Plasma Physics

The hydrogen plasma is studied at temperatures T ~ 10^4 - 10^6 K using the free energy minimization method. A simple analytic free energy model is proposed which is accurate at densities up to 1 g/cc and yields convergent internal partition function of atoms. The occupation probability formalism is modified for solving the ionization equilibrium problem. The ionization degree and equation of state are calculated and compared with the results of other models.

The long-time relaxation of ideal two dimensional magnetohydrodynamic turbulence subject to the conservation of two infinite families of constants of motion---the magnetic and the "cross" topology invariants--is examined. The analysis of the Gibbs ensemble, where all integrals of motion are respected, predicts the initial state to evolve into an equilibrium, stable coherent structure (the most probable state) and decaying Gaussian turbulence (fluctuations) with a vanishing, but always positive temperature. The non-dissipative turbulence decay is accompanied by decrease in both the amplitude and the length scale of the fluctuations, so that the fluctuation energy remains finite. The coherent structure represents a set of singular magnetic islands with plasma flow whose magnetic topology is identical to that of the initial state, while the energy and the cross topology invariants are shared between the coherent structure and the Gaussian turbulence. These conservation laws suggest the variational principle of iso-topological relaxation which allows us to predict the appearance of the final state from a given initial state. For a generic initial condition having X points in the magnetic field, the coherent structure has universal types of singularities: current sheets terminating at Y points. These structures, which are similar to those resulting from the 2D relaxation of magnetic field frozen into an ideally conducting viscous fluid, are observed in the numerical experiment of Biskamp and Welter. The Gibbs ensemble method developed in this work admits extension to other Hamiltonian systems with invariants not higher than quadratic in the highest-order-derivative variables. The turbulence in two dimensional Euler fluid is of a different nature: there the coherent structures are also formed, but the fluctuations about these structures are non-Gaussian.

The dynamics of relativistically strong electromagnetic (EM) wave propagation in hot electron-positron plasma is investigated. The possibility of finding localized stationary structures of EM waves is explored. It is shown that under certain conditions the EM wave forms a stable localized soliton-like structures where plasma is completely expelled from the region of EM field location.

The equilibrium of a cylindrical plasma with purely poloidal mass flow and cross section of arbitrary shape is investigated within the framework of the ideal MHD theory. For the system under consideration it is shown that only incompressible flows are possible and, conscequently, the general two dimensional flow equilibrium equations reduce to a single second-order quasilinear partial differential equation for the poloidal magnetic flux function ψ , in which four profile functionals of ψ appear. Apart from a singularity occuring when the modulus of Mach number associated with the Alfvén velocity for the poloidal magnetic field is unity, this equation is always elliptic and permits the construction of several classes of analytic solutions. Specific exact equlibria for a plasma confined within a perfectly conducting circular cylindrical boundary and having i) a flat current density and ii) a peaked current density are obtained and studied.

A four dimensional systematic mathematical approach for investigating propagation and coupling of wave modes in a slowly varying (in all space directions and time) anisotropic, absorbing plasma is represented. The formalism is especially useful for energy considerations of the waves. It is applicable to general cases of mode conversion in plasmas with general geometries of space-time and magnetic field configurations. A simple example of how this formalism can be applied to practical cases is given.

The profile of a Bennett hole induced by laser field in ionic distribution in collisional plasma is calculated. Influence of Chandrasekhar's dependence of coefficients of velocity space transport on the profile is included into the calculation for the first time. It is found that the hole narrows down as the field detuning frequency increases. Physical cause of the effect is the falling dependence of Coulomb collision frequency on the ionic velocity. Estimations show that the effect is quite observable under conditions of high-current gas-discharge plasma.

The conditions for the existence of negative-energy perturbations (which could be nonlinearly unstable and cause anomalous transport) are investigated in the framework of linearized collisionless Maxwell-drift kinetic theory for the case of equilibria of magnetically confined, circularly cylindrical plasmas and vanishing initial field perturbations. For wave vectors with a non-vanishing component parallel to the magnetic field, the plane equilibrium conditions (derived by Throumoulopoulos and Pfirsch [Phys Rev. E {\bf 49}, 3290 (1994)]) are shown to remain valid, while the condition for perpendicular perturbations (which are found to be the most important modes) is modified. Consequently, besides the tokamak equilibrium regime in which the existence of negative-energy perturbations is related to the threshold value of 2/3 of the quantity η ν = ∂ln T ν ∂ln N ν , a new regime appears, not present in plane equilibria, in which negative-energy perturbations exist for {\em any} value of η ν . For various analytic cold-ion tokamak equilibria a substantial fraction of thermal electrons are associated with negative-energy perturbations (active particles). In particular, for linearly stable equilibria of a paramagnetic plasma with flat electron temperature profile ( η e =0 ), the entire velocity space is occupied by active electrons. The part of the velocity space occupied by active particles increases from the center to the plasma edge and is larger in a paramagnetic plasma than in a diamagnetic plasma with the same pressure profile. It is also shown that, unlike in plane equilibria, negative-energy perturbations exist in force-free reversed-field pinch equilibria with a substantial fraction of active particles.

A phenomenon analogous to the conical refraction widely known in the crystalooptics and crystaloacoustics is discovered for the magnetohydrodynamical waves in the collisionless plasma with anisotropic thermal pressure. Angle of the conical refraction is calculated for the medium under study which is predicted to be 18 ∘ 26 ′ . Possible experimental corroborating of the discovered phenomenon is discussed.

A phenomenon analogous to the conical refraction well-known in the crystalooptics and crystaloacoustics is considered for the magnetohydrodynamical waves in a collisionless plasma with anisotropic thermal pressure. Imposing the most general (generalization of Tsiklauri, 1996, Phys. Plasmas, 3, 800) condition for the existence of the phenomenon, angle of the conical refraction is calculated which appeared to be dependent on the ratio of the Alfven velocity and sound speed measured in the perpendicular direction in respect to the external magnetic field. Feasible ways of experimental demonstration of the phenomenon are discussed and a novelty brought by the general consideration is outlined.

It is planned to use atomic processes to spread out most of the heating power over the first wall and side walls to reduce the heat loads on the plasma facing components in ITER to ~ 50 MW. Calculations indicate that there will be 100 MW in bremstrahlung radiation from the plasma center, 50 MW of radiation from the plasma edge inside the separatrix and 100 MW of radiation from the scrape-off layer and divertor plasma, leaving 50 MW of power to be deposited on the divertor plates. The radiation losses are enhanced by the injection of impurities such as Neon or Argon at acceptably low levels (~0.1 % Argon, etc.)