Hydrodynamic states of phonons in insulators

The Chapman-Enskog method is generalized for accounting the effect of kinetic modes on hydrodynamic evolution. Hydrodynamic states of phonon system of insulators have been studied in a small drift velocity approximation. For simplicity, the investigation was carried out for crystals of the cubic class symmetry. It has been found that in phonon hydrodynamics, local equilibrium is violated even in the approximation linear in velocity. This is due to the absence of phonon momentum conservation law that leads to a drift velocity relaxation. Phonon hydrodynamic equations which take dissipative processes into account have been obtained. The results were compared with the standard theory based on the local equilibrium validity. Integral equations have been obtained for calculating the objects of the theory (including viscosity and heat conductivity). It has been shown that in low temperature limit, these equations are solvable by iterations. Steady states of the system have been considered and an expression for steady state heat conductivity has been obtained. It coincides with the famous result by Akhiezer in the leading low temperature approximation. It has been established that temperature distribution in the steady state of insulator satisfies a condition of heat source absence.Comment: 10 page

Experimental study of a transformer with superconducting elements for fault current limitation and energy redistribution

Numerous proposed and developed superconducting fault current limiters and self-limiting transformers limit successfully fault currents but do not provide uninterrupted supplying of consumers. A design investigated in the work combines the functions of a conventional transformer with the functions of fast energy redistribution and fault protection. The device constitutes a transformer containing an additional high-temperature superconducting (HTS) coil short-circuited by a thin film HTS switching element. Fault current limitation and redistribution of the power flow to a standby line are achieved as a result of a fast transition of the superconducting switching element from the superconducting into the normal state. Transient and steady-state characteristics were experimentally investigated. A mathematical model of the device operation was proposed, and the calculated results were found to be in good agreement with the experimental data. The application field and basic requirements to such devices were discussed and it was shown that the proposed device meets these requirements.Comment: 15 pages incl. 4 figures. Submitted to "Cryogenics

AC losses in type-II superconductors induced by nonuniform fluctuations of external magnetic field

Magnetic field fluctuations are inevitable in practical applications of superconductors and it is often necessary to estimate the AC losses these fluctuations induce. If the fluctuation wavelength is greater than the size of a superconductor, known estimates for an alternating uniform external magnetic field can be employed. Here we consider the opposite case and analyze, using a model critical-state problem, penetration of spatially nonuniform fluctuations into type-II superconductors. Numerical simulation is based on a variational formulation of the Bean model. The analytical solutions, found in a weak penetration limit, are used to evaluate AC losses for two types of fluctuations: the running and standing waves. It is shown that for spatially nonuniform fluctuations the losses are better characterized by the fluctuation penetration depth than by the fluctuation amplitude. The results can be used to estimate the AC losses in flywheels, electric motors, magnetic shields, etc.Comment: 18 pages, 5 fugure

Generalization of the Grad method in plasma physics

The Grad method is generalized based on the Bogolyubov idea of the functional hypothesis for states at the end of relaxation processes in a system. The Grad problem (i.e., description of the Maxwell relaxation) for a completely ionized spatially uniform two-component electron-ion plasma is investigated using the Landau kinetic equation. The component distribution functions and time evolution equations for parameters describing the state of a system are calculated, and corrections are obtained to the known results in a perturbation theory in a small electron-to-ion mass ratio.Comment: 10 pages, 2 table