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In this paper we review some theoretical aspects of the dynamics of the mesoscale filaments extending along the magnetic field lines in the edge plasma, which are often called ‘blobs’. We start with a brief historical survey of experimental data and the main ideas on edge and SOL plasma transport, which finally evolved into the modern paradigm of convective very-intermittent cross-field edge plasma transport. We show that both extensive analytic treatments and numerical simulations demonstrate that plasma blobs with enhanced pressure can be convected coherently towards the wall. The mechanism of convection is related to an effective gravity force (e.g. owing to magnetic curvature effects), which causes plasma polarization and a corresponding E× B convection. The impacts of different effects (e.g. X-point magnetic geometry, plasma collisionality, plasma beta, etc.) on blob dynamics are considered. Theory and simulation predict, both for current tokamaks and for ITER, blob propagation speeds and cross-field sizes to be of the order of a few hundred meters per second and a centimeter, respectively, which are in reasonable agreement with available experimental data. Moreover, the concept of blobs as a fundamental entity of convective transport in the scrape-off layer provides explanations for observed outwards convective transport, intermittency and non-Gaussian statistics in edge plasmas, and enhanced wall recycling in both toroidal and linear machines.

Recent measurements show that non-diffusive, intermittent transport of particles can play a major role in the scrape-off-layer (SOL) of fusion experiments. A possible mechanism for fast convective plasma transport is related to the plasma filaments or blobs observed in the SOL with fast cameras and probes. In this paper, physical arguments suggesting the importance of blob transport [S. I. Krasheninnikov, Physics Letters A 283, 368 (2001)] have been extended by calculations using a three-field fluid model, treating the blobs as coherent propagating structures. The properties of density, temperature and vorticity blobs, and methods of averaging over ensembles of blobs to get the average SOL profiles, are illustrated. The role of ionization of background neutrals in sustaining the density blob transport is also discussed. Many qualitative features of the experiments, such as relatively flat density profiles and transport coefficients increasing toward the wall, are shown to emerge naturally from the blob transport paradigm.

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An analytic theory of the resistive X-point (RX) mode in the edge region of a diverted tokamak is developed by employing an outgoing-evanescent wave boundary condition along the field lines. This result is employed to deduce a new categorization of edge instabilities in the presence of X-points. A regime diagram shows the relationship of the RX mode to the ideal and conventional resistive ballooning modes. In addition to describing growth rates of linear instabilities, the analysis also yields regimes and scalings for nonlinear convective "blob" propagation velocities. The regime diagram and a knowledge of experimental and BOUT code simulation results, suggests that the quasicoherent mode seen in the Alcator C-Mod tokamak [M. Greenwald et al., Phys. Plasmas 6, 1943 (1999)] can be classified as an electromagnetic RX mode. Analytical scalings for the existence of this mode compare well with experimental trends, as does the solution of a model radial eigenvalue problem. Finally, using a finite Larmor radius assumption to eliminate the perpendicular wavenumber, the instability regime diagram can be converted to an edge phase space diagram. X-point physics adds a new region to this edge parameter space that is postulated to be the enhanced D-alpha (EDA) regime.

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Predictive modeling of radiofrequency wave propagation in high-power fusion experiments requires accounting for nonlinear losses of wave energy in the plasma edge and at the wall. An important mechanism of "anomalous" power losses is the acceleration of ions into the walls by rf sheath potentials. Previous work computed the "sheath power dissipation" non-self-consistently by post-processing fields obtained as the solution of models which did not retain sheaths. Here, a method is proposed for a self-consistent quantitative calculation of sheath losses by incorporating a sheath boundary condition (SBC) in antenna coupling and wave propagation codes. It obtains the self-consistent sheath potentials and spatial distribution of the time-averaged power loss in the solution for the linear rf fields. It can be applied for ion cyclotron and (in some cases) lower hybrid waves. The use of the SBC is illustrated by applying it to the problem of an electron plasma wave propagating in a waveguide. This model problem is relevant to understanding the low heating efficiency in direct ion-Bernstein wave launch.Implications for calculating sheath voltages driven by fast-wave antennas are also discussed.

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