Localized electrostatic structures in bounded plasmas

This project deals with localized electrostatic structures that appear in bounded plasmas (acronym BPLES`s), such as sheaths (which appear under all circumstances), double layers (which appear under special circumstances), and gradient-driven structures in space and fusion plasmas. A common feature of these structures is that the plasma properties within them are subject to sudden changes over very short distances. Instead of exhibiting almost perfect quasi-neutrality and thermodynamic equilibrium, BPLES`s are highly non-neutral regions dominated by strong electric fields, where energy is exchanged between the field and the particles via many physical processes typical of plasmas far from thermodynamic equilibrium. This situation is especially complicated, but nevertheless highly important, for space, laboratory and fusion plasmas, where BPLES`s form in the presence of a magnetic field. Our task in this project is to study the particle and energy transport within BPLES`s both parallel and perpendicular to the magnetic field lines. Both open and closed magnetic-field configurations will be studied, with special attention given to the general phenomenon known as E B shear flow. The method for investigating this topic is computer simulation, in particular the particle-in-cell (PIC) method. For performing this task it is mandatory to upgrade present-day PIC codes (such as XPDP or XOOPIC) for solving the field equations and the single-particle equations of motion over non-uniform (nonlinear) grids. This is basically the second (but by no means a secondary) task of the BPLES project, for the following reason: In the standard electrostatic field solver, which is of the finite- difference type and second-order accurate on uniform grids, nonlinear grids give rise to error terms causing significant problems, so that a wider finite-difference stencil is required to maintain second-order accuracy. Other methods of achieving increased local spatial resolution, including adaptive-mesh methods as well as ones avoiding the mesh for the field solve altogether (such as particle-particle methods), are intended be employed as well. This work is well aligned with ongoing research activities on basic and fusion-related plasma theory and simulation in Austria, other European countries, and the U.S.

Unlike other states of matter (solid, liquid and gas, or simply - material), which usually exhibit rather sharp boundaries, the "plasma state" is characterized by a plasma "body" with negligible electric fields, terminated by plasma localised electrostatic structures (LESs) in which excessively strong electric fields are localised. These LESs may be plasma sheaths (PSs) or double/ multiple structures of this kind, commonly known as double layers (DLs). The general achievement of the present project is a new qualitative and quantitative characterisation of the common plasma-LES boundary (PLB), around which the electric field suddenly changes its strength and a "magic" transformation of electron thermal energy into ion directional energy takes place. Understanding, quantifying and predicting how this happens in detail for given external boundary conditions (BCs) enables one to avoid complicated calculations of the particle, heat and energy fluxes within the LES, but instead requires such only at the PLB and at the far side of the LES. Solutions to this problem were available previously for various physical scenarios restricted by the assumption that the plasma ions are created from neutrals at rest ("cold" ion sources). In the present project, a complete archetypal bounded plasma system with a warm ion source has been modelled theoretically (full-scale approach), and in addition a model with separate plasma and sheath regions (two-scale approach) has been developed. All models are kinetic (microscopic) and their solutions have been obtained by means of advanced mathematical tools with extremely high reliability, so they are referred to as exact ones. In each model, relevant experimentally observable fluid (macroscopic) variables have been calculated, at positions close to each other (dense grid), for different ion-source temperatures in the range from zero to asymptotically high values. Highly reliable analytic approximations have been found in spite of initial doubts that such would ever be feasible for warm ion sources. Thus, extension of the well-established cold-ion-source (singular) bounded-plasma model to (regular) bounded-plasma models with arbitrary finite ion-source temperatures has been achieved. The newly found compatibility conditions for the two-scale approach have enabled construction of approximate analytic full- scale solutions. Comparison of the exact solutions with the constructed ones permits identification of the PEB in a real plasma. Moreover, this project introduces the unified Bohm criterion, which is universally valid for both warm and cold, and for both kinetic and fluid scenarios, thus completely removing previous theoretical controversies related to the "official" Bohm criterion. The new theory is a scientific breakthrough accompanied by highly reliable quantitative results important for plasma physics and engineering. The methodological advances achieved and the results obtained, in collaboration with a strong team of associates from Austria and other countries, have already been published to a significant extent in several high-ranking journals, with further dissemination being in progress.