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

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.

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BIREFRINGENCE IN CRYSTALS AND IN THE IONOSPHERE

Canadian Journal of Physics ◽

10.1139/p54-003 ◽

1954 ◽

Vol 32 (1) ◽

pp. 16-34 ◽

Cited By ~ 2

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.

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

Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Mathematical or Physical Character ◽

10.1098/rsta.1924.0003 ◽

1924 ◽

Vol 224 (616-625) ◽

pp. 95-140 ◽

Cited By ~ 6

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.

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Monte Carlo calculation of the energy parameters and spatial distribution of the cathodic arc ions while passing through the macro-particles filters

International Journal of Computational Physics Series ◽

10.29167/a1i1p30-34 ◽

2018 ◽

Vol 1 (1) ◽

pp. 30-34 ◽

Cited By ~ 2

Author(s):

Alexey Chernogor ◽

Igor Blinkov ◽

Alexey Volkhonskiy

Keyword(s):

Magnetic Field ◽

Mass Transfer ◽

Monte Carlo ◽

Monte Carlo Calculation ◽

Inhomogeneous Magnetic Field ◽

Flow Energy ◽

Wide Range ◽

Field Concentrator ◽

Cathodic Arc ◽

The Magnetic Field

The flow, energy distribution and concentrations profiles of Ti ions in cathodic arc are studied by test particle Monte Carlo simulations with considering the mass transfer through the macro-particles filters with inhomogeneous magnetic field. The loss of ions due to their deposition on filter walls was calculated as a function of electric current and number of turns in the coil. The magnetic field concentrator that arises in the bending region of the filters leads to increase the loss of the ions component of cathodic arc. The ions loss up to 80 % of their energy resulted by the paired elastic collisions which correspond to the experimental results. The ion fluxes arriving at the surface of the substrates during planetary rotating of them opposite the evaporators mounted to each other at an angle of 120° characterized by the wide range of mutual overlapping.

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No-z Model for Magnetic Fields of Different Astrophysical Objects and Stability of the Solutions

Data ◽

10.3390/data6010004 ◽

2021 ◽

Vol 6 (1) ◽

pp. 4

Author(s):

Evgeny Mikhailov ◽

Daniela Boneva ◽

Maria Pashentseva

Keyword(s):

Magnetic Field ◽

Magnetic Fields ◽

Large Scale ◽

Point Of View ◽

Accretion Discs ◽

Wide Range ◽

Astrophysical Objects ◽

Alpha Effect ◽

The Stability ◽

The Magnetic Field

A wide range of astrophysical objects, such as the Sun, galaxies, stars, planets, accretion discs etc., have large-scale magnetic fields. Their generation is often based on the dynamo mechanism, which is connected with joint action of the alpha-effect and differential rotation. They compete with the turbulent diffusion. If the dynamo is intensive enough, the magnetic field grows, else it decays. The magnetic field evolution is described by Steenbeck—Krause—Raedler equations, which are quite difficult to be solved. So, for different objects, specific two-dimensional models are used. As for thin discs (this shape corresponds to galaxies and accretion discs), usually, no-z approximation is used. Some of the partial derivatives are changed by the algebraic expressions, and the solenoidality condition is taken into account as well. The field generation is restricted by the equipartition value and saturates if the field becomes comparable with it. From the point of view of mathematical physics, they can be characterized as stable points of the equations. The field can come to these values monotonously or have oscillations. It depends on the type of the stability of these points, whether it is a node or focus. Here, we study the stability of such points and give examples for astrophysical applications.

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The role of slow magnetostrophic waves in dipole formation in rapidly rotating dynamos

10.5194/egusphere-egu21-15480 ◽

2021 ◽

Author(s):

Aditya Varma ◽

Binod Sreenivasan

Keyword(s):

Magnetic Field ◽

Threshold Value ◽

Dipole Field ◽

Wave Frequency ◽

Alfven Wave ◽

Inertial Waves ◽

Axial Dipole ◽

Wide Range ◽

The Magnetic Field

It is known that the columnar structures in rapidly rotating convection are affected by the magnetic field in ways that enhance their helicity. This may explain the dominance of the axial dipole in rotating dynamos. Dynamo simulations starting from a small seed magnetic field have shown that the growth of the field is accompanied by the excitation of convection in the energy-containing length scales. Here, this process is studied by examining axial wave motions in the growth phase of the dynamo for a wide range of thermal forcing. In the early stages of evolution where the field is weak, fast inertial waves weakly modified by the magnetic field are abundantly present. As the field strength(measured by the ratio of the Alfven wave to the inertial wave frequency) exceeds a threshold value, slow magnetostrophic waves are spontaneously generated. The excitation of the slow waves coincides with the generation of helicity through columnar motion, and is followed by the formation of the axial dipole from a chaotic, multipolar state. In strongly driven convection, the slow wave frequency is attenuated, causing weakening of the axial dipole intensity. Kinematic dynamo simulations at the same parameters, where only fast inertial waves are present, fail to produce the axial dipole field. The dipole field in planetary dynamos may thus be supported by the helicity from slow magnetostrophic waves.

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Radio Emission Model of a 'Typical' Pulsar

Australian Journal of Physics ◽

10.1071/ph870755 ◽

1987 ◽

Vol 40 (6) ◽

pp. 755 ◽

Cited By ~ 10

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.

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Decaying turbulence and magnetic fields in galaxy clusters

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/stz1918 ◽

2019 ◽

Vol 488 (3) ◽

pp. 3439-3445 ◽

Cited By ~ 1

Author(s):

Sharanya Sur

Keyword(s):

Magnetic Field ◽

Magnetic Fields ◽

Galaxy Clusters ◽

Power Law ◽

Dynamo Action ◽

Wide Range ◽

Major Merger ◽

Decaying Turbulence ◽

Field Decay ◽

The Magnetic Field

Abstract We explore the decay of turbulence and magnetic fields generated by fluctuation dynamo action in the context of galaxy clusters where such a decaying phase can occur in the aftermath of a major merger event. Using idealized numerical simulations that start from a kinetically dominated regime we focus on the decay of the steady state rms velocity and the magnetic field for a wide range of conditions that include varying the compressibility of the flow, the forcing wavenumber, and the magnetic Prandtl number. Irrespective of the compressibility of the flow, both the rms velocity and the rms magnetic field decay as a power law in time. In the subsonic case we find that the exponent of the power law is consistent with the −3/5 scaling reported in previous studies. However, in the transonic regime both the rms velocity and the magnetic field initially undergo rapid decay with an ≈t−1.1 scaling with time. This is followed by a phase of slow decay where the decay of the rms velocity exhibits an ≈−3/5 scaling in time, while the rms magnetic field scales as ≈−5/7. Furthermore, analysis of the Faraday rotation measure (RM) reveals that the Faraday RM also decays as a power law in time ≈t−5/7; steeper than the ∼t−2/5 scaling obtained in previous simulations of magnetic field decay in subsonic turbulence. Apart from galaxy clusters, our work can have potential implications in the study of magnetic fields in elliptical galaxies.

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Magnetic Rayleigh–Taylor instability at a contact discontinuity with an oblique magnetic field

Astronomy and Astrophysics ◽

10.1051/0004-6361/201936490 ◽

2020 ◽

Vol 634 ◽

pp. A96

Author(s):

E. Vickers ◽

I. Ballai ◽

R. Erdélyi

Keyword(s):

Magnetic Field ◽

Growth Rate ◽

Dispersion Relation ◽

Contact Discontinuity ◽

Homogeneous Magnetic Field ◽

Taylor Instability ◽

Wide Range ◽

Rayleigh Taylor Instability ◽

The Magnetic Field ◽

Theoretical Results

Aims. We investigate the nature of the magnetic Rayleigh–Taylor instability at a density interface that is permeated by an oblique homogeneous magnetic field in an incompressible limit. Methods. Using the system of linearised ideal incompressible magnetohydrodynamics equations, we derive the dispersion relation for perturbations of the contact discontinuity by imposing the necessary continuity conditions at the interface. The imaginary part of the frequency describes the growth rate of waves due to instability. The growth rate of waves is studied by numerically solving the dispersion relation. Results. The critical wavenumber at which waves become unstable, which is present for a parallel magnetic field, disappears because the magnetic field is inclined. Instead, waves are shown to be unstable for all wavenumbers. Theoretical results are applied to diagnose the structure of the magnetic field in prominence threads. When we apply our theoretical results to observed waves in prominence plumes, we obtain a wide range of field inclination angles, from 0.5° up to 30°. These results highlight the diagnostic possibilities that our study offers.

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Magnetic Ordering of Perovskite-Like La-, Nd-, and Gd-Doped Bismuth Ferrite

MRS Advances ◽

10.1557/adv.2019.327 ◽

2019 ◽

Vol 4 (36) ◽

pp. 1989-1999 ◽

Cited By ~ 1

Author(s):

Valery Sobol ◽

Barys Korzun ◽

Olga Mazurenko ◽

Temirkhan Bizhigitov ◽

Sabit Tomaev

Keyword(s):

Magnetic Field ◽

Exchange Interaction ◽

Bismuth Ferrite ◽

Magnetic Ordering ◽

Solid State Reaction Method ◽

Nonlinear Dependence ◽

X Ray Diffraction ◽

Wide Range ◽

Pure Grade ◽

The Magnetic Field

ABSTRACTBismuth ferrite (BiFeO3) and La-, Nd- and Gd-substituted bismuth ferrite of the Bi1-xLaxFeO3, Bi1-xNdxFeO3, and Bi1-xGdxFeO3 types with the atomic part of the substitution element x equal up to 0.20 were synthesized by the solid-state reaction method using powders of oxides Bi2O3, Fe2O3, and La2O3, or Nd2O3, or Gd2O3 of pure grade quality and investigated using X-ray diffraction analysis. The magnetization was measured in the magnetic field up to 6.5⋅106 A/m at 5 and 300 K. It was found that the total substitution up to 0.20 atomic part of Bi by La, Nd, and Gd leads to the paramagnetic behavior of the doped bismuth ferrite at low temperatures in a wide range of magnetic field. Strong nonlinear dependence of magnetization on the magnetic field was detected and a ferromagnetic-like dependence of magnetization was observed for small magnetic fields. This can be explained by the exchange interaction between doping magnetic ions, as well as by the exchange interaction of these ions with ions of iron. The enhancement of magnetic properties with the increase of the content of the substitution is monotone and is more pronounced for the Bi1-xGdxFeO3 ceramics.

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First measurements of the Mesospheric Magnetic Field in the Auroral Zone by means of laser

10.5194/egusphere-egu2020-7839 ◽

2020 ◽

Author(s):

Magnar G. Johnsen ◽

Njål Gulbrandsen ◽

Paul Hillman ◽

Craig Denman ◽

Jürgen Matzka ◽

...

Keyword(s):

Magnetic Field ◽

Time Scales ◽

Optical Pumping ◽

Sodium Atom ◽

Auroral Zone ◽

Geomagnetic Variations ◽

Sum Frequency ◽

Sodium Layer ◽

Magnetic Field Magnitude ◽

The Magnetic Field

In December 2019, for the first time, we were able to remotely measure the magnetic field in the mesospheric sodium layer, in the auroral zone.By means of laser optical pumping and Larmor-resonance detection, it is possible to use the naturally occurring sodium layer in the mesosphere to measure Earth&#8217;s magnetic field magnitude at 90 km above ground. This is an altitude otherwise only accessible by rockets, which only will provide point measurements of very short time scales.During the winter of 2019-20 we have applied a cw sum-frequency fasor/laser for probing the sodium-atom Larmor resonance at the Artic Lidar Observatory for Mesospheric Research (ALOMAR) at And&#248;ya in northern Norway in order to measure and monitor the magnetic field in situ in the high latitude mesosphere over longer time scales.The technique, which has been proved earlier at mid-latitudes, has now been confirmed and applied to high latitudes in the auroral zone during disturbed auroral and geomagnetic conditions. The magnetic field in the auroral zone is close to vertical making our measurements a notable achievement since the beam is closer to parallel with the magnetic field, contary to earlier measurements being closer to perpendicular as shown as best by theory.This opens up for a completely new domain of measurements of externally generated geomagnetic variations related to currents in the magnetosphere-ionosphere system.Here we report on the instrumental setup, and discuss our measurements of the mesospheric magnetic field.

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