scholarly journals Stability of Compressible Hollow Jet Pervaded by a Transverse Varying Magnetic Field

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Samia S. Elazab ◽  
Samy A. Rahman ◽  
Alfaisal A. Hasan ◽  
Nehad A. Zidan
Keyword(s):  
Magnetic Field ◽  
Capillary Force ◽  
Electromagnetic Force ◽  
Transverse Field ◽  
Singular Solutions ◽  
Uniform Field ◽  
Axial Field ◽  
Axisymmetric Perturbation ◽  
Basic Equations ◽  
Stable Domains

The magnetohydrodynamic stability of an ordinary compressible hollow cylinder pervaded by a transverse varying magnetic field, under the influence of capillary, inertia, and Lorentz force, has been developed. The problem is modelized. The basic equations formulated, solved, and, upon applying appropriate boundary conditions, the singular solutions are excluded. The eigenvalue relation has been derived and discussed. The capillary force has destabilizing influence only for long wavelengths in the axisymmetric perturbation but it is stabilizing in the rest and also so in the nonaxisymmetric perturbations. The compressibility increases the stable domains and simultaneously decreases those of instability. The electromagnetic force has different effects due to the axial uniform field and varying transverse one. The axial field is stabilizing for all wavelengths in all kinds of perturbations. The transverse field is stabilizing or not according to restrictions. Here, the high compressibility increases rapidly the magnetodynamic stable domains and leads to shrinking those of instability.

Magnetohydrodynamic stability of a streaming gas jet

1993 ◽  
Vol 49 (1) ◽  
pp. 3-15
Author(s):  
Samia S. Elazab
Keyword(s):  
Magnetic Field ◽  
Capillary Force ◽  
Electromagnetic Force ◽  
Radial Distance ◽  
Gas Jet ◽  
Axisymmetric Perturbation ◽  
Mhd Stability ◽  
The Magnetic Field

The MHD stability of a gas jet surrounded by a streaming radially finite liquid cylinder (with solid cylindrical edge) is studied. The system is acted upon by capillary, electromagnetic and inertial liquid forces. The eigenvalue relation is established to all kinds of perturbations. The streaming has a strong destabilizing influence that is independent of all problem parameters. The capillary force is destabilizing only for small axisymmetric modes and stable for the rest. The electromagnetic force is strongly stabilizing whatever the intensities of the magnetic field. If the influence of the latter is sufficiently strong, the influence of the streaming can be completely suppressed. It is found that for an axisymmetric perturbation the domain of instability is the same whatever the value of the liquid radial distance.

scholarly journals Magnetohydrodynamic Stability of Streaming Jet Pervaded Internally by Varying Transverse Magnetic Field

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Alfaisal A. Hasan
Keyword(s):  
Magnetic Field ◽  
Numerical Analysis ◽  
Transverse Magnetic Field ◽  
Capillary Force ◽  
Present Model ◽  
Transverse Magnetic ◽  
Exterior Field ◽  
Stabilizing Effect ◽  
Basic Equations ◽  
The Stability

The Magnetohydrodynamic stability of a streaming cylindrical model penetrated by varying transverse magnetic field has been discussed. The problem is formulated, the basic equations are solved, upon appropriate boundary conditions the eigenvalue relation is derived and discussed analytically, and the results are verified numerically. The capillary force is destabilizing in a small axisymmetric domain and stabilizing otherwise. The streaming has a strong destabilizing effect in all kinds of perturbation. The toroidal varying magnetic field interior the fluid has no direct effect at all on the stability of the fluid column. The axial exterior field has strong stabilizing effect on the model. The effect of all acting forces altogether could be identified via the numerical analysis of the stability theory of the present model.

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 The Combined Effect of Rotation and Magnetic Field on Finite-Amplitude Thermal Convection

1973 ◽  
Vol 26 (5) ◽  
pp. 617 ◽  
Author(s):  
R Van der Borght ◽  
JO Murphy
Keyword(s):  
Magnetic Field ◽  
Mean Field ◽  
Field Approximation ◽  
Finite Amplitude ◽  
Combined Effect ◽  
Mean Field Approximation ◽  
Free Boundaries ◽  
Wide Range ◽  
The Mean ◽  
Basic Equations

The combined effect of an imposed rotation and magnetic field on convective transfer in a horizontal Boussinesq layer of fluid heated from below is studied in the mean field approximation. The basic equations are derived by a variational technique and their solutions are then found over a wide range of conditions, in the case of free boundaries, by numerical and analytic techniques, in particular by asymptotic and perturbation methods. The results obtained by the different techniques are shown to be in excellent agreement. As for the linear theory, the calculations predict that the simultaneous presence' of a magnetic field and rotation may produce conflicting tendencies.

Schwingung eines Plasmazylinders in einem äußeren Magnetfeld

1957 ◽  
Vol 12 (10) ◽  
pp. 815-821 ◽  
Author(s):  
K. Körper
Keyword(s):  
Magnetic Field ◽  
Axial Direction ◽  
Homogeneous Magnetic Field ◽  
Index Of Refraction ◽  
Infinite Length ◽  
Induced Current ◽  
Resonance Frequencies ◽  
Small Density ◽  
Basic Equations ◽  
Hydromagnetic Waves

Es werden die durch elektromagnetische Strahlung erregten Schwingungen einer kreiszylindrischen, homogenen, unendlich langen, einem homogenen axialen statischen Magnetfeld ausgesetzten Plasmasäule behandelt. Die zwei möglichen Schwingungstypen lassen sich durch die Richtung des im Plasma induzierten Stromes relativ zum Magnetfeld unterscheiden. Bei Strömen parallel zum Magnetfeld werden die Schwingungen durch den EccLEsschen Brechungsindex charakterisiert. Ströme senkrecht zum Magnetfeld liefern einen Brechungsindex, der zwei von der Teilchendichte des Plasmas und dem statischen Magnetfeld abhängige Resonanzfrequenzen (Ionenresonanz, Elektronenresonanz) besitzt. Dieser Brechungsindex geht für kleine Frequenzen in den für magnetohydrodynamische Wellen über. — Aus den Grundgleichungen wird der Energiesatz des Plasmas hergeleitet; er enthält neben der elektromagnetischen Strahlungsleistung, der JOULESchen Wärme und den Zeitableitungen der elektrischen und magnetischen Energiedichte noch die der kinetischen Energien der Elektronen und Ionen.The oscillations of a plasma cylinder of infinite length have been analyzed. The plasma is assumed to be homogeneous and to be exposed to a static homogeneous magnetic field in axial direction. There are two different types of oscillations. In one case the induced current is parallel to the magnetic field, and is therefore not influenced by it. In the other case where the induced current is perpendicular to the field two resonance frequencies exist. In the limit of small density and high magnetic field these are the gyrofrequencies of the iones and the electrons. The index of refraction for both types in the limit of small frequencies is that of the “hydromagnetic waves”. — From the basic equations the energy conservation theorem is derived. Besides the usual terms giving the electromagnetic radiation, JOULE’S losses, the electromagnetic energy density, it contains the kinetic energy of the ions and electrons of the plasma.

scholarly journals A Supernova at 50 PC: Effects on the Earth’s Atmosphere and Biota

2017 ◽  
Author(s):  
A.L Melott ◽  
B.C. Thomas ◽  
M. Kachelrieß ◽  
D.V. Semikoz ◽  
A.C. Overholt
Keyword(s):  
Magnetic Field ◽  
Transverse Field ◽  
Cosmic Ray ◽  
Magnetic Field Effects ◽  
Field Orientation ◽  
Local Bubble ◽  
Coherent Field ◽  
Computational Procedures ◽  
Cosmic Ray Flux ◽  
Disordered Magnetic

ABSTRACTRecent 60Fe results have suggested that the estimated distances of supernovae in the last few million years should be reduced from ∼100 pc to ∼50 pc. Two events or series of events are suggested, one about 2.7 million years to 1.7 million years ago, and another may at 6.5 to 8.7 million years ago. We ask what effects such supernovae are expected to have on the terrestrial atmosphere and biota. Assuming that the Local Bubble was formed before the event being considered, and that the supernova and the Earth were both inside a weak, disordered magnetic field at that time, TeV-PeV cosmic rays at Earth will increase by a factor of a few hundred. Tropospheric ionization will increase proportionately, and the overall muon radiation load on terrestrial organisms will increase by a factor of ∼150. All return to pre-burst levels within 10kyr. In the case of an ordered magnetic field, effects depend strongly on the field orientation. The upper bound in this case is with a largely coherent field aligned along the line of sight to the supernova, in which case TeV-PeV cosmic ray flux increases are ∼104; in the case of a transverse field they are below current levels. We suggest a substantial increase in the extended effects of supernovae on Earth and in the “lethal distance” estimate; more work is needed. This paper is an explicit followup to Thomas et al. (2016). We also here provide more detail on the computational procedures used in both works.

The Theory of Special Relativity

2017 ◽  
Author(s):  
Hanoch Gutfreund ◽  
Jürgen Renn
Keyword(s):  
Electromagnetic Field ◽  
Special Relativity ◽  
Euler Equations ◽  
Lorentz Transformation ◽  
Electromagnetic Force ◽  
Momentum Tensor ◽  
Perfect Fluids ◽  
Dimensional Spacetime ◽  
Tensor Formulation ◽  
Basic Equations

This chapter shows how the principle of special relativity and the principle of the constancy of the velocity of light uniquely determine the Lorentz transformation. Unlike in pre-relativity physics, space and time are not separate entities. They are combined into a four-dimensional spacetime continuum, which is most clearly demonstrated in the formulation of the theory of special relativity due to Hermann Minkowski. The chapter then defines vectors and tensors with respect to the Lorentz transformation, leading to a tensor formulation of Maxwell's equations, of the electromagnetic force acting on charges and currents, and of the energy-momentum of the electromagnetic field and its conservation law. It also introduces the energy-momentum tensor of matter and discusses the basic equations of the hydrodynamics of perfect fluids (the Euler equations).

Evaluation of an elliptically polarized undulator for the future Taiwan Photon Source

2021 ◽  
Vol 16 (12) ◽  
pp. P12017
Author(s):  
H.-W. Luo ◽  
T.-Y. Chung ◽  
C.-H. Lee ◽  
C.-S. Hwang
Keyword(s):  
Magnetic Field ◽  
Electron Beam ◽  
Synchrotron Radiation ◽  
Transverse Field ◽  
Longitudinal Direction ◽  
X Ray ◽  
Elliptically Polarized ◽  
Transverse Position ◽  
Photon Source ◽  
Field Integral

Abstract The resonant photon energy of an adjustable-phase undulator (APU) is varied with the relative motion of the magnet arrays along the longitudinal direction. There exists, however, a transverse field gradient (TFG) of order 100 T/m in an APU of small gap (∼10 mm). Whereas the TFG might affect the electron beam as it contributes to the dynamic field integral and the radiation integrals, the TFG might also degrade the performance of the synchrotron radiation due to the transverse position-dependent magnetic field. The effects of the TFG on the present Taiwan Photon Source (TPS) and future TPS-upgraded are analyzed to investigate the feasibility of an APU that operates in the soft x-ray region.

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