scholarly journals Universal dynamo paradigm for solar activity, Higgs fields and disasters

2021 ◽  
Vol 254 ◽  
pp. 02017
Author(s):  
Boris Shevtsov
Keyword(s):  
Field Theory ◽  
Solar Activity ◽  
Relaxation Oscillator ◽  
Restoring Force ◽  
Mexican Hat ◽  
Induction Equation ◽  
Champagne Bottle ◽  
Dynamo Effect ◽  
Higgs Fields ◽  
Magnetic Induction Equation

There is still a problem of a correct and accurate description of the dynamo and its uses in various fields of physics. To solve this problem, a special and universal representation of dynamo is proposed. The magnetic induction equation of dynamo is presented in the form of a Lienard relaxation oscillator with cubic nonlinear restoring force corresponding to the Mexican hat or champagne bottle potential which is used to determine the Higgs fields which are considered here in its general sense. Universal dynamo paradigm in field theory which can be used to describe disasters is proposed. Using solar activity as an example, it is shown how a dynamo induces a magnetic analogue of the Higgs fields with a broken symmetry of the magnetic field. Various dynamo modes are considered and different dynamo numbers are estimated. The dynamo effect can be used in field theory as an alternative to spontaneous symmetry breaking. Opportunities for the promotion of the new dynamo paradigm are discussed.

Inversion of the geomagnetic induction problem

1970 ◽  
Vol 315 (1521) ◽  
pp. 185-194 ◽  
Keyword(s):  
Frequency Spectrum ◽  
Real Data ◽  
Real Analytic Function ◽  
Numerical Application ◽  
Geomagnetic Induction ◽  
Induction Equation ◽  
Real Analytic ◽  
Principle Of Causality ◽  
Magnetic Potentials ◽  
Magnetic Induction Equation

An algorithm has been found for inverting the problem of geomagnetic induction in a con­centrically stratified Earth. It determines the (radial) conductivity distribution from the frequency spectrum of the ratio of internal to external magnetic potentials of any surface harmonic mode. The derivation combines the magnetic induction equation with the principle of causality in the form of an integral constraint on the frequency spectrum. This algorithm generates a single solution for the conductivity. This solution is here proved unique if the conductivity is a bounded, real analytic function with no zeros. Suggestions are made regarding the numerical application of the algorithm to real data.

scholarly journals Stable upwind schemes for the magnetic induction equation

2009 ◽  
Vol 43 (5) ◽  
pp. 825-852 ◽  
Author(s):  
Franz G. Fuchs ◽  
Kenneth H. Karlsen ◽  
Siddharta Mishra ◽  
Nils H. Risebro
Keyword(s):  
Magnetic Induction ◽  
Upwind Schemes ◽  
Induction Equation ◽  
Magnetic Induction Equation

Planar velocity dynamos in a sphere

2006 ◽  
Vol 462 (2072) ◽  
pp. 2439-2456 ◽  
Author(s):  
A.A Bachtiar ◽  
D.J Ivers ◽  
R.W James
Keyword(s):  
Magnetic Field ◽  
Outer Core ◽  
Magnetic Reynolds Number ◽  
Main Magnetic Field ◽  
Dynamo Action ◽  
Field Growth ◽  
Planar Velocity ◽  
Induction Equation ◽  
Planar Flows ◽  
Magnetic Induction Equation

The Earth's main magnetic field is generally believed to be due to a self-exciting dynamo process in the Earth's fluid outer core. A variety of antidynamo theorems exist that set conditions under which a magnetic field cannot be indefinitely maintained by dynamo action against ohmic decay. One such theorem, the Planar Velocity Antidynamo Theorem , precludes field maintenance when the flow is everywhere parallel to some plane, e.g. the equatorial plane. This paper shows that the proof of the Planar Velocity Theorem fails when the flow is confined to a sphere, due to diffusive coupling at the boundary. Then, the theorem reverts to a conjecture. There is a need to either prove the conjecture, or find a functioning planar velocity dynamo. To the latter end, this paper formulates the toroidal–poloidal spectral form of the magnetic induction equation for planar flows, as a basis for a numerical investigation. We have thereby determined magnetic field growth rates associated with various planar flows in spheres. For most flows, the induced magnetic field decays with time, supporting a planar velocity antidynamo conjecture for a spherical conducting fluid. However, one flow is exceptional, indicating that magnetic field growth can occur. We also re-examine some classical kinematic dynamo models, converting the flows where possible to planar flows. For the flow of Pekeris et al . (Pekeris, C. L., Accad, Y. & Shkoller, B. 1973 Kinematic dynamos and the Earth's magnetic field. Phil. Trans. R. Soc. A 275 , 425–461), this conversion dramatically reduces the critical magnetic Reynolds number.

Kinematic dynamo action in a network of screw motions; application to the core of a fast breeder reactor

1999 ◽  
Vol 382 ◽  
pp. 137-154 ◽  
Author(s):  
F. PLUNIAN ◽  
P. MARTY ◽  
A. ALEMANY
Keyword(s):  
Magnetic Field ◽  
Experimental Studies ◽  
Magnetic Reynolds Number ◽  
Liquid Sodium ◽  
Dynamo Action ◽  
Periodic Cell ◽  
The Core ◽  
Induction Equation ◽  
Breeder Reactors ◽  
Dynamo Effect

Most of the studies concerning the dynamo effect are motivated by astrophysical and geophysical applications. The dynamo effect is also the subject of some experimental studies in fast breeder reactors (FBR) for they contain liquid sodium in motion with magnetic Reynolds numbers larger than unity. In this paper, we are concerned with the flow of sodium inside the core of an FBR, characterized by a strong helicity. The sodium in the core flows through a network of vertical cylinders. In each cylinder assembly, the flow can be approximated by a smooth upwards helical motion with no-slip conditions at the boundary. As the core contains a large number of assemblies, the global flow is considered to be two-dimensionally periodic. We investigate the self-excitation of a two-dimensionally periodic magnetic field using an instability analysis of the induction equation which leads to an eigenvalue problem. Advantage is taken of the flow symmetries to reduce the size of the problem. The growth rate of the magnetic field is found as a function of the flow pitch, the magnetic Reynolds number (Rm) and the vertical magnetic wavenumber (k). An α-effect is shown to operate for moderate values of Rm, supporting a mean magnetic field. The large-Rm limit is investigated numerically. It is found that α=O(Rm−2/3), which can be explained through appropriate dynamo mechanisms. Either a smooth Ponomarenko or a Roberts type of dynamo is operating in each periodic cell, depending on k. The standard power regime of an industrial FPBR is found to be subcritical.

Time-dependent kinematic dynamos with stationary flows

1989 ◽  
Vol 425 (1869) ◽  
pp. 407-429 ◽  
Keyword(s):  
Reynolds Number ◽  
Numerical Solutions ◽  
Magnetic Reynolds Number ◽  
Velocity Models ◽  
Stationary Flows ◽  
Induction Equation ◽  
Steady Solutions ◽  
Simple Flows ◽  
Magnetic Induction Equation ◽  
Stationary Velocity

Numerical solutions to the magnetic induction equation in a sphere have been obtained for a number of stationary velocity models. By searching for non-steady magnetic fields and in some circumstances showing that all magnetic field modes decay, the inability of several earlier researchers to find convergent steady solutions is explained. Results of previous authors are generally confirmed, but also extended to cover non-steady fields, different values of magnetic Reynolds number and other parameters, and higher truncation limits. Some non-decaying fields are found where only decaying or non-convergent results have previously been reported. Two flows ∊ s 0 2 + t 0 2 and ∊ s 0 2 + t 0 1 , each consisting of two very simple axisymmetric rolls are seen to sustain growing fields provided that (i) the magnetic Reynolds number R and the poloidal to toroidal flow ratio ∊ are of appropriate magnitudes, and (ii) the meridional s 0 2 flow is directed inwards along the equatorial plane and out towards the poles. An even simpler axisymmetric single roll flow ∊ s 0 1 + t 0 1 is also seen to support growing fields for appropriate ∊ and R . These simple flows dispel the somewhat prevalent belief that dynamo maintenance relies on the supporting flow being complex, and having length scale significantly less than that of the conducting fluid volume.

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