Generation of a longitudinal current by a transverse electromagnetic field in collisional degenerate plasma

From the Vlasov–Boltzmann kinetic equation for a collisional degenerate plasma, the electron distribution function is constructed in the quadratic approximation in the electric field strength. A formula for calculating the electric current is derived. It is shown that nonlinearity leads to the rise of a longitudinal electric current directed along the wave vector. The longitudinal current is orthogonal to the known transverse classical current obtained in the linear analysis. When the collision frequency tends to zero, all results obtained for a collisional plasma pass into the corresponding results for a collisionless plasma. The case of small wavenumbers is considered. It is shown that, when the collision frequency tends to zero, the expression for the current passes into the corresponding expression for the current in a collisionless plasma. Graphic analysis of the real and imaginary parts of the current density is performed. The dependence of the electromagnetic field oscillation frequency and electron–plasma-particle collision frequency on the wavenumber is studied.     

Transverse electrical conductivity of a quantum collisional plasma in the Mermin approach

We derive formulas for the transverse electrical conductivity and the permittivity in a quantum collisional plasma using the kinetic equation for the density matrix in the relaxation approximation in the momentum space. We show that the derived formula becomes the classical formula when the Planck constant tends to zero and that when the electron collision rate tends to zero (i.e., the plasma becomes collisionless), the derived formulas become the previously obtained Lindhard formulas. We also show that when the wave number tends to zero, the quantum conductivity becomes classical. We compare the obtained conductivity with the conductivity obtained by Lindhard and with the classical conductivity     

Wave function and the probability current distribution for a bound electron moving in a uniform magnetic field

We study the effects of electromagnetic fields on nonrelativistic charged spinning particles bound by a short-range potential. We analyze the exact solution of the Pauli equation for an electron moving in the potential field determined by the three-dimensional δ-well in the presence of a strong magnetic field. We obtain asymptotic expressions for this solution for different values of the problem parameters. In addition, we consider electron probability currents and their dependence on the magnetic field. We show that including the spin in the framework of the nonrelativistic approach allows correctly taking the effect of the magnetic field on the electric current into account. The obtained dependences of the current distribution, which is an experimentally observable quantity, can be manifested directly in scattering processes, for example.     

Electromagnetic force on the wall of cylindrical waveguide

When transverse electric (TE) wave or transverse magnetic (TM) wave propagates inside a cylindrical waveguide, the electromagnetic force on the wall is investigated. The characteristics of surface charge, current, electric force, magnetic force and electromagnetic force are studied. The results show that the electric force is tension and magnetic force is press. The surface density of electromagnetic force on the wall can be calculated by the difference between magnetic and electric energy density there. For TE wave, the electromagnetic force distribution on the walls may be either tension or pressure in general. However, the electromagnetic force is always pressure for TM wave.     

A complementary theory of light scattering by homogeneous spheres

A theory of the scattering of electromagnetic waves by homogeneous spheres, the so-called Mie theory, is presented in a unique and coherent manner in this paper. We begin with Maxwell's equations, from which the vector wave equations are derived and solved by means of the two orthogonal solutions to the scalar wave equation. The transverse incident electric field is mapped in spherical coordinates and expanded in known mathematical functions satisfying the scalar wave equation. Determination of the unknown coefficients in the scattered and internal fields is achieved by matching the electromagnetic boundary conditions on the surface of a sphere. Far-field solutions for the electric field are then given in terms of the scattering functions. Transformation of the electric field to the reference plane containing incident and scattered waves is carried out. Extinction parameters and the phase matrix are derived from the electric field perpendicular and parallel to the reference plane. On the basis of the independent-scattering assumption, the theory is extended to cases involving a sample of homogeneous spheres.     

Sopra un problema di interazione di onde elettromagnetiche in un plasma non lineare a geometria sferica

We consider the problem of the approximate determination of the electromagnetic field generated by two oscillating electric dipoles in the center of a spherical cavity imbedded in a nonlinear plasma. The influence of the nonlinearities of the plasma upon the field are investigated by means of a perturbative solution of the relevant equations, deduced from the ‘quasi-hydrodynamic’ approach. Analytical and numerical results, which illustrate several nonlinear effects, as well as the influence of the rarefaction and ionization of the gas, are included. The main result of the paper is the prediction of an observable second harmonic field.     

Sur un problème inverse pour les équations de Maxwell dans un réseau doublement périodique

Consider an electromagnetic plane wave incident on a doubly periodic structure in ø³. We prove that the knowledge of the tangential component of the electric field on an elementary section determines the electric permittivity of the grating.     

Low Frequency Electromagnetic Radiation

The field scattered by a dielectric body irradiated by a lowfrequency electromagnetic wave can be expressed, to a firstapproximation, in terms of a scattering tensor. Variationalprinciples are obtained for the elements of this tensor. Boundsbased on these principles permit estimates of the rate of changeof the tensor with dielectric constant and shape. In particular,it is shown that the trace of the tensor is stationary for thesphere among shapes of equal volume. For scatterers possessingrotational symmetry the longitudinal component can be relatedto the transverse component of the adjugate problem.     

Transversal line defects induced by an electric field in a period-2 oscillatory medium

The dynamical behavior of spiral waves in a period-2 oscillatory medium is investigated under the influence of an external applied alternating current field. Open and closed transversal line defects which wiggle along the direction parallel to the wave fronts, are generated in the spiral-wave patterns when the stimulus frequency of the electric field is equal to one, three or five times of the local oscillatory frequency in the period-2 state. Their generations are directly related with the change in the spatial wavelength induced by the electric field. These wigglings proliferate along the transverse direction parallel to the wave fronts as the stimulus strength increases, and become denser when the stimulus frequency increases by multiples of the period-2 oscillatory frequency.     

The scattering of electromagnetic wave at oblique incidence in a homogeneous chiral medium

We consider the scattering of a time-harmonic electromagnetic wave by a perfectly and imperfectly conducting infinite cylinder at oblique incidence respectively. We assume that the cylinder is embedded in a homogeneous chiral medium and the cylinder is parallel to the z axis. Since the x components and y components of electric field and magnetic field can be expressed in terms of their z components, we can derive from Maxwell's equations and corresponding boundary conditions that the scattering problem is modeled as a boundary value problem for the z components of electric field and magnetic field. By using Rellich's lemma and variational approach, the uniqueness and the existence of solutions are justified.     

Nonlinear electrodynamic lensing of electromagnetic waves in a magnetic dipole field

We consider propagation of electromagnetic waves in magnetic dipole and gravitational fields proceeding in accordance with the nonlinear vacuum electrodynamics laws. We derive formulas describing the effect of nonlinear electrodynamic lensing of electromagnetic waves in the magnetic dipole field. We show that rotation of the magnetic dipole moment about an axis noncoincident with this moment leads to a nonlinear electrodynamic modulation of the electromagnetic radiation intensity by frequencies that are multiples of the dipole rotation frequency. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 150, No. 1, pp. 85–94, January, 2007.     

Quantum theoretic explanation of the Schwarz-Hora effect

Following the path-integral approach we show that the Schwarz-Hora effect is a one-electron quantum-mechanical phenomenon in that the de Broglie wave associated with a single electron is modulated by the oscillating electric field. The treatment brings out the crucial role played by the crystal in providing a discontinuity in the longitudinal component of the electric field. The expression derived for the resulting current density shows the appropriate oscillatory behaviour in time and distance. The possibility of there being a temporal counterpart of Aharonov-Bohm effect is briefly discussed in this context.

     

Mathematical modeling of the vertical magnetic dipole field in a two-dimensional nonhomogeneous medium

We consider a quasi-three-dimensional problem of remote marine sounding by a high-power stationary source located on land. A transition from the three-dimensional problem to a family of parametric two-dimensional problems is performed. The solution of the remote marine sounding problem is obtained with high accuracy after solving about 20 two-dimensional problems. The integral equations are solved by the modified integral current method, which has proved highly efficient for field computations inside a strongly conducting anomaly. The electric field amplitude is observed to increase with depth. The width of the coastal current channel is estimated by analyzing the vertical magnetic field component.     

Plasma waves reflection from a boundary with specular accommodative boundary conditions

In the present work the linearized problem of plasma wave reflection from a boundary of a half-space is solved analytically. Specular accommodative conditions of plasma wave reflection from plasma boundary are taken into consideration. Wave reflectance is found as function of the given parameters of the problem, and its dependence on the normal electron momentum accommodation coefficient is shown by the authors. The case of resonance when the frequency of self-consistent electric field oscillations is close to the electron (Langmuir) plasma oscillations frequency, namely, the case of long-wave limit is analyzed in the present paper.     

The linear sampling method for the inverse electromagnetic scattering problem for screens

We consider the inverse electromagnetic scattering problem of determining the shape of a screen from a knowledge of the electric far field pattern of the scattered wave at fixed frequency. We adapt the linear sampling method invented by Colton and Kirsch (Inverse Problems 12 (1996) 383-393) for the case of obstacles with nonempty interior. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Behavior of a plasma with the collision rate proportional to the electron velocity in an external electric field

We solve the problem of the behavior of a gas plasma in a half-space analytically using the kinetic equation with the collision rate proportional to the modulus of the electron velocity. The plasma is in a variable external electric field. The specular reflection of electrons from the plasma boundary is used as a boundary condition. We use the solution to find the screened electric field. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 153, No. 3, pp. 409–421, December, 2007.     

Regular and chaotic charged particle dynamics in low frequency waves and role of separatrix crossings

We consider interaction of charged particles with an electromagnetic (electrostatic) low frequency wave propagating perpendicular to a uniform background magnetic field. The effects of particle trapping by the wave and further acceleration of a surfatron type are discussed in details. Method for this analysis based on the adiabatic theory of separatrix crossing is used. It is shown that particle can unlimitedly accelerate in the trapping in electromagnetic waves and energy of particle does not increase for the system with electrostatic wave.     

Effect of cold plasma permittivity on the radiation of the dominant TEM‐wave by an impedance loaded parallel‐plate waveguide radiator

The effects of wall impedances on the radiation of the dominant transverse electromagnetic wave by an impedance loaded parallel‐plate waveguide radiator immersed in a cold plasma have been analyzed. The solution to the governing mathematical model in cold plasma is determined while using the Wiener–Hopf technique. It is observed that the amplitude of the radiated field increases with increasing permittivity of the plasma. The work presented may be of great interest to quantify the effects of ionosphere plasma on the communicating signals between Earth station and an artificial satellite in the Earth's atmosphere. Copyright © 2015 John Wiley & Sons, Ltd.     

Inverse diffraction by a doubly periodic structure

Let us consider the scattering of electromagnetic waves by a doubly periodic structure. Above the structure, the medium is assumed to be homogeneous with a fixed real dielectric coefficient. The medium is a perfect conductor below the structure. For a given incident plane wave, the tangential electric field is measured away from the structure. An inverse problem arises: To what extent can one determine the location of the periodic structure that separates the dielectric medium from the conductor? In this paper, results on uniqueness and stability are established for the inverse problem. A crucial step in our proof is to obtain a lower bound for the first eigenvalue of an eigenvalue problem.     

Global existence and asymptotic behavior of solutions to the nonisentropic bipolar hydrodynamic models

In this paper, we consider a one-dimensional bipolar nonisentropic hydrodynamical model from semiconductor devices. This system takes the nonisentropic Euler-Poisson form with electric field and frictional damping added to the momentum equations. First, we prove global existence of smooth solutions to the Cauchy problem. Next, we also discuss the asymptotic behavior of the smooth solutions. We find that in large time, the densities of electron and hole tend to the same nonlinear diffusive wave, the momentums tend to the Darcy's law, and the temperatures tend to the ambient device temperature. Finally, we can obtain the algebraic decay rate of the densities to the same nonlinear diffusive wave, the momentums to the Darcy's law and the temperatures to the ambient device temperature, and the exponential decay of their difference and the electric field to zero. We can show our results by precise energy methods.