Inter-ELM power exhaust in tokamak fusion reactors W.Fundamenski1,3, T.Eich2, D.Moulton3, F.Militello1, C.Lowry4, G.Maddison1, E.Havlickova1, D.Ward1, R.Kemp1, M.Wischmeier2, D.C.McDonald1

Recent infra-red measurements of divertor power loads on JET and AUG [1], revealed that the inter-ELM power width at the outer mid-plane in attached ELMy H-modes, λQ, does not exhibit any noticeable scaling with machine size [1]. Making use of these results to calculate the effective radial heat diffusivity, χ⊥, and then including this χ⊥ in parametrized expressions based on edge plasma fluid simulations, it is possible to estimate the peak interELM divertor power loads, Qmax t , in future fusion devices with conventional divertor designs. Two additional constraints are imposed: (i) power flow across the separatrix must exceed the L−H access power, PL−H , as given by an empirical scaling [2], in order to maintain Hmode operation, i.e., Psol = fL−HPL−H , with fL−H > 1, and (ii) the upstream separatrix density is given by some fraction, f sep GW < 1, of the Greenwald density, nGW ∼ Ip/πa, while line average density is set equal to nGW . Affecting the calculation yields the following expression: Qmax t ∝ f sep−0.75 GW f 1.47 LH q −0.84B2. 57 T R 0. 15κ0.2ε−0.23Z0. 31 e f f . Hence, Q max t increases only weakly with reactor size and should be comparable in future and present devices, for comparable levels of fGW , fLH , q, BT and θ⊥. Calibrating the scaling against a high density JET shot with nitrogen seeding, and allowing for an additional factor of two reduction due to divertor closure, leads to an estimate of Qmax t in ITER and DEMO (R = 8.5 m, BT = 5.7 T, qcyl = 2, Ze f f = 3) as 8− 16 MW/m2 and 20− 50 MW/m2, respectively. It thus appears that H-mode operation of a tokamak fusion reactor cannot be reconciled with the thermo-mechanical properties of leading candidate materials (< 5 MW/m2 for irradiated W), and the power exhaust cabilities of conventional divertors, requiring either advanced materials and/or advanced divertor solutions. The main uncertainties in the above prediction are the upper limit on the separatrix density, distribution of divertor radiation and the impact of divertor closure. Letter to the Editor 2 Recent infra-red measurements of divertor power loads on JET and AUG [1], revealed that the inter-ELM power width at the outer mid-plane in attached ELMy H-modes, λQ = |∇⊥Q‖/Q‖|, can be approximated by, λQ ≈ 0.73 ·B−0.78±0.25 T q 1.2±0.27P0. 1±0.11 sol R 0.02±0.2. (1) Here parallel power e-folding length, λQ, is in mm, the toroidal magnetic field, BT , is in T, the power entering the SOL, Psol , Psol = Pcore−P rad = f core rad Pcore, (2) is in MW and the central major radius R is in m, while the cylindrical safety factor, q≡ qcyl = 2πεκaBT μ0Ip , (3) is dimensionless. The remarkable, and at first glance deeply worrying, feature of (1) is the fact that λQ is virtually independent of reactor size. In this letter, we examine the implication of this lack of size scaling on the peak divertor (target) power load, Qmax t , and the peak divertor electron temperature, T max et in future tokamak reactors. In order to make this prediction, we resort to results of 2-D plasma fluid simulations in which the plasma density, power entering the SOL, reactor size and heat diffusivity in the SOL were all varied independently [4]. In the high density (high recycling) regime of SOL operation, the results were found to agree reasonably well with the following expressions: Qmax ‖t [MW/m 2]≈ 1120×n−1.82 eu (Psol/S⊥)χ ⊥ q 0.52R0. 33 (4) T max et [eV ]≈ n−5.52 eu (Psol/S⊥)χ ⊥ q 0.18R−0.66 (5) nmax et [10 20m−3]≈ n3.36 eu (Psol/S⊥)χ ⊥ q 0.37R1. 15 (6) where the peak parallel divertor (target) power density, Qmax ‖t is in MW/m 2, upstream separatrix density, neu is in 1020m−3, power into the SOL, Psol is in MW , the plasma surface area S⊥ is in m2, radial heat diffusivity, χ⊥, is in m2/s, the cylindrical safety factor q is dimensionless, and R is in m. It is worth noting that ELMs were absent from the simulations, such that comparison with experiment requires replacing Psol by the power entering the SOL in between ELMs, Pi−E sol , which is defined as some fraction of Psol , Pi−E sol = f i−E P Psol. (7) Since the effects of radial transport enter (4)-(6) via the SOL radial heat diffusivity, χ⊥, it is necessary to estimate this quantity based on the experimental power e-folding length, λQ, (1). For this purpose we employ a well known expression [3], λQ/L‖ ∼ √ κ⊥/κ‖e = √ χ⊥/χ‖e, (8) which is obtained by assuming energy conservation in the absence of source/sinks, ∇ ·Q= 0, and purely conductive transport in both parallel and perpendicular directions, Q‖ ≈ Q‖e ≈ κ‖e∇‖Te, Q⊥ ≈ κ⊥∇⊥Te. (9) Letter to the Editor 3