scholarly journals Dynamo mechanism in a rotating spherical shell: competition between magnetic field and convection vortices

2002 ◽  
Vol 465 ◽  
pp. 1-32 ◽  
Author(s):  
NORIO ISHIHARA ◽  
SHIGEO KIDA
Keyword(s):  
Magnetic Field ◽  
Spherical Shell ◽  
Magnetic Energy ◽  
Outer Boundary ◽  
Magnetic Flux Density ◽  
Primary Role ◽  
Electrically Conducting ◽  
Magnetic Dipole Field ◽  
Boussinesq Fluid ◽  
The Magnetic Field

A strong axial magnetic dipole field with magnetic energy 15 times larger than the kinetic energy of thermal convection is realized by a direct numerical simulation of the magnetohydrodynamic equation of an electrically conducting Boussinesq fluid in a rotating spherical shell which is driven by a temperature difference between the outer and inner boundaries against a gravity force pointed towards the system centre. Cyclonic and anticyclonic convection vortices are generated and play a primary role in the magnetic field intensification. The magnetic field is enhanced through the stretching of magnetic lines in four particular parts of the convection fields, namely inside anticyclones, between cyclones and their western neighbouring anticyclones at middle as well as low latitudes, and between anticyclones and the outer boundary. A ‘twist-turn’ loop of intense magnetic flux density is identified as a fundamental structure which yields dominant contributions both to the toroidal and poloidal components of the longitudinally averaged magnetic field. Various types of competitive interaction between the magnetic field and convection vortices are observed. Among these, a creation-and-annihilation cycle in a statistically equilibrium state is particularly important. It is composed of three sequentially recurrent dynamical processes: the generation of convection vortices by the Rayleigh–Bénard instability, the growth of anticyclones and the intensification of magnetic field by a concentrate-and-stretch mechanism, and the breakdown of vortices by the Lorentz force followed by diminution of the magnetic field. The energy transfer from the velocity to the magnetic fields takes place predominantly in this dynamical cycle.

A detailed analysis of a dynamo mechanism in a rapidly rotating spherical shell

2012 ◽  
Vol 701 ◽  
pp. 228-250 ◽  
Author(s):  
F. Takahashi ◽  
H. Shimizu
Keyword(s):  
Magnetic Field ◽  
Spherical Shell ◽  
Large Scale ◽  
Magnetic Energy ◽  
Thin Sheet ◽  
Dynamo Model ◽  
Current Loop ◽  
Flow Acceleration ◽  
Dynamo Mechanism ◽  
The Magnetic Field

AbstractMechanisms of magnetic field intensification by flows of an electrically conducting fluid in a rapidly rotating spherical shell are investigated using a numerical dynamo model with an Ekman number of $1{0}^{\ensuremath{-} 5} $. A strong dipolar solution with a magnetic energy 55 times larger than the kinetic energy of thermal convection is obtained. In a regime of small viscosity and inertia with the strong magnetic field, the convection structure consists of a few large-scale retrograde flows in the azimuthal direction and localized thin sheet-like plumes. A detailed term-by-term analysis of the magnetic field amplification processes shows that the magnetic field is amplified through stretching of magnetic lines, which occurs typically through four types of flow: the retrograde azimuthal flow near the outer boundary, the downwelling flow of the sheet plume, the prograde azimuthal flow near the rim of the tangent cylinder, and the cylindrical-radially alternating flows of the plume cluster. The current loop structure emerges as a result of stretching the magnetic lines along the magnetic field by the flow acceleration. The most remarkable effects of the generated magnetic field on the flow come from the strong azimuthal (toroidal) magnetic field. Similarities of the present model in the convection and magnetic field structures to previous studies at larger and even smaller Ekman numbers suggest universality of the dynamo mechanism in rotating spherical dynamos.

scholarly journals Design of a New 1D Halbach Magnet Array with Good Sinusoidal Magnetic Field by Analyzing the Curved Surface

Sensors ◽  
2021 ◽  
Vol 21 (7) ◽  
pp. 2522
Author(s):  
Guangdou Liu ◽  
Shiqin Hou ◽  
Xingping Xu ◽  
Wensheng Xiao
Keyword(s):  
Magnetic Field ◽  
Magnetic Flux ◽  
Permanent Magnet ◽  
Flux Density ◽  
Permanent Magnets ◽  
Air Gap ◽  
Curved Surface ◽  
Magnetic Flux Density ◽  
Sinusoidal Magnetic Field ◽  
The Magnetic Field

In the linear and planar motors, the 1D Halbach magnet array is extensively used. The sinusoidal property of the magnetic field deteriorates by analyzing the magnetic field at a small air gap. Therefore, a new 1D Halbach magnet array is proposed, in which the permanent magnet with a curved surface is applied. Based on the superposition of principle and Fourier series, the magnetic flux density distribution is derived. The optimized curved surface is obtained and fitted by a polynomial. The sinusoidal magnetic field is verified by comparing it with the magnetic flux density of the finite element model. Through the analysis of different dimensions of the permanent magnet array, the optimization result has good applicability. The force ripple can be significantly reduced by the new magnet array. The effect on the mass and air gap is investigated compared with a conventional magnet array with rectangular permanent magnets. In conclusion, the new magnet array design has the scalability to be extended to various sizes of motor and is especially suitable for small air gap applications.

scholarly journals Calculation of Transient Magnetic Field and Induced Voltage in Photovoltaic Bracket System during a Lightning Stroke

2021 ◽  
Vol 11 (10) ◽  
pp. 4567
Author(s):  
Xiaoqing Zhang ◽  
Yaowu Wang
Keyword(s):  
Magnetic Field ◽  
Time Derivative ◽  
Equivalent Circuit Model ◽  
Magnetic Flux Density ◽  
Induced Voltage ◽  
Lightning Stroke ◽  
Transient Magnetic Field ◽  
Lightning Current ◽  
Time Space ◽  
The Magnetic Field

An effective method is proposed in this paper for calculating the transient magnetic field and induced voltage in the photovoltaic bracket system under lightning stroke. Considering the need for the lightning current responses on various branches of the photovoltaic bracket system, a brief outline is given to the equivalent circuit model of the photovoltaic bracket system. The analytic formulas of the transient magnetic field are derived from the vector potential for the tilted, vertical and horizontal branches in the photovoltaic bracket system. With a time–space discretization scheme put forward for theses formulas, the magnetic field distribution in an assigned spatial domain is determined on the basis of the lightning current responses. The magnetic linkage passing through a conductor loop is evaluated by the surface integral of the magnetic flux density and the induced voltage is obtained from the time derivative of the magnetic linkage. In order to check the validity of the proposed method, an experiment is made on a reduced-scale photovoltaic bracket system. Then, the proposed method is applied to an actual photovoltaic bracket system. The calculations are performed for the magnetic field distributions and induced voltages under positive and negative lightning strokes.

scholarly journals 46. The störmertron

1958 ◽  
Vol 6 ◽  
pp. 446-447
Author(s):  
Willard H. Bennett
Keyword(s):  
Magnetic Field ◽  
Charged Particles ◽  
Mercury Vapor ◽  
Electron Gun ◽  
Conducting Film ◽  
New Developments ◽  
Electrically Conducting ◽  
The Earth ◽  
Magnetic Dipole Field ◽  
Glass Tubes

A tube has been developed in which the shapes of streams of charged particles moving in the earth's magnetic field can be produced accurately to scale. The tube has been named the Störmertron in honor of Carl Störmer who calculated many such orbits. New developments which have made this tube possible include a method for coating the inside of large glass tubes with a transparent electrically conducting film, and an electron gun producing gas-focused streams in less than ½ micron of mercury vapor, a nearly vapor-free grease joint, and a nearly vapor-free carbon black. The magnetic dipole field of the earth is simulated with an Alnico magnet capped with properly shaped soft iron caps. The stream is deflected using two pairs of yoke coils near the gun.

scholarly journals Homotopy Analysis Solution of Hydromagnetic Mixed Convection Flow Past an Exponentially Stretching Sheet with Hall Current

2012 ◽  
Vol 2012 ◽  
pp. 1-26 ◽  
Author(s):  
Mohamed Abd El-Aziz ◽  
Tamer Nabil
Keyword(s):  
Magnetic Field ◽  
Mixed Convection ◽  
Convection Flow ◽  
Mixed Convection Flow ◽  
Electrically Conducting ◽  
Hall Parameter ◽  
Homotopy Analysis ◽  
Continuous Sheet ◽  
Exponentially Stretching ◽  
The Magnetic Field

The effect of thermal radiation on steady hydromagnetic heat transfer by mixed convection flow of a viscous incompressible and electrically conducting fluid past an exponentially stretching continuous sheet is examined. Wall temperature and stretching velocity are assumed to vary according to specific exponential forms. An external strong uniform magnetic field is applied perpendicular to the sheet and the Hall effect is taken into consideration. The resulting governing equations are transformed into a system of nonlinear ordinary differential equations using appropriate transformations and then solved analytically by the homotopy analysis method (HAM). The solution is found to be dependent on six governing parameters including the magnetic field parameterM, Hall parameterm, the buoyancy parameterξ, the radiation parameterR, the parameter of temperature distributiona, and Prandtl number Pr. A systematic study is carried out to illustrate the effects of these major parameters on the velocity and temperature distributions in the boundary layer, the skin-friction coefficients, and the local Nusselt number.

Gas-ionizing shocks in a magnetic field

1967 ◽  
Vol 1 (1) ◽  
pp. 37-54 ◽  
Author(s):  
M. D. Cowley
Keyword(s):  
Magnetic Field ◽  
Electric Field ◽  
Wave Speed ◽  
Normal Velocity ◽  
Electrically Conducting ◽  
Shock Stability ◽  
The Face ◽  
Arbitrary Velocity ◽  
Flow Plane ◽  
The Magnetic Field

Ionizing shocks for plane flows with the magnetic field lying in the flow plane are considered. The gas is assumed to be electrically conducting downstream, but non-conducting upstream. Shocks whose downstream state has a normal velocity component less than the slow magneto-acoustic-wave speed and whose upstream state is supersonic are found to be non-evolutionary in the face of plane magneto-acoustic disturbances, unless the upstream electric field in a frame of reference where the gas is at rest is arbitrary. Velocity conditions are also determined for shock stability with the electric field not arbitrary.Shock structures are found for the case of large ohmic diffusion, the initial temperature rise and ionization of the gas being caused by a thin transition having the properties of an ordinary gasdynamic shock. For the case where shocks are evolutionary when the upstream electric field is arbitrary, the shock structure requirements only restrict the electric field by limiting the range of possible values. When shocks are evolutionary with the electric field not arbitrary, they can only have a structure for a particular value of the electric field. Limits to the current carried by ionizing shocks and the effects of precursor ionization are discussed qualitatively.

CHOICE OF CONDITIONS FOR MHD SIMULATIONS ABOVE THE ACTIVE REGION, ALLOWING THE STUDY OF THE SOLAR FLARE MECHANISM

2021 ◽  
Vol 44 ◽  
pp. 92-95
Author(s):  
A.I. Podgorny ◽  
◽  
I.M. Podgorny ◽  
A.V. Borisenko ◽  
N.S. Meshalkina ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Active Region ◽  
Solar Flare ◽  
Magnetic Energy ◽  
Solar Radius ◽  
Computational Domain ◽  
Mhd Simulations ◽  
Flare Energy ◽  
Numerical Instabilities ◽  
The Magnetic Field

Primordial release of solar flare energy high in corona (at altitudes 1/40 - 1/20 of the solar radius) is explained by release of the magnetic energy of the current sheet. The observed manifestations of the flare are explained by the electrodynamical model of a solar flare proposed by I. M. Podgorny. To study the flare mechanism is necessary to perform MHD simulations above a real active region (AR). MHD simulation in the solar corona in the real scale of time can only be carried out thanks to parallel calculations using CUDA technology. Methods have been developed for stabilizing numerical instabilities that arise near the boundary of the computational domain. Methods are applicable for low viscosities in the main part of the domain, for which the flare energy is effectively accumulated near the singularities of the magnetic field. Singular lines of the magnetic field, near which the field can have a rather complex configuration, coincide or are located near the observed positions of the flare.

scholarly journals The development of magnetic field line wander by plasma turbulence

2017 ◽  
Vol 83 (4) ◽  
Author(s):  
Gregory G. Howes ◽  
Sofiane Bourouaine
Keyword(s):  
Magnetic Field ◽  
Field Line ◽  
Magnetic Field Line ◽  
Large Scale ◽  
Magnetic Energy ◽  
Plasma Turbulence ◽  
Alfven Wave ◽  
Astrophysical Plasmas ◽  
Field Lines ◽  
The Magnetic Field

Plasma turbulence occurs ubiquitously in space and astrophysical plasmas, mediating the nonlinear transfer of energy from large-scale electromagnetic fields and plasma flows to small scales at which the energy may be ultimately converted to plasma heat. But plasma turbulence also generically leads to a tangling of the magnetic field that threads through the plasma. The resulting wander of the magnetic field lines may significantly impact a number of important physical processes, including the propagation of cosmic rays and energetic particles, confinement in magnetic fusion devices and the fundamental processes of turbulence, magnetic reconnection and particle acceleration. The various potential impacts of magnetic field line wander are reviewed in detail, and a number of important theoretical considerations are identified that may influence the development and saturation of magnetic field line wander in astrophysical plasma turbulence. The results of nonlinear gyrokinetic simulations of kinetic Alfvén wave turbulence of sub-ion length scales are evaluated to understand the development and saturation of the turbulent magnetic energy spectrum and of the magnetic field line wander. It is found that turbulent space and astrophysical plasmas are generally expected to contain a stochastic magnetic field due to the tangling of the field by strong plasma turbulence. Future work will explore how the saturated magnetic field line wander varies as a function of the amplitude of the plasma turbulence and the ratio of the thermal to magnetic pressure, known as the plasma beta.

scholarly journals Modified boundary integral method for pressure driven MHD duct flow

1989 ◽  
Vol 12 (1) ◽  
pp. 159-174
Author(s):  
B. D. Aggarwala ◽  
P. D. Ariel
Keyword(s):  
Magnetic Field ◽  
Integral Method ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Duct Flow ◽  
Rectangular Duct ◽  
Computationally Efficient ◽  
Electrically Conducting ◽  
Flow Through ◽  
The Magnetic Field

In this paper, we investigate the flow of a viscous, Incompressible, electrically conducting fluid through a rectangular duct in the presence of a magnetic field, when one of the boundaries perpedicular to the magnetic field is partly conducting and partly Insulating, by a modified Boundary Integral Method.Three problems are considered (i) flow through an infinite channel, (ii) flow through a rectangular duct when the conducting part is symmetrically situated, and (iii) flow through a rectangular duct when the conducting part is arbltrarily positioned.Such problems have been studied before by asymptotic means for large values of M, the Hartmann number. Hoverer, the present modification of the Boundary Integral Method renders the problem computationally efficient and provides a reliable numerical solution for all values of M. For large M, our coputation time decreases significantly.

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.

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