A minimal two-field fluid approach is followed to describe the radio-frequency (RF) wave propagation in the bounded scrape-off layer plasma of magnetic fusion devices self-consistently with direct current (DC) biasing of this plasma. The RF and DC parts are coupled by non-linear RF and DC sheath boundary conditions at both ends of open magnetic field lines. The physical model is studied within a simplified framework featuring slow wave (SW) only and lateral walls normal to the straight confinement magnetic field. The possibility is however kept to excite the system by any realistic 2D RF field map imposed at the outer boundary of the simulation domain. The self-consistent RF + DC system is solved explicitly in the asymptotic limit when the width of the sheaths gets very large, for several configurations of the RF excitation and of the target plasma. In the case of 3D parallelepipedic geometry, semi-analytical results are proposed in terms of asymptotic waveguide eigenmodes that can easily be implemented numerically. The validity of the asymptotic treatment is discussed and is illustrated by numerical tests against a quantitative criterion expressed from the simulation parameters. Iterative improvement of the solution from the asymptotic result is also outlined. Throughout the resolution, key physical properties of the solution are presented. The radial penetration of the RF sheath voltages along lateral walls at both ends of the open magnetic field lines can be far deeper than the skin depth characteristic of the SW evanescence. This is interpreted in terms of sheath-plasma wave excitation. Therefore, the proper choice of the inner boundary location is discussed as well as the appropriate boundary conditions to apply there. The asymptotic scaling of various quantities with the amplitude of the input RF excitation is established.

This paper summarizes recent experimental characterization of radio frequency (RF)-induced scrape-off layer (SOL) modifications in ASDEX-Upgrade (AUG), JET and Tore Supra (TS). Geometrical aspects are emphasized: complex SOL patterns are observed by several indicators visualized in one or two dimensions transverse to the magnetic field lines. Results are ascribed to inhomogeneous RF-induced SOL biasing around powered ion cyclotron range of frequencies antennas and associated E × B 0 density convection (D'Ippolito et al 1993 Phys. Fluids B 5 3603). Within a simple RF sheath model (Perkins 1989 Nucl. Fusion 29 583), the shape of convective cells on TS can be interpreted in terms of RF-sheath generation by parallel RF currents. Some lessons are drawn for future machines.

Long pulse operation on the Tore Supra tokamak has entered a new phase, characterized by the use of heating power level in excess of 10 MW, during pulses lasting several tens of resistive times. This has been made possible by the use of ion cyclotron range of frequency (ICRF) heating (9 MW coupled to the plasma at 57 MHz), combined with lower hybrid current drive (LHCD: 3 MW at 3.7 GHz) and efficient fuelling techniques (supersonic gas injection, pellets). This paper addresses key technological, operational and physics issues related to the long pulse operation of the Tore Supra ICRF system and required for a reactor: R&D on the ICRF plant, real-time control and safety procedures, integration with other tokamak subsystems, experimental investigation and theoretical modelling of the edge ICRF physics (wave coupling, heat loads on antenna front faces). As far as possible lessons are drawn from the experience gained on Tore Supra for the design and operation of a next-step device.

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