2.2 RMP impact on the edge impurity radiation and stability of detached plasma

The large helical device, LHD, is a heliotron-type fusion machine, in which the magnetic field is produced by superconducting coils with poloidal and toroidal

#### Figure 1.

The pattern of the connection length LC in the edge stochastic layer of LHD (a); the tomographic reconstruction of the emission from carbon ions CII (514 nm) (b) and CIV (466 nm) (c), recorded just before the detachment onset, at line averaged plasma density ne = 5 1019 <sup>m</sup><sup>3</sup> .

winding numbers l = 2 and n = 10, respectively [23]. Figure 2(b) displays a poloidal cut of the calculated magnetic field structure in the edge region and the distribution of connection length LC. The magnetic field in helical devices is completely generated by currents in external coils and has a broad spectrum of Fourier harmonics of different mode numbers m and n. Each of those generates magnetic islands, and by overlapping of the islands, the magnetic field structure becomes stochastic. The divertor legs, named left and right legs, are connected to the L and R divertor plates, respectively, rotating helically by moving in the toroidal direction. The lower half of the Figure 2 presents the LC distribution with RMP of m/n = 1/1, where the remnant island structure embedded into the stochastic layer is visible.

Figure 3 shows the time evolution of several plasma parameters in discharges with and without RMP where the density ramp up was performed without auxiliary impurity seeding, and the edge radiation was coming mainly from carbon impurity sputtered from the divertor target plates. On the one hand, without RMP (blue lines), the growth of the density leads to a sudden increase of the radiated power, see Figure 3(b), and, finally, to the radiation collapse of the whole plasma. On the other hand, with the RMP application (red lines), the radiated power is saturated at a higher level and the state with the plasma detached from the divertor targets is sustained during the whole later phase of the discharge. This is demonstrated in Figure 3(a) by the evolution of the heat load onto the divertor target. The strong cooling of the edge plasma by impurity radiation leads to the decrease of the plasma column effective radius a99 displayed in Figure 3(d).

Figure 4 shows the radial profiles of the electron temperature Te, density ne, and pressure in the edge region along the LHD mid-plane, in the attached and detached discharge phases [24]. With the RMP application, a clear flattening of the T<sup>e</sup> profile due to the magnetic island is observed at the outboard, R = 4.60–4.75 m, in the attached phase. The increase in the density leads to the lowering of Te, and during the detached phase,T<sup>e</sup> inside the island is sustained at 20 eV. It is also interesting to note that with the growing ne, the width of the region with the profile flattening becomes slightly narrower, and at the same time, a region with the flattening appears

#### Figure 2.

Top view of the LHD torus with the position of divertor probe arrays at the inboard, indicated by numbers and letters "L"& "R" (a); LC distribution in the edge region of LHD, without (upper half) and with (lower half) RMP application (b). The right and left legs, indicated in the figure, are connected to L and R divertor arrays, respectively.

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

#### Figure 3.

Time evolution of plasma parameters in the LHD density ramp-up discharges, with (red) and without (blue) the RMP application: The power load onto divertor targets measured by probes (a), the radiated power measured by AXUV (b), line averaged density (c), and the effective plasma minor radius a99 defined as that of the flux surface, containing 99% of the total plasma energy (d).

#### Figure 4.

Radial profiles of the plasma parameters in the LHD edge region: electron temperature (a, d, g), density (b, e, h), and pressure (c, f, i); the panels (a–f) correspond to discharges with RMP, (g–i)—without RMP. The region of the Te flattening caused by the magnetic island is indicated by yellow patch [24].

at the inboard, R = 3.1–3.2 m. This is interpreted as a result of the plasma response to the external RMP field. Indeed, the measurements with a saddle loop coil indicate the reduction of the total field perturbation by RMP induced by the currents in the plasma under the attached conditions and its amplification during the detached phase [20, 25, 26]. A similar flattening appears in the pressure profiles, while density is relatively flat in the entire edge region with some modulations around the magnetic island. Without RMP application, there is no such flattening except for a small modulation due to the inherent small remnant islands of higher mode numbers.

The edge impurity radiation profiles are estimated using the T<sup>e</sup> and n<sup>e</sup> profiles presented in Figure 4 and by assuming a concentration of carbon of 1% with respect to ne. Figure 5 shows the temporal evolution of the radiation profiles together with LC distributions [24]. Without RMP, Figure 5(b), the impurity radiation starts to peak around the X-point of the divertor leg, at R 4.8 m, and later moves gradually radially inward due to the decrease in the temperature as the density increases; the X-point of the divertor leg should be distinguished from that of the magnetic island created by the RMP. Finally, the radiation penetrates into the confinement region at t = 4 sec, leading to the radiation collapse, as shown in Figure 3. With the RMP application, Figure 5(a), a bundle of flux tubes of long connection length appears at the edge, as a remnant island. The radiation starts to peak at the X-point of the divertor leg and moves radially inward, similarly to the case without RMP. It is, however, stopped at the periphery of the edge of the island, R 4.75 m, without penetrating into the confinement region at the detachment transition, t 2.9 sec. Then, the discharge is sustained until the end of NBI heating due to the stabilization of the radiation profile by the island.

Radiation profile measurements have been performed to capture the change of the global structure of impurity emission due to RMP and are compared with numerical transport simulations with the code EMC3-EIRENE [20–22]. Figure 6 shows the calculated impurity radiation distribution, with and without RMP, and

#### Figure 5.

The calculated LC distribution in the outboard edge region (upper panels); time evolution of the carbon radiation estimated from Te and ne profiles as shown in Figure 4, by assuming 1% carbon concentration and noncoronal cooling rate at neτ = 1017 m<sup>3</sup> s (lower panels), with (a) and without (b) RMP [24].

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

Figure 6.

Carbon impurity radiation distribution calculated by EMC3-EIRENE at poloidal cross section, together with line-integrated profile of the simulation and measurements by AXUV, on the right panel, without (a) and with (b) RMP [20].

the radiation profile measured by the AXUV diagnostics [20]. Without the RMP application, the impurity radiation is enhanced at the inboard as it is demonstrated in Figure 6(a). The line integrated radiation profile found both in the measurements and in simulations are shown in the right panel. Both profiles have maxima at the center channels, which pass through the enhanced radiation at the inboard location. With the RMP, the peak of the radiation moves to the bottom of the plasma, where the X-point of the m/n = 1/1 island is located (note that the toroidal angle positions of the cross sections are different in Figures 2(b) and 6). The simulation also shows a peak at the bottom channel in accordance with the measurement. The measurements by imaging bolometer also indicate enhanced radiation around X-point in agreement with the numerical simulation [21].

The impact of RMP on the impurity emission intensity was also investigated in the VUV range with the diagnostic equipment [22], viewing the entire plasma toroidal cross section. Density dependence of the radiated power measured by the resistive bolometer, together with emissions from different charge states, CIII (C2+), CIV (C3+), CV (C4+), and CVI (C5+), measured with the spectrometer [27] is plotted in Figure 7. Here, the plasma density is normalized to the density limit in helical devices, nsudo [28]. It is seen that without RMP, the radiated power shows rapid increase around the density limit, that is, <sup>∂</sup> Pbolo ∂ ne without RMP! . This means that any small density perturbation leads to a significant change in the radiation; that is, the system in question is becoming unstable. With RMP, the radiation is enhanced in the low-density range even in the attached phase. The increase of the radiation with RMP is interpreted due to the enlarged volume inside the edge magnetic island with a low Te, of 10–20 eV where the radiation of low charged carbon ions approaches its maximum. After the detachment transition, there appears a region where the radiation is insensitive to the density, that is, <sup>∂</sup> Pbolo ∂ ne with RMP!0. This provides a possibility to the radiation level control and, thereby, the detachment stability. One can see that the "flat" region extends slightly beyond the density limit, which results in an extension of density operation range for the case with RMP. Very similar density dependence as for the bolometer measurement is observed in the emission of CIII and CIV species, being the dominant radiating charge states, see Figure 7(b) and (c). As it is analyzed in Ref. [16], CIV is providing the largest contribution to the total radiated power. On contrary, with RMP, the radiation of CV and CVI ions increases monotonically with the plasma density, and is larger than without RMP. Since the ionization energies of CV and CVI ions, 392 and 490 eV, respectively, are much higher than the Te inside the magnetic island, the higher emission intensity might indicate enhanced penetration of impurity toward the core boundary. The contribution of CV and CVI to the total radiated power is, however, small compared to the states of lower charges [16].

#### Figure 7.

Density dependence of the radiated power measured by the bolometer (a), the emissivity of CIII (b), CIV (c), CV (d), and CVI (e) species measured by VUV spectrometer without (triangles) and with (circles) RMP. The density is normalized to the density limit in helical devices, nsudo [27].

The results above clearly show the difference of edge impurity radiation and transport with and without RMP. This is of high importance for the detachment stabilization in the former situation. The mechanism of the stabilization of the radiation layer is under investigation by taking into account the magnetic geometry, the particle, and the energy transport, both parallel and perpendicular to the field lines within and out of the magnetic island. Similar observations of the detached plasma stabilization with large island were also found in W7-AS [29]. The recent results on the successful detachment control in W7-X with the island divertor also suggest an important role of the edge magnetic island for the detached plasma stability [30].

#### 2.3 Change of divertor footprint with RMP application

The toroidal variation of the particle fluxes onto divertor plates with RMP has been investigated with Langmuir probe array installed around the mid-plane of the targets at the inboard side [17, 31]. It has been found that the time evolution of the divertor particle flux exhibits substantial difference between toroidal locations, that is, some plates are becoming detached earlier than others; at some plates, the flux even increases after detachment [27]. The summary of this behavior is shown in Figure 8, where the divertor particle flux normalized to its value without RMP is plotted for different toroidal sections. In the attached case, there is an n = 1 mode structure for both left (L) and right (R) divertor arrays, which are connected to the left and right legs, respectively, as indicated in Figure 2. In the detached phase, the n = 1 structure remains, but the toroidal phase is shifted by one section. The relation between the divertor flux and LC profiles is presented in Figure 9 for several toroidal cross sections [27]. At the section 6L (Figure 9(a) and (b)), a bundle of flux tubes of 6.5 mm width is connected to the divertor plate. By applying RMP, the footprint shifts toward the right side with increased LC. The measured particle flux increases in the absolute values due to the longer LC, as seen also in Figure 9(a).

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

#### Figure 8.

The toroidal distributions of the particle flux onto divertor targets with RMP normalized by the values without RMP on attached (a) and detached (b) discharge phases. Red circles correspond to the left divertor and blue diamonds to the right divertor arrays, as it is indicated in Figure 2 by the toroidal section number [27].

The flux profile becomes more asymmetric with respect to the central peak, being increased at the right side, which reflects the right shift of the LC footprint. On the other hand, the 2R plate shows decrease of the particle flux with the RMP application, as seen in Figure 9(c). This is interpreted by the decrease in LC, as shown in the figure, where the long LC bundle at the central region almost disappears with RMP, and thus, the particle flux decreases as well. These results show that, to a certain extent, the particle transport is well correlated with the LC distribution calculated in the vacuum approximation, i.e., without a plasma response to RMP, and thus can be controlled by the RMP application in the attached phase. In the detached phase, the particle flux both at 6L and 2R decreases in the entire region with respect to the case without RMP, as shown in Figure 9(b) and (d).

In Figure 9(e) and (f), the observations in section 2L are presented. By applying RMP, the particle flux becomes smaller in the attached phase with respect to the reference case without RMP. The flux, however, increases at the detached phase, as shown in Figure 9(f). At this plate, the fraction of long flux tubes with LC > 100 m decreases, but those with LC 30 m increases with RMP. The reduction of the flux at the attached phase may be due to the reduction of the contribution from the tubes with LC > 100 m. On the other hand, in the detached phase, the increases of the flux could be attributed to the change of the particle transport channel from long, LC > 100 m, to the medium, LC 30 m, flux tubes. This effect has to be investigated by analyzing in detail the relation between the magnetic field structure and the ionization front. It has to be taken into account that there is a significant

Figure 9.

LC (solid lines) and divertor particle flux (dashed lines with circles) profiles along the divertor probe pins, with (red) and without (black) RMP. (a and b) 6L, (c and d) 2R, and (e and f) 2L toroidal section, respectively [27].

plasma response to the RMP, which is different in the attached and detached phases, as mentioned above.

During the detached phase, there are large oscillation in both divertor particle flux and radiation. Figure 10 presents the time traces of the particle flux to the divertor targets and of the radiation losses measured by AXUV during the detached phase, where oscillation with 60–90 Hz is visible. The particle flux and radiation are oscillating in phase. Similar behavior was also observed in the particle flux to the first wall [32]. The mechanism of the oscillation is discussed later in this chapter.
