Abstract. A study of three-dimensional perturbed magnetic field structures and transport for edge localized mode control experiments with resonant magnetic perturbations at DIII-D is presented. We focus on ITER-Similar Shape plasmas at ITER relevant electron pedestal collisionalities ν * e ∼ 0.2. This study is performed in comparison to results from TEXTOR-Dynamic Ergodic Divertor circular limiter plasmas. For both experiments the magnetic field structure is analyzed in the vacuum paradigm -superimposing the external RMP field on the unperturbed equilibrium. At TEXTOR this description holds for normalized poloidal flux Ψ N > 0.7 without tearing modes driven by the RMP field. For DIII-D H-mode plasmas the validity of this approach still needs to be established. In this paper a method is discussed to diagnose the degree of edge stochastization based on a comparison between modeled magnetic footprints on the divertor targets and experimental data. Clear evidence is presented for the existence of a generic separatrix perturbation causing striation of target particle fluxes. However, heat fluxes into these striations are small. This observation can be explained by accounting for the different heat and particle source locations and the 3D trajectories of the open, perturbed field lines towards the divertor target. Analysis of the transport characteristics filling the perturbed separatrix lobes based on initial EM C3/EIREN E modeling suggests the existence of open field lines connecting the stochastic edge to the target pattern. However, the width and inward most extent of the stochastic layer can not yet be quantified.

It is shown that neoclassical theory explains quite well the origin of the co-current toroidal rotation velocity measured in the core of stationary Alcator C-Mod edge localized mode (ELM)-free Ohmic high confinement (H)-mode discharges. Both edge and core toroidal rotation velocity profiles are determined to a good approximation by the edge ion temperature and density pedestals, where the gradients are large and the plasma is in the high collisionality regime. Under these conditions, the predicted radial electric field profile is similar to those measured in the DIII-D tokamak whereas the usual expression for the poloidal velocity is modified by finite Larmor radius (FLR) effects. Over the entire plasma cross section, the expression of the toroidal velocity can approximately be cast as the product of a dimensionless non-local functional of the pedestal normalized profiles T i (r)/T i (r inf) and N i (r)/N i (r inf) with powers of the plasma density, temperature, safety factor and magnetic field at the pedestal inflexion point r inf provided the FLR related corrections are independent of the latter parameters. The collapse of the core toroidal rotation velocity when either an internal transport barrier forms (that leads to impurity accumulation), or the plasma experiences a transition from the H-to the low confinement (L)-mode, or ELMs appear, and the spin up at the L-H transition are also explained. In the edge region, power balance is consistent with the prediction from subneoclassical ion energy transport theory at high collisionality. The role of charge exchange neutrals is discussed and the critical density above which they are expected to noticeably slow down the rotation is estimated. The toroidal velocity gradient predicted by theory at the edge of the ELM-free Ohmic H-mode discharge mainly under study (q s = 3.4) is near the onset value for the Kelvin-Helmholtz (K-H) parallel velocity shear (PVS) instability; this result is very interesting since a transition from ELM-free to enhanced D α (EDA) H-modes occurs at q ∼ = 3.5-4; the PVS K-H instability appears to have the characteristics of the 'quasi-coherent' mode that is present in all EDA plasmas, but not in ELM-free H-modes.

The first results of the Dynamic Ergodic Divertor in TEXTOR, when operating in the m=n 3=1 mode configuration, are presented. The deeply penetrating external magnetic field perturbation of this configuration increases the toroidal plasma rotation. Staying below the excitation threshold for the m=n 2=1 tearing mode, this toroidal rotation is always in the direction of the plasma current, even if the toroidal projection of the rotating magnetic field perturbation is in the opposite direction. The observed toroidal rotation direction is consistent with a radial electric field, generated by an enhanced electron transport in the ergodic layers near the resonances of the perturbation. This is an effect different from theoretical predictions, which assume a direct coupling between rotating perturbation and plasma to be the dominant effect of momentum transfer. Helical magnetic field perturbations are introduced in tokamak plasmas to study, on the one hand, the ergodic divertor concept [1,2] and, on the other hand, the interaction of such perturbations with the magnetohydrodynamics (MHD) stability of the plasma [3,4]. Recent experiments, for instance, suggest a control method to mitigate edge localized modes while maintaining the pedestal pressure and thus plasma confinement [5][6][7]. However, open questions remain, in particular, with regard to the influence on the momentum transport of the plasma. Indeed, one motivation to equip the tokamak TEXTOR with the Dynamic Ergodic Divertor (DED) [8] was to be able to study the interaction between helical magnetic field perturbations and plasma transport and stability.The DED consists of 16 magnetic perturbation coils (four quadruples), plus two additional coils for the compensation of the magnetic field imperfections at the feeder regions of the coils. The coils wind helically around the inner side of the torus (major radius: R 1:75 m; minor radius of the circular plasma cross section typically a 0:47 m) with a pitch corresponding to the magnetic field lines of the magnetic flux surface with a safety factor of q 3. Depending on the choice of coil connections to the power supplies, base modes with different poloidal and toroidal mode numbers can be produced. For the DED these are m=n 12=4, 6=2, and 3=1. The penetration depth into the plasma strongly depends on the mode numbers: While the m=n 12=4 affects the edge plasma only, the m=n 3=1 mode reaches into the plasma center (the maximum radial magnetic field component achievable by the DED at the q 2 surface is 10 ÿ3 of the total magnetic field).In this Letter we present results obtained by the m=n 3=1 mode operation. Covering about one-third of the poloidal cross section of the torus, the mode spectrum of the DED does not contain many sidebands. For the m=n 3=1 configuration the three dominant resonant components inside the plasma are m 1, 2, and 3. In Fig. 1 their strengths at the respective resonances are PRL 94, 015003 (2005) P H Y S I C A L

The concept of the dynamic ergodic divertor (DED) is based on plasma edge ergodization by a resonant perturbation. Such a divertor concept is closely related to helical or island divertors in stellerators. The base mode of the DED perturbation field can be m/n = 12/4, 6/2 or 3/1. The 3/1 base mode with its deep penetration of the perturbation field provides the excitation of tearing modes. This topic was presented elsewhere. In this contribution we concentrate on the divertor properties of the DED. We report on the characterization of the topology, transport properties in ergodic fields, impurity transport and density limit behaviour.The 12/4 base where the perturbation is restricted to the plasma edge is suitable for divertor operation. With increasing perturbation field island chains are built up at the resonance layers. Overlapping islands lead to ergodization. The plasma is guided in the laminar region via open field lines of short connection length to the divertor target. The magnetic topology is not only controlled by the coil current but especially by the edge safety factor. For appropriate edge safety factor we observe a strong temperature drop in the plasma edge, indicating an expansion of the laminar region, which is necessary to decouple the divertor plasma from the core plasma. The modifications of

The impact of the helical perturbations, which can act as a momentum source or sink, on the rotation velocity is calculated on the basis of the ambipolarity constraint and the parallel momentum equation of the revisited neoclassical theory; this theory allows prediction of the parallel and poloidal flow speeds, v , and v , respectively, and therefore the radial electric field E r via the usual radial momentum balance equation. Source terms account for the momentum deposition by neutral beam injection, pressure anisotropization and the j × B force density, the latter two due to Fourier components of (rotating) helical fields. However, the neoclassical theory cannot account for the effect of the electrostatic turbulence on rotation in, e.g. TEXTOR L-modes. This is included by replacing the neoclassical viscosity η 2 by an anomalous one due to turbulence. The main results can be summarized as follows. Using in the case of JET the data of shot #59316 the maximum rotation speed can be reproduced with an accuracy of 10%. A similar result is obtained for the TEXTOR shot #91269. If the angular velocity of the (m = 2, n = 1) Fourier component of the helical field is at low slip frequencies ω p − ω f (ω p is the plasma rotation frequency and ω f the rotation frequency of the helical field) gradually reduced to zero, a localized minimum appears and the gradient of the toroidal velocity becomes around 4 × 10 5 s −1 (JET). However, if the slip frequency is larger than a critical value, the rotation profile of the rotation velocity is not influenced as observed at JET. Although it is possible to create a large velocity shear around the singular surface, this shear is nonetheless limited by the reduction of the central velocity. Therefore, it might not be possible to trigger an ITB by plasma braking at the singular surface.