BIREFRINGENCE IN CRYSTALS AND IN THE IONOSPHERE

1954 ◽  
Vol 32 (1) ◽  
pp. 16-34 ◽  
Author(s):  
C. H. M. Turner
Keyword(s):  
Magnetic Field ◽  
Dielectric Constant ◽  
Electromagnetic Waves ◽  
Plane Waves ◽  
Diagonal Matrix ◽  
Effective Dielectric Constant ◽  
Normal Velocity ◽  
Electron Collisions ◽  
Velocity Of Propagation ◽  
The Magnetic Field

Propagation of plane electromagnetic waves in a homogeneous ionized gas in a uniform magnetic field is compared with the propagation of light in an optically inactive birefringent crystal. It is well known that propagation in a crystal may be described by using a system of real orthogonal axes for which the dielectric constant is given by a diagonal matrix. This paper shows that propagation of plane waves in the ionosphere may be described in a similar manner, the medium having an effective dielectric constant given by a diagonal matrix, provided that a system of "complex" orthogonal axes is used for the description of the components of the field vectors. This set of component axes (which is quite different from and not to be confused with coordinate axes) is equivalent to resolving the field vectors into components parallel to the magnetic field and two contrarotating circular components in a plane perpendicular to the magnetic field. An expression giving the velocity of each of the two modes of propagation in a given direction and expressions for the amplitude of each component of the field vectors are obtained (equations 43 and 44). Provided that one accepts the concept of a complex velocity of propagation, the results hold when electron collisions are included. When electron collisions are neglected, it is possible to form a double-sheeted surface, called the normal velocity surface, which is of some assistance in visualizing the manner in which the velocity of propagation of the plane waves in each mode changes with direction.

THE MAGNETIC FIELD AT THE SURFACE OF A STRATIFIED FLAT CONDUCTOR IN THE FIELD OF PLANE WAVES WITH APPLICATION TO GEOPHYSICS

1962 ◽  
Vol 40 (11) ◽  
pp. 1583-1592 ◽  
Author(s):  
H. W. Dosso
Keyword(s):  
Magnetic Field ◽  
Surface Layer ◽  
Electromagnetic Waves ◽  
Plane Waves ◽  
Geomagnetic Variations ◽  
Wide Range ◽  
The Magnetic Field

The problem of plane electromagnetic waves incident on a stratified flat conductor is considered. Expressions for the amplitude and phase of the components of the resultant magnetic field at the surface of the conductor are obtained and evaluated for a wide range of frequencies, conductivities, surface layer depths, and angles of incidence. The frequencies f = 10−3 to 103 cycles/sec and the conductivities σ = 10−11 to 10−16 emu considered are of interest in studying geomagnetic variations.

scholarly journals III.—The distribution of the magnetic field and return current round a submarine cable carrying alternating current.—Part 1

1924 ◽  
Vol 224 (616-625) ◽  
pp. 95-140 ◽  
Keyword(s):  
Magnetic Field ◽  
Electromagnetic Waves ◽  
Sea Water ◽  
Plane Waves ◽  
Practical Importance ◽  
Control Mechanisms ◽  
Submarine Cable ◽  
Low Frequencies ◽  
Submarine Cables ◽  
The Magnetic Field

Among the scientific problems to which the late war gave rise, one of the greatest fundamental and practical importance is the determination of the conditions of propagation of impulses or disturbances of every kind below and above the surface of the sea. As sea water is a medium of fairly high electrical conductivity, the propagation of electromagnetic waves, especially of high frequencies, is greatly affected by the absorption in the water and the distortion at the surface. In view of the applications to signalling, the guiding of ships over submarine cables, and the actuation of mechanisms, a knowledge of the distribution of the intensity and direction of the magnetic field produced by a submarine cable or loop is of the greatest practical importance, apart from its scientific interest. The investigations described in the present paper commenced in January, 1918, when the writer was called to the Admiralty Experimental Station at Parkeston Quay, Harwich, for the purpose of devising control mechanisms actuated by submarine cables. It was immediately obvious that absorption by the sea water might prove to be a serious factor in diminishing the intensity of the magnetic field, and that low frequencies would therefore be preferable. Calculations were therefore made concerning the propagation of electromagnetic waves in the sea, but as these applied only to plane waves in an infinite medium it was also decided to make a few direct measurements on the absorption of the field produced by a 300 by 200 yard loop which had been laid down at the mouth of Harwich harbour, the result being to show that absorption had no serious effect at frequencies of 30 to 20 ~ per second. This result was sufficient for the immediate purpose.

Gas-ionizing shocks in a magnetic field

1967 ◽  
Vol 1 (1) ◽  
pp. 37-54 ◽  
Author(s):  
M. D. Cowley
Keyword(s):  
Magnetic Field ◽  
Electric Field ◽  
Wave Speed ◽  
Normal Velocity ◽  
Electrically Conducting ◽  
Shock Stability ◽  
The Face ◽  
Arbitrary Velocity ◽  
Flow Plane ◽  
The Magnetic Field

Ionizing shocks for plane flows with the magnetic field lying in the flow plane are considered. The gas is assumed to be electrically conducting downstream, but non-conducting upstream. Shocks whose downstream state has a normal velocity component less than the slow magneto-acoustic-wave speed and whose upstream state is supersonic are found to be non-evolutionary in the face of plane magneto-acoustic disturbances, unless the upstream electric field in a frame of reference where the gas is at rest is arbitrary. Velocity conditions are also determined for shock stability with the electric field not arbitrary.Shock structures are found for the case of large ohmic diffusion, the initial temperature rise and ionization of the gas being caused by a thin transition having the properties of an ordinary gasdynamic shock. For the case where shocks are evolutionary when the upstream electric field is arbitrary, the shock structure requirements only restrict the electric field by limiting the range of possible values. When shocks are evolutionary with the electric field not arbitrary, they can only have a structure for a particular value of the electric field. Limits to the current carried by ionizing shocks and the effects of precursor ionization are discussed qualitatively.

scholarly journals Radio Emission Model of a 'Typical' Pulsar

1987 ◽  
Vol 40 (6) ◽  
pp. 755 ◽  
Author(s):  
AZ Kazbegi ◽  
GZ Machabeli ◽  
G Melikidze
Keyword(s):  
Magnetic Field ◽  
Electromagnetic Waves ◽  
Emission Model ◽  
Radio Waves ◽  
Resonance Case ◽  
Pulsar Magnetosphere ◽  
Pulsar Emission ◽  
Dipole Magnetic Field ◽  
New Type ◽  
The Magnetic Field

The generation of radio waves in the plasma of the pulsar magnetosphere is considered taking into account the inhomogeneity of the dipole magnetic field. It is shown that the growth rate of the instability of the electromagnetic waves calculated in the non-resonance case turns out to be of the order of 1/ TO (where TO is the time of plasma escape from the light cylinder). However, the generation of electromagnetic waves from a new type Cherenkov resonance is possible, occurring when the particles have transverse velocities caused by the drift due to the inhomogeneity of the magnetic field. Estimates show that the development of this type of instability is possible only for pulsars with ages which exceed 104 yr. We make an attempt to explain some peculiarities of 'typical' pulsar emission on the basis of the model developed.

The magnetic field dependence of the dielectric constant of liquids

1981 ◽  
Vol 62 (1-2) ◽  
pp. 207-216
Author(s):  
T.M. Plantenga ◽  
J. Bulthuis ◽  
J.P. Van Dieren ◽  
W. Mels ◽  
C. MacLean
Keyword(s):  
Magnetic Field ◽  
Dielectric Constant ◽  
Field Dependence ◽  
Magnetic Field Dependence ◽  
The Magnetic Field

Conduction electron diamagnetism in alloys and magnetic-field-dependent dielectric constant of a Fermi gas

1964 ◽  
Vol 280 (1380) ◽  
pp. 85-96 ◽  
Keyword(s):  
Magnetic Field ◽  
Dielectric Constant ◽  
Free Electrons ◽  
Impurity Potential ◽  
First Order ◽  
Dilute Alloys ◽  
A Value ◽  
Field Dependent ◽  
Self Consistency ◽  
The Magnetic Field

The diamagnetism of free electrons in the presence of charged impurity centres which are sufficiently dilute to be non-interacting is calculated to first order in the strength of the potential of the impurity centre. This is done by combining the density-matrix treatment of Landau diamagnetism with the impurity-screening theory o f March & Murray. The susceptibility involves the integrated value of the impurity potential through the crystal, and its first derivative with respect to the magnetic field, B. If the impurity potential is assumed to have a value appropriate to B — 0, then the result for the change in diamagnetic susceptibility on alloying agrees with that of Kohn & Luming (1963). It is shown, however, that the impurity potential is modified in the presence of the magnetic field, and in particular it has angular dependence. The correction to the dia­magnetic susceptibility due to this self-consistency is shown to be significant (25% ). The relevance of the theory to experimental results on dilute alloys is briefly discussed. Finally, as a by-product of the investigation, we have obtained interesting results about the form of the field-dependent dielectric constant.

A semianalytical solution for the propagation of electromagnetic waves in 3‐D lossy orthotropic media

Geophysics ◽  
2001 ◽  
Vol 66 (4) ◽  
pp. 1141-1148 ◽  
Author(s):  
José M. Carcione ◽  
Fabio Cavallini
Keyword(s):  
Magnetic Field ◽  
Plane Wave ◽  
Electromagnetic Waves ◽  
Plane Waves ◽  
Computer Experiment ◽  
Transverse Magnetic ◽  
Wave Analysis ◽  
Helmholtz Equations ◽  
Magnetic Surfaces ◽  
Time Histories

We derive an analytical solution for electromagnetic waves propagating in a 3‐D lossy orthotropic medium for which the electric permittivity tensor is proportional to the magnetic permeability tensor. The solution is obtained through a change of coordinates that transforms the spatial differential operator into a pure Laplace operator and the differential equations for the electric and magnetic field components into pure Helmholtz equations. A plane‐wave analysis gives the expression of the slowness and attenuation surfaces as a function of frequency and propagation direction. The transverse electric and transverse magnetic surfaces degenerate to one repeated sheet so that, in any direction, the two differently polarized plane waves have the same slowness. A computer experiment with realistic geophysical parameters has shown that the anisotropic propagation and dissipation properties emerging from plane‐wave analysis agree with the different time histories of the magnetic field computed at a number of representative receiver locations.

Whistler instability in plasmas with anisotropic and non-Maxwellian velocity distributions

1971 ◽  
Vol 6 (3) ◽  
pp. 449-456 ◽  
Author(s):  
Kai Fong Lee
Keyword(s):  
Magnetic Field ◽  
Electromagnetic Waves ◽  
Maxwell Equations ◽  
Transverse Velocity ◽  
Distribution Functions ◽  
Loss Cone ◽  
Circularly Polarized ◽  
Electron Plasmas ◽  
Thermal Spread ◽  
The Magnetic Field

The instability of right-handed, circularly polarized electromagnetic waves, propagating along an external magnetic field (whistler mode), is studied for electron plasmas with distribution functions peaked at some non-zero value of the transverse velocity. Based on the linearized Vlasov-Maxwell equations, the criteria for instability are given both for non-resonant instabilities arising from distribution functions with no thermal spread parallel to the magnetic field, and for resonant instabilities arising from distribution functions with Maxwellian dependence in the parallel velocities. It is found that, in general, the higher the average perpendicular energy, the more is the plasma susceptible to the whistler instability. These criteria are then applied to a sharply peaked ring distribution, and to loss-cone distributions of the Dory, Guest & Harris (1965) type.

scholarly journals Propagation of an electromagnetic soliton in a ferromagnetic medium

2002 ◽  
Vol 44 (1) ◽  
pp. 103-110
Author(s):  
V. Veerakumar ◽  
M. Daniel
Keyword(s):  
Magnetic Field ◽  
Electromagnetic Waves ◽  
Ferromagnetic Material ◽  
Linear Charge ◽  
Electromagnetic Soliton ◽  
Induction Components ◽  
Charged Medium ◽  
A Charge ◽  
The Magnetic Field ◽  
Ferromagnetic Medium

AbstractWe study the propagation of electromagnetic waves (EMWs) in both isotropic and anisotropic ferromagnetic material media. As the EMW propagates through linear charge-free isotropic and anisotropic ferromagnetic media, it is found that the magnetic field and the magnetic induction components of the EMW and the magnetization excitations of the medium are in the form of solitons. However, the electromagnetic soliton gets damped and decelerates in the case of a charged medium. In the case of a charge-free nonlinear ferromagnetic medium we obtain results similar to those for the linear case.

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