Probability Density, Diagrammatic Technique, and Epsilon Expansion in the Theory of Wave Turbulence

We apply the methods of Field Theory to study the turbulent regimes of statistical systems. First we show how one can find their probability densities. For the case of the theory of wave turbulence with four-wave interaction we calculate them explicitly and study their properties. Using those densities we show how one can in principle calculate any correlation function in this theory by means of direct perturbative expansion in powers of the interaction. Then we give the general form of the corrections to the kinetic equation and develop an appropriate diagrammatic technique. This technique, while resembling that of $\varphi^4$ theory, has many new distinctive features. The role of the $\epsilon=d-4$ parameter is played here by the parameter $\kappa=\beta + d - \alpha - \gamma$ where $\beta$ is the dimension of the interaction, $d$ is the space dimension, $\alpha$ is the dimension of the energy spectrum and $\gamma$ is the ``classical'' wave density dimension. If $\kappa > 0$ then the Kolmogorov index is exact, and if $\kappa < 0$ then we expect it to be modified by the interaction. For $\kappa$ a small negative number, $\alpha<1$ and a special form of the interaction we compute this modification explicitly with the additional assumption of the irrelevance of the IR divergencies which still needs to be verified.Comment: 26 pages, PUPT-146

Global gyrokinetic simulations of intrinsic rotation in ASDEX Upgrade Ohmic L-mode plasmas

Non-linear, radially global, turbulence simulations of ASDEX Upgrade (AUG) plasmas are performed and the nonlinear generated intrinsic flow shows agreement with the intrinsic flow gradients measured in the core of Ohmic L-mode plasmas at nominal parameters. Simulations utilising the kinetic electron model show hollow intrinsic flow profiles as seen in a predominant number of experiments performed at similar plasma parameters. In addition, significantly larger flow gradients are seen than in a previous flux-tube analysis (Hornsby et al {\it Nucl. Fusion} (2017)). Adiabatic electron model simulations can show a flow profile with opposing sign in the gradient with respect to a kinetic electron simulation, implying a reversal in the sign of the residual stress due to kinetic electrons. The shaping of the intrinsic flow is strongly determined by the density gradient profile. The sensitivity of the residual stress to variations in density profile curvature is calculated and seen to be significantly stronger than to neoclassical flows (Hornsby et al {\it Nucl. Fusion} (2017)). This variation is strong enough on its own to explain the large variations in the intrinsic flow gradients seen in some AUG experiments. Analysis of the symmetry breaking properties of the turbulence shows that profile shearing is the dominant mechanism in producing a finite parallel wave-number, with turbulence gradient effects contributing a smaller portion of the parallel wave-vector

Surface modification of aluminum by runaway electron preionized diffuse discharges in different gases at atmospheric pressure

The paper presents the results of an examination of aluminum samples exposed to runaway electron preionized diffuse discharges in air, nitrogen, and argon at atmospheric pressure. The changes in the chemical composition, structure, and hardness of the aluminum surface layers caused by the action of the discharge were investigated. It has been found that the oxygen and carbon concentrations in the surface layers depend on the number of discharge pulses and on the chemical composition of the working gas. The goal of the study was to find possible uses of runaway electron preionized diffuse discharges in research and industry

Influence of sulphide Cu (I) promoting additives concentration on acid and catalytic properties of high-silica zeolites in straight-run gasoline conversion

In present article the influence of Cu[2]S promoting additives concentration on acid and catalytic properties of high silica MFI-type zeolites is investigated in the process of conversion of straight-run gasoline fractions of gas condensate into high octane components of motor fuels. It was shown that zeolite modified with 1% of Cu[2]S nanoscaled powder possesses the highest acid centers concentration and highest catalytic activity

Modification of various metals by volume discharge in air atmosphere

The results of the modification of stainless steel, niobium and titanium by volume discharge induced by a beam of runaway electrons in air under normal pressure are presented. Changes in the chemical composition of the surface layers of metal by the action of the discharge, structural changes and changes of hardness were studied. It has been found that the concentration of oxygen and carbon in the surface layers of the samples depend on the number of discharge pulses. The aim of this work is to find possible application of this type of discharge in science and industrial production

Modification of the surface layers of copper by a diffuse discharge in atmospheric pressure air

The paper presents the results of examination of copper samples exposed to a diffuse discharge initiated by a runaway electron beam in air under normal pressure. The changes in the chemical composition of the surface layers of copper caused by the action of the discharge were investigated. It has been found that the oxygen and carbon concentrations in the surface layers depend on the number of discharge pulses. The study was aimed at finding possible ways of using this type of discharge in research and industry