2.4 Operation space of detachment: amplitude and radial location of resonance layer of RMP

The parameter space of a stable discharge performance with the RMP and the plasma detached from the divertor targets has been investigated by varying the

Experimental Studies of and Theoretical Models for Detachment in Helical Fusion Devices DOI: http://dx.doi.org/10.5772/intechopen.87130

Figure 10.

Time traces of the radiation losses, measured by the AXUV (green line), and that of the particle flux to divertor targets (red and blue lines) during detached phase with RMP.

RMP amplitude and location of its resonance layer. Figure 11(a) shows the density dependence of the radiated power at different RMP amplitudes quantified by the ratio Br=B<sup>0</sup> scanned from 0 to 0.12%. The densities at the detachment onset and the radiation collapse are plotted as a function of Br=B<sup>0</sup> in Figure 11(b). The density range between the detachment transition and thermal collapse corresponds to the operation range with a stable detached plasma. One can see that the density at the collapse is almost independent of the RMP amplitude. With decreasing the amplitude, the detachment transition density shifts to higher density and finally merges with that where the collapse happens. For Br=B<sup>0</sup> < 0.07%, the RMP is almost completely suppressed by the plasma response, and thus, no stable detachment was realized. As it is seen in Figure 11(a), the radiation level attained in the detached phase is almost independent of the RMP amplitude.

The radial position of the resonance layer of the m/n = 1/1 RMP was scanned by changing the rotational transform ι, which is an inverse value of safety factor q normally used for tokamaks. The radial profiles of Te for different ι-configurations are plotted in Figure 12, where radial shift of the region with a flat Te profile is demonstrated. As the resonance layer with ι = n/m = 1 moves radially inward, the Te in the flattening region becomes higher. This is because the island gradually penetrates into the confinement region through the LCFS, and flux surfaces in the island are becoming closed. In the configurations with the magnetic axis at Raxis = 3.90 and 3.85 m, the island is marginally outside LCFS and is embedded into the stochastic layer. The stable detachment has been realized so far only for these two configurations. The openness of the flux surfaces in the island thus ensures a low enough level

#### Figure 11.

The radiated power as a function of density for different RMP amplitudes (a) and density at the detachment transition (circles) and radiation collapse (triangles) as a function of RMP amplitude (b).

Figure 12.

Radial profiles of Te for different profiles of the rotational transform. Configurations differ by the position of the magnetic axis, Rax. The stable detachment was realized for Rax = 3.85 and 3.90 m so far.

Te in the island and consequently a high level of the edge radiation from impurity ions of low charges.

The findings discussed above are summarized in Figure 13, where the radial location of the island is represented by the distance between the island X-point and the LCFS [12]. Here, the results from W7-AS are also incorporated. The operation spaces for two devices are not overlapping, which means that probably some hidden parameters important for the detachment stabilization are still missed. Nevertheless, it is seen that for stable sustainment of a detached plasma, there is a threshold value of Br=B0, which is nearly the same in the LHD and W7-AS, and a certain distance between the island and the confinement region is necessary.

#### 2.5 Compatibility with core plasma performance

The compatibility of a stable detached plasma with a good performance in the plasma core is an important issue for a fusion reactor. Temporal evolution of the radial profiles of Te, ne, and the electron pressure measured by Thomson scattering are plotted in Figure 14; ne=nsudo = 0.43 and ≥ 0.5 correspond to the attached and detached phases, respectively. From the Te and pressure profiles, one can see the shrinkage of the plasma volume observed as the RMP is applied, which is due to low Te within the edge magnetic island. It is found that with the RMP application, the increasing density leads to a peaking of the pressure profile. This is due to the increase in ne at the central region since the Te profiles are almost the same with and without RMP. The energy confinement time, τE, and central pressure, Pe0, are plotted in Figure 15, as functions of the line averaged plasma density [27]. Systematically, τ<sup>E</sup> is smaller with RMP, because of the plasma volume shrinkage. Without RMP, τ<sup>E</sup> becomes saturated around the density limit, while with RMP, it increases with density slightly beyond the density limit. In Figure 15, one can see that the pressure peaking with RMP is enhanced especially in the detached phase. Near the

Experimental Studies of and Theoretical Models for Detachment in Helical Fusion Devices DOI: http://dx.doi.org/10.5772/intechopen.87130

#### Figure 13.

The operation space in the plane ΔxLCFS�islandð Þ ΔxLCFS�div , Br/B0 with a stable detached plasma in the heliotrons LHD and W7-AS [12].

#### Figure 14.

Radial profiles of (a–c) electron pressure, (d–f) ne, and (g–i) Te, with (red) and without (black) RMP, for different densities, ne=nsudo = 0.43, 0.5, and 1.0.

thermal collapse density limit, the fusion triple product, n0τET0, becomes comparable for both cases, with and without RMP.

The global parameters are significantly affected by the change in the plasma volume caused by the RMP application. In order to study the local plasma transport characteristics, a core plasma energy transport has been analyzed with the 1-D transport code TASK3D [33]. This code calculates the heating source profile, in the present case by the NBI, by taking into account the beam slowing down and solves a heat conduction equation with ne and Te values measured experimentally.

Figure 16 shows the resulting NBI power deposition profiles and effective heat conductivity, χ eff¼0:5 χ <sup>e</sup>þχ<sup>i</sup> ð Þ, where χ <sup>e</sup> and χ<sup>i</sup> are those for electrons and ions and ρ¼reff =a<sup>99</sup> is the normalized minor radius. In the attached phase, ne=nSudo = 0.43, the NBI power deposition profiles are almost identical for the both cases with and

Figure 15.

Density dependence of energy confinement time, τE, (a) and of the central pressure, Pe0, (b), obtained with (circles) and without (triangles) RMP [27].

#### Figure 16.

Radial profiles of (a–c) χeff ¼ 0:5 χ<sup>e</sup> þ χ<sup>i</sup> ð Þ, and (d–f) NBI deposition, with (red) and without (black) RMP, for ne=nSudo = 0.43 (attached), 0.5 (detached), and 1.0 (detached), calculated by core transport code TASK3D.

without RMP, while χ eff is smaller with the RMP in the plasma central region. The larger χ eff in the very core without RMP is attributed to the flat pressure profile there, see Figure 14(a). In the detached phase with ne=nSudo = 0.50 and 1.0, the NBI heating power is deposited more at the central region with RMP. This is because of a deeper penetration of the NBI due to the shrinkage of the plasma volume with the edge radiation cooling. The increased energy deposition at the central region with RMP, �0.3 MW/m3 , provides an addition to the particle source density ΔSp of the order of 1019 1/s/m3 , estimated for an NBI particle energy of 180 keV. According to a simple

Experimental Studies of and Theoretical Models for Detachment in Helical Fusion Devices DOI: http://dx.doi.org/10.5772/intechopen.87130

picture of a diffusive particle transport, this ΔSp leads to a density increment of <sup>Δ</sup>n�SpΔr<sup>2</sup>=<sup>D</sup> <sup>¼</sup>1017�1018m�<sup>3</sup>, with <sup>Δ</sup><sup>r</sup> <sup>0</sup>:1�0:<sup>4</sup> <sup>m</sup> (Δ<sup>ρ</sup> <sup>0</sup>:2�0:8), <sup>D</sup> <sup>¼</sup><sup>1</sup> <sup>m</sup><sup>2</sup>=s. This level is too low to be responsible for the density increase of 1019 m�<sup>3</sup> observed at the plasma axis with RMP, Figure 14(e) and (f). In the inner plasma region, ρ < 0:6, χ eff decreases significantly both with and without RMP with the increasing density, although χ eff remains slightly smaller in the case with RMP. Together with the negligible effects of the NBI particle source, this indicates that the pressure peaking is probably due to the reduction of the transport. On the other hand, at the periphery, ρ>0:8, χ eff becomes larger with RMP. This could be due to additional stochastization caused by the RMP application. Here, the radial transport can be enhanced by flows along braiding magnetic field lines [34, 35]. The larger impurity emission with RMP, see Figure 7, could also lead to larger χ eff because TASK3D currently does not take into account the volumetric power loss. The present findings suggest that with the RMP application, there is no significant transport degradation in the central plasma region during the detached plasma phase, compared to the case without RMP.
