Debye Potentials Research Articles

Positronium formation in positron-helium collisions in Debye plasma

SynopsisPositronium formation processes in positron-helium collisions with Debye potentials are studied using the screening approximation model in incident energy range from the threshold to 100 eV for screening parameters μ=0.00-0.25.

Positronium formation in collisions between positrons and Rb, Cs atoms with screened Coulomb interaction

SynopsisPositronium formation processes in collisions between positrons and Rb, Cs atoms with Debye potentials are studied using the screening approximation model for screening parameters μ=0.00-0.25 at incident energy range 2-60 eV.

Investigation of Dusty Plasma Based on the Ornstein—Zernike Integral Equation for a Multicomponent Fluid

The electrostatic interaction between charged particles in a dusty plasma has been studied using the Ornstein—Zernike integral equation for a multicomponent plasma. The transition to the one-component approximation has been performed for the nonideal plasma subsystem. It has been shown that the interaction between charged plasma particles at the coupling parameter Γ of the dust subsystem less than unity is well described by the Debye potential with the complete screening constant. The static dielectric function in the region of low wavenumbers becomes negative at Γ > 1 and this region expands with increasing Γ. As a result, attraction between likely charged particles and repulsion between oppositely charged ones occur in a certain distance range. In this case, the total pressure, specific heat at constant volume, and isothermal compressibility of the dusty plasma remain positive in the entire studied range of the nonideality parameter Γ < 250, but the isothermal compressibility of only the dust nonideal subsystem becomes negative at Γ ≈ 2.

Probing a chiral drug using long period fiber gratings.

The electromagnetic field theory for a step-index fiber geometry is developed to sense a surrounding chiral drug via long-period fiber gratings (LPFGs). This theory employs Debye potentials and electromagnetic fields for cladding modes in the LPFGs by introducing constitutive relations for a chiral drug. The fields in the chiral drug are transformed and decomposed into right- and left-hand circularly polarized components to account for the magnetoelectric coupling due to the chirality. The solving process for complex propagation constants is given. Numerical results show that responses of the LPFGs to refractive index and chirality changes are different. The two minimum transmissions of a coated LPFG are very sensitive to the variation of the complex chirality. On the other hand, the two resonance wavelengths keep invariant as real and imaginary parts of the comparatively small chirality change. This work enriches the electromagnetic field theory for better design of LPFGs against the highly sensitive chirality detection.

Perturbation theory of optical resonances of deformed dielectric spheres

We analyze the optical resonances of a dielectric sphere whose surface has been slightly deformed in an arbitrary way. Setting up a perturbation series up to second order, we derive both the frequency shifts and modified linewidths. Our theory is applicable, for example, to freely levitated liquid drops or solid spheres, which are deformed by thermal surface vibrations, centrifugal forces or arbitrary surface waves. A dielectric sphere is effectively an open system whose description requires the introduction of non-Hermitian operators characterized by complex eigenvalues and not normalizable eigenfunctions. We avoid these difficulties using the Kapur-Peierls formalism which enables us to extend the popular Rayleigh-Schr\"{o}dinger perturbation theory to the case of electromagnetic Debye's potentials describing the light fields inside and outside the near-spherical dielectric object. We find analytical formulas, valid within certain limits, for the deformation-induced first- and second-order corrections to the central frequency and bandwidth of a resonance. As an application of our method, we compare our results with preexisting ones finding full agreement.

Influence of plasma screening on the energies and transition properties of the Al9+ ion using Debye and ion-sphere models

Investigations on the energies and radiative properties of a highly charged ion embedded in plasma in the weak- and strong-coupling regimes are made, taking the Al9+ ion as an example. The Debye and ion-sphere (IS) potentials are adopted to describe the plasma screening effects, respectively. The multiconfiguration Dirac-Fock (MCDF) method is employed to describe the relativistic and electronic correlation effects in the above atomic system. The screening effects on the ionization potential (IP), transition energies, and radiative rates are estimated. Results obtained are compared with the available results in the literature. Comparisons between the Debye and IS models results are also carried out considering similar plasma conditions. The present data are useful for diagnostics of astrophysical and laboratory plasmas.

Symmetries of linearized gravity from adjoint operators

Based on operator identities and their formal adjoints, we derive two symmetry operators for the linearized Einstein operator on vacuum backgrounds of Petrov type D and, in particular, the Kerr spacetime. One of them is of differential order four and coincides with a result of Cohen and Kegeles. The other one is a new operator of differential order six. The corresponding operator identities are based on the Teukolsky equation and the Teukolsky-Starobinsky identities, respectively. The method applies to other field equations as well, which is illustrated with the Maxwell equation. The resulting symmetry operators are connected to Hertz and Debye potentials as well as to the separability of the Teukolsky equation for both Maxwell and linearized gravity.

Energy spectra of three‐dimensional harmonium under Debye potential obtained using the shifted 1/N expansion approach

In this work, the problem of harmonium was investigated using the method of the shifted 1/N expansion. The energy eigenvalues and the classical equilibrium interelectron distance were calculated for ground and few first excited states under Debye potential as a function of both the Debye screening length and the harmonic confinement strength. It was found that harmonium becomes a Wigner molecule at the strong‐correlation limit in which the two electrons oscillate about the classical equilibrium interelectron distance r0. The results show reasonable agreement with the previous results both quantitatively and qualitatively.

Potentials of a moving test charge during the solar wind interaction with dusty magnetosphere of Jupiter

The electrostatic Debye screening and wakefield potentials caused by a test charge are investigated in a positively charged dusty plasma. A modified dielectric constant of the dust-acoustic waves to account for the beam electrons and protons from solar wind is employed and analyzed the electrostatic potentials both analytically and numerically. This model is essentially applied to Jupiter’s magnetosphere that contains positively charged dust grains, Maxwellian electrons and ions, as well as solar wind streaming electrons and protons. The normalized Debye potential decreases exponentially by variation of axial distance while the normalized wakefield potential is strongly influenced by the plasma temperatures and streaming speeds of solar wind electrons and protons.

Diffraction of light by plasma in the solar system

We study the propagation of electromagnetic (EM) waves in the solar system and develop a Mie theory that accounts for the refractive properties of the free electron plasma in the extended solar corona. We use a generic model for the electron number density distribution and apply the eikonal approximation to find a solution in terms of Debye potentials, which is then used to determine the EM field both within the inner solar system and at large heliocentric distances. As expected, the solution for the EM wave propagating through the solar system is characterized by a plasma-induced phase shift and related change in the light ray’s direction of propagation. Our approach quantitatively accounts for these effects, providing a wave-optical treatment for diffraction in the solar plasma. As such, it may be used in practical applications involving big apertures, large interferometric baselines or otherwise widely distributed high-precision astronomical instruments.

Electron transport in nonideal and degenerate plasmas

In this article, various methods of calculation for the Coulomb logarithm in the kinetic theory of electron transfer are considered. It is assumed that the interaction of electrons with ions is described by the Debye potential with a screening constant, which is determined either with or without the contribution of the ionic component. In order to take into account ion–ion correlations, the Ornstein–Zernike integral equation in the hypernetted chain approximation is solved numerically. The behavior of the collision cross section of electrons with ions has been studied in detail on the basis of the phase shift method.

Influence of ion shadowing effect on average inter-particle distance in dusty plasma crystals

Average distance between particles of dust in dusty plasma crystals is sensitive to the temperature of neutral atoms in a glow discharge plasma. In some experiments a significant decrease of average inter-particle distance after cooling to low temperatures is observed: the distance at 100 K is up to 4 times less than at 300 K. In this work dusty plasma system is studied by the method of numerical solving of Newton equations which is similar to the method of molecular dynamics. It is shown that the model of dusty plasma interaction including only the Debye potential and electrostatic parabolic trap may be not enough to explain this effect. Adding ion shadowing potential to this model increases the difference between the values of inter-particle distance at 100 and 300 K by 2–3 times. Comparison of theoretical results with experiments of other groups shows that some of the experimental points may be well approximated by this model.

Wave-optical treatment of the shadow cast by a large sphere

We study the electromagnetic (EM) field in the shadow cast by a large opaque sphere. For this, we consider the scattering of a high frequency monochromatic EM wave by the large sphere and develop a Mie theory that accounts for the presence of this obscuration. Applying fully absorbing boundary conditions, we find a solution for the Debye potentials, which we use to determine the EM field in the shadow in the wave zone at large distances from the sphere. We use the standard tools available from the nuclear scattering theory to develop the wave-optical treatment of the problem. Based on this treatment, we demonstrate that there is no EM field deep in the shadow, except for the field that is diffracted into the shadow by the edges of the sphere, as anticipated.

Two-photon transitions in confined hydrogenic atoms

Two-photon transitions from ground state to excited and ionized states are studied. The energy levels and radial matrix elements of animpenetrable spherically confined hydrogenic atom embedded in plasma environment are evaluated using accurate Bernstein-polynomial(B-polynomial) method. Transition probability amplitudes, transparency frequencies and resonance enhancement frequencies for varioustransitions, namely, $1s-2s$, $1s-3s$ and $1s-3d$ are evaluated for various values of confining Debye potential parameter. The effect ofspherical confinement is studied and explained.

Adsorption of mixtures of the Yukawa-ions near a hard wall: A density functional study based on the third-order Ornstein-Zernike relation

We examine the adsorption of the primitive-model “ionic” mixtures modeled in terms of the screened Debye potentials on a hard structureless wall. It is well-known that the screened Debye potentials are of the Yukawa form. They could approach the Coulomb potentials when the screen parameter λ vanishes. Thus the study of the mixtures of repulsive and attractive Yukawa molecules can mimic the ionic fluid behavior at small λ. One of the advantages of using this Yukawa potential is that it avoids the long-range interactions and mitigates the complications inherent in the Coulomb potential.We have previously developed a third-order Ornstein-Zernike relation (OZ3) and have adapted it to the adsorption of many types of fluids on hard walls. Specifically, a new generation of closures was developed for use in the Euler-Lagrange equations of the density functional theory (DFT) for determining the non-uniform densities of various fluid types: such as the Lennard-Jones fluid, as well as the regular Yukawa fluids (with finite λ values) on an inhomogeneous substrate. In this work, we examine the applicability of the OZ3-inspired bridge functions to the adsorption of the “small-λ” Yukawa fluids. The mixtures of these Yukawa fluids are, for simplicity, called the Yukawa ions, in contrast to the Coulomb ions. The results shall mimic the electrical double layers in electrochemistry.The Euler-Lagrange equations for the binary mixtures are solved with new OZ3 closures. Two types of closures are investigated: one derived from the Jackson-Feenberg approximation, and the other derived from the linear cavity approximation. The results are compared with the Monte-Carlo results on primitive-model symmetric ions and asymmetric ions on a neutral hard structureless wall. Satisfactory agreements are obtained. It is noted that the contact value theorems (i.e. the hard-wall sum rules) play an instrumental role in obtaining the accurate results.

Spectra of confined positronium

Positronium is studied under the effect of spherically confined plasma environment. Exponentially Cosine Screened Coulomb potential (ECSC) has been used to include the dense plasma screening effect on positronium. Time independent Schrodinger equation is solved numerically. Various physical parameters such as energy eigenvalues, radial matrix elements, oscillator strengths, and polarizability are well explored as a function of confinement parameters. Oscillator strength gets drastically modified under confinement. We have also obtained the results for Ps confined under spherically confined Debye potential and compared with results of ECSC potential. Also incidental degeneracy for different values of confinement parameters has been reported for the first time for positronium.

Diffraction of electromagnetic waves in the gravitational field of the Sun

We consider the propagation of electromagnetic (EM) waves in the gravitational field of the Sun within the first post-Newtonian approximation of the general theory of relativity. We solve Maxwell's equations for the EM field propagating on the background of a static mass monopole and find an exact closed form solution for the Debye potentials, which, in turn, yield a solution to the problem of diffraction of EM waves in the gravitational field of the Sun. The solution is given in terms of the confluent hypergeometric function and, as such, it is valid for all distances and angles. Using this solution, we develop a wave-theoretical description of the solar gravitational lens (SGL) and derive expressions for the EM field and energy flux in the immediate vicinity of the focal line of the SGL. Aiming at the potential practical applications of the SGL, we study its optical properties and discuss its suitability for direct high-resolution imaging of a distant exoplanet.

Quantum screened interactions in moderately dense plasmas and atomic contributions to thermodynamics

The screened Coulomb interaction φ through which particles interact in the path integral description of quantum plasmas is studied analytically and numerically. This interaction, which is a key ingredient in quantum Mayer diagrams, is closely related to the random‐phase approximation potential known from finite‐temperature many‐body perturbation theory. An efficient way to compute numerically φ and its contributions in quantum Mayer diagrams under weak degeneracy conditions is proposed. Two key contributions to the thermodynamics of a moderately dense hydrogen plasma are studied using this method: polarization of the plasma and the electron– proton cluster function which accounts for the contributions from hydrogen atoms at finite density and finite temperature. The calculations include effects from dynamical screening and from shifts as well as broadening of spectral lines. When κ λ≪1, with κ the inverse Debye screening length and λ the electronic thermal de Broglie wavelength, a simple fast‐to‐evaluate approximation for φ can be used without loss of accuracy. The error induced on the electron– proton cluster function by the common approximation of replacing φ by a statically screened Debye potential is assessed for κ λ in the range 0⩽κ λ⩽0.5.

Spectra of electron pair under harmonic and Debye potential

Two electron systems confined by harmonic potential is known as harmonium. Such a system has been studied for many reasons in the literature. In this work we study harmonium under Debye potential. We use higher order finite difference method for the solution of Schrodinger equation. Complete energy spectrum of harmonium and harmonium under Debye potential is studied. Debye screening length shows considerable effect on the energy levels and the radial matrix elements. The results are analysed in the light of existing results and the comparison with available results shows remarkable agreement.

Применение потенциалов Дебая для расчета первичного поля в изотропной упругой среде, возбуждаемой вертикальным источником

An analytical solution of the problem of exciting an isotropic elastic medium by a vertical point source is proposed. This problem is a model one and is also a part of the solution of other model problems such as wave excitation in a plane-layered medium. The solution is based on the method of Debye potentials, which is widely used in solving various problems of electrodynamics. The range of these problems includes radiation from an antenna of a fairly arbitrary kind over a plane-layered dielectric medium, consideration of the effect an intricate fairing of an aircraft has on the operation of the radar station antenna system (the effect on the antenna pattern and the direction-finding characteristics of the system as a whole), designing slit radiators with a feeding resonator, and radiation from horn and waveguide antennas into a magnetodielectric semi-space. In many cases, it is possible to obtain an analytical solution of the problem; if an analytical solution is not available, numerical methods developed using the Debye potentials are effective from the computational point of view. The significance of an analytical solution lies in the simplicity and clarity of the interpretation and understanding of the wave propagation processes in contrast to a numerical solution. However, the fundamental difference between the problems of exciting elastic bodies from electrodynamic ones is in that two types of waves, namely, transverse and longitudinal ones, propagate in elastic media. This feature substantially complicates both the analytical solution and the elastic wave propagation process in comparison with electromagnetic waves. In view of this specific feature, a technique for calculating the excitation of an isotropic elastic medium using the apparatus of Debye potentials is proposed. It is shown that the displacement field of an isotropic elastic medium excited by a vertical source is represented as the sum of longitudinal and transverse wave fields, and symmetrically in the plane perpendicular to the source axis. Simple analytic expressions for calculating the displacement field at an arbitrary point in space are obtained. The results of calculations using analytical formulas are compared with the data of numerical modeling in the COMSOL Multiphysics 3.5a computer program. In view of the fact that the COMSOL Multiphysics 3.5a computer program is intended for calculating structures with finite dimensions, an original model of unlimited elastic medium in the form of a large-radius sphere (around 20 wavelengths) with radially-symmetrical absorption was developed.