RESPONSE OF DYKE TO OSCILLATING DIPOLE

Geophysics ◽  
1958 ◽  
Vol 23 (1) ◽  
pp. 128-133 ◽  
Author(s):  
James Paul Wesley
Keyword(s):  
Magnetic Field ◽  
Closed Form ◽  
Scalar Potential ◽  
Three Dimensions ◽  
Electromagnetic Response ◽  
Dipole Source ◽  
First Approximation ◽  
Sulfide Ore ◽  
Infinite Conductivity ◽  
The Magnetic Field

A dyke of sulfide ore may be geophysically prospected by observing its electromagnetic response to a slowly oscillating magnetic dipole source. An excellent first approximation of the fields generated is obtained by considering the idealized case of a dyke of infinite conductivity and vanishing thickness in a vacuum. Surprisingly, this idealized problem can be solved exactly in terms of a newly discovered Green’s function for Laplace’s equation (in three dimensions) which is simply expressed in closed form. The magnetic scalar potential and the magnetic field are given for final results.

RESPONSE OF THIN DYKE TO OSCILLATING DIPOLE

Geophysics ◽  
1958 ◽  
Vol 23 (1) ◽  
pp. 134-143 ◽  
Author(s):  
James Paul Wesley
Keyword(s):  
Exact Solution ◽  
Magnetic Dipole ◽  
Analytical Continuation ◽  
Dipole Source ◽  
Finite Conductivity ◽  
First Approximation ◽  
Sulfide Ore ◽  
Infinite Slab ◽  
Infinite Conductivity

A dyke of sulfide ore may be geophysically prospected by observing its response to a slowly oscillating magnetic dipole source. To a first approximation the field produced by a thin dyke is given by a dyke of infinite conductivity and vanishing thickness in a vacuum (Wesley, 1958, Geophysics, v. 23, p. 128). In order to identify the ore and to estimate the size of the deposit, it is necessary to consider further approximations involving the conductivity and thickness of the dyke. By a type of analytical continuation an approximation is found which agrees both with the exact solution for a dyke of infinite conductivity and vanishing thickness and with the exact solution (approximated only for ωσ large and also for σ small) for an infinite slab of finite conductivity and nonvanishing thickness, the dyke appearing as an infinite slab when both source and observer are near the dyke but far removed from the edge. The solution is very good provided the dyke is geometrically thin.

The Magnetic Anisotropy of Stretched Rubber as a Function of the Tension to Which It Is Subjected

1945 ◽  
Vol 18 (1) ◽  
pp. 8-9 ◽  
Author(s):  
Eugénie Cotton-Feytis
Keyword(s):  
Magnetic Field ◽  
Magnetic Anisotropy ◽  
Uniaxial Crystal ◽  
Horizontal Magnetic Field ◽  
First Approximation ◽  
The Difference ◽  
The Times ◽  
Angular Displacements ◽  
The Magnetic Field ◽  
Oscillation Method

Abstract From the standpoint of its magnetic anisotropy, stretched rubber is comparable in a first approximation to a uniaxial crystal, in which the direction of the axis is the same as the direction of elongation. It is possible to measure this anisotropy by means of the oscillation method used by Krishnan, Guha and Banerjee in studying crystals. The sample to be examined is suspended in a uniform horizontal magnetic field in such a manner that its axis is horizontal. It is then so arranged that the torsion of the suspension wire is zero when the rubber sample is in a position of equilibrium in the field. The times of oscillation T′ and T for very small angular displacements around this position, in the presence and then in the absence of the magnetic field, are then recorded. In this way the difference between the specific susceptibilities in the direction of the axis and in the horizontal direction perpendicular to the axis is calculated by application of the equation:

Static magnetic fields in vacuum

2018 ◽  
Author(s):  
J. Pierrus
Keyword(s):  
Magnetic Field ◽  
Problem Solving ◽  
Magnetic Fields ◽  
Vector Potential ◽  
Scalar Potential ◽  
Multipole Expansion ◽  
Magnetic Vector Potential ◽  
Magnetic Dipoles ◽  
Static Magnetic Fields ◽  
The Magnetic Field

Wherever possible, an attempt has been made to structure this chapter along similar lines to Chapter 2 (its electrostatic counterpart). Maxwell’s magnetostatic equations are derived from Ampere’s experimental law of force. These results, along with the Biot–Savart law, are then used to determine the magnetic field B arising from various stationary current distributions. The magnetic vector potential A emerges naturally during our discussion, and it features prominently in questions throughout the remainder of this book. Also mentioned is the magnetic scalar potential. Although of lesser theoretical significance than the vector potential, the magnetic scalar potential can sometimes be an effective problem-solving device. Some examples of this are provided. This chapter concludes by making a multipole expansion of A and introducing the magnetic multipole moments of a bounded distribution of stationary currents. Several applications involving magnetic dipoles and magnetic quadrupoles are given.

Closed-form formula of magnetic gradient tensor for a homogeneous polyhedral magnetic target: A tetrahedral grid example

Geophysics ◽  
2017 ◽  
Vol 82 (6) ◽  
pp. WB21-WB28 ◽  
Author(s):  
Zhengyong Ren ◽  
Chaojian Chen ◽  
Jingtian Tang ◽  
Huang Chen ◽  
Shuanggui Hu ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Closed Form ◽  
Magnetization Vector ◽  
Gradient Tensor ◽  
Magnetic Gradient ◽  
Closed Form Solutions ◽  
Tetrahedral Grid ◽  
Pipeline Model ◽  
The Magnetic Field ◽  
Closed Form Formula

A closed-form formula is developed for the full magnetic gradient tensor of a polyhedral body with a homogeneous magnetization vector. It is based on the direct derivative technique on the closed form of the magnetic field. These analytical expressions are implemented into an easy-to-use C++ package which simultaneously calculates the magnetic potential, the magnetic field, and the full magnetic gradient tensor for magnetic targets. Modern unstructured tetrahedral grids are adopted to represent the polyhedral body so that our code can deal with arbitrarily complicated magnetic targets. A prismatic body is tested to verify the accuracies of our closed-form formula. Excellent agreements are obtained between our closed-form solutions and solutions of a prismatic magnetic body with differences up to machine precision. A pipeline model is used to demonstrate its capability to deal with complicated magnetic targets. This C++ code is freely available to the magnetic exploration community.

TRANSIENT ELECTROMAGNETIC RESPONSE OF AN INHOMOGENEOUS CONDUCTING SPHERE

Geophysics ◽  
1970 ◽  
Vol 35 (2) ◽  
pp. 331-336 ◽  
Author(s):  
Saurabh K. Verma ◽  
Rishi Narain Singh
Keyword(s):  
Magnetic Field ◽  
Rise Time ◽  
Mineral Deposits ◽  
Electromagnetic Response ◽  
Radial Coordinate ◽  
Induced Magnetic Field ◽  
Transient Electromagnetic ◽  
Unit Step ◽  
Analytic Expressions ◽  
The Magnetic Field

Analytic expressions for the quasi‐static electromagnetic response of a sphere in presence of unit‐step and ramp‐type time varying magnetic fields are derived. The conductivity inside the sphere is assumed to vary linearly with radius, i.e. [Formula: see text], where ρ is radial coordinate, [Formula: see text] is a constant and a is the radius of sphere. Curves showing the decay of the magnetic field for both types of fields are presented. In the case of ramp‐type applied magnetic field, the magnitudes of maxima of the induced magnetic field are found to decrease with increase in the rise time of the applied field and, hence, exciting pulses having small values of rise time should be used. It is believed that the analysis will be useful in the geoelectric exploration for highly conducting mineral deposits.

Compressible magnetoconvection in three dimensions: planforms and nonlinear behaviour

1995 ◽  
Vol 305 ◽  
pp. 281-305 ◽  
Author(s):  
P. C. Matthews ◽  
M. R. E. Proctor ◽  
N. O. Weiss
Keyword(s):  
Magnetic Field ◽  
Shear Flow ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Nonlinear Behaviour ◽  
Two Dimensional ◽  
Horizontal Shear ◽  
Mean Flow ◽  
The Magnetic Field

Convection in a compressible fiuid with an imposed vertical magnetic field is studied numerically in a three-dimensional Cartesian geometry with periodic lateral boundary conditions. Attention is restricted to the mildly nonlinear regime, with parameters chosen first so that convection at onset is steady, and then so that it is oscillatory.Steady convection occurs in the form of two-dimensional rolls when the magnetic field is weak. These rolls can become unstable to a mean horizontal shear flow, which in two dimensions leads to a pulsating wave in which the direction of the mean flow reverses. In three dimensions a new pattern is found in which the alignment of the rolls and the shear flow alternates.If the magnetic field is sufficiently strong, squares or hexagons are stable at the onset of convection. Both the squares and the hexagons have an asymmetrical topology, with upflow in plumes and downflow in sheets. For the squares this involves a resonance between rolls aligned with the box and rolls aligned digonally to the box. The preference for three-dimensional flow when the field is strong is a consequence of the compressibility of the layer- for Boussinesq magnetoconvection rolls are always preferred over squares at onset.In the regime where convection is oscillatory, the preferred planform for moderate fields is found to be alternating rolls - standing waves in both horizontal directions which are out of phase. For stronger fields, both alternating rolls and two-dimensional travelling rolls are stable. As the amplitude of convection is increased, either by dcereasing the magnetic field strength or by increasing the temperature contrast, the regular planform structure seen at onset is soon destroyed by secondary instabilities.

Small-scale magnetic fields in turbulence: Saffman's approximation revisited

1980 ◽  
Vol 99 (3) ◽  
pp. 481-493
Author(s):  
Ralph Baierlein
Keyword(s):  
Magnetic Field ◽  
Numerical Evaluation ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Small Scale ◽  
Fluid Element ◽  
Relative Time ◽  
Fourier Decomposition ◽  
The Subject ◽  
The Magnetic Field

The subject is the small-scale structure of a magnetic field in a turbulent conducting fluid, ‘small scale’ meaning lengths much smaller than the characteristic dissipative length of the turbulence. Philip Saffman developed an approximation to describe this structure and its evolution in time. Its usefulness invites a closer examination of the approximation itself and an attempt to place sharper limits on the numerical parameters that appear in the approximate correlation functions, topics to which the present paper is addressed.A Lagrangian approach is taken, wherein one makes a Fourier decomposition of the magnetic field in a neighbourhood that follows a fluid element. If one construes the viscous-convective range narrowly, by ignoring magnetic dissipation entirely, then results for a magnetic field in two dimensions are consistent with Saffman's approximation, but in three dimensions no steady state could be found. Thus, in three dimensions, turbulent amplification seems to be more effective than Saffman's approximation implies. The cause seems to be a matter of geometry, not of correlation times or relative time scales.Strictly-outward spectral transfer is a characteristic of Saffman's approximation, and this may be an accurate description only when dissipation suppresses the contributions from inwardly directed spectral transfer. In the spectral region where dominance passes from convection to dissipation, one can generate expressions for the parameters that arise in Saffman's approximation. Their numerical evaluation by computer simulation may enable one to sharpen the limits that Saffman had already set for those parameters.

Numerical modelling of MHD waves in the solar chromosphere

2005 ◽  
Vol 364 (1839) ◽  
pp. 395-404 ◽  
Author(s):  
Mats Carlsson ◽  
Thomas J Bogdan
Keyword(s):  
Magnetic Field ◽  
Acoustic Waves ◽  
Mode Conversion ◽  
Three Dimensions ◽  
Mhd Waves ◽  
Solar Chromosphere ◽  
Fast Mode ◽  
Reflected Waves ◽  
The Waves ◽  
The Magnetic Field

Acoustic waves are generated by the convective motions in the solar convection zone. When propagating upwards into the chromosphere they reach the height where the sound speed equals the Alfvén speed and they undergo mode conversion, refraction and reflection. We use numerical simulations to study these processes in realistic configurations where the wavelength of the waves is similar to the length scales of the magnetic field. Even though this regime is outside the validity of previous analytic studies or studies using ray-tracing theory, we show that some of their basic results remain valid: the critical quantity for mode conversion is the angle between the magnetic field and the k-vector: the attack angle. At angles smaller than 30° much of the acoustic, fast mode from the photosphere is transmitted as an acoustic, slow mode propagating along the field lines. At larger angles, most of the energy is refracted/reflected and returns as a fast mode creating an interference pattern between the upward and downward propagating waves. In three-dimensions, this interference between waves at small angles creates patterns with large horizontal phase speeds, especially close to magnetic field concentrations. When damping from shock dissipation and radiation is taken into account, the waves in the low–mid chromosphere have mostly the character of upward propagating acoustic waves and it is only close to the reflecting layer we get similar amplitudes for the upward propagating and refracted/reflected waves. The oscillatory power is suppressed in magnetic field concentrations and enhanced in ring-formed patterns around them. The complex interference patterns caused by mode-conversion, refraction and reflection, even with simple incident waves and in simple magnetic field geometries, make direct inversion of observables exceedingly difficult. In a dynamic chromosphere it is doubtful if the determination of mean quantities is even meaningful.

scholarly journals Theory of magnetic reconnection in solar and astrophysical plasmas

2012 ◽  
Vol 370 (1970) ◽  
pp. 3169-3192 ◽  
Author(s):  
David I. Pontin
Keyword(s):  
Magnetic Field ◽  
Magnetic Reconnection ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Astrophysical Plasmas ◽  
Current State ◽  
Fundamental Process ◽  
Recent Developments ◽  
The Magnetic Field ◽  
Theoretical Results

Magnetic reconnection is a fundamental process in a plasma that facilitates the release of energy stored in the magnetic field by permitting a change in the magnetic topology. In this paper, we present a review of the current state of understanding of magnetic reconnection. We discuss theoretical results regarding the formation of current sheets in complex three-dimensional magnetic fields and describe the fundamental differences between reconnection in two and three dimensions. We go on to outline recent developments in modelling of reconnection with kinetic theory, as well as in the magnetohydrodynamic framework where a number of new three-dimensional reconnection regimes have been identified. We discuss evidence from observations and simulations of Solar System plasmas that support this theory and summarize some prominent locations in which this new reconnection theory is relevant in astrophysical plasmas.

scholarly journals Transport properties through graphene with sequence of alternative magnetic barriers and wells in the presence of time-periodic scalar potential

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Fatemeh Pakdel ◽  
Mohammad Ali Maleki
Keyword(s):  
Magnetic Field ◽  
Transport Properties ◽  
Potential Barrier ◽  
Scalar Potential ◽  
Angle Of Incidence ◽  
Matrix Formalism ◽  
Oscillating Potential ◽  
Filtering Effect ◽  
Magnetic Barriers ◽  
The Magnetic Field

AbstractWe investigate the electronic transport properties of a graphene sheet under the magnetic barriers and wells through the oscillating scalar potential combined with the static scalar potential barrier having two types of uniform and alternative profiles. We compute the total sideband transmission of the system by additional sidebands at energy, in presence of oscillating potential, $$V_1$$ V 1 , using the transfer-matrix formalism and the Floquet sidebands series. The oscillating potential, generally, suppresses the Klein tunneling and the confinement of the charge carriers. In the absence of $$V_1$$ V 1 , both profiles show the wave vector filtering effect for the carriers by controlling the energy E relative to the potential barrier height, $$V_0$$ V 0 . The $$(N-1)$$ ( N - 1 ) -fold resonance splittings are observed through a region around $$E=V_0$$ E = V 0 with reduction of the transmission. The transmission vanishes in this region upon increasing the number of magnetic blocks N, strength of the magnetic field B in both configurations. We present an estimate relation for the width of the reduction region expressed in terms of E, $$V_0$$ V 0 , B and the angle of incidence of the quasiparticles. We observe, in the second profile, $$(N-1)$$ ( N - 1 ) -fold resonances in the transmission for special values of $$E=V_0$$ E = V 0 with a separation depending on the width of the magnetic blocks. The magnetic field and the width of the magnetic blocks have critical values, where the transmission reduces to zero. All the features observed in the transmission reflect to the conductance. In both configurations, there are some peaks in the conductance corresponding to the resonances of the transmission. The oscillations of the conductance are obtained which was observed in the experimental results. We, also, find the possibility for switching the transport properties of the system by changing the characteristic parameters of the magnetic system.

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