DEVELOPMENT OF ADVANCED DIVERTOR CONCEPTS FOR STEADY-STATE TOKAMAKS H. Guo1*, D. Hill1, L. Lao1, A. Leonard1, P. Stangeby2, D. Thomas1 1General Atomics, 2University of Toronto *Email: [email protected] The need for advanced divertor solutions to efficiently dissipate heat from fusion reactors is critical because the maximum steady-state power load for envisioned plasma-facing components 2 (PFC) is limited to qt ≤ 10 MW/m on PFC surfaces, whether solid or liquid, while the undissipated power loads will be an order of magnitude higher. Adequate reactor lifetime dictates near zero-erosion at the divertor surface, so the divertor plasma temperature at the divertor target plates must be maintained at a low temperature with Tt ≤ 5 eV to suppress erosion [1]. In addition, these boundary plasma conditions must be maintained with a core plasma density and neutral and impurity influx consistent with robust high performance (H-mode) operation and efficient current drive. These requirements pose a grand challenge for long-pulse tokamaks, e.g., for a Fusion Nuclear Science Facility [2] and the China Fusion Engineering Test Reactor (CFETR) [3], which will have lower plasma density than ITER for high performance long-pulse current drive or high duty cycle operations, with a normalized Greenwald density fraction, ne/nGW ~ 0.5, in contrast to ne/nGW = 1 for ITER. 1. TECHNOLOGY TO BE ASSESSED We propose an innovative small angle slot (SAS) divertor concept (Fig. 1) [4] to address the challenge of efficient divertor heat dispersal compatible with non-inductive current drive in future tokamaks, and expect that this can be achieved with minimized divertor volume without internal magnetic coils, thereby maximizing the plasma Fig. 1. Sketch of an SAS divertor on the DIII-D volume for fusion energy production. tokamak [4]. The SAS concept was developed SAS features a small (glancing) angle using the 2D plasma-fluid Monte-Carlo-neutral target and a narrow (~ a few λq wide) slot boundary plasma SOLPS-EIRENE code package for typical H-mode plasmas in DIII-D. progressively flaring out from the strike point to amplify both neutral/molecular and impurity dissipation of power in the divertor. SOLPS (B2-EIRENE) edge code analysis finds that a SAS divertor can achieve strong plasma cooling when the strike point is placed near the small- angle side target, leading to low electron temperature across the entire divertor target at a given upstream plasma density. This is enabled by strong coupling between a gas tight slot and directed neutral recycling resulting from the small angle target to enhance neutral buildup near the target. SAS modeling exhibits the following key benefits:

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• Preferentially enhancing the buildup of neutral density in a localized region near the plasma strike point on the divertor target to achieve detachment at lower upstream densities for facilitating current drive and ensuring core fusion performance • Spreading the cooling front across the divertor target with the slot gradually flaring out from the strike point, thus effectively reducing both heat flux and erosion along the entire divertor target 2. APPLICATION OF THE TECHNOLOGY Development of a viable divertor solution for the control of the heat loading and erosion of the plasma-facing components is now recognized to be critical throughout the fusion community worldwide, and needs to be urgently addressed for high power long pulse operation in modern long pulse fusion devices such as EAST (China), KSTAR (Korea) and JT60-SA (Japan), as well as next-step fusion devices. A recent Fusion Energy Sciences workshop has pointed out the need to develop the scientific basis for design and operation of an advanced divertor to evaluate boundary plasma solutions applicable to next step fusion experiments beyond ITER. A new SAS divertor concept is now being developed in DIII-D to address the challenge of efficient divertor heat dispersal at the relatively low plasma density required for non-inductive current drive in future steady-state tokamaks. 3. CRITICAL VARIABLES Advanced divertor designs for a fusion reactor should feature (i) highly dissipative operation, limiting surface heat and erosion to tolerable levels; (ii) controlled density, neutral fueling, and impurity influx compatible with high performance core plasma operation. In particular, it is imperative to satisfy the following requirements for steady-state operation: 2 • Divertor target heat load: qt ≤ 10 MW/m

• Divertor target plasma temperature: Tt ≤ 5 eV across the entire target

• Wide opening ranges with a Greenwald density fraction: ne/nGW ≥ 0.5 • Compatible with high performance core One of the grand challenges of fusion is to satisfy these three requirements since there are currently no proven divertor solutions available. The ITER divertor is expected to achieve the 2 first key requirement, qt ≤ 5-10 MW/m , and partially achieve the second one, Tt ≤ 5 eV near the strike point, but Tt remains high elsewhere on the target while operating at high ne/nGW ~ 1. 4. DESIGN VARIABLES The undissipated parallel heat flux in next-step fusion devices could be as much as an order of magnitude higher than in current experiments. A large fraction of power (> 90%) must be removed by impurity radiation in the core and divertor/SOL. However, as the plasma is cooled down to Tt ≤ 10 eV, neutral and molecular dissipation becomes critical for further cooling the plasma down to Tt < 5 eV to ultimately achieve detachment. Thus, the SAS concept specifically uses innovation in target shaping to bootstrap power and momentum dissipation of recycling neutrals to enable plasma detachment at minimal upstream density. SAS features the following critical design parameters:

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Small field line-to-target angle: The most critical feature of the SAS divertor is its small angle at the outboard side end of the divertor slot, Fig. 1. SOLPS analysis shows that reducing the target angle reduces , the electron temperature at the Outer Strike Point (OSP) for a given upstream density, nu, with an abrupt transition occurring as the target angle is made 𝑇𝑇𝑡𝑡 𝑂𝑂𝑂𝑂𝑂𝑂 sufficiently small, e.g., below ~20°, for a tight and fixed degree of closure to neutrals [4]. Progressive target flaring outboard of the strike point: The second major beneficial feature of SAS is that, by employing a progressive increase in the target angle on the outboard side of the slot, low electron temperatures can be achieved across the entire divertor target plate in contrast to the small-angle ITER-like vertical target [4], Fig. 2. A common feature of ITER- like vertical target configurations is the achievement of the ‘partial detachment’ condition where only the plasma near the strike point is detached, while the plasma further out has rather high Tt and is attached. This is tolerable for low duty cycle tokamaks like ITER, but is unacceptable for high duty cycle tokamaks due to the net erosion associated with the high Tt of the outer regions of the target. Narrow slot width ~ a few λq: Recent analysis suggests the characteristic radial width for the parallel heat flux λq scales as ~1/Ip independent of machine size [5]. If this scaling is realized in future devices, λq < 1 mm could result. With the SAS configuration, the slot width would only necessarily need to Fig. 2. Radial profiles of Te and q⊥, the accommodate the flux surfaces outside the separatrix deposited power flux density across the divertor target surface at upstream within a few λq, i.e., a few cm wide at the target plate. 19 -3 density, nu ~ 4x10 m , for different SOLPS shows that the coupling between such a slot divertors [4]. narrow slot and a small angel target leads to a significant reduction in the upstream density at the onset of detachment. The slot length does not seem be as sensitive as the above variables, although a longer slot length should be desirable, in principle, to further improve divertor retention of neutrals. These findings potentially identify a new avenue by which the divertor can be optimized for power exhaust while minimizing the divertor volume. For power flow across the separatrix into the divertor/SOL, PSOL ~ 100 MW, for a reactor with R ~ 6 m, a narrow slot of ~10 cm deep in principle suffices for radiative power removal even if the radiation occurs entirely inside the slot, assuming a uniform radiation loading of 10 MW/m2 over the divertor surface. The SAS divertor concept has recently been tested in DIII-D for a range of plasma configurations and conditions, and has qualitatively demonstrated the key features predicted by the models. In confirmation of SOLPS predictions, a sharp transition is observed when the strike point is moved to the critical outer corner near the small angle target of SAS. A set of Langmuir probes imbedded in SAS show that the radial profile of the ion saturation current, which is

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peaked at the strike point when it is located away from the SAS corner, becomes flattened when it is placed in the corner and the electron temperature, Te, becomes low across the target. The density ramp-up with precise control of slot strike point location shows that the detachment occurs at significantly lower pedestal density in the unpumped SAS for a typical H-mode than in the open divertor at the bottom. 5. RISKS, UNCERTAINTIES, AND MATURITY In the present code analysis, carbon is the radiating low-Z impurity. Initial tests on DIII-D with carbon PFCs have qualitatively reproduced the key SAS features as predicted by the code. Tokamaks with tungsten PFCs will inject low-Z impurity gases such as nitrogen, so it is believed that the present results should be largely applicable to the case of W PFCs with injection of nitrogen, which has similar radiative properties to carbon. The present SOLPS analysis has neglected divertor pumping. Accordingly, the plasma conditions at the target represent the upper limit of what can be achieved with SAS since pumping in the slot should decrease neutral concentration in the slot. An AT employing an unbalanced double-null (DN) divertor configuration may allow the particle and heat exhaust channels to be strategically decoupled: one of the outer divertors may be designed to take the bulk of power load, while the gas pumping load and He ash removal would be accomplished by the other outer divertor. Accordingly, the divertor that required the stronger SAS effect would not have to be pumped as strongly. The present SAS design was done with SOLPS5.0, which employs a version of the EIRENE Monte Carlo neutral code that does not include neutral-neutral (n-n) collisions. The n-n collisions exhibit little influence on the divertor plasma conditions [6], although they can have a significant impact on divertor pumping, i.e., in the regions outside the plasma [7]. In order to establish that there is a viable window for application to a fusion reactor, further code analyses are necessary, e.g., with SOLPS-ITER, including full classical drifts, n-n collisions, pumping, as well as extrinsic impurity seeding, to identify the sensitivity of the dissipative/detached divertor conditions to various input parameters such as PSOL, and to establish scaling to reactor conditions. 6. TECHNOLOGY DEVELOPMENT FOR FUSION APPLICATIONS The configuration flexibility of existing US fusion facilities provides a unique opportunity to explore and quantify key divertor design parameters controlling divertor detachment and energy dissipation in a single device, and to validate models for extrapolation to reactor conditions. Utilizing staged divertor modifications through model-based variations, we expect these efforts to lead to experimental and model evaluation of the SAS divertor for developing a scientific basis for advanced divertor solutions for next-step devices, bringing this new technology to Technology Readiness Level 4.

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7. REFERENCES [1] P. C. Stangeby and A. W. Leonard, 2011, “Obtaining reactor-relevant divertor conditions in tokamaks”, Nucl. Fusion 51, 063001. [2] A. M. Garofalo et al., 2014, “A Fusion Nuclear Science Facility for a fast-track path to DEMO”, Fusion Eng. Des. 89, 876–881. [3] V. S. Chan et al., 2015, “Evaluation of CFETR as a Fusion Nuclear Science Facility using multiple system codes”, Nucl. Fusion 55, 023017. [4] H. Y. Guo et al., 2017, “Small angle slot divertor concept for long pulse advanced tokamaks”, Nucl. Fusion 57, 044001. [5] T. Eich et al., 2013, “Scaling of the tokamak near the scrape-off layer H-mode power width and implications for ITER”, Nucl. Fusion 53, 093031. [6] V. Kotov et al., 2008, “Numerical modelling of high density JET divertor plasma with the SOLPS4.2 (B2-EIRENE) code”, Plasma Phys. Control. Fusion 50, 105012. [7] A. S. Kukushkin et al., 2011, “Finalizing the ITER divertor design: The key role of SOLPS modeling”, Fusion Engineering and Design 86, 2865.

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