Magnetomechanical Instabilities in Elastic-Plastic Cylinders, Part I: Elastic Response

1996 ◽  
Vol 63 (3) ◽  
pp. 734-741 ◽  
Author(s):  
D. L. Littlefield
Keyword(s):  
Magnetic Field ◽  
Electromagnetic Fields ◽  
Threshold Value ◽  
Substantial Effect ◽  
Elastic Response ◽  
Linear Perturbation ◽  
Azimuthal Magnetic Field ◽  
Physical Mechanisms ◽  
Linear Perturbation Theory ◽  
The Stability

The effects of electromagnetic fields on instabilities in metal cylinders are considered in this analysis. The cylinder is assumed to be infinitely long and perfectly conducting. An axial electric current is introduced in the cylinder, giving rise to an azimuthal magnetic field in the surrounding vacuum, causing mechanical distortion in the cylinder. The current is assumed to be small so that the deformation remains elastic; in an accompanying paper (Littlefield, 1996) larger currents are considered where plastic flow becomes important. After solutions to the idealized motion of the cylinder under uniaxial strain conditions are developed, small perturbations to the motion are considered. The equations governing the motion of these disturbances are derived using linear perturbation theory. Solutions to the equations indicate that electromagnetic fields can have a substantial effect on the stability spectrum in the cylinder. In general, the frequency of oscillating perturbations is suppressed by the azimuthal magnetic field, and distending instabilities are possible if the magnetic field is above a threshold value. The underlying physical mechanisms contributing to these deviations are proposed.

The Instability of a Viscoelastic Conducting Cylindrical Interface Supporting Free-surface Currents

2002 ◽  
Vol 57 (3-4) ◽  
pp. 159-176 ◽  
Author(s):  
Yusry O. El-Dib ◽  
Galal M. Moatimid
Keyword(s):  
Magnetic Field ◽  
Free Surface ◽  
Perturbation Technique ◽  
Linear Perturbation ◽  
Surface Currents ◽  
Azimuthal Magnetic Field ◽  
Special Cases ◽  
Viscoelastic Effects ◽  
The Stability ◽  
Complex Coefficients

The stability of a viscoelastic interface acted upon by an oscillating azimuthal magnetic field is studied. The interface separates two rigid magnetic fluid columns. Only azimuthal disturbrance modes are considered in a linear perturbation technique. Weak viscoelastic effects are taken into consideration, so that their contributions are demonstrated in the boundary conditions. The presence or absence of free surface currents resulted in a dispersion equation with complex coefficients of the Mathieu type. It is found that the surface currents disappear when the stratified magnetic field becomes unity. The phenomenon of coupled resonance is observed. Several special cases are reported. A set of graphs are drawn to illustrate the influence of the various parameters on the stability of the considered system.

scholarly journals Spiral-arm instability – III. Fragmentation of primordial protostellar discs

2019 ◽  
Vol 491 (1) ◽  
pp. L24-L28 ◽  
Author(s):  
Shigeki Inoue ◽  
Naoki Yoshida
Keyword(s):  
Gravitational Instability ◽  
Finite Thickness ◽  
Linear Perturbation ◽  
Gas Cooling ◽  
Formation And Evolution ◽  
Linear Perturbation Theory ◽  
The Stability ◽  
Protostellar Discs ◽  
Self Gravity ◽  
Spiral Arm

ABSTRACT We study the gravitational instability and fragmentation of primordial protostellar discs by using high-resolution cosmological hydrodynamics simulations. We follow the formation and evolution of spiral arms in protostellar discs, examine the dynamical stability, and identify a physical mechanism of secondary protostar formation. We use linear perturbation theory based on the spiral-arm instability (SAI) analysis in our previous studies. We improve the analysis by incorporating the effects of finite thickness and shearing motion of arms, and derive the physical conditions for SAI in protostellar discs. Our analysis predicts accurately the stability and the onset of arm fragmentation that is determined by the balance between self-gravity and gas pressure plus the Coriolis force. Formation of secondary and multiple protostars in the discs is explained by the SAI, which is driven by self-gravity and thus can operate without rapid gas cooling. We can also predict the typical mass of the fragments, which is found to be in good agreement with the actual masses of secondary protostars formed in the simulation.

The instability of a pinched fluid with a longitudinal magnetic field

1958 ◽  
Vol 245 (1241) ◽  
pp. 222-237 ◽  
Keyword(s):  
Magnetic Field ◽  
Longitudinal Magnetic Field ◽  
Short Wave ◽  
Longitudinal Field ◽  
Plasma Equilibrium ◽  
Azimuthal Magnetic Field ◽  
Long Wave ◽  
Pinched Plasma ◽  
Pinch Current ◽  
The Stability

The stability of a pinched plasma equilibrium with a longitudinal magnetic field superimposed on the characteristic azimuthal magnetic field of the pinch current is studied theoretically. The linearized solutions are developed as helical perturbations of the plasma surface, and the behaviour of these is given for the different cases of uniform longitudinal, longitudinal field zero inside the plasma, and for helices of the same and opposite sense to the helix which describes the total magnetic field. Approximately, the conclusions are: that the longitudinal field has the effect of stabilizing short-wave perturbations, but that some long-wave perturbations remain unstable no matter how large the externally imposed longitudinal magnetic field.

Instabilities of Steady, Periodic, and Quasi-Periodic Modes of Convection in Porous Media

1987 ◽  
Vol 109 (2) ◽  
pp. 350-355 ◽  
Author(s):  
S. Kimura ◽  
G. Schubert ◽  
J. M. Straus
Keyword(s):  
Saturated Porous Medium ◽  
Temporal Frequency ◽  
Time Dependent ◽  
Linear Perturbation ◽  
Complex Eigenvalue ◽  
Periodic State ◽  
Linearized System ◽  
Linear Perturbation Theory ◽  
The Stability ◽  
Convection In Porous Media

Instabilities of steady and time-dependent thermal convection in a fluid-saturated porous medium heated from below have been studied using linear perturbation theory. The stability of steady-state solutions of the governing equations (obtained numerically) has been analyzed by evaluating the eigenvalues of the linearized system of equations describing the temporal behavior of infinitesimal perturbations. Using this procedure, we have found that time-dependent convection in a square cell sets in at Rayleigh number Ra=390. The temporal frequency of the simply periodic (P(1)) convection at Rayleigh numbers exceeding this value is given by the imaginary part of the complex eigenvalue. The stability of this (P(1)) state has also been studied; transition to quasi-periodic convection (QP2) occurs at Ra ≈ 510. A reverse transition to a simply periodic state (P(2)) occurs at Ra ≈ 560; a slight jump in the frequency of the P(2) state occurs at Ra between 625 and 640. The jump coincides with a second narrow (in terms of Ra) region of quasi-periodicity.

scholarly journals Stability of nonaxisymmetric ferrofluid flow in rotating cylinders with magnetic field

2005 ◽  
Vol 2005 (23) ◽  
pp. 3727-3737 ◽  
Author(s):  
Jitender Singh ◽  
Renu Bajaj
Keyword(s):  
Magnetic Field ◽  
Applied Magnetic Field ◽  
Critical Value ◽  
Annular Space ◽  
Rotating Cylinders ◽  
The Stability

Effect of an axially applied magnetic field on the stability of a ferrofluid flow in an annular space between two coaxially rotating cylinders with nonaxisymmetric disturbances has been investigated numerically. The critical value of the ratioΩ∗of angular speeds of the two cylinders, at the onset of the first nonaxisymmetric mode of disturbance, has been observed to be affected by the applied magnetic field.

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

Data ◽  
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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