A collisionless electric sheath model between a metal surface and a magnetized plasma is given. The magnetic field is assumed to be uniform and has a small angle of incidence with respect to the surface. It is shown that the ambipolar wall potential is essentially independent of the angle of incidence. The finite Larmor radius and secondary electron effects on the wall potential are derived. The sheath thickness is shown to depend strongly on the surface absorption characteristics.

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.

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Finite Larmor radius effects and inertia become important in the edge region, where the scale lengths of the plasma parameters are intermediate between the ion Larmor radius and the connection length. In contrast to standard neoclassical theory the ambipolarity constraint and the parallel momentum equation of the revisited neoclassical theory [2] allow to predict the parallel and poloidal flow speeds and therefore the radial electric field Er via the usual radial momentum balance equation. The crucial parameter Λ entering both equations measures the ratio of the contributions arising from perpendicular viscosity to those from the parallel viscosity. The theory also accounts for the friction with the recycled neutral gas due to charge exchange. The solution method of the second order equation obtained in this case is validated by comparing with analytical results obtained at vanishing neutral gas density. Indeed, the deviations of the maxima of the flow velocities and of the minima of the electric field are smaller than ≈10%. Comparison of the analytical and numerical results with the measurements at ALCATOR C‐MOD shows good agreement.

An asymptotic solution is given for the ion-drift-kinetic equation with a full Fokker–Planck term for the limiter-scrape-off layer in a tokamak. In this layer, the plasma is assumed to consist of hot, collisionless ions, and cold, collisional electrons. From the solution of the boundary-layer problem, ion and electron particle and energy losses to the limiter are calculated. Limiter load profiles due to ions are explicitly given as functions of the poloidal angle.