Stretch, Twist, Fold: The Fast Dynamo

ISBN-13: 9783662140147 / Angielski / Miękka / 2013 / 408 str.

Stephen Childress; Andrew D. Gilbert

Opis

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.

Recenzje

"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

Spis treści

Introduction: Ideas and Examples.- The Fast Dynamo Problem.- Fast Dynamo Action in Flows.- Fast Dynamos in Maps.- Methods and Their Application.- Dynamos and Non-dynamos.- Magnetic Structure in Steady Integrable Flows.- Upper Bounds.- Magnetic Structure in Chaotic Flows.- Nearly Integrable Flows.- Spectra and Eigenfunctions.- Strongly Chaotic Systems.- Random Fast Dynamos.- Dynamics.

Blurb

This monograph addresses those interested in the study of planetary or solar magnetic fields, astronomers and geophysicists, researchers and students alike. The authors explore dynamo action under conditions appropriate to large astrophysical bodies, the magnetic Reynolds number of the flow being large compared to unity. In this limit dynamo action becomes closely linked with stretching properties of the flow. The concept of a fast dynamo is explained and studied using various methods from dynamical systems theory. Emphasis is placed on explicit, simple examples of fast dynamos. These examples suggest the beginnings of a theory of fast dynamo action, and link the physical process to the analysis of the stretching, folding, and twisting properties of the flow. A number of special formulations are considered, including dynamo action in almost integrable flows, dynamo action in the anti-integrable limit, and the analysis of random fast dynamos.