An electron in a quantized plane wave and in a constant magnetic field

The Dirac equation is considered for an electron in a constant homogeneous magnetic field and in a quantized electromagnetic plane wave propagating along the direction of the former. This problem is shown to be reduced to the Schrödinger equation for a system of many interacting oscillators. The corresponding Hamiltonian is diagonalized. An equation is established relating the total energy with the moment of a system along the magnetic field. Approximate solutions of this equation are given. A behaviour of a system close to cyclotron resonance is discussed.     

Spin connection resonance in magnetic motors

A mechanism is proposed for rotation of magnetic assemblies by a torque consisting of the magnetic dipole moment of the assembly and a magnetic field generated from space–time in Einstein–Cartan–Evans (ECE) field theory. It is shown that when the magnetic assembly is stationary, the space–time is described by a Helmholtz wave equation in the tetrad as eigenfunction. This is a balance condition in which the Cartan torsion of the space–time is zero, but in which the tetrad and spin connection are non-zero. This balance may be broken by a driving current density produced by the magnetic assembly. The Helmholtz equation becomes an undamped oscillator equation. At resonance the torque on the magnetic assembly may be amplified sufficiently to cause the whole assembly to rotate, as observed experimentally in a repeatable and reproducible manner.     

Exact quantum mechanical description of the motion of spin-1/2 particles and of spin motion in a uniform magnetic field

The Dirac-Pauli equation is used to obtain the exact equation of spin motion for spin-1/2 particles with an anomalous magnetic moment in a constant and uniform magnetic field. Exact formulas are established for the angular velocity of the revolution of such particles along circular orbits and the rotation of the particle spin with respect to momentum. Finally, a quantum mechanical equation for the motion of the particles in a strong magnetic field is derived. Zh. éksp. Teor. Fiz. 114, 448–457 (August 1998)     

An analytical solution of the Klein–Fock–Gordon equation for a 2D pion atom moving in a constant uniform magnetic field

The Klein–Fock–Gordon equation is solved for a 2D pion moving in a constant uniform magnetic field. A relativistic energy spectrum is calculated for fixed values of the angular momentum and magnetic field Н. An analysis of the results of these calculations allows us to conclude that the Klein–Fock–Gordon equation, unlike the Schr?dinger equation, cannot describe the energy of the particle s-state in the magnetic field. It is elucidated that a correction for the relativistic energy level caused by the constant magnetic field is noticeable for the magnetic field H > 100. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 91–96, March, 2009.     

An analytic solution of the Boltzmann equation in the presence of self-generated magnetic fields in astrophysical plasmas

Through relating a self-generated magnetic field to the regular motion of free electrons that is responsible for the magnetic field generation in astrophysical plasmas, we solve the Boltzmann kinetic equation in the presence of the self-generated magnetic fields to obtain a steady-state, collisional invariant analytic solution of the equation.     

Dynamics of spinor condensates and stochastic approach

The dynamics of the collective spin for Bose-Einstein condensates with nonlinear interactions, is studied within the framework of the two-component spinor. We discuss the spin resonance when the system is submitted to a periodically-modulated magnetic field at the zero temperature. In this case, the nonlinearity parameter controls the critical change between a localized and a homogeneous spin state. When the temperature is finite – or a random magnetic field is considered – the movement of the collective spin is governed by the Landau-Lifshitz-Gilbert equation, from which the complete Fokker-Planck equation is derived. This equation is the essential tool to describe the time-evolution of the probability distribution function for the collective spin. The functional integral approach is used to solve analytically examples of BEC spin behavior in a static magnetic field at finite temperature. We show how such a method can lead effectively to the complete solution of the Fokker-Planck equation for this kind of problems.     

任意两共轴圆线圈间的互感系数及磁感线的分布

从一个圆电流的矢势出发,导出了任意两共轴圆线圈间互感系数的函数表达式,根据其函数表达式,由数学软件MatLab绘出了互感系数随两线圈间距离及两线圈半径变化的分布图.然后再从一个圆电流的矢势出发,导出了任意两共轴圆电流线圈磁感线所满足的方程,按照磁感线方程也绘出了其磁感线在空间的分布图.     

On the influence of a weak magnetic field on the drift motion of charged particles

The results obtained in [1] are generalized to the case when an arbitrarily oriented magnetic field is present by allowance for the influence of a magnetic field with cyclotron frequency less than the collision frequency on the dependence of the drift velocity on the velocity of random motion (Langevin equation). A study is made of the influence of a magnetic field on the equation of drift motion derived in [1] and this field is allowed for in the previously obtained results of the solution of that equation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 69–72, May, 1972.     

Classical spin theory

Tensor and vector equations of motion of a classical charged particle with spin have been derived within the framework of the special theory of relativity on the basis of Frenkel's tensor. The anomalous magnetic moment of the particle is considered in a natural manner in deriving the equations. The expression for the forces acting on the particle is constructed with consideration of the effect of spin on the motion trajectory. The spin equations proved to coincide with those obtained previously by Nyborg and Good. The properties of these equations have been studied, and it has been shown that the various equations are in fact variant forms of one and the same equation. In the absence of an anomalous magnetic moment the tensor equation coincides with Frenkel's spin equation, and in the same situation the vector equation transforms to the equation obtained by Tamm. In the special case of homogeneous fields the vector equation coincides with the well-known Bargmann-Michel-Telegdi equation. In conclusion we present spin motion equations for a particle with electric and magnetic charges.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 67–76, February, 1980.     

Zur Statistik neutraler Fermionen mit anomalem magnetischen Moment im äußeren Magnetfeld

In this paper we calculate the equation of state of a relativistic uncharged Fermi particle gas in a magnetic field, using the exact solutions of the Dirac-Pauli equation for an uncharged Fermi particle with an anomalous magnetic moment. We find that the stressenergy tensor is anisotropic. The anisotropy is introduced by the anisotropy of energy states.     

Inverted satellites of a solitary oscillating pearl vortex in a thin magnetic superconductor film

An electrodynamic equation is derived for the magnetic field of an isolated Pearl vortex moving along an arbitrary trajectory in an ultrathin film of a magnetic superconductor. This equation is valid for any type of magnetic order in the magnetic subsystem. The magnetic structure of an isolated oscillating Pearl vortex is investigated in a thin magnetic superconductor film. Oscillations of the vortex and the presence of the magnetic subsystem are shown to lead to a significant renormalization of the vortex field in comparison with the Pearl solution. New phenomena of inverted satellites are predicted in which an inverted precursor appears in front of the vortex and an inverted wake is formed behind the latter at a distance of the order of 10λ_eff from the vortex center. These phenomena can be observed in magnetooptical experiments.     

Inhomogeneous configurations of magnetization of ferromagnetic films with biaxial anisotropy

The system of the Landau-Lifshitz equations and magnetostatic equations for a ferromagnetic film with biaxial anisotropy and a Q-factor smaller than unity is reduced to a single scalar equation for the magnetostatic potential. Such a procedure is possible if the magnetization modulation scale in the sample considerably exceeds the characteristic magnetic length. The solutions to this equation describing inhomogeneous periodic magnetic configurations are obtained. The energy analysis of these configurations is carried out.     

Transport Equations of Plasma in a Curvilinear Magnetic Field

The problem of transport equations of a collisional plasma in a curvilinear magnetic field is studied. Two main approaches to this problem are presented: that based on using the Boltzmann kinetic equation and the drift kinetic equation approach. In the frame of the first approach a multimoment transport equation set is found which is more general than the transport equation sets of Braginskii and Grad. The tensor equations of this set are described in an arbitrary curvilinear coordinate system. This allow to use these equations in problems of a plasma confined in toroidal magnetic configurations. Simplification of the multimoment transport equation set in the case of high magnetic field is performed. In the frame of the drift kinetic equation approach, a generalization of the drift transport equations derived earlier by the authors (Zh. Eksp. Teor. Fiz. 83 (1982) 139) is given.     

Classical Theory of Hot-Electron Transport in Electric and Magnetic Fields

Balance equation approach to the hot-electron transport in electric and magnetic fields is reformulated.The balance equations are re-derived from the Boltzmann equation. A new expression for the distribution function isreported in the present paper. It is homogeneous steady solution of the Boltzmann equation in constant relaxation timeapproximation. It holds when ωocτ < i or ωc < Te. As an example, the mobility of 2D electron gas in the GaAs-AlGaAsheterojunction is computed as a function of electric field and magnetic field.     

Passage of polarized neutrons through magnetic media. Depolarization by magnetized inhomogeneities

The behavior of a neutron polarization vector for neutrons passing through magnetic media characterized by a magnetic fluctuation tensor is described by Bloch-type equation. Coherent and incoherent spin flow motions on the surface of an unit three-dimension sphere are reflected by the equation. The applicability of the equation is based on two factors: (a) the SU(2) group analysis of the neutron spin behaviour in a magnetic field; and (b) consecutive averaging of spin trajectories in the SU(2) group manifold over all neutrons passing through a thin sample layer. Halpern-Holstein's and Maleyev-Ruban's depolarizations are discussed.     

On the effect of a magnetic field on fast charged particles passing through a substance

A transport equation in the small-angle approximation is obtained for a curvilinear beam of fast charged particles passing through a substance in a nonuniform magnetic field. Green functions for this equation are found for an annular beam in a weak-focusing field and for a helical beam in the nonuniform magnetic field.     

Equivalent representation of orthogonal-field electrodynamics by system of covariant lines of force

It is shown that the electrodynamics of orthogonal magnetic and electric fields can be represented as the dynamics of covariant lines of force. Such a representation is provided for the Lienard-Wichert field of an arbitrary moving charge and the field of a charge that moves uniformly about a circle. The four vector of the electric lines of force is written as the sum of the four vector of the charge and the radius four vector directed along the light cone to the observation point. This vector is a solution of an equation that formally coincides with the equation of motion of the magnetic moment in external fields for a zero intrinsic magnetic moment. The electromagnetic field is reconstructed according to a system of lines that correspond to the total equation of motion of the magnetic moment. Such a field for a uniformly circulating charge is examined.Erevan Physics Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 35, Nos. 3, 4, pp. 313–323, March–April, 1992.     

霍尔推力器放电通道溅射腐蚀计算

为了预示霍尔推力器的寿命,建立了推力器粒子束放电通道的2维电磁场模型,模拟的推进剂为氙。利用PIC方法跟踪粒子在电磁场中的运动。磁场的求解采用拉普拉斯方程,电场的求解采用泊松方程。电子由阴极喷入通道,并在电磁场中与原子发生电离碰撞生成离子。在跟踪离子的过程中记录下撞击到内外壁面的离子个数、角度和能量。利用记录下的参数进行腐蚀计算,得到当溅射阈值能量分别为10,20,30,40,50 eV时通道壁面的腐蚀速率。推力器放电通道出口附近的最大腐蚀速率约为1.7×10-9 m/s。