Influence of the spin Brownian motion on the negative magneto-rheological effect in a rod-like haematite particle suspension

We have shown the basic equation of the orientational distribution function of prolate spheroidal haematite particles with rotational Brownian motion in a simple shear flow under an applied magnetic field. The equation has been solved numerically in order to investigate the influence of the spin Brownian motion on the orientational distribution, the negative magneto-rheological effect and the characteristics of magnetisation. With respect to the orientational distribution, the present results are in good agreement with those of the theory without that motion, which shows that the spin Brownian motion does not significantly influence the orientational distribution. In contrast, the influence of the spin Brownian motion appears more significantly in the negative viscosity: the negative viscosity effect decreases in comparison with that of the previous theory without the spin Brownian motion. Moreover, a more significant negative magneto-rheological effect is obtained for a larger particle aspect ratio. Since the magnetisation has a strong relationship with the orientation of the magnetic moment, the effect of the spin Brownian motion appears more significantly in this characteristic.     

The filling of neutron star magnetospheres with plasma: Dynamics of the motion of electrons and positrons

We consider the motion of charged particles in the vacuum magnetospheres of rotating neutron stars with a strong surface magnetic field, B ≳ 10¹² G. The electrons and positrons falling into the magnetosphere or produced in it are shown to be captured by the force-free surface E · B = 0. Using the Dirac-Lorentz equation, we investigate the dynamics of particle capture and subsequent motion near the force-free surface. The particle energy far from the force-free surface has been found to be determined by the balance between the power of the forces of an accelerating electric field and the intensity of curvature radiation. When captured, the particles perform adiabatic oscillations along the magnetic field lines and simultaneously move along the force-free surface. We have found the oscillation parameters and trajectories of the captured particles. We have calculated the characteristic capture times and energy losses of the particles through the emission of both bremsstrahlung and curvature photons by them. The capture of particles is shown to lead to a monotonic increase in the thickness of the layer of charged plasma accumulating near the force-free surface. The time it takes for a vacuum magnetosphere to be filled with plasma has been estimated.     

Quantum mechanical equations of motion of particles and spin in polarized media

Quantum mechanical equations of motion are obtained for particles and spin in media with polarized electrons in the presence of external fields. The motion of electrons and their spins is governed by the exchange interaction, while the motion of positrons and their spin is governed by the annihilation interaction. For particles with spin S ≥ 1, second-order terms in spin are taken into account. The equations obtained can be applied to describe the motion of particles and spin both in magnetic and nonmagnetic media.     

Mössbauer relaxation spectra of the spherical superparamagnetic particles with zero energy of anisotropy

Superoperator equations of Fokker-Planck type, describing the common dynamics of the hyperfine field and the nuclear spin are derived under the conditions of diffusional motion of the magnetic moment of the particles. The solution of this equation in the case of particles with zero energy of magnetic anisotropy is considered. Mössbauer spectra of⁵⁷Fe nuclei are calculated over a large range of the diffusion coefficient.     

Polarization of spin-1/2 particles in an axisymmetric magnetic field

The present paper shows that the nature of the polarization of charged spin-1/2 particles moving in a uniform magnetic field changes dramatically in a relatively weak transverse axisymmetric magnetic field. The direction along which the spin projection is quantized has a fixed orientation with respect to the axes of a cylindrical coordinate system and can form a substantial angle with the direction of the uniform magnetic field. The presence of spin quantization is proved both by the fact that the commutator of the Hamiltonian operator and the projection of the polarization operator in the direction of quantization is zero and by analyzing the Bargmann-Michel-Telegdi equation for this given case. Finally, the possibilities of detecting this effect and utilizing it are discussed. Zh. éksp. Teor. Fiz. 114, 1153–1161 (October 1998)     

The motion of a classical spinning particle in a Riemann-Cartan space-time

A consistent set of equations of motion for classical charged particles with spin and magnetic dipole moment in a Riemann-Cartan space-time is generated from a constrained Lagrangian formalism. The equations avoid the spurious free helicoidal solutions and at the same time conserve the canonical condition of normalization of the 4-velocity. The 4-velocity and the mechanical moment are parallel in this theory, where the condition of orthogonality between spin and 4-velocity is treated as a nonholonomic constraint. A generalized BMT precession equation is obtained as one of the results of the formalism.     

Toward a nonlinear theory of acceleration of charged particles in a linearly polarized EH-ubitron field

The motion of charged particles in a linearly polarized EH-ubitron field with sinusoidal time dependence of the variable component of the magnetic field is investigated. It is shown that, depending on the parameters of the system and the initial conditions of entry of the particle into the EH-field region, three different types of motion are possible: ballistic motion, capture in the vicinity of one of the maxima of the magnetic field, and escape of particles from the EH-field region. An analytical expression is found for the criterion determining the type of motion of the particles, along with analytical solutions for the energy of the particles in the approximation of slow variation of the magnetic field amplitude in time. Peculiarities of the motion of the particles in EH fields with arbitrary rate of change of the magnetic field amplitude in time are investigated numerically. Zh. Tekh. Fiz. 69, 87–93 (January 1999)     

Field theory onR×S 3 topology. VI: Gravitation

We extend to curved space-time the field theory on R×S³ topology in which field equations were obtained for scalar particles, spin one-half particles, the electromagnetic field of magnetic moments, an SU₂ gauge theory, and a Schrödinger-type equation, as compared to ordinary field equations that are formulated on a Minkowskian metric. The theory obtained is an angular-momentum representation of gravitation. Gravitational field equations are presented and compared to the Einstein field equations, and the mathematical and physical similarity and differences between them are pointed out. The problem of motion is discussed, and the equations of motion of a rigid body are developed and given explicitly. One result which is worth emphazing is that while general relativity theory yields Newton's law of motion in the lowest approximation, our theory gives Euler's equations of motion for a rigid body in its lowest approximation.On leave from the Center for Theoretical Physics, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel.     

Equations of motion of a spinning relativistic particle in external fields

We consider the motion of a spinning relativistic particle in external electromagnetic and gravitational fields to first order in the external field but to arbitrary order in the spin. The influence of the spin on the particle trajectory is properly accounted for by describing the spin noncovariantly. Specific calculations are performed through second order in the spin. A simple derivation is presented for the gravitational spin-orbit and spin-spin interactions of a relativistic particle. We discuss the gravimagnetic moment (GM), a particular spin effect in general relativity. We show that for a Kerr black hole the gravimagnetic ratio, i.e., the coefficient of the GM, equals unity (just as the gyromagnetic ratio equals 2 for a charged Kerr hole). The equations of motion obtained for a spinning relativistic particle in an external gravitational field differ substantially from the Papapetrou equations. Zh. éksp. Teor. Fiz. 113, 1537–1557 (May 1998)     

EXACT SOLUTION OF THE PAULI EQUATION IN THE FIELD OF A 'T HOOFT-POLYAKOV MONOPOLE

In this paper, the motion for the spin one half particles with arbitrary isospin in the field of a't Hooft-Polyakov magnetic monopole (in the Prasad-Sommerfield limit) is studied by the method of the moving frame. An exact solution of the Pauli equation for the total angular momentum J=0 and isospin I=1/2 is presented. The question of Proton decay catalysis is briefly discussed.     

Transit of beams of charged particles through a non-adiabatic magnetic field

The possibility of obtaining beams of particles with high transverse energies in a strong magnetic field is discussed. The motion of particles in a weakly non-adiabatic field is described by a linear non-homogeneous equation. The non-adiabaticity of motion is caused, in the first approximation, by the curvature of the magnetic lines of force. The conditions for a small spread of magnetic moments of the beam particles are established by solving the equation of motion. The transverse energy of particles and its spread can be varied by varying the shape of the magnetic field and the initial radial velocities of the particles. As a result of the conditions for a small spread of magnetic moments, a beam traversing a steep magnetic field gains a smaller magnetic moment than a beam passing through a field with a lesser slope.The author is indebted to Dr M. Seidl, DrSc, for valuable discussions on the subject, and to Dr M. Ondráek, CSc for help in the computer 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.     

Brownian dynamics simulations with spin Brownian motion on the negative magneto-rheological effect of a rod-like hematite particle suspension

We have investigated the behaviour of a suspension of magnetic rod-like hematite particles in a simple shear flow with the addition of an applied magnetic field. A significant feature of the present hematite particle suspension is the fact that the magnetic moment of the hematite particle lies normal to the particle-axis direction. From simulations, we have attempted to clarify the dependence of the negative magneto-rheological effect on the particle aggregation and orientational distribution of particles. The present Brownian dynamics method has a significant advantage in that it takes into account the spin rotational Brownian motion about the particle axis in addition to the ordinary translational and rotational Brownian motion. The net viscosity is decomposed into three components and discussed at a deeper level and in detail: these three viscosity components arise from (1) the torque due to the magnetic particle–field interaction, (2) the torque and (3) the force due to the interaction between particles. It is found that a slight change in the orientational distribution has a significant influence on the negative magneto-rheological effect. In a relatively dense suspension, the viscosity components arising from an applied magnetic field and the interaction between particles come to change rapidly for a certain strength of the magnetic particle–particle interaction, which is due to the onset of the formation of raft-like clusters.     

Generation of electromagnetic radiation in the motion of vortices in magnetically coupled superconducting films

We examine theoretically the generation of electromagnetic radiation in the relative motion of vortex lattices in magnetically coupled films in the dc transformer geometry. We establish the conditions under which the force of mutual pinning of the vortex lattices varies according to a harmonic law as a function of the relative displacement of the vortices in the films within a given range of magnetic field inductions. In this case the equation describing the viscous flow of vortex lattices in magnetically coupled films is the same as the equation of the resistively shunted Josephson junction model. We show that magnetically coupled superconductors exhibit the properties of a Josephson element without any restrictions on the geometrical size of such a system imposed by the coherence length ξ. The frequency f of the electromagnetic radiation generated by the relative motion of vortex lattices in magnetically coupled superconductors depends on the spatial period of the vortex lattices and the velocity of relative vortex motion, which means that the frequency of the radiation can be tuned by applying a magnetic field or a current. Zh. éksp. Teor. Fiz. 113, 1319–1338 (April 1998)     

Die Rotation des Elektronenspins beim ebenen Tunnelprozeß mit überlagertem homogenem Magnetfeld

Measurements of the spin polarization of field emitted electrons from various ferromagnetic (Gd, Ni, Fe) and nonferromagnetic metals (W) show a steady increase of the angle? _s between momentum and electron spin with increasing external magnetic field (spin rotation). This effect is refered to the coupling between the magnetic moment of the electron and the strong electric field in the potential barrier at the emitter surface during the tunneling process. A formal application of the equation of spin motion derived by Bargmann, Michel and Telegdi for an electron moving in homogeneous electromagnetic fields delivers a quantitative agreement with the experimental results.     

Passage of relativistic magnetic dipole moments through magnetic fields

We have solved the Dirac equation with an anomalous moment Pauli-coupling exactly for a constant magnetic field and derived the general relativistic formulas for phase changes due to translational motion and spin rotations. We also give transmission and reflection coefficients, spin rotation for tunnelling and barrier penetration. For ultrarelativistic particles the spin rotation angle on the path of lengthL is equal to (2μB L/ħc)[1 +m ² c ⁴/(E²-μ ² B ²)].

     

Current-induced domain wall motion with adiabatic and nonadiabatic spin torques in magnetic nanowires

We investigate current-driven domain wall (DW) propagation in magnetic nanowires in the framework of the modified Landau-Lifshitz-Gilbert equation with both adiabatic and nonadiabatic spin torque (AST and NAST) terms. By employing a simple analytical model, we can demonstrate the essential physics that any small current density can drive the DW motion along a uniaxial anisotropy nanowire even in absence of NAST, while a critical current density threshold is required due to intrinsic anisotropy pinning in a biaxial nanowire without NAST. The DW motion along the uniaxial wire corresponds to the asymptotical DW oscillation solution under high field/current in the biaxial wire case. The current-driven DW velocity weakly depends on the NAST parameter β in a uniaxial wire and it is similar to the β = α case (α: damping) in the biaxial wire. Apart from that, we discuss the rigid DW motion from both the energy and angular momentum viewpoints and point out some physical relations in between. We also propose an experimental scheme to measure the spin current polarization by combining both field- and current-driven DW motion in a usual flat (biaxial) nanowire.