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Wide divertor heat-flux width in ITER from self-organization between the neoclassical and turbulent transports across the separatrix surface C.S. Chang1, M. Churchill1, R. Hager1, S. Ku1, R. Maingi1, J. Menard1, A. Loarte2, R. Pitts2, V. Parail3, M. Romanelli3, F. Köchl4 1Princeton Plasma Physics Laboratory, Princeton University, Princeton, NJ 08543-451, USA 2ITER Organization, Route de Vinon sur Verdon, 13067 St Paul Lez Durance, France 3Culham Centre for Fusion Energy, Culham Science Centre, Abingdon OX14 3DB, UK 4Atominstitut, Technische Universität Wien, Stadionallee 2, 1020 Vienna, Austria

Corresponding Author’s email: cschang@pppl.gov

Abstract Prediction from the edge gyrokinetic code XGC1 for the divertor heat-flux width on representative NSTX, DIII-D, C-Mod and JET plasmas agrees with experimental data regression formulas within regression error bar. However, it is found that the divertor heat-flux width λq, measured on the outer divertor surface and mapped to the outboard midplane along flux-surfaces, in a full-current ITER plasma (Ip=15MA) is about 6mm, instead of ≲1mm as predicted by regression from the present tokamak data. On the other hand, in a low-current ITER plasma with Ip=5MA, which is modeled after a first-phase operation plasma, λq agrees with regression from the present tokamak data. A detailed physics study shows that this λq behavior is related to turbulence bifurcation from the “blob-like” to the “streamer-like” pattern as ρi/a decreases from the present tokamak plasmas, and from the 5MA ITER plasma, to the 15MA ITER plasma. It is also found, from some NSTX-U simulations, that a high triangularity plasma shape could enhance λq.

1. INTRODUCTION A serious concern for ITER operation is the

ability for the divertor to withstand the steady plasma exhaust heat that will be deposited on the divertor surface along a narrow toroidal strip. A simple, data-based regression from experimental measurements in present devices shows that the heat-flux width follows a scaling 1/Bpol

γ where Bp is the magnitude of the poloidal magnetic field at outboard-midplane separatrix, and γ~1. For ITER operation at IP=15 MA with q95 = 3, this regression yields λq≲1mm for the heat-flux width λq when mapped to outboard midplane. Such a narrow λq leads to very large local power flux density in attached divertor conditions beyond the design limits of the ITER’s stationary heat loads, thus requiring the achievement of detached divertor operation. The operational range in which such a detached operation can be achieved decreases with smaller λq, and is restricted to a dangerously high plasma separatrix density (nsep/nGW>0.6 for λq≈1mm) amenable to plasma

Fig. 1. Experimental results for the divertor heat-flux width in all the major present-day tokamaks are in filled colored shapes (MAST, NSTX, C-Mod, AUG, DIII-D and JET). Black open symbols show the XGC simulation results on DIII-D, C-Mod, NSTX, JET, and ITER. The full-current (15MA) ITER result is shown at far right with a black flower symbol, while the 5MA ITER result is shown with the mark “1st phase ITER.”

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disruption and an uncomfortably high radiative fraction. In addition such a small λq poses challenges for the control of the detached divertor conditions since the power fluxes during transient re-attachment exceed by factor of several over the stationary heat flux design limits of the ITER divertor.

However, one could question if such a simple extrapolation is valid as there may be differences in fundamental edge physics between ITER plasma and those in present devices. Therefore, any extrapolation from present experiments to ITER needs to have a solid physics basis, which is one of the goals of the gyrokinetic edge code XGC1. Here, we report a substantial new physics understanding that has been achieved after the 2016 IAEA-FEC [1].

2. SIMULATION RESULTS AND TURBULENCE BIFURCATION In the 2016 IAEA-FEC paper, prediction for λq by XGC1 has been validated on several

representative C-Mod, DIII-D, and NSTX plasma conditions [1]. These simulation results, marked with the open black symbols “☐, O, and ∇" in Fig. 1, stay within the regression error bars (the dashed lines) from the multi-machine experimental regression curve λq ∝1/Bpol

1.19 (solid line) by Eich et al. [2]. In addition, a recent XGC1 simulation of a high current JET also satisfies the Eich scaling (see the ♢ mark at Bpol≈0.9T). Since this JET plasma has its linear physical size as large as half and its poloidal magnetic field strength almost 75% of the full-current ITER plasma, its obeyance of the empirical λq ∝1/Bpol

1.19 rule has a significant meaning.

However, when the same XGC1 code is applied to a model ITER plasma at the full-current,

Ip=15MA, surprisingly, λq≈6mm is obtained [1] (the flower mark at the far right) instead of the regression value λq≲1mm. Understanding the physics origin of both the present 1/Bpol

γ scaling with γ~1 and the much wider λq in ITER is of critical importance. An in-depth investigation of

Fig. 2. A typical “blob-type” edge turbulence in tokamaks that obey Eich scaling. Shown here is from a model DIII-D plasma. Blobs normally exist at ΨN≳0.97.

Fig. 3. Extension of the “streamer-type” edge turbulence into the separatrix region in 15MA ITER model plasma. Notice the ~3X compressed physical scale compared to Fig. 2. White line is the separatrix.

δn/n

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the XGC1 data reveals an interesting competition effect between the neoclassical and turbulent transports. Figures 2 and 3, respectively, depict existence of the “blob-type” edge turbulence across the magnetic separatrix in the present tokamaks that obey the Eich scaling, and the “streamer-type turbulence” in ITER at 15MA that shows λq much above the Eich-scaling value. When the turbulence pattern is of blob type, the neoclassical ion orbit motion (mostly from the “X-point ion orbit loss motion [3]) is the main contributor to the divertor heat-flux and makes λq to follow the Eich scaling. This finding confirms the previous XGC0 finding [4] and the ion-drift model [5]. On the other hand, when the turbulence pattern is of streamer type, the turbulence transport is the main contributor to λq. In the present tokamaks, the streamer type turbulence is found only well-inside the separatrix ΨN<0.97, and is in general highly efficient in driving the radial transport across the magnetic surface. Moreover, in the full-current ITER case, XGC1 finds that the pressure and potential perturbation in the streamer-type turbulence across the separatrix are highly off-phase from each other (Fig. 4). The fluctating density and electrostatic potential even shows an anticorrelation across the magnetic separatrix (Fig. 5). Both observations indicate the dominant role played by non-adiabatic electron physics.

In order to examine whether the change in the λq behavior between the present tokamaks and the full-current ITER is from the absolute size effect or the relative size effect in the ratio ρi/a, we have also performed an XGC1 study for a low-current, first-phase ITER (Ip=5MA), keeping the same plasma size and a similar safety factor q. Possibility for the absolute ρi effect has been assumed to be low due to the experimental evidence in C-Mod that an ITER-similar ρi value does

Fig. 5. XGC1 shows that there is an anti-correlation between fluctuating density δne and electrostatic potential δΦ in the streamer-type edge turbulence across the magnetic separatrix surface (black line) in the full-current ITER case.

Fig. 4. XGC1 shows that the density perturbation contours (color) deviate significantly from the potential contours (solid and dotted lines) across the magnetic separatrix in the full-current ITER case. This is an indication of the strong role played by the non-adiabatic electrons.

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not produce an enhanced λq, which is to be validated in XGC in the near future. XGC finds that λq in this low current-ITER case follows the Eich scaling, as can be seen in Fig. 1 with the mark “1st phase ITER.” Turbulence in this case is also blobby as shown in Fig. 6 (left), as for the

present tokamaks that follow the Eich scaling. Figure 6 presents a direct comparison of the turbulence structure between the 5MA ITER (left) and 15MA ITER (right). This study shows that the wide λq and the change in the turbulence pattern to the streamer type in the full-current ITER plasm is not from the absolute size effect but from the dimensionless parameter ρi/a. Somewhere between the high current JET and the full-current ITER, there is a physics bifurcation. One of the highest priority aims by the on-going XGC1 study is to understand this bifurcation physics, which may allow us to find a method to induce the bifurcation and, thus, to widen significantly the divertor heat-load width.

Another interesting abnormality is noticed recently by XGC1 from a couple of higher current (2 & 1.5 MA), high triangulariry (δ≈0.6) NSTX-U model plasma simulations (Bpol=0.58 & 0.44T), as marked with ▼ in Fig. 7. The XGC1 obtains λq values are ≈2-3X greater than the Eich’s multi-machine regression value in these high-triangularity

Fig. 7. High triangularity (δ≈0.8 at single-null X-point, and average δ≈0.6) in NSTX-U plasmas shows enhanced divertor heat-load width. 1.5MA and 2MA cases are shown. The light-blue filled ∇ symbol is for high-triangularity NSTX plasma and two black filled ∇ symbols are for high-triangularity NSTX-U plasmas. When a sufficient divertor heat loss is turned on (modeling the radiative loss) in the 2MA NSTX-U case, the divertor heat-flux width decreases somewhat.

Fig. 6. Appearance of a blob-type turbulence across the magnetic separatrix in a 5MA ITER plasma while a streamer-type turbulence exists in a 15MA ITER plasma. Smaller-size view-window in the 15MA ITER case is shown as in insert box in the 5MA figure.

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NSTX-U model plasmas, while the normal triangularity NSTX plasmas obey the Eich scaling. The higher the plasma current is, the bigger the λq enhancement is over the Eich value. Turbulence pattern is mixed between the blob and streamer type in the high-triangularity NSTX-U cases. In the high-triangularity NSTX-U case, a preliminary XGC simulation also shows some reduction in λq by a (radiative) heat loss in the divertor chamber. This phenomenon has not been seen in other tokamaks at moderate triangularity values. More simulations are to be performed in the near future to understand the relation between the results from NSTX-U and ITER, and the effect of the (radiative) heat-loss from the divertor chamber. 3. SUMMARY AND DISCUSSION

When the neoclassical ion X-point orbit-loss mechanism is sufficient to transport a significant portion of the heat across the separatrix surface, the mechanism mostly determines the divertor heat-flux width. The turbulent electron transport plays a support role in keeping the plasma loss ambipolar and in expelling the corresponding convective electron heat across the separatrix surface. There is a large sheared ExB flow across the separatrix that prevents the formation of the streamer-type turbulence. Turbulence is of “blob” type.

However, in the full-current ITER edge, the neoclassical ion drift effect is weak due to the smallness of ρi/a. The plasma across the separatrix self-organizes to produce a streamer-type turbulence with an increased role played by the non-adiabatic electron, and broadens the divertor heat-flux width well-above the ion neoclassical level. The weak mean ExB-shear across the separatrix surface, due to the small ρi/a effect, allows the formation of the streamer type turbulence. The blob-type turbulence disappears. We note here that a strong ExB-shearing layer re-appears at ΨN<0.97 from the non-local X-point orbit loss effect, and a strong co-rotation is established across the separatrix to offset the weak radial electric force, which supports a reasonably strong pedestal that is ≳2X wider than the MHD predicted width in the full-current ITER plasma.

There appears to be an edge-physics bifurcation at a ρi/a value somewhere between the highest current JET and the full-current ITER, which leads to the change of a blob-type turbulence with narrow λq to a streamer-type turbulence with wide λq. A substantial XGC effort will be devoted in the near future to understand the basic physics behind this bifurcation, which may lead to some method for inducing the bifurcation by an external actuator.

High triangularity study on NSTX-U model plasmas shows a substantially enhanced divertor heat-load width, while a normal triangularity NSTX plasmas show Eich-type heat-load width. Turbulence across the last closed flux surface is mixed between blobs and streamers in the high-triangularity case. Understanding this phenomenon may also lead to a valuable insight in widening λq in ITER and future reactors. Acknowledgement This material is mostly based upon work funded through the SciDAC program by the U.S. Department of Energy, Office of Fusion Energy Science and Office of Advanced Scientific Computing Research under Contract Number DE-AC02-09CH11466. This research used resources of the Oak Ridge Leadership Computing Facility (OLCF) and the National Energy Research Scientific Computing Center (NERSC), which are DOE Office of Science User Facilities supported under Contract Numbers DE-AC05-00OR22725 and DE-AC02-05CH11231, respectively.

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Disclaimer: ITER is the Nuclear Facility INB no. 174. The views and opinions expressed herein do not necessarily reflect those of the ITER Organization.

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22, (2015) 092511 [5] R. Goldston, Nucl. Fusion 52, 013009 (2012)