The Dynamo Theory

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Celestial Magnetic Fields The Dynamo Theory -Dynamo theory describes the process through which motion of a conductive body in the presence of a magnetic field acts to regenerate that magnetic field. -The Earth’s molten outer core circulates due to: Convection currents Earth’s rotation (Coriolis Effect) -This electrically conducting iron moves in the presence of Earth’s magnetic field. -Electric currents are induced, and the magnetic field is regenerated. -The Magnetic field flips approximately every 200,000 years, but it has been 750,000 years since its last flip. The Sun -"Magnetic field causes most of what we see in the corona because of its interaction with the solar atmosphere (plasma)." -Magnetic Flux and Magnetic Field Lines are conserved. -The sun switches its magnetic poles every 11 years. -Sunspots are areas of extremely dense magnetic field lines. The Planets’ Magnetospheres -Jupiter’s magnetic field is huge and causes strong radio wave emissions -Saturn’s rotation axis and magnetic axis are the same (axisymmetric) -Uranus has a strange magnetosphere with a corkscrewing magneto-tail caused by a 39° difference between the rotation axis and magnetic axis -Very little is known about Uranus’s and Neptune’s magnetic field due to their distance from Earth. -Earth’s magnetic field affects experiments on earth along with a lot more! Life -Magnetic Field protects us from the solar wind. -The Solar Wind would strip our atmosphere of important elements like hydrogen and oxygen. (ingredients for water). -Mars and Venus have a weak magnetic field and therefore could not produce or sustain life. Magnetospheres and Auroras -Reactions between charged particles from the solar wind and atoms in the earth's atmosphere give rise to light emissions which form colored light displays called auroras. -Magnetosphere: area of space controlled by a planet's magnetic field. -Interplanetary magnetic field: this is the Sun's magnetic field which is carried over to other planets through the solar wind -The shape of the Magnetosphere is affected by the solar wind, which compresses the magnetosphere on the day side and creates a tail on the night side, overall creating a bullet shape. .

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Dynamo Theory 1 Dynamo Theory
Dynamo theory 1 Dynamo theory In geophysics, dynamo theory proposes a mechanism by which a celestial body such as the Earth or a star generates a magnetic field. The theory describes the process through which a rotating, convecting, and electrically conducting fluid can maintain a magnetic field over astronomical time scales. History of theory When William Gilbert published de Magnete in 1600, he concluded that the Earth is magnetic and proposed the first theory for the origin of this magnetism: permanent magnetism such as that found in lodestone. In 1919, Joseph Larmor proposed that a dynamo might be generating the field.[1] [2] However, even after he advanced his theory, some prominent scientists advanced alternate theories. Einstein, believed that there might be an asymmetry between the charges of the electron and proton so that the Earth's magnetic field would be produced by the entire Earth. The Nobel Prize winner Patrick Blackett did a series of experiments looking for a fundamental relation between angular momentum and magnetic moment, but found none.[3] [4] Walter M. Elsasser, considered a "father" of the presently accepted dynamo theory as an explanation of the Earth's magnetism, proposed that this magnetic field resulted from electric currents induced in the fluid outer core of the Earth. He revealed the history of the Earth's magnetic field through pioneering the study of the magnetic orientation of minerals in rocks. In order to maintain the magnetic field against ohmic decay (which would occur for the dipole field in 20,000 years) the outer core must be convecting.
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Dynamo Theory and GFD
Dynamo theory and GFD Steve Childress 16 June 2008 1 Origins of the dynamo theory Dynamo theory studies a conducting fluid moving in a magnetic field; the motion of the body through the field acts to generate new magnetic field, and the system is called a dynamo if the magnetic field so produced is self-sustaining. 1.1 Early ideas point the way In the distant past, there was the idea that the earth was a permanent magnet. In the 1830s Gauss analyzed the structure of the Earth's magnetic field using potential theory, decomposing the field into harmonics. The strength of the dominant field was later found to change with time. In 1919 Sir Joseph Larmor drew on the induction of currents in a moving conductor, to suggest that sunspots are maintained by magnetic dynamo action. P. M. Blackett proposed that magnetic fields should be produced by the rotation of fluid bodies. The `current consensus' is that the Earth's magnetic field is the result of a regenerating dynamo action in the fluid core. The mechanism of generation of the field is closely linked dynamically with the rotation of the Earth. Similar ideas are believed to apply to the solar magnetic field, to other planetary fields, and perhaps to the magnetic field permeating the cosmos. 1.2 Properties of the Earth and its Magnetic Field The magnetic field observed at the Earth's surface changes polarity irregularly. The non- dipole components of the surface field also vary with time over many time scales greater than decades, and have a persistent drift to the west.
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Lecture 2: Dynamo Theory
Lecture 2: Dynamo theory Celine´ Guervilly School of Mathematics, Statistics and Physics, Newcastle University, UK Basis of electromagnetism: Maxwell’s equations Faraday’s law of induction: if a magnetic field B varies with time then an electric field E is produced. @B r × E = - @t Ampere’s` law (velocity speed of light) r × B = µ0j where j is the current density and µ0 is the vacuum magnetic permeability. Gauss’s law (electric monopoles from which electric field originates) ρ r · E = 0 with ρ the charge density and 0 the dielectric constant. No magnetic monopole (no particle from which magnetic field lines radiate) r · B = 0 Ohm’s law Relates current density j to electric field E. In a material at rest, we assume the simple form j = σE with σ the electrical conductivity. In the reference frame moving with the fluid, the electric, magnetic fields and current become E0 = E + u × B, B0 = B, j0 = j In the original reference, Ohm’s law is j = σ(E + u × B) A conducting wire is wound around the disc and joins the rim and the axis: electric current flows in the wire and across the disc. Winding is such that the induced magnetic field B reinforces the applied magnetic field B0. Dynamo: conversion of kinetic energy into magnetic energy. If the disc rotation rate exceeds a critical value, B0 can be switched off and the dynamo will continue to operate: the dynamo has become self-excited. Homopolar disc dynamo A solid electrically conducting disk rotates about an axis. Uniform magnetic field B0 aligned with the rotation axis.
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Ye= Pfl,'3(Cos 0) [Cos M#O, Sin M,]
Proc. Nat. A cad. Sci. USA Vol. 68, No. 6, pp. 1111-1113, June 1971 The Magnetic Field Induced by the Bodily Tide in the Core of the Earth (dynamo theory/coupling coefficient) C. L. PEKERIS Department of Applied Mathematics, The Weizmann Institute, Rehovot, Israel Corninunicated March 15, 1971 ABSTRACT The motion in the liquid core of the earth The coupling term V X H in (1) generates combination due to the bodily tide can induce a periodic magnetic field having the frequency a of the tide as well as multiple fre- frequencies, including a steady term of zero frequency. quencies, including a steady term. The coupling coefficient The periodic components of H will not be observed at for the steady term between the convectively inducing the surface of the earth because of damping of the field and induced fields is estimated to be of the order of crH2/X, where H denotes the height of the equilibrium tide, and by conduction in passing through the mantle [3]. The only X = 1/4K7rK, K denoting the electrical conductivity of the component of the magnetic field induced by the bodily core. With a = 1.4 X 10-4 sec-', H = 20 cm, and K = 3 X tide that would be observed at the surface is the one of 10-6 emu, the coupling coefficient comes out only of the order of 10-6, as against unity in the case of the dynamo zero frequency. In the homogeneous dynamo theory theory. [3 ], the steady field is visualized to be maintained through the convection by a process of bootstrapping.
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The Current State of Ionospheric Wind Dynamo Theory Is Reviewed
J. Geomag. Geoelectr., 31, 287-310, 1979 Ionospheric Wind Dynamo Theory: A Review A. D. RICHMOND SpaceEnvironment Laboratory, National Oceanic and Atmospheric Administration,Boulder, Colorado 80302, U. S. A. (Accepted June 10, 1978) The current state of ionospheric wind dynamo theory is reviewed. Observation- al and theoreticaladvances in recent yearshave permitted more accurate models of the dynamo mechanismto be presentedthan previously,which have lent further credenceto the validity of dynamo theory as the main explanation for quiet-day ionosphericelectric fields and currents at middle and low latitudes. The diurnal component of the wind in the upper E region and lower F region appears to be primarily responsiblefor averagequiet-day currents, although other wind compo- nents give significantcontributions. Observationally,there is a need for better spatial and temporal coverage of wind and electric field data. Theoretically, there is a need for further considerationof the mutual dynamiccoupling among winds, conductivities,electric fields, and electric currents, and for better modeling of nighttimeconditions. 1. Introduction This paper is intended to review the present state of knowledge concerning the theory of the ionospheric wind dynamo. The main emphasis is on current theoreti- cal conceptions, with historical aspects, observational evidence, and treatments of temporal and spatial variability covered more briefly. For further information on dynamo theory and ionospheric currents, previous reviews (K. MAEDA and KATO, 1966; MATSUSHITA, 1967, 1968, 1971a, 1973, 1975, 1977; H. MAEDA, 1968; PRICE, 1969a, b; WAGNER, 1971; AKASOFU and CHAPMAN, 1972; MATSUSHITA and MOZER, 1973; VOLLAND, 1974a; FATKULLIN, 1975; KANE, 1976) will be found useful. 2. Formulation of Dynamo Theory The basic features of ionospheric wind dynamo theory can be formulated as follows.
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By EDWARD HAROLD BLISH B.S., Syracuse University (1963)
AN ANALYSIS OF IQSY METEOR WIND AND GEOMAGNETIC FIELD DATA by EDWARD HAROLD BLISH B.S., Syracuse University (1963) SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENT FOR THE DEGREE OF MASTER OF SCIENCE at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY September 29, 1969 Teo I ) Signature of Author ( Department of Meteorology, 29 September 1969 Certified by 4 Thesis Supervisor 1i 4 Accepted by Departmental Committee on Graduate Students ftWN AN ANALYSIS OF IQSY METEOR WIND AND GEOMAGNETIC FIELD DATA by Edward Harold Blish Submitted to the Department of Meteorology on 29 September 1969 in partial fulfillment of the requirement for the degree of Master of Science ABSTRACT Meteor wind observations at Sheffield, U.K. for forty weekly twenty-four hour periods during the IQSY were harmoni- cally analyzed for their prevailing, solar tidal, and short- period components. Corresponding magnetic field measurements at Hartland, U.K. were similarly analyzed for their harmonic components. The results were compared to other published values and to those of tidal and dynamo theory. Significant linear correlations between the amplitudes and phase angles of the meteor wind and magnetic field harmonic components demonstrate the existence of systematic relationships between the magnetic field and ionospheric wind variations as predicted by the dynamo theory. Significant correlations re- producable by a simple dynamo mechanism were also found between the magnetic activity indices, the magnetic field, and the pre- vailing ionospheric wind components. Ionospheric current densities and electric fields were esti- mated using the overhead Sq approximation, a simplified conduc- tivity model, and the horizontal current-layer dynamo theory equations. The ionospheric dynamo electric field alone was found to be too small to account for the observed quiet-day magnetic field variations inferring that an additional ionos- pheric electric field of possible magnetospheric origin is probably the primary driving force for the ionospheric currents.
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PERGAMON International Journal of Engineering Science 36 (1998) 1325±1338 Dynamo theory then and now Gary A. Glatzmaier a, Paul H. Roberts b aLos Alamos National Laboratory, Los Alamos, NM 87545, U.S.A. bUniversity of California, Los Angeles, CA 90095, U.S.A. Abstract A brief history of dynamo theory is presented, from its earliest beginnings, through the development of successful kinematic models (those in which only the electrodynamic equations are solved), up to the present time when fully magnetohydrodynamic simulations have successfully reproduced the main features of the Earth's magnetic ®eld. A particular focus of this paper is the role of the solid inner core of the Earth on the dynamics of its ¯uid core. Some new results are presented concerning the age and topography of the inner core. # 1998 Elsevier Science Ltd. All rights reserved. 1. The kinematic geodynamo Although it has been known for many centuries that the Earth is magnetic [1±3], the reason for this, and for many puzzling features of the Earth's magnetic ®eld, have been convincingly explained only during the present century. The key was the discovery in 1906 that the Earth possesses a ¯uid core [4]. To be sure, the curious time scales of the ®eld, long compared with those of the atmosphere and oceans, but short compared with geological processes, had suggested to people like Halley [5] and Hansteen [6] that ¯uid motions within the Earth must somehow be involved, but nothing was certain until 1906. The density of the ¯uid core, deduced from seismological observations, ranges from 9904 kg m3 at the top to 12166 kg m3 at the bottom [7].
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Exploring the Physics of the Earth's Core with Numerical Simulations
Exploring the physics of the Earth’s core with numerical simulations Nathanaël Schaeffer To cite this version: Nathanaël Schaeffer. Exploring the physics of the Earth’s core with numerical simulations. Geophysics [physics.geo-ph]. Grenoble 1 UJF - Université Joseph Fourier; Université Grenoble Alpes, 2015. tel- 01241755 HAL Id: tel-01241755 https://tel.archives-ouvertes.fr/tel-01241755 Submitted on 11 Dec 2015 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Distributed under a Creative Commons Attribution - NonCommercial - ShareAlike| 4.0 International License Habilitation a` Diriger des Recherches Universite´ Grenoble Alpes Exploring the physics of the Earth’s core with numerical simulations Nathanael¨ Schaeffer soutenue le 30 septembre 2015, devant le jury composéde : Emmanuel DORMY Ecole´ Normale Supérieure(Paris) Rapporteur BérengèreDUBRULLE Centre d’Etudes´ Atomiques (Saclay) Rapporteur Johannes WICHT Max Planck Institute (Göttingen) Rapporteur Thierry ALBOUSSIERE` UniversitéClaude Bernard (Lyon) Examinateur Franck PLUNIAN UniversitéGrenoble Alpes (Grenoble) Examinateur Abstract In the first chapter of this report, I discuss some of my work of the past 7 years, since I joined the geodynamo team at ISTerre as a CNRS researcher. This work most often involves numerical simulations with codes that I have written.
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Introduction to Hydromagnetic Dynamo Theory with Applications to the Sun and the Earth
Introduction Basic electrodynamics Kinematic turbulent dynamos The solar dynamo Magnetohydrodynamical dynamos and geodynamo simulations Introduction to Hydromagnetic Dynamo Theory with Applications to the Sun and the Earth Dieter Schmitt Max Planck Institute for Solar System Research IMPRS Solar System School 18–20 June 2013 Dieter Schmitt Hydromagnetic Dynamo Theory Introduction Basic electrodynamics Kinematic turbulent dynamos The solar dynamo Magnetohydrodynamical dynamos and geodynamo simulations Outline Mean-field coefficients 1 Introduction Mean-field dynamos Magnetic field of the Earth 4 The solar dynamo Magnetic field of the Sun Basic incredients Dynamo hypothesis Convection zone dynamos Homopolar dynamo Overshoot layer dynamos 2 Basic electrodynamics Interface dynamos Pre-Maxwell theory Flux transport dynamos Induction equation 5 Magnetohydrodynamical dynamos Alfven’s theorem and geodynamo simulations Magnetic Reynolds number Equations and parameters Poloidal and toroidal magnetic Proudman-Taylor theorem and fields convection in a rotating sphere 3 Kinematic turbulent dynamos A simple geodynamo model Antidynamo theorems Advanced models Parker’s helical convection Reversals Mean-field theory 6 Literature Dieter Schmitt Hydromagnetic Dynamo Theory Introduction Magnetic field of the Earth Basic electrodynamics Magnetic field of the Sun Kinematic turbulent dynamos Dynamo hypothesis The solar dynamo Homopolar dynamo Magnetohydrodynamical dynamos and geodynamo simulations Geomagnetic field 1600 Gilbert, De Magnete: ”Magnus magnes ipse est globus terrestris.” (The Earth’s globe itself is a great magnet.) 1838 Gauss: Mathematical description of geomagnetic field l+1 P m − P r m − P r R m m m B = l;m Bl = Φl = R r Pl (cos #) gl cos mφ + hl sin mφ sources inside Earth l number of nodal lines, m number of azimuthal nodal lines l = 1; 2; 3;::: dipole, quadrupole, octupole, ..
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A Brief Introduction to Dynamos
A brief introduction to dynamos Steve Tobias (Leeds) 5th Potsdam Thinkshop, 2007 Geophysical and Astrophysical Magnetism: The Earth Earth has magnetic field! Paleomagnetism: around for long time Largely Dipolar Reverses every million or so years Geophysical and Astrophysical Magnetism: Solar System Planets These tend to have magnetic fields Geophysical and Astrophysical Magnetism: The Sun and Stars These tend to have magnetic fields (more on this later) Geophysical and Astrophysical Magnetism: Galaxies These tend to have magnetic fields M51 Spiral Galaxy Geophysical and Astrophysical Magnetism: Experiments These tend not to have magnetic fields VKS dynamo experiment See Jean-Francois and Cary’s talks A brief introduction to dynamos “In mathematics the art of proposing a question must be held of higher value than solving it” Georg Cantor “There are more questions than answers…” Johnny Nash A brief introduction to dynamos Review of basics of dynamo theory: C.A. Jones “Dynamo Theory” (Les Houches Lectures) http://www-lgit.obs.ujf-grenoble.fr/houches/ H.K. Moffatt “Magnetic Field Generation in Electrically Conducting Fluids”, 1978, CUP. Turbulent small-scale dynamos (and MHD turbulence): “MHD Dynamos and Turbulence”, Tobias, S.M., Cattaneo, F. & Boldyrev, S. in “Ten Chapters on Turbulence” eds Davidson, Kaneda and Sreenivasan CUP (2013) http://www1.maths.leeds.ac.uk/~smt/tcb_review13.pdf The Induction Equation stretching For what choices of u does B remain for large times? Clearly if u=0 then the field will decay away on diffusive timescale. Magnetic Reynolds Number Rm For geophysical and astrophysical flows Rm is large enough that stretching wins. In fact theoretical problems can arise because Rm is so large (see later) Earth’s Core Jupiter Solar Convection Zone Galaxy Experiments (though see Cary’s talk for plasma Rm!) Stretching vs Diffusion The induction equation is a linear problem in B.
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On the Genesis of the Earth's Magnetism
IOP PUBLISHING REPORTS ON PROGRESS IN PHYSICS Rep. Prog. Phys. 76 (2013) 096801 (55pp) doi:10.1088/0034-4885/76/9/096801 On the genesis of the Earth’s magnetism Paul H Roberts1,3 and Eric M King2 1 Institute of Geophysics and Planetary Physics, University of California, Los Angeles, CA 90095, USA 2 Earth and Planetary Science, University of California, Berkeley, CA 94720, USA E-mail: [email protected] Received 23 January 2011, in final form 26 June 2013 Published 4 September 2013 Online at stacks.iop.org/RoPP/76/096801 Abstract Few areas of geophysics are today progressing as rapidly as basic geomagnetism, which seeks to understand the origin of the Earth’s magnetism. Data about the present geomagnetic field pours in from orbiting satellites, and supplements the ever growing body of information about the field in the remote past, derived from the magnetism of rocks. The first of the three parts of this review summarizes the available geomagnetic data and makes significant inferences about the large scale structure of the geomagnetic field at the surface of the Earth’s electrically conducting fluid core, within which the field originates. In it, we recognize the first major obstacle to progress: because of the Earth’s mantle, only the broad, slowly varying features of the magnetic field within the core can be directly observed. The second (and main) part of the review commences with the geodynamo hypothesis: the geomagnetic field is induced by core flow as a self-excited dynamo. Its electrodynamics define ‘kinematic dynamo theory’. Key processes involving the motion of magnetic field lines, their diffusion through the conducting fluid, and their reconnection are described in detail.
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Hydromagnetic Dynamo Theory Appears Closed Loops Shown in Fig
RE+VIEWS OF MODERN PHYSICS VOLUME 28, NUMBER 2 APRIL, 1956 ::—::ycromagnetic .'Dynamo '..'.xeory WAl.rEn M. KLSASSER Department of Physics, University of Utah, Salt Lake City, Utah CONTE1VTSt The problem on which we report here is that of using the mechanism whereby the 1. Introductory Survey. 135 these equations to study fieMs, those of the 2. The Induction Equation. 137 most conspicuous cosmic magnetic earth, of sunspots and the sun, and of magnetic stars 3. Electric Fields, Potentials. 138 maintained. This is only a segment 4. The Hydromagnetic Equations, Waves . 140 are generated and of the broader dynamics of hydromagnetic fields, but 5. Conservation Theorems. 142 perhaps the most intriguing of its aspects. A system 6. Turbulence, Eddy Stresses . 143 which can maintain magnetic fields (either stationary 7. The Cauchy Integral, Amplification. 145 fields or least average fields) owing to motions in 8. Transverse Modes of the Sphere. 148 at will be designated as a 9. Mechanics of a Rotating Fluid. 150 electrically conducting fluids, hydromugneHc 10. The Toroidal Field. 153 dynamo. of these 11. The Feedback Mechanism 155 The most ancient and. the most important 12. Motions in the Earth's Core 158 problems is of course that of the magnetic field of the 13. Appendix: Periodic Dynamos, Reversals. 160 earth. Some of our mathematics will be specifically adapted to this problem. The geomagnetic field is the 14. Bibliography. ~ . 163 result of convective motions in the earth's Quid metallic 1. INTRODUCTORY SURVEY core. The author has elsewhere (1950) reviewed the geophysical setting and the extensive array of observa- E use the term hydromagnetism synonymously tional data substantiating the model of the geophysical ~ with magnetohydrodynamics which is preferred has for a ~ dynamo.
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