Steady‐State Theory of a Discharge Column in a Magnetic Field: Separable Solutions for a Finite Cylinder

1972 ◽  
Vol 43 (6) ◽  
pp. 2620-2623 ◽  
Author(s):  
D. B. Ilić ◽  
S. A. Self
Keyword(s):  
Magnetic Field ◽  
Steady State ◽  
State Theory ◽  
Finite Cylinder ◽  
Discharge Column

Particle balance in a steady state plasma in a dipole magnetic field

2019 ◽  
Vol 1 (4) ◽  
pp. 045005 ◽  
Author(s):  
Anuj Ram Baitha ◽  
Ayesha Nanda ◽  
Sargam Hunjan ◽  
Sudeep Bhattacharjee
Keyword(s):  
Magnetic Field ◽  
Steady State ◽  
Dipole Magnetic Field ◽  
Particle Balance ◽  
State Plasma

scholarly journals Magnetoactive elastomers for magnetically tunable vibrating sensor systems

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Tatiana I. Becker ◽  
Yuriy L. Raikher ◽  
Oleg V. Stolbov ◽  
Valter Böhm ◽  
Klaus Zimmermann
Keyword(s):  
Magnetic Field ◽  
Steady State ◽  
Smart Materials ◽  
Excitation Frequency ◽  
Experimental Studies ◽  
Uniform Field ◽  
Sensor Systems ◽  
Ongoing Research ◽  
Amplification Ratio ◽  
Field Distortion

Abstract Magnetoactive elastomers (MAEs) are a special type of smart materials consisting of an elastic matrix with embedded microsized particles that are made of ferromagnetic materials with high or low coercivity. Due to their composition, such elastomers possess unique magnetic field-dependent material properties. The present paper compiles the results of investigations on MAEs towards an approach of their potential application as vibrating sensor elements with adaptable sensitivity. Starting with the model-based and experimental studies of the free vibrational behavior displayed by cantilevers made of MAEs, it is shown that the first bending eigenfrequency of the cantilevers depends strongly on the strength of an applied uniform magnetic field. The investigations of the forced vibration response of MAE beams subjected to in-plane kinematic excitation confirm the possibility of active magnetic control of the amplitude-frequency characteristics. With change of the uniform field strength, the MAE beam reveals different steady-state responses for the same excitation, and the resonance may occur at various ranges of the excitation frequency. Nonlinear dependencies of the amplification ratio on the excitation frequency are obtained for different magnitudes of the applied field. Furthermore, it is shown that the steady-state vibrations of MAE beams can be detected based on the magnetic field distortion. The field difference, which is measured simultaneously on the sides of a vibrating MAE beam, provides a signal with the same frequency as the excitation and an amplitude proportional to the amplitude of resulting vibrations. The presented prototype of the MAE-based vibrating unit with the field-controlled “configuration” can be implemented for realization of acceleration sensor systems with adaptable sensitivity. The ongoing research on MAEs is oriented to the use of other geometrical forms along with beams, e.g. two-dimensional structures such as membranes.

scholarly journals Mapping of steady-state electric fields and convective drifts in geomagnetic fields – Part 1: Elementary models

2016 ◽  
Vol 34 (1) ◽  
pp. 55-65 ◽  
Author(s):  
A. D. M. Walker ◽  
G. J. Sofko
Keyword(s):  
Magnetic Field ◽  
Steady State ◽  
Electric Field ◽  
Electric Fields ◽  
Magnetic Field Line ◽  
Geomagnetic Field ◽  
Geomagnetic Field Models ◽  
Spatial Derivatives ◽  
Field Lines ◽  
The Magnetic Field

Abstract. When studying magnetospheric convection, it is often necessary to map the steady-state electric field, measured at some point on a magnetic field line, to a magnetically conjugate point in the other hemisphere, or the equatorial plane, or at the position of a satellite. Such mapping is relatively easy in a dipole field although the appropriate formulae are not easily accessible. They are derived and reviewed here with some examples. It is not possible to derive such formulae in more realistic geomagnetic field models. A new method is described in this paper for accurate mapping of electric fields along field lines, which can be used for any field model in which the magnetic field and its spatial derivatives can be computed. From the spatial derivatives of the magnetic field three first order differential equations are derived for the components of the normalized element of separation of two closely spaced field lines. These can be integrated along with the magnetic field tracing equations and Faraday's law used to obtain the electric field as a function of distance measured along the magnetic field line. The method is tested in a simple model consisting of a dipole field plus a magnetotail model. The method is shown to be accurate, convenient, and suitable for use with more realistic geomagnetic field models.

scholarly journals Levitation of non-magnetizable droplet inside ferrofluid

2018 ◽  
Vol 857 ◽  
pp. 398-448 ◽  
Author(s):  
Chamkor Singh ◽  
Arup K. Das ◽  
Prasanta K. Das
Keyword(s):  
Magnetic Field ◽  
Steady State ◽  
Viscosity Ratio ◽  
Temporal Dynamics ◽  
Liquid Droplet ◽  
Droplet Surface ◽  
Two Dimensions ◽  
Projection Algorithm ◽  
The Stability ◽  
The Individual

The central theme of this work is that a stable levitation of a denser non-magnetizable liquid droplet, against gravity, inside a relatively lighter ferrofluid – a system barely considered in ferrohydrodynamics – is possible, and exhibits unique interfacial features; the stability of the levitation trajectory, however, is subject to an appropriate magnetic field modulation. We explore the shapes and the temporal dynamics of a plane non-magnetizable droplet levitating inside a ferrofluid against gravity due to a spatially complex, but systematically generated, magnetic field in two dimensions. The coupled set of Maxwell’s magnetostatic equations and the flow dynamic equations is integrated computationally, utilizing a conservative finite-volume-based second-order pressure projection algorithm combined with the front-tracking algorithm for the advection of the interface of the droplet. The dynamics of the droplet is studied under both the constant ferrofluid magnetic permeability assumption as well as for more realistic field-dependent permeability described by Langevin’s nonlinear magnetization model. Due to the non-homogeneous nature of the magnetic field, unique shapes of the droplet during its levitation, and at its steady state, are realized. The complete spatio-temporal response of the droplet is a function of the Laplace number $La$ , the magnetic Laplace number $La_{m}$ and the Galilei number $Ga$ ; through detailed simulations we separate out the individual roles played by these non-dimensional parameters. The effect of the viscosity ratio, the stability of the levitation path and the possibility of existence of multiple stable equilibrium states is investigated. We find, for certain conditions on the viscosity ratio, that there can be developments of cusps and singularities at the droplet surface; we also observe this phenomenon experimentally and compare with the simulations. Our simulations closely replicate the singular projection on the surface of the levitating droplet. Finally, we present a dynamical model for the vertical trajectory of the droplet. This model reveals a condition for the onset of levitation and the relation for the equilibrium levitation height. The linearization of the model around the steady state captures that the nature of the equilibrium point goes under a transition from being a spiral to a node depending upon the control parameters, which essentially means that the temporal route to the equilibrium can be either monotonic or undulating. The analytical model for the droplet trajectory is in close agreement with the detailed simulations.

Non-steady-state stimulated scattering: a convenient solution in terms of convolution integrals

1977 ◽  
Vol 352 (1671) ◽  
pp. 539-555
Keyword(s):  
Steady State ◽  
Input Pulse ◽  
State Theory ◽  
Spatial Modulation ◽  
Bragg Angle ◽  
Stimulated Scattering ◽  
Scattering Spectrum ◽  
Convolution Integrals ◽  
Beam Incident ◽  
Scattered Beam

A non-steady-state theory of stimulated light scattering, which places particular emphasis on the effects induced in the scattering medium, is developed. It is shown that a spatial modulation of the dielectric constant is induced whose amplitude and phase can be expressed in terms of simple convolution integrals. These involve only the input pulse shape, the steady-state scattering spectrum and the frequency shift between the laser and scattered beams. The effect of the induced modulation on the scattered beam and on any weak independent beam incident at the Bragg angle is also considered.

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