3D effects of edge magnetic field configuration on divertor/sol transport and optimization possibilities for a future reactor

1 OV/4-4 3D effects of edge magnetic field configuration on divertor/sol transport and optimization possibilities for a future reactor M. Kobayashi 1, Y. Feng, O. Schmitz 3, K. Ida 1, T.E. Evans 4, H. Frerichs 3, F.L. Tabares 5, Y. Liang 6, Y. Corre 7, Ph. Ghendrih 7, G. Ciraolo 7, A. Bader 3, Y. Xu 8, H.Y. Guo 4,9, J.W. Coenen 6, D. Reiter 6, Z.Y. Cui 8, U. Wenzel, N. Asakura 10, N. Ohno 11, D. Tafalla 5, S. Morita 1, S. Masuzaki 1, B.J. Peterson 1, K. Itoh 1, H. Yamada 1 1 National Institute for Fusion Science, Toki, Japan, Max-Planck-Institute fuer Plasmaphysik, Greifswald, Germany, 3 University of Wisconsin Madison, WI, USA, 4 General Atomics, San Diego, CA, USA, 5 Laboratorio Nacional de Fusion. Ciemat, Madrid, Spain, 6 Forschungszentrum Jülich GmbH, Jülich, Germany, 7 IRFM, CEA Cadarache ST Paul Lez Durance, France, 8 Southwestern Institute of Physics, Chengdu, China, 9 Institute of Plasma Physics, CAS, Hefei, China, 10 Japan Atomic Energy Agency, Rokkasho, Aomori, Japan, 11 Nagoya University, Nagoya, Japan E-mail contact of main author: kobayashi.masahiro@lhd.nifs.ac.jp Abstract. Recent progress on the experimental identification and physics interpretation of 3D effects of magnetic field geometry/topology on divertor transport is overviewed. In this paper, the 3D effects are elucidated as a consequence of competition between transports parallel (//) and perpendicular ( ) to magnetic field, in open field lines cut by divertor plates, or in magnetic islands. The competition process has strong impacts on the divertor functions, such as density regime, impurity screening, and detachment control. The effects of magnetic perturbation on the edge electric field and turbulent transport are also discussed. Based on the experiments and numerical simulations, key parameters governing the 3D transport physics for the individual divertor functions, are discussed, suggesting demanding issues to be addressed for divertor optimization in future reactors. 1. Introduction The divertor optimization with the 3D edge magnetic field structure is inevitable in helical devices due to intrinsic non-axisymmetric magnetic configurations [,,,,,], and also in tokamaks with the application of symmetry breaking magnetic perturbation (MP) fields aimed at edge transport control [,,] or at ELM mitigation/suppression [,,]. Understanding of the 3D effects is, therefore, prerequisite to divertor optimization for a future reactor, exploring advanced magnetic configurations. Recent development of 3D numerical simulation codes [,,] as well as systematic experiments [,,,,] have revealed various transport aspects in the 3D magnetic configurations. In these contexts, this paper overviews the recent progress on the experimental identification and physics interpretation of 3D effects of magnetic field geometry/topology on divertor transport, and suggests key parameters that control the effects, in order to provide a perspective on divertor optimization for future reactors. The 3D effects have been investigated so far intensively in various devices and these investigations have made significant progress in the understanding the transport features [,

OV/4-4,,,,,]. The modifications of transport are caused by the stochasticity of field lines or by the 3D deformation of magnetic flux tubes [,], i.e., the laminar zone []/edge surface layers [] where parallel correlation along field lines still persists to some extent, i.e., L K (Kolmogorov length) > L C (connection length to divertor plates). Particularly in the present study, in order to obtain simple picture, the 3D effects are defined as follows. The 3D effects emerge when the //-transport starts to compete with the -transport to deliver particle, momentum or energy from upstream (i.e., around the last closed flux surface, LCFS, or around midplane in X-point divertor) to the downstream (i.e., divertor region). This situation occurs either in open field lines or in magnetic islands, as shown in Fig.1. The //- transport time becomes finite along an open field line or inside the island to circulate therein, which then competes with the - transport. The condition for such a situation can be written as, B θ in eq.(1) instead of B r ), where typically B θ ~ 0. 1 B, and it results in B Γ θ // >> Γ, t B t thus the //-transport dominates over transport. On the other hand, in the stochastic layer in the helical devices or in the tokamaks with resonant magnetic perturbation (RMP) field, as Br 4 3 well as in the island divertor configuration, where typically = 10 ~ 10, the situation Bt allows the -transport to contribute substantially to deliver the plasma quantity, and thus Divertor plates B r Γ // ~ Γ. The parameter domain in which this effect becomes significant is elucidated Bt in Fig.8 in ref.[]. For momentum transport, which is vector field, the direction of the flow or of the field line connection is also important. When the flow fields, which have (toroidally) opposite streaming directions, interact with each other due to the proximity of the counter connecting field lines, they loses the //-momentum via dissipation caused by -viscosity. Such a situation can occur in the island divertor [] or in the stochastic layer [], as shown in Fig.. In the D axi-symmetric X-point divertor, the separation of counter directional flux r r Γ Γ // Field lines (magnetic island) Γ // Field lines (stochastic, opened) Γ FIG.1 Schematics of transport in stochastic field lines (top) and in magnetic island (bottom). Γ //, represents flux of any physical quantity (particle, momentum, energy) that are parallel, perpendicular to magnetic field Br, Γ θ lines. // ~ Γ, (1) Bt where B r,θ, Bt are radial or poloidal component of magnetic field and toroidal field, respectively. Γ //, represents flux of any physical quantity (particle, momentum, energy) that is parallel, perpendicular to magnetic field lines, respectively. The ratio Γ // / Γ ranges from 10 5 to 10 8, depending on the physical quantities as well as on the plasma parameters. In the scrape-off layer (SOL) of D axi-symmetric X-point divertor tokamaks, (in that case we take Γ Γ//

3 OV/4-4 tubes, i.e., inner and outer divertor legs, are usually large, and thus the momentum loss effect is considered to be negligible. The enhancement of -transport also occurs in the situation where short and long connection length flux tubes are touching each other and they are squeezed due to the magnetic shear, as shown in Fig.3. In this case, the exchange of physical quantities such as particle and energy between the different flux tubes is considered to be enhanced due to the enlarged interface area between them. It is noted that, in closed nested flux surfaces, otherwise, the //-transport just uniformly distributes plasma parameters along the flux surfaces, but does not contribute to net transport from LCFS to divertor plates (or net radial direction), even with non-axisymmetric deformation of magnetic flux surfaces. In the following sections, we investigate how these 3D effects are reflected in the experimental observations and then give rise to possible impacts on divertor functions.. Impact on divertor density regime D axi-symmetric divertor Pressure conservation along flux tube radial Divertor plate +V // (+ φ) poloidal -V // (- φ) 3D configuration (e.g. stochastic layer, ID) radial //-Momentum loss due to counter flows Divertor plate +V // -V // poloidal Open field lines Divertor plate FIG. Schematics of formation of //-flow towards divertor plates in D axisymmetric (top) and in 3D divertor (bottom) configurations. In the 3D case, the spatial separation between counterstreaming flows, λ m, becomes short and thus momentum loss of //-flow via - viscosity takes place. The divertor density regime in the D axi-symmetric X-point divertor configuration is known for strong recycling enhancement at the divertor region, which is sustained with sufficient energy input from the upstream and with effective neutral confinement. The divertor (downstream) density is strongly coupled to the upstream (LCFS or midplane) density, for example, 3 n down nup, Tdown nup, which is derived from the pressure conservation along flux tubes between the upstream and the downstream. Such the density regime is called high-recycling regime or conduction limited regime, and the relation has been confirmed in experiments []. However, in the 3D divertor configurations such as helical devices, W7-AS [,], LHD [] and tokamaks with RMP, TEXTOR-DED [], it has been often found that the dependency becomes modest, i.e., ~ 1 up, ~1 up n down n Tdown n, and also that the downstream density never exceeds the upstream density, n down < nup, while in the D configuration usually we observe n >>. down n up The phenomena have been interpreted as due to the loss of //-momentum as shown in Fig., which was first Long L C B ~ r Short L C Magnetic shear exchange exchange enhanced FIG.3 Schematics of deformation of flux tubes in the stochastic layers. Through bending by B r and stretching by magnetic shear, the flux tubes of long and short L C are squeezed. The resultant interaction area increases and exchange of plasma quantity is enhanced.

4 OV/4-4 investigated in the island divertor configuration of W7-AS [], using the 3D edge transport code EMC3-EIRENE [,]. In the W7-AS island divertor, due to the smallness of the island, the counter-streaming plasma flows along the island fans interact with each other and lose //-momentum, as discussed in the section 1. The similar effect has been identified in the stochastic layer of LHD, where the squeezing effect of counter-directional flux tubes (i.e., flows) due to the strong magnetic shear enhances further the loss of //-momentum []. The numerical analysis in HSX has also shown the absence of high recycling regime due to the momentum loss in the edge island structure []. The effect of //-momentum loss can be formulated as the ratio between momentum transport time in parallel and perpendicular to magnetic field, τ m // D L// =, () τ V λ m // m α ndiv n LCFS where D, L//, V// are the perpendicular particle high recycling regime ( α 3 ), where α diffusivity, //-characteristic scale length for ndown n up. The larger the momentum transport, i.e., connection length ( L C ) or τ m // / τ m or q e / q// e are, the Kolmogorov length ( L K ) of field lines. λ m is the weaker the upstream and downstream -characteristic scale length for momentum coupling, i.e., density dependence, is. transport, i.e., the distance between the counterstreaming flows. The ratio corresponds to the momentum loss factor f m discussed in refs.[,]. The larger the ratio is, the larger the -loss of //-momentum is. In TEXTOR-DED with m/n=6/ mode of RMP operation, the detailed analysis of the 3D edge transport simulation has shown that the replacement of //-energy flux ( q // e ) with - transport ( q e ), as discussed in Fig.1, as well as with the convection flux ( q // e, conv ) due to the substantial upstream ionization source, are responsible for the modification of density regime []. The effect of convection energy flux was also pointed out in ref.[]. Both effects lead to the reduction of //-conduction energy ( q // e, cond ) and weaken the upstream and downstream coupling as elucidated in ref.[]. The contribution of q e can be formulated as, q e n χ e =, (3) q.5 // e ( Br / Bt ) κ0e Te where χ e, κ0e are perpendicular heat diffusivity and coefficient for //-heat conductivity, respectively. The effect of convection energy flux, q // e, conv / q// e, cond is strongly dependent on the divertor geometry because the neutral penetration into the edge plasma is largely controlled by the configuration of divertor plates and baffles. In the X-point divertor tokamaks, these plates are usually situated to avoid neutral leakage from the divertor region, so that the upstream ionization source is almost negligible, i.e., q // e, conv / q// e, cond << 1. On the other hand, in some 3D divertor configurations, such as TEXTOR-DED, which have 10 1 10 0 10-1 10-10 -3 10-4 Tore Supra (m/n=18/6) LHD (m/n~5/10, strong shear) W7-X (m/n=5/5) DIII-D (m/n 10/3) ITER (m/n~10/3) High recycling( α 3) No High recycling(α < 3) 10-3 10-10 -1 10 0 10 1 / q q e // e W7-AS (m/n=9/5) (m/n=4/4) HSX (m/n=7/8) TEXTOR-DED (m/n=1/4) TEXTOR-DED (m/n=6/) TEXTOR-DED (m/n=3/1) FIG.4 Divertor density regime of various devices in terms of loss of //-momentum, τ m // / τ m, and replacement of //-energy flux with - flux, q e / q// e. Red: no high recycling regime ( α < 3 ), blue: with

5 OV/4-4 open divertor configuration, the neutral penetration into upstream occurs to a certain extent and thus gives rise to the convection flux. The estimation of q // e, conv / q// e, cond is, however, not straightforward and one needs detailed numerical analysis taking into account the 3D geometry of edge plasma and of divertor/baffle structures. The larger the q e / q// e or q // e, conv / q// e, cond are, the weaker the upstream and downstream coupling, i.e., density dependence, is. The strong upstream and downstream coupling, i.e., the high recycling regime, is recovered in a certain situation of the 3D divertor configuration. It has been achieved in Tore Supra [], TEXTOR-DED with m/n=3/1 mode []. The numerical simulations with EMC3-EIRENE on W7-X and on HSX with large island size have also shown clear high recycling regime [,]. For these cases, either or both of τ m // / τ m and q e / q// e are considered to be small enough to maintain the robust upstream and downstream coupling. Figure 4 summarizes the density regime of various devices in terms of τ m // / τ m and q e / q// e. The λ m has been estimated as λm π a / m, assuming that the counter streaming flows are regulated in poloidal direction as shown in Fig., except for LHD, where the strong magnetic shear squeezes the flux tubes and thus λ m becomes much smaller e.g. ~ a few cm [], as depicted in Fig.3. For the calculations of τ m // / τ m and q e / q// e, the half values of the plasma parameters at LCFS, i.e., 0.5 TLCFS and 0.5 nlcfs are assumed as representative values. It has been also assumed that for the devices with stochastic edge layer L// LK ~ π R q based on the argument in ref.[], while for the island divertor configurations (W7-AS/X) L// LC ~100 m [,]. Mach number of 0.5 is used for the calculation of V //. This is a rather rough estimate but Fig.4 shows a clear tendency of the transition from the high recycling regime to the cases of absence of high recycling regime as moving in to higher τ m // / τ m and q e / q// e. It is noted that for the case of ITER, it has been shown that the strong magnetic shear deforms the flux tubes significantly and reduces the λ m down to ~ several cm []. If we take the value, the ITER case with RMP will move vertically in Fig.4 closer to the border between the cases with and without high recycling regime. However, there is a fundamental difference between the X-point poloidal divertor with RMP and the other devices, LHD, W7-AS/X, Tore Supra, TEXTOR-DED, etc. In the latter case, the radial projection of //-flux due to B r directly competes with the -transport. In the former case, on the other hand, the dominant diverting field is still B θ, since B θ / Bt ~0.1 and B r / Bt ~10-3. The flow field, therefore, might be dominantly poloidal without significant deviation from the case without RMP in terms of //- momentum transport. We need further detailed investigation both in experiments and numerical simulations for this issue. 3. Impact on SOL/divertor impurity transport There have been many observations of impurity screening/core decontamination in tokamaks with RMP application [,,], in helical devices with the stochastic layer [,] or with the island divertor configurations [,]. Although it is not clear yet at all whether these phenomena are caused by the edge impurity screening or attributed to the core transport or some other effects such as change of source characteristic, etc., here we discuss the 3D geometrical/topological effects on the edge impurity transport. A simple

6 OV/4-4 picture for impurity screening in the 3D divertor configuration is as follows: Based on the //- momentum balance equation for impurity, the resultant profile is considered to be determined by competition between friction force and ion thermal force acting on the impurity [], Vz // V// Vz // mz mz + Ci // Ti +..., (4) t τ s where mz, Vz //, V//, τ s are mass of impurity, //-velocity of impurity and background plasma, and collision time (slowing down time of impurity) between impurity and plasma, respectively. The friction force drags the impurity towards the plasma flow direction (i.e., towards divertor region assuming that the flow is pointing towards divertor plates) through the friction between plasma and impurity, while the ion thermal force drives impurity towards upstream because of the //-temperature gradient pointing upstream. With B r of MP, the outward (radial) plasma flow can be enhanced due to the radial projection of V // and thus the friction force becomes more effective. It is also noted that effective screening are often observed at higher density range, i.e., at higher collisionality [,,,]. This is also consistent with the picture of friction force that is inversely proportional to collision time τ s. The effects of friction force have been pointed out so far in many publications [,,,,,], and here we use the following expression to measure the effect, Dst ( Br / Bt ) V// L// =, (5) D D where D is -particle diffusivity, which ranges from 0.4 to 1.0 m /s, depending upon the devices. Here, however, one should also note that the high collisional plasma also develop //- temperature gradient, thus ion thermal force. In the case of the 3D divertor configurations, this is avoided by increasing -energy flux at the high collisionality plasma, which replaces the //-energy flux as shown in Fig.1, and thus it hinders //-temperature gradient. This effect has been pointed out in the numerical simulation with EMC3-EIRENE on W7-AS [] and also later confirmed in LHD []. The effect can be formulated as [], q i n χ i =, (6) q.5 // i ( Br / Bt ) κ 0i Ti similarly as eq.(3) but now for ion. In the case of D axi-symmetric X-point divertor, where q i B θ / B t ~0.1 is used instead of B r / Bt as discussed in section 1, << 1 and the q// i suppression of ion thermal force never happens. In the 3D divertor, on the other hand, due to the very small B r / Bt =10-4 ~ 10-3, the condition ~ 1 is fulfilled. The comparison q// i between experiments and modelling that takes into account these effects has been conducted in LHD [] with respect to carbon emission, where at least qualitatively good agreement has been found for CIV profile and density dependence of CIII, CIV, and CV, indicating existence of such the mechanisms in the edge stochastic layer. The systematic experiments in LHD with varying the radial thickness of stochastic layer have shown that a thicker stochastic layer seems more effective to screening the impurity []. This is considered to be due to an increase of radial extension of the friction force dominant region. Since the friction dominant region favours low temperature and substantial high density condition with higher plasma velocity, the region tends to be located at the downstream, while the upstream is favoured by the thermal force dominant region. The q i

7 OV/4-4 thicker stochastic layer can provide a thicker friction force region, which thus reduces the impurity that penetrates directly into the thermal force dominant region as neutrals that then build up at the upstream. Analyses are underway to compare the impurity screening results from different D devices using the parameters such as st q i, and λ st SOL q λ etc., where λst SOL and D λimp are the radial thickness of stochastic layer or the island divertor SOL and the impurity penetration length. At the moment, however, clear operation domain for screening is not yet identified for these parameter space. It indicates that there exist hidden parameters that characterizes the impurity transport, such as injection energy, recycling location, drift, electric field, turbulence transport, etc. Indeed, the clear changes of the electric field as well as turbulent transport have been observed with RMP application as discussed in section 5. // i imp 4. Impact on detachment 0.15 Because of the fast //-transport with respect to -transport, it is considered that the change of magnetic geometry/topology can modify the edge radiation structure. This has been demonstrated in Tore Supra ergodic divertor with MP applied to lower hybrid current drive (LHCD) discharges []. It has been found that with relatively low density, 0.1 ρ = π a < n > / I 0., m e0 MARFE is obtained during MP application + LHCD, where the radiated power is almost doubled compared to the phase without MP. The MARFE is positionally stable at the high field side with more than 90% radiation of total input power. In W7-AS, it has been found that with proper choice of the edge island geometry, i.e., large island and with short connection length, an operation domain with stable partial detachment is realized [, ]. In such cases, the 3D numerical simulation with EMC3-EIRENE shows that the radiation region moves to the inboard side being peaked around island X-points. In the case with small island and long connection length, otherwise, the intense radiation remains in front of divertor plate and it leads to radiation collapse. The divertor radiation lowers the temperature at the recycling zone and the island becomes p Stable detach. Radiation collapse 0.000.0x10-4 coil ( b ~ 1.0x10-3.0x10-3 r / B0) vac Δx Remnant island of m/n=1/1 LCFS island LCFS Confinement region transparent to the neutral penetration into core region. It is considered that the sudden increase of neutral penetration into core at the detachment transition drives an instability resulting in the collapse. On the other hand, in the case of the larger island with the inboard side radiation instead of the divertor radiation, the island has screening effect against the neutral penetration and thus stabilizes detachment []. (m) 0.10 0.05 Healing Stable detach. FIG.5 Operation domain for stable detachment in LHD in terms of the distance between the island X-point and the LCFS, Δ xlcfs island, and the RMP strength, B r / B t []. The stable detachment : circles. Radiation collabpse : triangles. The larger Δ xlcfs island and the larger B r / B t are preferred for the stable detachment.

8 OV/4-4 In LHD, it has been found that the application of RMP with m/n=1/1, which creates remnant island structure in the stochastic region, has a stabilizing effect on the detachment []. Without RMP, otherwise, the discharge goes to radiation collapse. The divertor probe array measurements show that the particle flux profile has n=1 mode structure in toroidal direction during detachment []. In this sense, it is considered as a partial detachment. The 3D numerical simulation with EMC3-EIRENE shows that with RMP application the intense radiation is formed along the trajectory of the X-point of m/n=1/1 island, while without RMP the radiation is localized at the inboard side throughout the torus []. The radiation distribution measurements with both AXUVD as well as imaging bolometer show the signature of the intense X-point radiation, confirming, at least qualitatively, agreement with the code prediction for modification of 3D radiation structure [,,]. The operation domain for the stable detachment with RMP is shown in Fig.5 in terms of the distance between the island X-point and the LCFS, Δ x, and the RMP strength, LCFS island B r / B t []. It is seen that in order to realize the stable detachment one needs both the larger Δ xlcfs island and B r / Bt. Although the mechanism of the stabilization is under investigation, the similar tendency in Δ xlcfs island of LHD as that in Δ xlcfs div of W7- AS indicates the importance of the decoupling between core and divertor recycling region to avoid instability caused by the sudden neutral penetration at the detachment transition. The stability analysis with perturbation method also shows that flattening of temperature profile at the island plays a key role to prevent inward penetration of radiation []. It is also found that the larger the B r / Bt is, the lower the detachment onset density, which is a similar trend observed in the MARFE onset in Tore Supra discussed above. In TEXTOR-DED, it has been observed that application of rotating RMP to the NBI heated plasma avoids the MARFE onset compared to the case without RMP []. The experimental results shows that the threshold of the MARFE onset strongly depends on both the level and the poloidal distribution of recycling at the high field side, where the RMP coils are located. It is considered that both the smoothing of recycling and poloidal flow of plasma particles with moving field lines of rotating RMP are responsible for the effect []. The experimental observations shown above clearly indicate a possibility to control the edge radiation structure and the detachment stability in the 3D divertor configurations. 5. Impact on edge electric field and turbulence The change of edge magnetic geometry/topology by the application of RMP can affect turbulence/fluctuation via several effects caused by the magnetic field braiding: the radial component of field lines, B r, can induce radial electron current, radial transport such as D st (eq.(5)), modify the parallel wavelength of the modes, k // ( // = ( B 0 + Br ) ), increase sheath dissipation through the open field lines, etc. The measurements and analysis of the radial electric field and fluctuations with RMP application in tokamaks, helical devices and RFP have been conducted, i.e. in TEXTOR-DED [,,], Tore Supra [,], TEXT [,], CSTN-III [], MAST [,], LHD [], and RFX-mod []. In TEXTOR-DED, the RMP application leads to suppression of blob transport []. This is considered due to the suppression of large scale turbulence structure with RMP by changing the mode structure from k // 0 (without RMP) to finite k // (with RMP), as

9 OV/4-4 observed in experiments [,], which then reduces the blob size. This is also confirmed in numerical simulation []. Moreover, the enhanced sheath dissipation caused by the increased volume of open field lines with RMP is responsible for the reduction of blob radial velocity as observed in the numerical analysis in ref.[]. In TEXTOR-DED [] and MAST [], the reduction of long range correlation of potential fluctuations during RMP application has been observed, which suggests reduction of zonal flows. Possible mechanisms for this effect might be the suppression of large turbulent structure due to the nonzero k // with RMP as mentioned above, and also the decrease in Reynolds stress which is a drive for the zonal flows. The details of the mechanism are under investigation in refs.[,,,,] with sophisticated models. It is also noted that clear changes of plasma potential profile as well as the edge electric field have been observed [,,], where the radial electric field tends to change from negative (inward) to positive (outward). This is interpreted as due to the effect of open field lines produced by RMP, where the fast escaping electrons compared to ions must develop positive field to restore the ambipolarity. These results suggest that the stochastic layer induced by RMP can significantly affect edge turbulence and turbulent transport, and hence for plasma-wall interaction and also plasma confinement. 6. Summary The impacts of the 3D edge magnetic field geometry/topology on SOL/divertor transport have been discussed in regard to the divertor density regime, impurity screening and detachment control. The 3D effects are defined as it emerges when the -transport starts to compete with //-transport in the open field lines of the stochastic layer or in the magnetic island structure for delivering plasma quantity (particle, energy, momentum) from the upstream r, region (around LCFS) to the downstream region (divertor), i.e., Γ // ~ Γ. This Bt condition is met in the stochastic layer or in the edge islands in the island divertor configurations, where typically B / B =10-4 ~ 10-3, while in the D axi-symmetric r t B configuration with X-point divertor B θ / Bt ~0.1 and thus Γ θ // >> Γ. For the vector B t quantity such as momentum, the direction of field line connection to the divertor plates, i.e., plasma flow direction, becomes important. The spatial separation of opposite vector quantities, λ m, the -characteristic scale length for momentum transport, i.e., distance between the counter-streaming flows, is a key parameter to determine the loss of //-momentum through viscosity between the counter flows. Based on this picture, the controlling parameters of the 3D effects have been discussed for the individual divertor functions. Table 1 summarizes the parameters together with the experimental observations, devices, and physical interpretations. In addition to the 3D effects on the divertor functions, there have been reported many experimental observations of the impacts on the edge turbulence as well as on the electric field, as shown in section 5. Although the underlying mechanisms are under investigation, the change caused by the RMP application does have clear effects on the transport and thus on the present analysis through, for example, the values of D, χ, used in the parameters, and B θ

10 OV/4-4 ExB drift on the impurity transport. Comprehensive picture of the 3D effects on the SOL/divertor transport still must wait for these issues to be disclosed. Systematic understanding of the impact of 3D divertor configurations will open new perspectives on divertor optimization for future reactors, which is not available in the D axisymmetric configurations. For this purpose, further investigation with multi-machine comparison, which enables parameter scan study in substantial range, is mandatory. Table I. SUMMARY OF THE 3D EFFECTS ON THE SOL/DIVERTOR TRANSPORT. : Numerical simulations. The definitions of formulae are given in the text. Observations Devices Key parameters Interpretation Divertor functions α +1 n div n LCFS α T div n LCFS α = 1 (weak div-lcfs coupling) Core decontamination W7-AS, LHD, TEXTOR-DED, HSX TEXT, Tore Supra, W7-AS, W7-X, LHD, TEXTOR-DED, TJ-II τ m // / τ m >> 1 q / q// e >>1 q e q // conv / // cond D st q i / D >>1 / q// >>1 λ / λ st SOL i imp //-momentum loss p > LCFS p div Reduction of //-energy conduction Enhanced friction force Ion thermal force suppression Shallow penetration of neutral impurity Pumping efficiency Phys. Sputtering Detach. onset density (?) Impurity screening Detach. stabilization W7-AS, LHD, Tore Supra w island Δx LCFS div Δx LCFS island Radiation modulation by islands Core-edge decoupling particle fueling, core impurity penetration Heat removal MARFE onset delayed TEXTOR-DED f RMP Avoid localized cooling by spreading recycling region with RMP rotation Control of edge radiation Acknowledgements The authors are grateful to Drs. A. Loarte and T. Takizuka for their valuable comments. References N. Ohyabu et al., Nucl. Fusion 34 (1994) 387. R. Koenig et al., Plasma Phys. Control. Fusion 44 (00) 365. E. Strumberger, Nucl. Fusion 7 (1996) 891. C. Alejaldre et al., Plasma Phys. Control. Fusion 41 (1999) A539. D.T. Anderson et al., Fusion Sci. Technol. 50 (006) 171. T. Mizuuchi et al., J. Nucl. Mater. 176-177 (1990) 1070. Ph. Ghendrih, A. Grosman and H. Capes, Plasma Phys. Control. Fusion 38 (1996) 1653. Ph. Ghendrih et al., Nucl. Fusion 4 (00) 11. K.H. Finken et al., Nucl. Fusion 39 (1999) 637. T.E. Evans et al., Nature Physics (006) 419. O. Schmitz et al., J. Nucl. Mater. 438 (013) S194. T.E. Evans et al., Nucl. Fusion 53 (013) 09309. Y. Feng et al., Recent improvements in the EMC3-EIRENE code, PET conference Sep. 3-5, 013, Cracow, Poland.

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