Uniform growth rates for the magnetic field in a kinematic dynamo

2000 ◽  
Vol 33 (18) ◽  
pp. 3605-3611
Author(s):  
Manuel Núñez ◽  
Javier Sanz
Keyword(s):  
Magnetic Field ◽  
Growth Rates ◽  
Kinematic Dynamo ◽  
Uniform Growth ◽  
The Magnetic Field

Kinematic dynamo problem in a linear velocity field

1984 ◽  
Vol 144 ◽  
pp. 1-11 ◽  
Author(s):  
Ya. B. Zel'Dovich ◽  
A. A. Ruzmaikin ◽  
S. A. Molchanov ◽  
D. D. Sokoloff
Keyword(s):  
Magnetic Field ◽  
Spatial Distribution ◽  
Velocity Field ◽  
Random Matrix ◽  
Magnetic Energy ◽  
Linear Velocity ◽  
Finite Conductivity ◽  
Kinematic Dynamo ◽  
Linear Velocity Field ◽  
The Magnetic Field

A magnetic field is shown to be asymptotically (t → ∞) decaying in a flow of finite conductivity with v = Cr, where C = Cζ(t) is a random matrix. The decay is exponential, and its rate does not depend on the conductivity. However, the magnetic energy increases exponentially owing to growth of the domain occupied by the field. The spatial distribution of the magnetic field is a set of thin ropes and (or) layers.

Hydromagnetic wavelike instabilities in a rapidly rotating stratified fluid

1973 ◽  
Vol 61 (3) ◽  
pp. 609-624 ◽  
Author(s):  
D. J. Acheson
Keyword(s):  
Magnetic Field ◽  
Angular Velocity ◽  
Growth Rates ◽  
Homogeneous Model ◽  
Stratified Fluid ◽  
Generation Mechanism ◽  
Helmholtz Instability ◽  
Coaxial Cylinders ◽  
The Magnetic Field ◽  
Rotating Stratified Fluid

We examine the hydromagnetic stability of a radially stratified fluid rotating between two coaxial cylinders, with particular emphasis on the case when the angular velocity greatly exceeds both buoyant and Alfvén frequencies. If the magnetic field is predominantly azimuthal instabilities then have an essentially non-axisymmetric and wavelike character. Various bounds on their phase speeds and growth rates are derived, including a ‘quadrant’ theorem analogous to Howard's semicircle theorem for Kelvin–Helmholtz instability. Their strong tendency to propagate against the basic rotation (i.e. ‘westward’), previously noted by the author in the study of a more simplified (homogeneous) model, seems relatively insensitive to the generation mechanism (e.g. unstable gradient of magnetic field, angular velocity or density), but a number of counterexamples show that this constraint need not apply if the magnetic field displays significant spatial variations of direction as well as magnitude and that eastward-propagating amplifying modes are then possible.

Theory of Raman sidescatter from a magnetized plasma

1984 ◽  
Vol 32 (2) ◽  
pp. 331-346 ◽  
Author(s):  
H. C. Barr ◽  
T. J. M. Boyd ◽  
R. Rankin
Keyword(s):  
Magnetic Field ◽  
Electromagnetic Wave ◽  
Growth Rates ◽  
Scattered Light ◽  
Critical Density ◽  
Magnetized Plasma ◽  
Frequency Shifts ◽  
Wave Growth ◽  
Circularly Polarized ◽  
The Magnetic Field

The effects of a d.c. magnetic field on stimulated Raman sidescatter from laser-produced plasmas is studied. For exact sidescatter along the magnetic field, the Raman instability separates into two distinct decays in which the scattered light is either a right (RHCP) or left (LHCP) circularly polarized electromagnetic wave. Growth rates of the instabilities can be enhanced in the former case but are diminished in the latter. The magnetic field induced effects are greatest near the quarter critical density where frequency shifts can be especially significant, being equal to ± ¼Ωc for decay into RHCP and LHCP waves, respectively.

scholarly journals General Relativistic Mean-Field Dynamo Model for Proto-Neutron Stars

Universe ◽  
2020 ◽  
Vol 6 (6) ◽  
pp. 83 ◽  
Author(s):  
Kevin Franceschetti ◽  
Luca Del Zanna
Keyword(s):  
Magnetic Field ◽  
Neutron Stars ◽  
Growth Rates ◽  
Exponential Growth ◽  
Mean Field ◽  
Dynamo Model ◽  
Time Interval ◽  
General Relativistic ◽  
The Magnetic Field ◽  
Mean Field Dynamo

Neutron stars, and magnetars in particular, are known to host the strongest magnetic fields in the Universe. The origin of these strong fields is a matter of controversy. In this preliminary work, via numerical simulations, we study, for the first time in non-ideal general relativistic magnetohydrodynamic (GRMHD) regime, the growth of the magnetic field due to the action of the mean-field dynamo due to sub-scale, unresolved turbulence. The dynamo process, combined with the differential rotation of the (proto-)star, is able to produce an exponential growth of any initial magnetic seed field up to the values required to explain the observations. By varying the dynamo coefficient we obtain different growth rates. We find a quasi-linear dependence of the growth rates on the intensity of the dynamo. Furthermore, the time interval in which exponential growth occurs and the growth rates also seems to depend on the initial configuration of the magnetic field.

scholarly journals Magnetorotational instability in diamagnetic, misaligned protostellar discs

2019 ◽  
Vol 491 (4) ◽  
pp. 5481-5488
Author(s):  
Ebru Devlen ◽  
Ayse Ulubay ◽  
E Rennan Pekünlü
Keyword(s):  
Magnetic Field ◽  
Growth Rate ◽  
Growth Rates ◽  
Vertical Component ◽  
Radial Component ◽  
Magnetorotational Instability ◽  
Radial Gradient ◽  
Dipole Magnetic Field ◽  
Protostellar Discs ◽  
The Magnetic Field

ABSTRACT In this study, we addressed the question of how the growth rate of the magnetorotational instability is modified when the radial component of the stellar dipole magnetic field is taken into account in addition to the vertical component. Considering a fiducial radius in the disc where diamagnetic currents are pronounced, we carried out a linear stability analysis to obtain the growth rates of the magnetorotational instability for various parameters such as the ratio of the radial-to-vertical component and the gradient of the magnetic field, the Alfvenic Mach number, and the diamagnetization parameter. Our results show that the interaction between the diamagnetic current and the radial component of the magnetic field increases the growth rate of the magnetorotational instability and generates a force perpendicular to the disc plane that may induce a torque. It is also shown that considering the radial component of the magnetic field and taking into account a radial gradient in the vertical component of the magnetic field causes an increase in the magnitudes of the growth rates of both the axisymmetric (m = 0) and the non-axisymmetric (m = 1) modes.

scholarly journals Hydromagnetic Stability Analysis of a Partially Ionized Medium

2020 ◽  
pp. 53-57
Author(s):  
Pardeep Kumar ◽  
Hari Mohan
Keyword(s):  
Magnetic Field ◽  
Stability Analysis ◽  
Growth Rates ◽  
Variable Density ◽  
Composite Medium ◽  
Horizontal Magnetic Field ◽  
Stability And Instability ◽  
Stabilizing Effect ◽  
Rayleigh Taylor Instability ◽  
The Magnetic Field

Rayleigh-Taylor instability of a composite medium with variable density and viscosity is considered by taking into account the frictional effect of collisions of ionized with neutral atoms in the presence of a variable horizontal magnetic field. The criteria determining stability and instability are independent of the effects of viscosity and collisional effects. The magnetic field stabilizes the system which is otherwise unstable in the absence of the magnetic field. The viscosity of the medium has stabilizing as well as destabilizing effect on the growth rates. The collisional frequency has stabilizing effect on the growth rates, but has also destabilizing effect in some region.

scholarly journals On the connection between the magneto-elliptic and magneto-rotational instabilities

2012 ◽  
Vol 698 ◽  
pp. 358-373 ◽  
Author(s):  
Krzysztof A. Mizerski ◽  
Wladimir Lyra
Keyword(s):  
Magnetic Field ◽  
Angular Velocity ◽  
Shear Flow ◽  
Growth Rates ◽  
Radial Profile ◽  
Rotational Instability ◽  
Horizontal Instability ◽  
Flow Limit ◽  
Limiting Case ◽  
The Magnetic Field

AbstractIt has recently been suggested that the magneto-rotational instability (MRI) is a limiting case of the magneto-elliptic instability (MEI). This limit is obtained for horizontal modes in the presence of rotation and an external vertical magnetic field, when the aspect ratio of the elliptic streamlines tends to infinite. In this paper we unveil the link between these previously unconnected mechanisms, explaining both the MEI and the MRI as different manifestations of the same magneto-elliptic-rotational instability (MERI). The growth rates are found and the influence of the magnetic and rotational effects is explained, in particular the effect of the magnetic field on the range of negative Rossby numbers at which the horizontal instability is excited. Furthermore, we show how the horizontal rotational MEI in the rotating shear flow limit is linked to the MRI by the use of the local shearing box model, typically used in the study of accretion discs. In such a limit the growth rates of the two instability types coincide for any power-law-type background angular velocity radial profile with negative exponent corresponding to the value of the Rossby number of the rotating shear flow. The MRI requirement for instability is that the background angular velocity profile is a decreasing function of the distance from the centre of the disc, which corresponds to the horizontal rotational MEI requirement of negative Rossby numbers. Finally a physical interpretation of the horizontal instability, based on a balance between the strain, the Lorentz force and the Coriolis force, is given.

scholarly journals Kinematic dynamo action in large magnetic Reynolds number flows driven by shear and convection

2001 ◽  
Vol 435 ◽  
pp. 261-287 ◽  
Author(s):  
YANNICK PONTY ◽  
ANDREW D. GILBERT ◽  
ANDREW M. SOWARD
Keyword(s):  
Magnetic Field ◽  
Convective Instability ◽  
Lower Boundary ◽  
Ekman Layer ◽  
Magnetic Reynolds Number ◽  
Moving Frame ◽  
Dynamo Action ◽  
Kinematic Dynamo ◽  
Layer Flow ◽  
The Magnetic Field

A numerical investigation is presented of kinematic dynamo action in a dynamically driven fluid flow. The model isolates basic dynamo processes relevant to field generation in the Solar tachocline. The horizontal plane layer geometry adopted is chosen as the local representation of a differentially rotating spherical fluid shell at co-latitude ϑ; the unit vectors [xcirc ], ŷ and zˆ point east, north and vertically upwards respectively. Relative to axes moving easterly with the local bulk motion of the fluid the rotation vector Ω lies in the (y, z)-plane inclined at an angle ϑ to the z-axis, while the base of the layer moves with constant velocity in the x-direction. An Ekman layer is formed on the lower boundary characterized by a strong localized spiralling shear flow. This basic state is destabilized by a convective instability through uniform heating at the base of the layer, or by a purely hydrodynamic instability of the Ekman layer shear flow. The onset of instability is characterized by a horizontal wave vector inclined at some angle ∈ to the x-axis. Such motion is two-dimensional, dependent only on two spatial coordinates together with time. It is supposed that this two-dimensionality persists into the various fully nonlinear regimes in which we study large magnetic Reynolds number kinematic dynamo action.When the Ekman layer flow is destabilized hydrodynamically, the fluid flow that results is steady in an appropriately chosen moving frame, and takes the form of a row of cat's eyes. Kinematic magnetic field growth is characterized by modes of two types. One is akin to the Ponomarenko dynamo mechanism and located close to some closed stream surface; the other appears to be associated with stagnation points and heteroclinic separatrices.When the Ekman layer flow is destabilized thermally, the well-developed convective instability far from onset is characterized by a flow that is intrinsically time-dependent in the sense that it is unsteady in any moving frame. The magnetic field is concentrated in magnetic sheets situated around the convective cells in regions where chaotic particle paths are likely to exist; evidence for fast dynamo action is obtained. The presence of the Ekman layer close to the bottom boundary breaks the up–down symmetry of the layer and localizes the magnetic field near the lower boundary.

Hydromagnetic Instability Conditions for Viscoelastic Non-Newtonian Fluids

2000 ◽  
Vol 55 (3-4) ◽  
pp. 460-466
Keyword(s):  
Magnetic Field ◽  
Growth Rates ◽  
Stable Configuration ◽  
Horizontal Magnetic Field ◽  
Physical Conditions ◽  
Unstable Configuration ◽  
The Stability ◽  
Parameter Values ◽  
The Magnetic Field ◽  
Second Order Fluids

Abstract The effect of a horizontal magnetic field and a non-Newtonian stress tensor, as described by the Wal-ters B’ model, on the instability of two second order fluids of high kinematic viscosities and viscoelas-ticities is investigated. For the potentially stable configuration, it is found that the system is stable or unstable for a wavenumber range depending on the kinematic viscoelasticity. For the potentially un-stable configuration, it is found that the stability criterion is dependent on orientation and magnitude of the magnetic field which is found to stabilize a certain range of the unstable configuration related to the viscoelasticity values. The behaviour of growth rates with respect to Alfvén velocities are examined analytically, and it is found that the magnetic field has a dual role on the instability problem. For the exponentially varying stratifications, the system is found to be stable or unstable for the stable and un-stable stratifications under certain physical conditions, and the growth rates are found to increase or de-crease with increasing the stratification parameter values, according to some restrictions satisfied by the chosen wavenumbers range

Stability of magnetohydrodynamic shock waves

1967 ◽  
Vol 1 (4) ◽  
pp. 463-472 ◽  
Author(s):  
Martin Lessen ◽  
Narayan V. Deshpande
Keyword(s):  
Magnetic Field ◽  
Mach Number ◽  
Shock Waves ◽  
Growth Rates ◽  
Acoustic Waves ◽  
Normal Mode Analysis ◽  
Mode Analysis ◽  
Magnetohydrodynamic Shock ◽  
The Stability ◽  
The Magnetic Field

The stability of oblique magnetohycirodynamic shock waves is studied with respect to a disturbance that excites magneto-acoustic waves. The problem is solved numerically by the normal mode analysis and it is shown that slow shocks are unstable in the sense that the disturbance grows exponentially with time. Growth rates are calculated for a particular Mach number and for different values of the magnetic field and obliqueness. The fast shock appears to be stable.

Sign in / Sign up

Export Citation Format

Share Document