Some properties of an electron gas in a quantizing magnetic field

The electron gas neutralized by a rigid positive background and in a quantizing magnetic field, is studied in a ‘quasi-classical’ model previously proposed by the author and collaborators. The plasma oscillation of the electron gas shows an acoustic-type dispersion for small wave vector. The potential behind an ion moving along the direction of the magnetic field is calculated and is found to have a sinusoidal behaviour. Some consequences of this potential are pointed out. The energy loss by a moving charge in the electron gas is shown to exhibit some interesting properties. Other quantities such as light scattering and magneto-acoustic oscillations are also discussed. A derivation is given for a ‘quasi-classical’ linear response in the finite relaxation time approximation.     

Zur Quantentheorie der magnetischen Widerstandsänderung

Considering a system of free electrons and randomly fixed impurities in a homogenious magnetic field, a derivation of a Titeica-type-formula for the transvers electrical conductivity is given. This formula holds for all magnetic field strengths and powers of the density of impurities. The derivation avoids an ergodic hypothesis for bounded variables which is used byKubo and coworkers. Also, a transport equation is derived, correct to the first power of the impurity density, from which the conductivity parallel to the magnetic field may be calculated. In both cases singularities which arise in the Born approximation are removed byt-matrix approximations.     

Kinetic equation for a weakly interacting classical electron gas

A kinetic equation is derived for the two-time phase space correlation function in a dilute classical electron gas in equilibrium. The derivation is based on a density expansion of the correlation function and the resummation of the most divergent terms in each order in the density. It is formally analogous to the ring summation used in the kinetic theory of neutral fluids. The kinetic equation obtained is consistent to first order in the plasma parameter and is the generalization of the linearized Balescu-Guersey-Lenard operator to describe spatially inhomogeneous equilibrium fluctuations. The importance of consistently treating static correlations when deriving a kinetic equation for an electron gas is stressed. A systematic derivation as described here is needed for a further generalization to a kinetic equation that includes mode-coupling effects. This will be presented in a future paper.     

Temperature of a thermally insulated surface in a gas flow

An equation is derived for determining the temperature of a thermally insulated surface in a gas flow. The equation does not contain any empirical coefficients. The derivation is based on allowance for the work done by a jet arrested at an obstructing surface on the surrounding flow layers. The application of the equation to subsonic and supersonic flows is discussed. Zh. Tekh. Fiz. 68, 134–135 (April 1998)     

A microscopic derivation of the critical magnetic field in a superconductor

The propagator for a noninteracting many electron system in a constant magnetic field in three space time dimensions is computed. This formula and the results of [FT1,2] are used to give a microscopic derivation of a BCS-equation with magnetic field. It is shown that this equation has no solution if the magnetic field is sufficiently large. Perturbation theory in the interaction around the magnetic field propagator is discussed.     

A diffusion model for the Dirac equation

In previous work the author was able to derive the Schrödinger equation by an analytical approach built around a physical model that featured a special diffusion process in an ensemble of particles. In the present work, this approach is extended to include the derivation of the Dirac equation. To do this, the physical model has to be modified to make provision for intrinsic electric and magnetic dipoles to be associated with each ensemble particle.     

Transport mean free path for magneto-transverse light diffusion: an alternative approach

This paper presents a derivation of the transport mean free path for magneto-transverse light diffusion, ℓ*_⊥, in an arbitrary random mixture of Faraday-active and non-Faraday-active Mie scatterers. This derivation is based on the standard radiative transfer equation. The expression of the transport mean free path obtained previously from the Bethe-Salpeter equation, for the case where only Faraday-active scatterers are present, is recovered. This simpler formulation can include the case of homogeneous mixtures of Faraday-active and non-Faraday-active scatterers.     

Transport mean free path for magneto-transverse light diffusion: an alternative approach

Abstract

This paper presents a derivation of the transport mean free path for magneto-transverse light diffusion, ?*_⊥, in an arbitrary random mixture of Faraday-active and non-Faraday-active Mie scatterers. This derivation is based on the standard radiative transfer equation. The expression of the transport mean free path obtained previously from the Bethe–Salpeter equation, for the case where only Faraday-active scatterers are present, is recovered. This simpler formulation can include the case of homogeneous mixtures of Faraday-active and non-Faraday-active scatterers.     

Compton scattering of a spectrally narrow radiation flux by free electrons

A kinetic equation that includes spontaneous and induced Compton scattering is obtained for the propagation of electromagnetic radiation in a gas of free electrons. The derivation includes terms on the order on (v/c)² in the conservation laws. Numerical integration of the equation is performed for the case of plane-parallel propagation of the radiation flux in the electron gas.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 93–97, February, 1979.In conclusion, the author wishes to express his gratitude to S. Shikhovtsova for help in conducting the numerical calculations.     

Orbital motion of dust particles in an rf magnetron discharge. Ion drag force or neutral atom wind force

Microparticles with sizes up to 130 μm have been confined and the velocity and diameter of particles in a plasma trap of an rf magnetron discharge with an arc magnetic field have been simultaneously measured. The motion of the gas induced by electron and ion cyclotron currents has been numerically simulated using the Navier-Stokes equation. The experimental and numerical results confirm the mechanism of the orbital motion of dust particles in the magnetron discharge plasma that is associated with the orbital motion of the neutral gas accelerated by electron and ion drift flows in crossed electric and magnetic fields.     

Fluctuations and the magnetic equation of state

The influence of inhomogeneity of magnetization on the equation of state for a magnetic system has been considered in the approximation of homogeneous fluctuations of magnetic moment. The fluctuations have been described in the molecular field approximation. It has been shown that taking into account the fluctuations of magnetic moment at the derivation of the equation of state changes the relation among the variablesM, H andT, the temperature dependence of the spontaneous magnetization near the critical point, and shifts the critical temperature.The author would like to thank Prof. J.Kocinski and Prof. L.Wojtczak for their interest in the subject of the paper and for numerous elucidating discussions. The author is indebted to Prof. L.Valenta for his helpful remarks concerning this paper.     

Skyrmions on an elastic cylinder

For a spin-polarized electron gas on an elastic cylinder in an external axial magnetic field and an axial electric field we find that the corresponding Euler-Lagrange equation is the double sine-Gordon (DSG) equation with an exact 2π-skyrmion solution. The DSG skyrmion is stabilized, without Coulomb repulsion, by the curvature of the cylinder. It adopts a characteristic length ξ which is smaller than the radius of the cylinder. For an elastic cylinder this mismatch of length scales causes a deformation of the cylinder in the region of the skyrmion. Received 23 October 2001 / Received in final form 8 March 2002 Published online 2 October 2002 RID="a" ID="a"e-mail: rossen.dandoloff@ptm.u-cergy.fr     

On the extension of the Boltzmann equation to include pair correlations

The derivation of kinetic equations, including the effects of pair correlations, for a gas of particles interacting via purely repulsive forces is reported. An additional assumption on the form of the two-particle distribution function yields the Enskog equation for a dense hard-sphere gas. However, the true two-particle distribution function is not of this form.     

On the steady motions of a flat domain wall in a ferromagnet

A new derivation is presented of Walker's exact solution to Gilbert equation, a solution which mimicks the travelling-wave motion of a flat domain wall at 180^°. It is shown that a process during which the working of the applied magnetic field exactly compensates dissipation (the Walker condition) exists both under the constitutive circumstances considered in the standard Gilbert equation and when either the internal free-energy or the dissipation, or both, are generalized by the introduction of higher-gradient terms; but that such a process cannot solve the generalized Gilbert equation. It is also shown that, when dry-friction dissipation is considered and a suitable magnetic field is applied, the associated Gilbert equation has a Walker-type solution mimicking a flat wall, at 90^° this time, which however does not satisfy the Walker condition. Received 16 November 2001     

Dependence of the magnetization relaxation time of single-domain ferromagnetic particles on damping in the Brown model

Analytical expressions for the magnetization relaxation time τ of single-domain ferromagnetic particles with cubic or uniaxial anisotropy in a static transverse magnetic field are derived. The derivation is based on calculating the escape rate of a Brownian particle from a potential well; this technique is applicable at any damping and is generalized to the case of magnetic relaxation of superparamagnetic particles. The validity of the expressions obtained for τ is checked against a numerical solution of the Landau-Lifshitz-Gilbert equation over the whole range of damping (very low, intermediate, and high damping and the crossover region between low and intermediate damping).     

Kinetic Description of a Rayleigh Gas with Annihilation

In this paper, we consider the dynamics of a tagged point particle in a gas of moving hard-spheres that are non-interacting among each other. This model is known as the ideal Rayleigh gas. We add to this model the possibility of annihilation (ideal Rayleigh gas with annihilation), requiring that each obstacle is either annihilating or elastic, which determines whether the tagged particle is elastically reflected or removed from the system. We provide a rigorous derivation of a linear Boltzmann equation with annihilation from this particle model in the Boltzmann–Grad limit. Moreover, we give explicit estimates for the error in the kinetic limit by estimating the contributions of the configurations which prevent the Markovianity. The estimates show that the system can be approximated by the Boltzmann equation on an algebraically long time scale in the scaling parameter.

     

静压轴径轴承静态特性的数值模拟分析

气体润滑轴承具有摩擦小、寿命长、精度高等优点,已经在精密工程等许多领域有着十分广阔的应用。文中对气体润滑基本方程Reynolds方程进行了分析,利用FLUENT对透平膨胀机用静压轴径轴承模型进行了数值模拟,得到轴承表面的压力分布;并逐一研究了供气压力、偏心率和轴承结构参数等因素对静压气体轴承静态特性的影响规律。     

Numerical calculations of the driving force on an Abrikosov vortex

The driving force on an Abrikosov vortex is calculated numerically from the London equation and involved energies for a vortex perpendicular to the screening current near the surface of a superconductor. Compared with previous analytical derivation of the total force, the partial magnetic, kinematic, and external forces are also obtained so that the nature of the driving force may be deeply discussed. It is shown that the force is neither a Lorentz force nor a Magnus force as often believed and that in order to get a correct result, the image effects and the work done by the applied field must be taken into account. A name of London force is suggested for the driving force. A deep understanding of the nature of the driving force on Abrikosov vortices may also be important in the study of vortex pinning and dynamics in type-II superconductors.     

Equation of State in the Fugacity Format for the Two-Dimensional Coulomb Gas

We derive the general form of the equation of state, in the fugacity format, for the two-dimensional Coulomb gas. Our results are valid in the conducting phase of the Coulomb gas, for temperatures above the Kosterlitz–Thouless transition. The derivation of the equation of state is based on the knowledge of the general form of the short-distance expansion of the correlation functions of the Coulomb gas. We explicitly compute the expansion up to order in the activity ζ. Our results are in very good agreement with Monte Carlo simulations at very low density.     

Magnetostatic Green's functions for the description of spin waves in finite rectangular magnetic dots and stripes

We present derivation of the magnetostatic Green's functions used in calculations of spin-wave spectra of finite-size non-ellipsoidal (rectangular) magnetic elements. The elements (dots) are assumed to be single domain particles having uniform static magnetization. We consider the case of flat dots, when the in-plane dot size is much larger than the dot height (film thickness), and assume the uniform distribution of the variable magnetization along the dot height. The limiting cases of magnetic waveguides with rectangular cross-section and thin magnetic stripes are also considered. The developed method of tensorial Green's functions is used to solve the Maxwell equations in the magnetostatic limit, and to represent the Landau–Lifshitz equation of motion for the magnetization of a magnetic element in a closed integro-differential form.