Stretch, Twist, Fold: The Fast Dynamo

1. Front Matter

   Pages I-XI

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2. Introduction: Ideas and Examples

   1. The Fast Dynamo Problem

      Pages 1-30

   2. Fast Dynamo Action in Flows

      Pages 31-60

   3. Fast Dynamos in Maps

      Pages 61-87

3. Methods and Their Application

   1. Dynamos and Non-dynamos

      Pages 89-111

   2. Magnetic Structure in Steady Integrable Flows

      Pages 113-147

   3. Upper Bounds

      Pages 149-184

   4. Magnetic Structure in Chaotic Flows

      Pages 185-212

   5. Nearly Integrable Flows

      Pages 213-244

   6. Spectra and Eigenfunctions

      Pages 245-288

   7. Strongly Chaotic Systems

      Pages 289-317

   8. Random Fast Dynamos

      Pages 319-341

   9. Dynamics

      Pages 343-380

4. Back Matter

   Pages 381-406

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The study of the magnetic fields of the Earth and Sun, as well as those of other planets, stars, and galaxies, has a long history and a rich and varied literature, including in recent years a number of review articles and books dedicated to the dynamo theories of these fields. Against this background of work, some explanation of the scope and purpose of the present monograph, and of the presentation and organization of the material, is therefore needed. Dynamo theory offers an explanation of natural magnetism as a phenomenon of magnetohydrodynamics (MHD), the dynamics governing the evolution and interaction of motions of an electrically conducting fluid and electromagnetic fields. A natural starting point for a dynamo theory assumes the fluid motion to be a given vector field, without regard for the origin of the forces which drive it. The resulting kinematic dynamo theory is, in the non-relativistic case, a linear advection-diffusion problem for the magnetic field. This kinematic theory, while far simpler than its magnetohydrodynamic counterpart, remains a formidable analytical problem since the interesting solutions lack the easiest symmetries. Much ofthe research has focused on the simplest acceptable flows and especially on cases where the smoothing effect of diffusion can be exploited. A close analog is the advection and diffusion of a scalar field by laminar flows, the diffusion being measured by an appropriate Peclet number. This work has succeeded in establishing dynamo action as an attractive candidate for astrophysical magnetism.

• Chaotic Dynbamics
• Dynamo Theory
• Integrable Flows
• Natural Magnetism
• spectra

"This excellent book by two leading researchers in dynamo theory is highly recommended, both to those interested in the way magnetic fields are generated in the cosmos and also to mathematicians who wish to learn how modern nonlinear dynamics theory is being applied to a classic problem..." The Observatory

• Courant Institute of Mathematical Sciences, New York University, New York, USA

  Stephen Childress

• Department of Mathematics, Laver Building, University of Exeter, Exeter, UK

  Andrew D. Gilbert

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