Role of nonlinear coupling and density fluctuations in magnetic-fluctuation-induced particle transport

Three-wave nonlinear coupling among spatial Fourier modes of density and magnetic fluctuations is directly measured in a magnetically confined toroidal plasma. Density fluctuations are observed to gain (lose) energy from (to) either equilibrium or fluctuating fields depending on the mode number. Experiments indicate that nonlinear interactions alter the phase relation between density and magnetic fluctuations, leading to strong particle transport.     

Lorentz Invariance and Brownian Motion of Test Particles with Constant Classical Velocity in Electromagnetic Vacuum

We show that the velocity and position dispersions of a test particle with a nonzero constant classical velocity undergoing Brownian motion caused by electromagnetic vacuum fluctuations in a space with plane boundaries can be obgained from those of the static case by Lorentz transformation. We explicitly derive the Lorentz transformations relating the dispersions of the two cases and then apply them to the case of the Brownian motion of a test particle with a constant classical velocity parallel to the boundary between two conducting planes. Our results show that the influence of a nonzero initial velocity is negligible for nonrelativistic test particles.     

Bremsstrahlung of a neutral fermi particle in the field of a plane electromagnetic wave

The bremsstrahlung is considered from a neutral Fermi particle with anomalous magnetic and electric moments in the field of a screened Coulomb center and in the presence of a plane electromagnetic wave. The effect of the wave polarization on the scattering cross section and the behavior of the particle spin during the scattering process are considered. Cross sections are given for scattering of a particle at a Coulomb center in the presence of constant, crossed electric and magnetic fields which are equal in magnitude and also for a free particle. It is shown that the effect of the anomalous electric moment is often decisive.     

Brownian motion with active fluctuations

We study the effect of different types of fluctuation on the motion of self-propelled particles in two spatial dimensions. We distinguish between passive and active fluctuations. Passive fluctuations (e.g., thermal fluctuations) are independent of the orientation of the particle. In contrast, active ones point parallel or perpendicular to the time dependent orientation of the particle. We derive analytical expressions for the speed and velocity probability density for a generic model of active Brownian particles, which yields an increased probability of low speeds in the presence of active fluctuations in comparison to the case of purely passive fluctuations. As a consequence, we predict sharply peaked Cartesian velocity probability densities at the origin. Finally, we show that such a behavior may also occur in non-Gaussian active fluctuations and discuss briefly correlations of the fluctuating stochastic forces.     

Hydrodynamic Fluctuations in Laminar Fluid Flow. I. Fluctuating Orr-Sommerfeld Equation

In recent years it has become evident that fluctuating hydrodynamics predicts that fluctuations in nonequilibrium states are always spatially long ranged. In this paper we consider the application of fluctuating hydrodynamics to laminar fluid flow, using plane Couette flow as a representative example. Specifically, fluctuating hydrodynamics yields a stochastic Orr-Sommerfeld equation for the wall-normal velocity fluctuations, where spontaneous thermal noise acts as a random source.This stochastic equation needs to be solved subject to appropriate boundary conditions. We show how an exact solution can be obtained from an expansion in terms of the eigenfunctions of the Orr-Sommerfeld hydrodynamic operator. We demonstrate the presence of a flow-induced enhancement of the wall-normal velocity fluctuations and a resulting flow-induced energy amplification and provide a quantitative analysis how these quantities depend on wave number and Reynolds number.     

Theorie der Bewegung geladener Teilchen in richtungskonstanten zeitabhängigen Magnetfeldern und elektrischen Zusatzfeldern

The motion of a charged particle in spatially homogeneous electric and magnetic fields is calculated for the case of the magnetic field to have a constant direction and its intensity to vary with an arbitrary power of time. The special case of a linearly increasing magnetic field is treated in detail taking into account a friction force proportional to the particle velocity. Generally, the equations of motion are reduced to a single differential equation of second order which is integrated exactly. The higher transcendental functions appearing in the solution are then approximated by elementary functions. Thus asymptotic approximative equations of a very simple form are obtained for position, velocity, kinetic energy and magnetic moment of the particle. The dependence of the particle orbit on the initial values of position and velocity and on the properties of the magnetic field is studied, and it is shown, how the particle motion is a helical motion superposed by a drift. The influence of the electric field induced by the time dependent magnetic field on the particle motion is considered in detail. For an additional electric field being present a drift formula is derived which is a generalization of the well-known ?? × ?? 93 drift for constant fields.     

Diffraction of electromagnetic plane wave by a slit in a homogeneous bi-isotropic medium

We investigated the diffraction of an electromagnetic plane wave by an infinite slit embedded in a homogeneous bi-isotropic medium. With the aim of deriving explicit expressions for the left- and right-handed Beltrami fields, we used the Fourier integral transform, the Wiener–Hopf technique and the steepest descent asymptotic method. The electric and magnetic fields, E and H, were determined from the Beltrami fields. Our graphical results indicate that the strength of both electric and magnetic fields reduces with the dissipation of bi-isotropic medium. While matching the diffraction pattern with the existing plane wave solution, the objective was, and is, to see how well spherical wave solution performs when it is developed for plane wave solution.     

Random Motion of a Charged Test Particle with a Classical Constant Velocity in Vacuum in a Cylindrical Spacetime

We examine the random motion of a charged test particle with a nonzero classical velocity driven by quantum electromagnetic vacuum fluctuations in a cylindrical spacetime and calculate both the velocity and position dispersions of the test particle. It is found that the dispersions display different behaviour in different directions. These differences can be understood as a result of the topology of the configuration and initial physical conditions.     

Motion of a classical charged particle with spin in the external field of a plane electromagnetic wave

We obtain the solution to the equations of motion for a classical particle with spin, electric and magnetic charges, and electric and magnetic normal and anomalous moments, in the field of a plane electromagnetic wave. An explicit form of the solution is given for linearly polarized waves and monochromatic circularly polarized waves. The possibility is noted that due to the presence of the moments, the particle can be accelerated to speeds arbitrarily close to the speed of light.Translated from Izvestiya Vysshykh Uchebnykh Zavedenii, Fizika, No. 11, pp. 71–74, November, 1981.     

A high-sensitivity laser-pumped Mx magnetometer

We discuss the design and performance of a laser-pumped cesium vapor magnetometer in the M_x configuration. The device will be employed in the control and stabilization of fluctuating magnetic fields and gradients in a new experiment searching for a permanent electric dipole moment of the neutron. We have determined the intrinsic sensitivity of the device to be 15 fT in a 1 Hz bandwidth, limited by technical laser noise. In the shot noise limit the magnetometer can reach a sensitivity of 10 fT in a 1 Hz bandwidth. We have used the device to study the fluctuations of a stable magnetic field in a multi-layer magnetic shield for integration times in the range of 2–100 seconds. The residual fluctuations for times up to a few minutes are traced back to the instability of the power supply used to generate the field.     

Near-surface Brownian motor with synchronously fluctuating symmetric potential and applied force

A model is suggested which accounts for the unidirectional surface-parallel motion of a Brownian particle under the action of fluctuating surface-inclined unbiased external force. The surface-normal force component induces amplitude fluctuations of the symmetric periodic near-surface potential, whereas the surface-parallel component makes the particle move along the surface. The combined effect of synchronous fluctuations of the symmetric potential and the applied force leads to the longitudinal drift of the particle. It is shown that the temperature dependence of the motor velocity is nonmonotonic, with the maximum governed by the range of the near-surface potential.     

Electro-and magnetostatic fields in media with a nonuniform velocity

A motion-induced magnetic or electric field is calculated by the integral method in the first order of smallness in the ratio of the motion velocity to the speed of light for homogenous media with an arbitrary stationary velocity distribution that are placed in static electric or magnetic fields. For the case of rotation of a sphere, the validity of the results is corroborated by comparing with a solution obtained by joining the fields in the moving and quiescent parts of the medium. Estimates suggest the feasibility of experimentally observing this effect of continuum electrodynamics.     

Electric Chern–Simons term, enlarged exotic Galilei symmetry and noncommutative plane

The extended exotic planar model for a charged particle is constructed. It includes a Chern–Simons-like term for a dynamical electric field, but produces usual equations of motion for the particle in background constant uniform electric and magnetic fields. The electric Chern–Simons term is responsible for the noncommutativity of the boost generators in the 10-dimensional enlarged exotic Galilei symmetry algebra of the extended system. The model admits two reduction schemes by the integrals of motion, one of which reproduces the usual formulation for the charged particle in external constant electric and magnetic fields with associated field-deformed Galilei symmetry, whose commuting boost generators are identified with the nonlocal in time Noether charges reduced on-shell. Another reduction scheme, in which electric field transmutes into the commuting space translation generators, extracts from the model a free particle on the noncommutative plane described by the twofold centrally extended Galilei group of the nonrelativistic anyons.     

Positive-, negative-, and orthogonal-phase-velocity propagation of electromagnetic plane waves in a simply moving medium: Reformulation and reappraisal

Reformulating the issue of planewave propagation in a simply moving, dielectric-magnetic medium that is isotropic in the co-moving reference frame, using the Lorentz transformations of electric and magnetic fields and not the Minkowski constitutive relations-we reaffirm that plane waves which have positive phase velocity in the co-moving frame of reference can have negative phase velocity in certain non-co-moving frames of reference. Furthermore, this phenomenon occurs whether the medium is dissipative or not. For a fixed propagation direction, orthogonal phase velocity arises only at a unique velocity of the non-co-moving frame.     

Effect of Ergodic and Non-Ergodic Fluctuations on a Charge Diffusing in a Stochastic Magnetic Field

In this paper, we study the basic problem of a charged particle in a stochastic magnetic field. We consider dichotomous fluctuations of the magnetic field where the sojourn time in one of the two states are distributed according to a given waiting-time distribution either with Poisson or non-Poisson statistics, including as well the case of distributions with diverging mean time between changes of the field, corresponding to an ergodicity breaking condition. We provide analytical and numerical results for all cases evaluating the average and the second moment of the position and velocity of the particle. We show that the field fluctuations induce diffusion of the charge with either normal or anomalous properties, depending on the statistics of the fluctuations, with distinct regimes from those observed, e.g., in standard Continuous-Time Random Walk models.     

Transient radiation in an anisotropic magnetodielectric plate in a waveguide

We have considered transient radiation of a charged particle in an anisotropic magnetodielectric plate placed into a regular waveguide. It is assumed that the charged particle passes through the plate moving at a constant velocity perpendicularly to the waveguide axis. Wave equations and analytical expressions for transverse electric (TE) and transverse magnetic (TM) fields in different regions of the waveguide have been obtained. Energies of transient radiation of the moving particle have been calculated. The properties of transient radiation and Vavilov–Cherenkov radiation have been analyzed for the case of a rectangular waveguide. Energies of transient radiation have been calculated for the case of a “thin” plate in the waveguide, when the wavelength in the plate is much greater than the length of the plate.     

Independent particle Schrödinger fluid: Moments of inertia

The philosophy of the single particle Schrödinger fluid, especially as regards the velocity fields which find such a natural role therein, is applied to the study of the moments of inertia of independent fermion system. It is shown that three simplified systems exhibit the rigid-body rotational velocity field in the limit of large A, and that the leading deviations, both on the average and fluctuating, from this large-A limit can be described analytically, and verified numerically. For a single particle in a Hill-Wheeler box the moments are studied numerically, and their large fluctuations identified with the specific energy level degeneracies of its parallelepiped shape. The full assemblage of these new and old results is addressed to the question of the necessary and sufficient condition that the moment has the rigid value. Counter examples are utilized to reject some conditions, and the conjecture is argued that unconstrained shape equilibrium might be the necessary and sufficient condition. The spheroidal square-well problem is identified as a promising test case.     

Small-angle approximation for an ion beam in an external electromagnetic field

A small-angle approximation method is formulated for a curvilinear ion beam propagating in an electromagnetic field. The effects of particle velocity scatter and multiple elastic scattering on the beam path in a magnetic field, the electric field of a cylindrical capacitor, and mutually orthogonal electric and magnetic fields are considered. An analytical model for beam power compression is developed.     

Hall effect for neutral atoms

It is shown that polarizable neutral systems can drift in crossed magnetic and electric fields. The drift velocity is perpendicular to both fields, but, contrary to the drift velocity of a charged particle, it exists only if the fields vary in space or time. We develop an adiabatic theory of this phenomenon and analyze conditions for its experimental observation. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 8, 652–657 (25 April 1996) Deceased. Published in English in the original Russian journal. Edited by Steve Torstveit.     

Zur Theorie der Teilchenbewegung in zeitabhängigen elektromagnetischen Feldern

The Langevin equation – i.e. the equation of motion for a charged particle including a collision term proportional to the particle velocity – is solved for arbitrary time-dependent electric and magnetic fields by a new general method. Instead of the usual ansatz: particle velocity = cyclotron velocity + drift velocity the method given makes the ansatz: particle velocity = tensor = cyclotron velocity. The unknown tensor obeys a simple differential equation of the first order which can be generally solved at once. This method is a modification of the variation of constants method for inhomogeneous differential equations. The electromagnetic fields considered must be spatially homogeneous; for (weakly) inhomogeneous fields an iteration procedure of Pytte (1962) may be applied. Some examples are discussed shortly. The Langevin equation treated is completely equivalent to the equation of motion in a magnetohydrodynamic one-fluid theory.