Dielectric tensor and electromagnetic modes in magnetized non-ideal plasmas

2000 ◽  
Vol 63 (3) ◽  
pp. 239-253 ◽  
Author(s):  
V. M. RYLYUK ◽  
I. M. TKACHENKO ◽  
J. ORTNER
Keyword(s):  
Perturbation Theory ◽  
Classical Theory ◽  
Electromagnetic Waves ◽  
Hydrogen Plasma ◽  
Dielectric Tensor ◽  
Coulomb Correlations

The effect of Coulomb correlations on the spectrum of electromagnetic waves propagating in a non-ideal magnetized fully ionized hydrogen plasma is studied. We employ the dielectric tensor constructed by means of the classical theory of moments without using perturbation theory.

Global Perturbation of Nonlinear Eigenvalues

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Julián López-Gómez ◽  
Juan Carlos Sampedro
Keyword(s):  
Perturbation Theory ◽  
Spectral Parameter ◽  
Classical Theory ◽  
General Setting ◽  
Perturbation Parameter ◽  
Linear Operators ◽  
Fredholm Operators ◽  
Index Zero ◽  
Finite Dimensional ◽  
Nonlinear Eigenvalues

Abstract This paper generalizes the classical theory of perturbation of eigenvalues up to cover the most general setting where the operator surface 𝔏 : [ a , b ] × [ c , d ] → Φ 0 ⁢ ( U , V ) {\mathfrak{L}:[a,b]\times[c,d]\to\Phi_{0}(U,V)} , ( λ , μ ) ↦ 𝔏 ⁢ ( λ , μ ) {(\lambda,\mu)\mapsto\mathfrak{L}(\lambda,\mu)} , depends continuously on the perturbation parameter, μ, and holomorphically, as well as nonlinearly, on the spectral parameter, λ, where Φ 0 ⁢ ( U , V ) {\Phi_{0}(U,V)} stands for the set of Fredholm operators of index zero between U and V. The main result is a substantial extension of a classical finite-dimensional theorem of T. Kato (see [T. Kato, Perturbation Theory for Linear Operators, 2nd ed., Class. Math., Springer, Berlin, 1995, Chapter 2, Section 5]).

First-principle studies of the lattice dynamics of crystals, and related properties

2005 ◽  
Vol 220 (5/6) ◽  
Author(s):  
Xavier Gonze ◽  
Gian-Marco Rignanese ◽  
Razvan Caracas
Keyword(s):  
Perturbation Theory ◽  
First Principles ◽  
Lattice Dynamics ◽  
Density Functional ◽  
Computational Method ◽  
Dielectric Tensor ◽  
Atomic Temperature ◽  
Density Functional Perturbation Theory ◽  
Infra Red ◽  
Temperature Factors

AbstractThe crystal lattice is never rigid. Due to temperature, external fields or pressure, the nuclei vibrate, the lattice distorts, and instabilities can induce phase transitions. We review the basic concepts of density-functional perturbation theory, a computational method especially suited to determine from first-principles the microscopic parameters governing such behaviour. Then, we present the additional formalism leading to the following properties of minerals: the infra-red and Raman spectra; the prediction of (meta)stability or instability of a crystalline phase, based on the phonon spectrum; the computation of thermodynamics quantities like the free energy, entropy, specific heat; the atomic temperature factors. For each property, examples are given. When appropriate, we mention the computation of related properties, like dielectric tensor and Born effective charges that are needed to get infra-red spectra. Finally, we discuss briefly, on one hand, other applications of the density-functional perturbation theory, and, on the other hand, an alternative technique, the finite-difference computation of dynamical matrices.

scholarly journals Observation of gravitational waves by light polarization

2021 ◽  
Vol 81 (1) ◽  
Author(s):  
Chan Park ◽  
Dong-Hoon Kim
Keyword(s):  
General Relativity ◽  
Perturbation Theory ◽  
Gravitational Wave ◽  
Gravitational Waves ◽  
Electromagnetic Waves ◽  
Geometrical Optics ◽  
Light Polarization ◽  
Stokes Parameters ◽  
Phase Amplitude

AbstractWe provide analysis to determine the effects of gravitational waves on electromagnetic waves, using perturbation theory in general relativity. Our analysis is performed in a completely covariant manner without invoking any coordinates. For a given observer, using the geometrical-optics approach, we work out the perturbations of the phase, amplitude, frequency and polarization properties–axes of ellipse and ellipticity of light, due to gravitational waves. With regard to the observation of gravitational waves, we discuss the measurement of Stokes parameters, through which the antenna patterns are presented to show the detectability of the gravitational wave signals.

Resonant interaction of electron cyclotron waves with a plasma containing arbitrarily drifting suprathermal electrons

1985 ◽  
Vol 34 (2) ◽  
pp. 319-326 ◽  
Author(s):  
A. Orefice
Keyword(s):  
Electromagnetic Waves ◽  
Electron Distribution Function ◽  
Resonant Interaction ◽  
Electron Cyclotron ◽  
Dielectric Tensor ◽  
Suprathermal Electrons ◽  
Relativistic Treatment ◽  
Electron Cyclotron Waves ◽  
Plasma Dispersion ◽  
The Magnetic Field

A relativistic treatment of the plasma dispersion functions and of the dielectric tensor for electron cyclotron electromagnetic waves is given for non-thermal plasmas where the electron distribution function can be represented as a combination of Maxwellians with arbitrary drifts along the magnetic field.

scholarly journals Dispersive and effective properties of two-dimensional periodic media

2019 ◽  
Vol 475 (2227) ◽  
pp. 20180298
Author(s):  
Yuri A. Godin ◽  
Boris Vainberg
Keyword(s):  
Electromagnetic Waves ◽  
Effective Properties ◽  
Circular Cylinders ◽  
Dielectric Tensor ◽  
Two Dimensional ◽  
Rectangular Array ◽  
Electric And Magnetic Fields ◽  
Explicit Formulae ◽  
Propagation Of Waves ◽  
Transverse Propagation

We consider transverse propagation of electromagnetic waves through a two-dimensional composite material containing a periodic rectangular array of circular cylinders. Propagation of waves is described by the Helmholtz equation with the continuity conditions for the tangential components of the electric and magnetic fields on the boundaries of the cylinders. We assume that the cell size is small compared with the wavelength, but large compared with the radius a of the inclusions. Explicit formulae are obtained for asymptotic expansion of the solution of the problem in terms of the dimensionless magnitude q of the wavevector and radius a . This leads to explicit formulae for the effective dielectric tensor and the dispersion relation with the rigorously justified error of order O (( q 2  +  a 2 ) 5/2 ).

Alternative representation of the dielectric tensor for a relativistic magnetized plasma in thermal equilibrium

1990 ◽  
Vol 43 (2) ◽  
pp. 269-281 ◽  
Author(s):  
Peter H. Yoon ◽  
Ronald C. Davidson
Keyword(s):  
Thermal Equilibrium ◽  
Electromagnetic Waves ◽  
Dimensionless Parameter ◽  
Relativistic Effects ◽  
Magnetized Plasma ◽  
Dielectric Tensor ◽  
Alternative Representation ◽  
Formal Result ◽  
Weakly Relativistic Plasma ◽  
The Magnetic Field

An alternative representation of the dielectric tensor εij(k, ω) for a relativistic magnetized plasma in thermal equilibrium is presented. This representation involves an infinite series expansion in powers of , as well as an asymptotic expansion for large Here ωc = eB0/mc is the nonrelativistic cyclotron frequency, k⊥ is the wavenumber perpendicular to the magnetic field B0êz, and α is the dimensionless parameter defined by α = mc2/KBT. The present work generalizes Shkarofsky's (1966) representation. Moreover, unlike Trubnikov's (1958) formal result, in which the k⊥ and kz dependences of εij(k, ω) are inexorably coupled, the present representation naturally separates the k⊥ and kz dependences of εij(k, ω). As an application, the general expression is simplified for the case of a weakly relativistic plasma, and the dispersion relation is obtained for electromagnetic waves, including first-order relativistic effects. The method developed in this paper can be used for other non-thermal distributions.

Transverse electromagnetic modes in a hot cylindrical plasma column

1994 ◽  
Vol 52 (3) ◽  
pp. 471-481
Author(s):  
M. Shoucri
Keyword(s):  
Plasma Column ◽  
Cyclotron Frequency ◽  
Hydrogen Plasma ◽  
Electron Plasma ◽  
Dielectric Tensor ◽  
Cylindrical Plasma ◽  
Hot Plasma ◽  
Transverse Electromagnetic ◽  
Special Case ◽  
Cylindrical Plasma Column

We derive the dielectric tensor of a hot plasma by including the smallgyroradius corrections up to the first harmonic (ω ≈ 2ωcα). We show that these corrections introduce radial wavenumbers associated with transverse electromagnetic modes (TEM). The special case of a cylindrical plasma column is discussed for a hydrogen plasma at the ion-cyclotron frequency and for an electron plasma at the electron-cyclotron frequency and its first harmonic.

Internal relaxation, ionization and recombination in a dense hydrogen plasma I. Application of singular perturbation theory

1975 ◽  
Vol 345 (1641) ◽  
pp. 251-263 ◽  
Keyword(s):  
Perturbation Theory ◽  
Singular Perturbation ◽  
Equilibrium Distribution ◽  
Electron Number Density ◽  
Hydrogen Plasma ◽  
Singular Perturbation Theory ◽  
Number Density ◽  
Electron Number ◽  
Initial Transient ◽  
New Distribution

The master equation which describes internal relaxation, ionization and recombination in a dense hydrogen plasma at constant electron temperature is developed. An approximate solution is obtained by using singular perturbation theory based on the assumption that the internal relaxation time is much shorter than the time for ionization. The results show that there are two distinct time regimes in the relaxation of a given initial nonequilibrium population distribution to the final equilibrium distribution. The first phase, a fast initial transient, involves an internal redistribution of the atoms to form a new distribution. This new distribution decays slowly during the second and much longer phase to the equilibrium distribution. Only during this period is there any significant change in the electron number density. After the initial transient period the rate coefficient for ionization is related linearly to the smallest eigenvalue of the relaxation matrix, the rate-quotient law holds approximately and the ordinary differential equation describing the behaviour of the electron number density is the usual phenomenological rate equation.

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