ON AXIALLY SYMMETRIC ELECTRIC CURRENT INDUCED IN A CYLINDER UNDER A LINE SOURCE

Geophysics ◽  
1973 ◽  
Vol 38 (5) ◽  
pp. 971-974 ◽  
Author(s):  
Shri Krishna Singh
Keyword(s):  
Magnetic Field ◽  
Electric Current ◽  
Short Note ◽  
Cylindrical Wave ◽  
Wave Functions ◽  
Static Case ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Axially Symmetric ◽  
Infinite Line

An infinite conducting cylinder excited by an infinite line current located outside the cylinder is a useful model in the interpretation of electromagnetic prospecting data. Several authors, with geophysical applications in mind, have considered the problem of the source being parallel to the axis of the cylinder (Wait, 1952; Negi et al., 1972). In the latter paper, the cylinder is surrounded by a shell; conductivity of both the cylinder and the shell is a function of radius. The secondary fields are written in the form of an infinite series of cylindrical wave functions. This solution is then specialized to the quasi‐static case. For reasons not explained, the authors neglect the n = 0 term. In this short note, computed results are presented which show that the contribution from the n = 0 term (corresponding to an axially symmetric electric current induced in the cylinder causing a transverse secondary magnetic field outside) is significant and must be taken into account for the two‐dimensional problem.

Motion of a charged particle in superposed Heliotron and biconical cusp fields

1969 ◽  
Vol 3 (2) ◽  
pp. 255-267 ◽  
Author(s):  
M. P. Srivastava ◽  
P. K. Bhat
Keyword(s):  
Magnetic Field ◽  
Charged Particle ◽  
Magnetic Moment ◽  
Particle Trajectory ◽  
Three Dimensional ◽  
Equation Of Motion ◽  
Neutral Point ◽  
Two Dimensional ◽  
Axially Symmetric ◽  
Hybrid Type

We have studied the behaviour of a charged particle in an axially symmetric magnetic field having a neutral point, so as to find a possibility of confining a charged particle in a thermonuclear device. In order to study the motion we have reduced a three-dimensional motion to a two-dimensional one by introducing a fictitious potential. Following Schmidt we have classified the motion, as an ‘off-axis motion’ and ‘encircling motion’ depending on the behaviour of this potential. We see that the particle performs a hybrid type of motion in the negative z-axis, i.e. at some instant it is in ‘off-axis motion’ while at another instant it is in ‘encircling motion’. We have also solved the equation of motion numerically and the graphs of the particle trajectory verify our analysis. We find that in most of the cases the particle is contained. The magnetic moment is found to be moderately adiabatic.

On: “Time‐Dependent Electromagnetic Fields of an Infinite, Conducting Cylinder Excited by a Long Current‐Carrying Cable” by S. K. Verma (GEOPHYSICS, April 1973, p. 369–379)

Geophysics ◽  
1974 ◽  
Vol 39 (3) ◽  
pp. 355-355
Author(s):  
Shri Krishna Singh
Keyword(s):  
Magnetic Field ◽  
Frequency Domain ◽  
Electric Current ◽  
Electromagnetic Fields ◽  
Time Domain ◽  
Static Solution ◽  
Transverse Magnetic ◽  
Time Dependent ◽  
Axially Symmetric ◽  
The Time Domain

In this paper Verma obtains a time‐domain solution by inverting the frequency‐domain solution given by Wait (1952). However, it has been recently pointed out by Singh (1973a) (see also Wait, 1973) that there is an error in the quasi‐static solution of Wait. Wait neglected the axially symmetric inducted electric current in the cylinder giving rise to a secondary transverse magnetic field outside (the n=0 term in the scattered wavefield). Singh (1973a) has shown that this term dominates. [It should be noted that Wait in his other works on the cylinder retains this term (e.g., Wait, 1959).] It is clear that this term would be dominant in the time‐domain also. This has been shown by Singh (1972, 1973b). Since the theoretical solution given by Verma in the paper under discussion is incomplete, his interpretation schemes are meaningless.

A NOTE ON DIFFRACTION BY AN INFINITE SLIT

1960 ◽  
Vol 38 (1) ◽  
pp. 38-47 ◽  
Author(s):  
R. F. Millar
Keyword(s):  
Integral Equation ◽  
Normal Derivative ◽  
Cylindrical Wave ◽  
Narrow Slit ◽  
Angle Of Incidence ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Boundary Values ◽  
Transmission Coefficients ◽  
Differential Integral Equation

The two-dimensional problem of diffraction of a plane wave by a narrow slit is considered. The assumed boundary values on the screen are the vanishing of either the total wave function or its normal derivative. In the former case, a differential–integral equation is obtained for the unknown function in the slit; in the latter, a pure integral equation is found. Solutions to these equations are given in the form of series in powers of ε (where ε/π is the ratio of slit width to wavelength), the coefficients of which depend on log ε. Expressions are found for the transmission coefficients as functions of ε and the angle of incidence; these are compared with previous determinations of other authors.A brief outline is given for the treatment of diffraction of a cylindrical wave by the slit.

The effect of a strong magnetic field on two-dimensional flows of a conducting fluid

1963 ◽  
Vol 15 (3) ◽  
pp. 429-441 ◽  
Author(s):  
Stephen Childress
Keyword(s):  
Magnetic Field ◽  
Perturbation Technique ◽  
The Body ◽  
Conducting Fluid ◽  
Order Effects ◽  
Two Dimensional ◽  
Axially Symmetric ◽  
Exterior Region ◽  
Electrically Conducting ◽  
Higher Order Effects

The motion of a viscous, electrically conducting fluid past a finite two-dimensional obstacle is investigated. The magnetic field is assumed to be uniform and parallel to the velocity at infinity. By means of a perturbation technique, approximations valid for large values of the Hartmann number M are derived. It is found that, over any finite region, the flow field is characterized by the presence of shear layers fore and aft of the body. The limit attained over the exterior region represents the two-dimensional counterpart of the axially symmetric solution given by Chester (1961). Attention is focused on a number of nominally ‘higher-order’ effects, including the presence of two distinct boundary layers. The results hold only when M [Gt ] Re; Re = Reynolds number. However, a generalization of the procedure, in which the last assumption is relaxed, is suggested.

An experimental investigation of MHD quasi-two-dimensional turbulent shear flows

2002 ◽  
Vol 456 ◽  
pp. 137-159 ◽  
Author(s):  
KARIM MESSADEK ◽  
RENE MOREAU
Keyword(s):  
Magnetic Field ◽  
Energy Transfer ◽  
Turbulent Flow ◽  
Shear Layer ◽  
Electric Current ◽  
Turbulent Shear ◽  
Two Dimensional ◽  
Joule Dissipation ◽  
Layer Width ◽  
Wide Range

An extensive experimental study is carried out to examine the properties of a quasi-two-dimensional MHD turbulent shear flow. Axisymmetric shear of a mercury layer is enforced by the action of a steady vertical magnetic field and a radial horizontal electric current flowing between a ring set of electrodes and a cylindrical wall. This shear layer is unstable, and the properties of the turbulent flow are studied for a wide range of Hartmann (up to 1800) and Reynolds numbers (up to 106). The mean velocity profiles exhibit a turbulent free shear layer, of thickness larger than that predicted by the laminar theory by two orders of magnitude. The profiles yield the expected linear dependence between the total angular momentum and the electric current when the magnetic field is large enough, but demonstrate a systematic deviation when it is moderate (Ha [lsim ] 250). The quasi-two-dimensional turbulence is characterized by an energy transfer towards the large scales, which leads to a relatively small number of large coherent structures. The properties of these structures result from the competition between the energy transfer and the Joule dissipation within the Hartmann layers. In the intermediate range of wavenumbers (k[lscr ] < k < ki, where k[lscr ] is the integral-length-scale wavenumber and ki the injection wavenumber), the energy spectra exhibit a power law close to k−5/3 when the Joule dissipation is weak and close to k−3 when it is significant. The properties of the turbulent flow in this latter regime depend on only one non-dimensional parameter, the ratio (Ha/Re)(l⊥/h)2 (Ha is the Hartmann number, Re the Reynolds number based on the cell radius, l⊥ a typical transverse scale, and h the layer width).

scholarly journals The exact solutions of a (2 + 1)-dimensional Dirac oscillator under a magnetic field in the presence of a minimal length

2015 ◽  
Vol 93 (5) ◽  
pp. 542-548 ◽  
Author(s):  
Abdelmalek Boumali ◽  
Hassan Hassanabadi
Keyword(s):  
Magnetic Field ◽  
Exact Solutions ◽  
Momentum Space ◽  
Uniform Magnetic Field ◽  
Hypergeometric Functions ◽  
Minimal Length ◽  
Wave Functions ◽  
Two Dimensional ◽  
Dirac Oscillator ◽  
Energy Eigenvalues

Minimal length of a two-dimensional Dirac oscillator is investigated in the presence of a uniform magnetic field and illustrates the wave functions in the momentum space. The energy eigenvalues are found and the corresponding wave functions are calculated in terms of hypergeometric functions.

scholarly journals Two-dimensional boson oscillator under a magnetic field in the presence of a minimal length in the non-commutative space

2021 ◽  
Vol 67 (2 Mar-Apr) ◽  
pp. 226
Author(s):  
Z. Selema ◽  
A. Boumal
Keyword(s):  
Magnetic Field ◽  
Schrödinger Equation ◽  
Momentum Space ◽  
Schrodinger Equation ◽  
Minimal Length ◽  
Wave Functions ◽  
Two Dimensional ◽  
Commutative Space ◽  
Klein Gordon

Minimal length in non-commutative space of a two-dimensional Klein-Gordon oscillator isinvestigated and illustrates the wave functions in the momentum space. The eigensolutionsare found and the system is mapping to the well-known Schrodinger equation in a Pöschl-Teller potential.

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