List of Departments
Topmost Scientific Results

🗀 Archive 2010-2015

Department of Theory and Simulation of Plasma Processes

- A nonlinear model of a scalar field coupled to its gradient has been proposed. The model is shown to be suitable for the description of phase transitions accompanied by the formation of spatially inhomogeneous distributions of the scalar field in the ground state. Some solutions of the proposed model have been obtained; these can be related, e.g., to the cosmological scenario or the spinodal decomposition. The proposed model is analogical to the mechanical nonlinear oscillator with coordinate-dependent mass or velocity-dependent elastic modulus. This analogy is employed to reveal the existence of limit cycles and destruction of new phase bubbles.
*A.G. Zagorodny, B.I. Lev* - The superconductivity model wherein the energy gap is asymptotically tending to zero with decrease of temperature or magnetic field has been proposed. Formally, both critical temperature and magnetic field for such a superconductor are infinite ones. The free energy functional has been obtained and Ginzburg-Landau theory for such a superconductor has been developed. A simple quasi-classical statistical model for the description of electrons on a liquid-helium surface in an external electric field is proposed.
*A.G. Zagorodny, B.I. Lev, K.V. Grigorishin, V.B. Tymchyshyn* - We apply the reductive perturbation method to the simple electrostatic ion-temperature-gradient mode in an advanced fluid description. The fluid resonance turns out to play a major role for the excitation of zonal flows. This is the mechanism recently found to lead to the low-to-high (L-H) mode transition and to the nonlinear Dimits upshift in transport code simulations. It is important that we have taken the nonlinear temperature dynamics from the Reynolds stress as the convected diamagnetic flow. This has turned out to be the most relevant effect as found in transport simulations of the L-H transition, internal transport barriers and Dimits shift. This is the first time that an analytical method is applied to a system which numerically has been found to give the right experimental dynamics.
*A.G. Zagorodny* - The approach we proposed earlier for description of particle diffusion in two-dimensional random velocity field has been compared with the decorrelation trajectory method. A frozen turbulence as the most difficult test for the statistical theories has been considered. Different statistical closures of equations for averaged quantities were compared, and validity of subensemble concept was analyzed analytically and numerically to formulate the approach that combines advantages of both methods.
*O.M. Cherniak*

- Particle diffusion in a wave with jumping phase is studied. It is shown that such a wave is involved into the resonance interaction with more plasma particles than a regular wave, and thus can be used to accelerate and heat them. The evolution of statistical characteristics of particle ensemble in a wave is calculated numerically for various types of phase jumps. A strong dependence of the intensity of heating on the type of phase jumps is found.
*А.G. Zagorodny, V.I. Zasenko, O.M. Cherniak*

- The microscopic phase density and its generalizations are considered. The procedure of derivation of hydrodynamic-type nonlinear equations for average values is generalized. We show that the last can be obtained based on equivalent description of evolution process. We investigate a solution of Cauchy problem of equations for average values of general case observable. The solution is represented with respect to the arity index of observable, evolution of which is presented by the certain evolution operators. We analyze the generalized hydrodynamic-type evolution equation for one particle distribution function.
*V. Shtyk*