The equation describing the radial transport of toroidal momentum in a collisional subsonic plasma with steep gradients has been obtained via a systematic expansion of the two-fluid equations. The diffusion rate is classical; the poloidal rotation, driven by the temperature gradient, generates, in turn, a toroidal flow gradient, also in Ohmic discharges. Moreover, important modifications of the parallel momentum equation are found to arise if ⌳ 1 ϵ(i /⍀ i)(q 2 R 2 /rL T) is уO(1/3); the poloidal rotation velocity is then no longer unique but obeys a cubic equation which may allow for bifurcated equilibria under certain conditions. The toroidal velocities predicted for Ohmic discharges compare well with those measured in PLT ͓Princeton Large Torus; S. Suckewer et al., Nucl. Fusion 21, 1301 ͑1981͔͒; the relevance of the extended equation providing the poloidal rotation velocity to selected experimental edge plasmas is discussed.

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 two-dimensional multifluid code TECXY has been used to model the biasing (with respect to the first wall) of the toroidal belt limiter ALT-II on the tokamak TEXTOR-94 and of the new toroidal pump limiter being installed on Tore Supra tokamak in the framework of the CIEL project. It is well known that the edge flow pattern can be influenced by the poloidal electric drifts from imposing radial electric fields. The modelling with TECXY introduces imprinted bias currents in the scrape-off layer (SOL) for the case of negative (limiter) biasing, and imprinted bias potentials for the case of positive biasing. This allowed us to simulate sufficiently well the experimental I -V characteristics for either biasing of ALT-II and also reproduced the essential features and trends of the observed plasma profiles in the SOL of TEXTOR-94. For negative biasing a moderate improvement of the pumping exhaust efficiency can be achieved in the case of TEXTOR. For Tore Supra, however, only a negligible improvement of the limiter performance with biasing can be predicted, which is explained by the relatively weak drift flows in Tore Supra.

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