Kinetic studies of nonstationary MPWT layer

Developing and improving analytical and numerical methods for predictive analysis of plasma confinement in a next-generation fusion experimental facility of the tokamak type (ITER) are of prime importance for fusion research and, hence, for mankind`s long-term energy supply. Investi-gations of fusion edge plasmas, in particular, have attracted growing interest in recent years. By fusion edge plasma we mean the plasma region outside the last closed magnetic surface (separa-trix), i.e., the scrape-off layer (SOL), however with inclusion of and special emphasis on its material boundaries, the divertor plates. The SOL strongly influences and even controls the particle and energy fluxes from and to the core plasma, thus playing a crucial role for overall plasma confine-ment. As of today, the main tools for realistic SOL studies are large fluid codes such as B2-SOLPS, EDGE2D and UEDGE, which are mostly used for stationary (time-independent) SOL studies. However, in SOL plasmas there are a number of processes which cannot be described by fluid codes (in which the plasma is characterized by a few "macroscopic" parameters like density, pres-sure and temperature) but rather require genuinely kinetic treatments (considering of the much more detailed "microscopic" velocity distribution function of the plasma particles). As of today, however, appropriate kinetic approaches are often non-existent or insufficiently developed. A particularly important region dominated by kinetic effects is the plasma layer adjacent to the wall, the so-called plasma-wall transition (PWT) layer. In the case of the SOL, the PWT is in addition embedded in a strong magnetic field oblique to the divertor plate (magnetized PWT, MPWT). On the other hand, there up to now exists no consistent theory (neither kinetic nor fluid) describing the non-stationary behavior of the MPWT layer. Even for the unmagnetized PWT layer (UPWT), just very few attempts have been made at treating time-dependent phenomena, and these attempts are based on rather simplified UPWT models. The present project, the duration of which is envisaged to be 2.5 years, aims at contributing to filling these severe gaps by pursuing and achieving the following goals: (1) Kinetic investigations of selected aspects of spatio-temporal MPWT behavior, such as: dy-namics of sheath formation, penetration and reflection of external perturbations (in particular, electromagnetic and particle pulses created by bursts of edge-localized modes (ELMs)) into/by the MPWT layer, and response of the MPWT layer to a time-dependent bias voltage applied to the wall. (2) A comprehensive, self-consistent kinetic description of the entire non-stationary MPWT will be formulated with realistic assumptions. This will include (a) fundamental research on the non-stationary MPWT, and (b) formulation of boundary conditions at the divertor plates for fluid codes (and "gyro-kinetic" codes, describing the motion of charged particles averaged over the fast Larmor gyration). For each problem, the conceptual theoretical work required will be accompanied by adequate sets of simulation runs with input parameters relevant to existing and planned tokamaks. This work is well aligned with ongoing research activities on basic and fusion-related plasma theory and simulation in Austria, other European countries, the USA and Japan.

Up to present time there are no publications concerning consistent analytic kinetic theory of the magnetized plasma-wall transition (MPWT) layer. Time-dependent theory for the MPWT layer, namely the theory of its stability, is not considered in general. Moreover one can find only a few (experimental) publications even on the time-dependent theory of the un-magnetized PWT layers. We start from the construction of the analytic time-dependent theory for the Tonks-Langmuir (TL) model of the discharge, which represents a sample for the PWT theory whose results can be successfully generalized for the PWT layer of other types. The stability of the potential shape in the quasi-neutral pre-sheath (PS) of the TL discharge is investigated. Regarding high-frequency perturbations the PS is shown to be stable. At low-frequencies perturbations the equation can be reduced to analysis of the diffusion like equation describing the instability. Using the smallness of the tilting angle of the magnetic field to the wall the ion distribution functions are found for three sub-layers (the collisional (CPS) and magnetic (MPS) pre-sheaths and Debye sheath (DS)) in the analytic form. The MPS entrance and the related kinetic form of the Bohm-Codura condition are defined for the first time. In the asymptotic three-scale limit, (when the electron Debye length is smaller than the ion giro-radius, which is itself much smaller than the collision length), the time-dependent properties of the sub-layers can be investigated separately from each other. The analytic theory of the stability of the MPS and the CPS is presented. It is assumed that ion gas moves with the constant fluid velocity. The presence of an ion beam has required to modify the form of the Bohm-Chodura criterion It is found that instabilities both of the CPS and MPS grow proportional to the square root of time. A numerical method for matching of the non-neutral sheath and quasi-neutral PS solutions for a spherical probe is developed. The method allows to determine an optimal matching radius. Using this radius we can determine the matched potential profile in the entire plasma-probe transition region. We have also shown that the Bohm criterion is inapplicable in the present probe problem. Existing theories of the Bohm criterion (BC) imply its interpretation in the fluid and kinetic approximations separately. In the fluid approach the results involve clearly identified quantity an ion fluid velocity. In the kinetics the ion behavior is formulated via a quantity (the squared inverse velocity averaged by the ion distribution function) without any clear physical significance. Introducing a generalized polytropic coefficient function we have succeeded to determine the unified BC which holds irrespectively of whether the ions are described kinetically or in the fluid approximation.