An innovative divertor concept, the fish tail divertor, for reducing the surface temperature on the divertor target plate in EAST tokamak experiments

An innovative divertor concept, the fish tail divertor, is proposed in this paper, aimed at reducing the surface temperature on the tokamak divertor plate as well as that due to the edge localized modes. This new concept has been implemented in experiments to demonstrate its capability of strike point sweeping on the plate at a frequency range from 10 to 100 Hz by using an oscillating magnetic field. A strike point movement of 5–6 cm is achieved by applying a coil current of several percent of plasma current, leading to a significant reduction of divertor surface temperature. The result indicates a possible application in a fusion reactor.


Introduction
The divertor heat load is one of the most critical problems for a fusion reactor, where the maximal power flux at the tokamak divertor plate is estimated to be about 100 MW m −2 , being more than one order of magnitude larger than the allowed material limit for plasma facing components [1]. It is a big a See Wan et al 2017 (https://doi.org/10.1088/1741-4326/aa7861) for the EAST Team. * Authors to whom any correspondence should be addressed.
Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. challenge to design a divertor to handle such a huge heat flux while being compatible with good core energy confinement. The radiated divertor, by injecting impurity in the divertor region to detach the plasma near the strike point, is a possible approach to reduce the heat load on the target and has been extensively studied in tokamak experiments. This approach could be acceptable for ITER, but it might limit the operational space of plasma parameters of a fusion reactor like the China Fusion Engineering Test Reactor [2] and DEMO [3]. In the past decade, new divertor concepts, such as the snowflake divertor (SFD) [4], X divertor (XD) [5], super XD [6] and X-point target divertor [7], have been proposed as alternative approaches for reducing the peak heat flux [8]. Although the SFD has been demonstrated on TCV [9][10][11], NSTX [12][13][14], DIII-D [15], and EAST [16] tokamaks, a too-large poloidal coil current would be required to generate this type of configuration in a reactor, if the coils are located outside the toroidal field coils and far away from the plasma.
Sweeping of the strike point on the divertor plate, to spread the heat flux over a larger area, is also a possible way to reduce the surface temperature. This method was implemented in JET experiments [17][18][19][20][21]. A model-based algorithm [17] was integrated into the plasma-shape control system to move the plasma boundary between two different configurations at a frequency of 4 Hz. The decrease in the divertor plate temperature by the sweeping was found in numerical simulations [18][19][20] and in experiments [21]. On EAST, the configuration was varied periodically from upper single null (USN) to lower single null (LSN) in a period of 20 s, to reduce the divertor plate temperature during long-pulse operations [22]. In all these experiments, the movement of the strike point was achieved by modifying plasma configuration using external poloidal field coils, and therefore the sweeping frequency was limited.
A new divertor concept, the fishtail divertor (FTD), has been proposed [23,24], aimed at reducing the divertor surface temperature as well as that due to the edge localized modes (ELMs). By using an oscillating magnetic field, generated by the electric current of in-vessel coils installed behind the target plate, the strike point is swept along the divertor plate like the swing of a fishtail, as shown in figure 1. Since the coil location is close to the strike point but is far away from the X point, the required coil current for the sweeping is small, and the associated change of the plasma shape is small. The feasibility and capability of FTD have been demonstrated in EAST experiments. By applying a coil current, I FTD , of 4% of the plasma current I p , the strike point has been swept in a range of 5-6 cm, and the sweeping frequency is varied from 10 Hz to 100 Hz. Theoretical results further indicate that a sufficiently fast sweeping can also be utilized for ELM heat load mitigation, indicating a possible new method for reducing the divertor surface temperature in a fusion reactor.

FTD experimental demonstration
FTD configuration is simulated with the Tokamak Simulation Code (TSC) [25] by using a standard EAST equilibrium and adding the oscillating field. Figure 1 shows the configurations for I FTD = ±10 kA and I p = 500 kA. There is a significant movement of the strike point along the divertor target plate, while the lower X-point location only slightly changes. The positive coil current (cyan curve) leads to a larger movement than the negative one (blue) does on the outer divertor plate because of the shorter distance between the strike point and the coil.
To test it experimentally, an in-vessel coil (with inner watercooling pipe) was installed behind the outer divertor plate in EAST tokamak, locating at R = 1.844 m and Z = −1.079 m. This coil only has a length of one third of a toroidal turn along the toroidal direction due to the space limitation from existing in-vessel components. The power supply system can drive a sine-wave current in the coil with the maximum current I FTD = ±7 kA at the frequency ranges from 10 to 100 Hz [26]. A quasi-USN configuration together with a secondary null X point on lower divertor are utilized for our experiments, in order to limit the heat flux to be below 2 MW m −2 , the nominal heat removal capability of the lower carbon divertor. The L-mode plasma parameters are I p = 300-400 kA, n e = 2.5 × 10 19 m −3 and B t = −2.2 T, with the auxiliary heating power 1.5-3 MW. The vacuum response of poloidal magnetic flux detection-loops to the FTD field has first been measured, and then it is deduced from the real-time measurement during the discharge, since the flux loop signal is utilized for plasma shape/position control, while the installed coil only has one third of a toroidal turn, as mentioned above. After applying the FTD coil current, the X-point displacement is smaller than 1.5 cm, and the plasma shape and confinement are not affected too much. Figure 2 presents the time traces of heating power, density and H 89 for the typical L-mode discharge of #94480 with FTD and #94481 without FTD.
The strike point sweeping has been measured by Langmuir probes (LPs) and infrared (IR) camera. The ion saturation current density j s is obtained from the LPs, consisting of 20 graphite probe tips embedded in the lower outer (LO) divertor target plates, with a spatial resolution of 10-15 mm in the poloidal direction and a temporal resolution of 0.2 ms [27]. The IR camera measures the surface temperature with a spatial resolution of 5 mm and framing rates from 100 Hz to 1 kHz, and the perpendicular heat flux q t on the divertor is calculated with DFLUX code [28], but without taking different cooling coefficients during the sweeping into account. With the applied coil current/frequency of ±6 kA/10 Hz for the shot #94480 with I p = 300 kA, the time evolution of j s values along the LO divertor target plate is shown in figure 3(a), where s is the distance along the LO divertor target plate from the divertor corner. The j s peak location oscillates in phase with the coil current waveform shown by the black curve below the contour. The strike point location reconstructed from the EFIT  code, sp efit , is shown by the red curve, which slightly oscillates around s ∼ 9 cm, since the vacuum response of poloidal magnetic flux detection-loops to the FTD field has been excluded. Figure 3(b) shows contour plot of heat flux from IR camera for the coil current/frequency of ±7 kA/10 Hz in the shot #94478 with I p = 300 kA. Figure 3(c) is similar to 3(a) but for the shot #87693 with I p = 400 kA and the coil current/frequency of ±5 kA/20 Hz. The oscillation of the j s peak location is also in phase with that of the coil current. For the sweeping frequency 100 Hz with I FTD = ±5 kA, the divertor surface temperature measured by IR is shown for shot #115136 with I p = 400 kA in figure 3(d). The high temperature area shrinks with increasing coil current. Noting that here this result is achieved by a new loop of in-vessel coil installed in the new lower divertor of EAST, locating at R = 1527 mm and Z = −1146.8 mm [29]. A different control algorithm for the fast-sweeping of the strike point has been developed, to be reported in another paper . Figure 4(a) presents the j s values taken from LP data at t = 6.46 s, 6.52 s and 7.06 s in discharge #94480, corresponding to applied I FTD = −6 kA, +6 kA and 0. Their fitting curves are obtained by using the Eich function [30]. The free parameters in this function for each fitting are optimized by the least-squares method [31], to reach the degree of confidence R 2 > 90%. One can see that the j s peak moves to left (right) by a negative (positive) I FTD . The movement of the j s peak is about 5 cm as coil current changes from −6 kA to +6 kA, in which the contribution from the perturbation of sp efit has been excluded. Similar behavior and movement can also be seen in the heat fluxes from IR measurement at t = 5.56 s, 5.61 s and 7.1 s for discharge #94478. The perpendicular heat flux q t on the divertor, is shown in figure 4(b) for I FTD = −7 kA, +7 kA and 0. Their fitting curves are also obtained by using Eich function with the least-squares method and a degree of confidence R 2 > 80%. The q t peak moves a distance of 5.5 cm with a slightly larger coil current, consistent with the LPs measurement.
As the poloidal magnetic field in the divertor region is weakened (enhanced) by a positive (negative) coil current, the magnetic flux expansion from midplane to divertor is changed. TSC code calculation predicts a flux expansion increase from a value of 2.0 without sweeping to 2.29 for I FTD = +6 kA, but the value decreases to 1.48 for I FTD = −6 kA in our experiment. The change of particle or heat flux profiles during sweeping can be evaluated from their footprint widths along the divertor. It is defined as in which the subscript x is denoted by j s for the particle flux or by q for the heat flux, h is either the particle flux Γ or the heat flux q, h BG the background flux, and h max the peak value. In figure 4(a), comparing to the original width of λ js, int ∼ 7.91 cm without sweeping, the particle flux footprint width increases to 8.1 cm for I FTD = +6 kA, but it decreases to 6.54 cm for I FTD = −6 kA due to the flux expansion change. This leads to a larger j s peak for I FTD = −6 kA than that for I FTD = +6 kA. In addition, the better closure near the divertor corner can also influence the j s value. It is found from one LP measurement that the electron temperature T e increases when I FTD is negative, which may result in the potential issue with sputtering. In figure 4(b), the heat flux footprint width increases from λ q,int ∼ 6.16 cm to 8.42 cm for I FTD = +7 kA but it decreases to 5.68 cm for I FTD = −7 kA. The peak of heat flux without FTD is slightly larger than that with FTD, because change of the cooling coefficient has not been taken into account in calculating the heat flux by the DFLUX code. The strike point sweeping spreads the heat flux over a larger wettened area and therefore reduces the divertor surface temperature. Corresponding to the coil current waveform for discharges #94478 shown in figure 5(a), the change of the j s peak location (relative to sp efit ) is shown in figure 5(b), indicating a sweeping distance in the range of 5-6 cm and at the frequency of 10 Hz. Figure 5(c) shows the surface temperature measured by IR camera for discharge #94478. The temperature is reduced by the sweeping, compared to that without sweeping (#94481) shown in figure 5(d).
The time evolution of maximum surface temperature near the strike point is shown in figure 6(a). Compared to that without FTD, the surface temperature (cyan) at s = 10.2 cm, calculated from averaged value in each period of sweep, is lower after FTD current turns on. It is found that the temperature is reduced from 175 • C (red) to 150 • C (cyan) by FTD at t = 6.9 s, although the sweeping distance is comparable to the heat flux width, as shown in figure 4. Our experiment is performed on the carbon divertor with very limited cooling capability. The heat removal capability is stronger for a tungsten divertor with inner water-cooling tube. Using the experimental measurement for heat flux profiles evolved in a half period of sweep as input, the calculation with COMSOL software [32] shows that the surface temperature near s = 9.4 cm can be reduced from 145 • C to 110 • C at t = 6.9 s for a tungsten divertor with a sweeping distance of 5 cm, as shown in figure 6(b). Meanwhile the oscillation in the temperature almost disappears due to the larger heat capacity and conductivity of the W divertor than the carbon one. The detailed input parameters used for COMSOL analysis will be described in the next section.
The sweeping distances in discharges with I p = 300 kA and 400 kA are investigated. Figure 7(a) summarizes the j s peak movement, ∆s peak , as a function of the original strike point location for I FTD = ±5 kA. The value of ∆s peak decreases as the original strike point location moves away from the coil location marked by the vertical dashed line. A larger ∆s peak is obtained for a smaller plasma current, as expected. For the case with I p = 300 kA, the j s peak movement (relative to sp efit ) linearly depends on the coil current, as shown in figure 7(b), consistent with TSC simulation results shown by stars. The sweeping distance is about 5 cm for a coil current of 4%I p . A saturation in the sweeping distance is observed in experiments when the coil current is increased to ±6 kA, indicating that the control strategy for plasma shape and position should be optimized for a large coil current.

Theoretical extrapolation
The COMSOL software is used to further predict the change of the target surface temperature due to the strike point sweeping for the EAST [33] and ITER tungsten divertor [34].  For the EAST case, the target consists of 9 tungsten armor blocks with a dimension of 22 mm × 22 mm × 12 mm, connected by a copper alloy cooling tube (inner diameter of 12 mm). The water flow speed inside the tube is assumed to be 3 m s −1 with a temperature of 20 • C at the entrance. For the ITER case, the tungsten armor block has the dimension of 28 mm × 22 mm × 12 mm, and the water flow speed is taken to be 10 m s −1 with the pressure of 4 MPa and the temperature of 100 • C. The heat flux on the target is assumed to distribute in a Gaussian profile with the full width of 5 cm [35]. The footprint of heat flux starts at the center of the target and moves on the target surface along the direction of the cooling tube. During the sweep, the heat flux with the fixed profiles is assumed for simplicity, which over-estimates the thermal benefit by about 10% for the heat flux with a peak of 1 MW m −2 . Figure 8 shows the maximum surface temperature after saturation as a function of sweeping frequency for a sweeping distance of 5 cm, with a peak heat flux of 10 MW m −2 for EAST and ITER divertor. The temperature decreases as the sweeping frequency increases. A large decrease in the temperature is found at the frequency of 10 Hz, and the maximum surface temperature decreases from 1060 • C to 472 • C (1220 • C-543 • C) for EAST (ITER), indicating that a sweeping frequency of 10 Hz can reduce the surface temperature below 700 • C, the empirical threshold for tungsten damage [36,37], although the sweeping distance is comparable to heat flux width. A sweeping frequency of 1 Hz is also sufficient to reduce the surface temperature, which has been analyzed in the previous study [18]. It was found that from the thermal fatigue point of view, the divertor lifetime is longer for a higher sweeping frequency than that for 1 Hz [19].
FTD can be utilized for the heat load mitigation due to transient ELM heat pulses. Assuming there is a stationary heat flux of 10 MW m −2 and transient heat pulses due to type I ELMs with a peak heat flux of 500 MW m −2 , a frequency of 10 Hz and a time duration of 500 µs [38], the calculation results for ITER divertor are shown in figure 9. The maximum surface temperature increase ∆T is around 700 • C during an ELM  heat pulse (the background 1100 • C), as shown in figure 9(a). After FTD is applied with a sweeping distance of 10 cm, the ∆T is reduced to about 450 • C at the sweeping frequency of 100 Hz, and it further decreases to about 200 • C at the sweeping frequency of 500 Hz, corresponding to a sweeping speed of 10 cm ms −1 . It indicates that ∆T significantly decreases only if the sweep is fast enough to move the strike point with a sufficient amplitude during an ELM event, i.e. 5 cm during the 500 µs.

Conclusion
A new divertor concept, the FTD, is proposed for reducing the divertor surface temperature in a tokamak. The corresponding experiments have been carried out by using the in-vessel coil installed behind the target plate near the strike point. A sweeping distance of 5-6 cm of the strike point has been achieved by applying a coil current ∼4% of plasma current. The sweeping frequency is varied from 10 to 100 Hz. The surface temperature is found to be reduced by 14% on the C divertor in experiments, and is predicted to be reduced by 24% on the W divertor for a heat flux of 1 MW m −2 , when the sweeping distance is comparable to the heat flux width. For a heat flux of 10 MW m −2 , the temperature is theoretically found to be reduced by about 60%, indicating that the FTD is more effective for a higher heat flux. The experimental results agree with the simulation results, implying a possible application in a fusion reactor. It is also found in calculations that with a sweeping distance of 10 cm and frequency of 500 Hz, the FTD can be utilized for the heat load mitigation due to transient type I ELM heat pulses. FTD provides an economic and flexible approach to achieve fast strike point sweeping.
For a fusion reactor such as DEMO, the FTD coil should be located outside the blanket for avoiding neutron irradiation, and the X-point location and plasma shape can be affected more by the sweeping. This depends on the ratio of two distances: the distance between the coil and the strike point and that between the coil and the X point, which can be minimized in the device design, e.g. by using the long-legged divertor configuration [6]. Considering the shielding from the blanket and vacuum vessel, however, a strong power supply will be required to generate the required oscillating field for the sweeping with a sufficient distance and frequency, similar to the generation of a fast-changing horizontal field by invessel coils for vertical displacement control in a reactor. The required power is roughly estimated to be between a few ten and a few hundred megawatts for the FTD operation, depending on the frequency, the distance from the coil to the strike point and the inductance from surrounding conductors. A relatively smaller sweeping distance is required for a reactor due to a narrower heat flux predicted for it, which corresponds to a relatively smaller coil current. To reduce the required power, it is important to reduce the distance between the coil and the strike point as well as the inductance from surrounding conductors, by optimizing the design of the divertor configuration, the blanket and other relevant parts in a reactor. The long-legged divertor configuration seems to be better for these purposes.