Fig. 2(a). Notably, the pressure range exhibiting the steep temperature gradient in Fig. 2(c) corresponds closely to the region of the ne-p rollover. 1/Lne gradually increases up to approximately p = 1.5 Pa. The data reveal that 1/Lne exhibits a weak decreasing gradient or remains nearly uniform in the low-pressure region while showing a weak increasing gradient in the intermediate-pressure region. The pressure-dependent sign change of 1/Lne indicates the existence of a spatial density peak that moves upstream with increasing pressure.
In order to reconstruct the spatial profiles of Te(z) and ne(z) along the magnetic field line, the experimentally obtained pressure dependences of Te(p) and ne(p) are converted to their z-dependence. In the following discussion, we assume that the z-profiles of Te and ne maintain their shape but shift spatially with pressure changes along the field line. An equivalent change in z-direction is obtained from the difference in pressures:
|
z
(
p
i
+
1
)
=
z
(
p
i
)
+
(
p
i
+
1
−
p
i
)
d
z
d
p
|
p
i
+
1
/
2
,
| (2) |
where i represents the index of pressure ascending, pi+1/2≡(pi+1+pi)/2 is the average of neighbouring pressures. The boundary condition for z(p1) is set such that the pressure at the measurement port, z = 1.66 m, corresponds to pressure of interest. The derivative dz/dp is determined as follows:
|
d
z
d
p
=
d
T
e
(
p
)
d
p
/
d
T
e
d
z
(
p
)
.
| (3) |
In the right hand side of Eq. (3), the pressure derivative is obtained from the smoothed curve in Fig. 2(a), and the local gradient is taken from Fig. 2(c). Substituting Eq. (3) to Eq. (2) yields the equivalent position z for each pressure pi. The reconstructed z-profiles of Te(z) and ne(z) are presented in Figs. 3(a) and (b). To avoid the overestimation of Te, as mentioned earlier, the reconstruction is carried out in the pressure range p < 1.4 Pa. Fig. 3(a) demonstrates that Te decreases monotonically with increasing z. For ne, a rollover in the z-direction (ne-z rollover) is observed in Fig. 3(b). Specifically, the density gradually increases up to z = 1.66 m, then decreases sharply around z = 1.70 m.
Fig. 3.
Reconstructed spatial profiles of (a) Te and (b) ne along the magnetic field line at a gas pressure of p = 1.0 Pa.
In summary, direct measurements of Te and ne gradients along the magnetic field line were performed in helium recombining plasma using the linear plasma device NUMBER. The neutral gas pressure dependence reveals a steep temperature gradient, the scale length of which is shorter than the device length, for a certain pressure range. The density gradient reverses signs from positive to negative in high-pressure region indicating existence of a spatial density peak. The reconstruction of spatial Te and ne profiles demonstrates monotonically decreasing temperature and a spatially localized density peak, consistent with expectations from numerical simulations.
This work was supported by JSPS KAKENHI Grant Numbers 23H01148 and 23K25845.
