Über die Autorin bzw. den Autor

Eugene N. Parker

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"Nobody has contributed more, or more deeply, to our understanding of the physics of astrophysical magnetofluids than Eugene Parker. Conversations on Electric and Magnetic Fields in the Cosmos provides those of us who have had the privilege of learning directly from him a chance to revisit the elegant insight, structure, and breezy wit that Parker brings to the subject. For those who have not had that privilege, this book provides lasting opportunity to visit with a master."--Eugene H. Levy, Rice University

"This small book, which describes the basic physics that governs the electrodynamics of the cosmos, is graced by insights the author gleaned during a lifelong fascination with the subject matter. We owe to him the explanation of many natural phenomena including how the solar wind blows and why its magnetic field lines form Archimedian spirals. Another of his creations, the a-? dynamo model affords us our understanding of how the magnetic fields of planets are maintained against resistive decay and why the Sun's magnetic field reverses every eleven years."--Peter Goldreich, Institute for Advanced Study, Princeton

"This is a book by one of the leaders in the field of plasma astrophysics. Parker sets the record straight on many misunderstandings concerning electric and magnetic fields in the cosmos. The book also presents a revealing picture of the author's thinking and displays how he was able to arrive at such original solutions to so many important astrophysical problems."--Russell M. Kulsrud, author of Plasma Physics for Astrophysics

"This is a unique undertaking by a scientist who is one of the most accomplished and outstanding in our field. The book takes the reader from the elementary principles of Newtonian mechanics and Maxwell's equations to hydrodynamics and magnetohydrodynamics equations. The author has intended this book to be conversations, as the title indicates. The style is informal but the physical ideas and concepts are presented with precision."--B. C. Low, National Center for Atmospheric Research

"Parker is one of the leaders in the field and has his own novel approach to plasma astrophysics. I believe that both students and active researchers will benefit from this book."--David Spergel, Princeton University

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Conversations on Electric and Magnetic Fields in the Cosmos

Princeton University Press

Introduction

The theoretical structure of electric and magnetic fields is presented in the standard textbooks, and one may ask why further conversation on the subject is useful or interesting. What is new that has not already been said many times before? The reply is that the emphasis in the usual formulation of electromagnetism is directed toward static electric and magnetic fields and then to electromagnetic radiation, whereas we are interested here in the electromagnetism of the cosmos-the large-scale magnetic fields that are transported bodily in the swirling ionized gases (plasmas) of planetary magnetospheres, stars, and galaxies, and, indeed, throughout intergalactic space. The plasma and the magnetic fields appear to be everywhere throughout the universe. The essential feature is that no significant electric field can arise in the frame of reference of the moving plasma. Hence, the large-scale dynamics of the magnetic field is tied to the hydrodynamics (HD) of the swirling plasma in the manner described by theoretical magnetohydrodynamics (MHD). So we shall have a fresh look at the theoretical foundations of both HD and MHD. The conventional derivations of the basic equations of HD and MHD are correct, of course, but the derivations ignore some fundamental questions, allowing a variety of misconceptions to flourish in the scientific community. We work out a minimal physical derivation, laying bare the simplicity of the necessary and sufficient conditions for the validity of HD and MHD to describe the large-scale bulk motion of plasmas and their magnetic fields. The essential condition for HD is that there be enough particles to give a statistically precise definition of the local plasma density; the essential condition for MHD is that there be enough free electrons and ions that the plasma cannot support any significant electric field in its own moving frame of reference. Both of these requirements are satisfied almost everywhere throughout the cosmos, with the result that HD and MHD accurately describe the large-scale bulk dynamics of the plasmas and fields. The magnetic field is transported bodily with the bulk motion of the plasma, and the dynamics is basically the mechanical interaction between the stresses in the magnetic field B and the pressure [p.sub.ij] and bulk momentum density NMv of the plasma velocity v. The associated electric current j and the electric field E in the laboratory frame of reference play no direct role in the dynamics. They are created and driven by the varying B and v. If needed for some purpose, they are readily computed once the dynamics has provided B and v.

It is here that a fundamental misunderstanding has become widely accepted, mistaking the electric current j and the electric current E (the E, j paradigm) (Parker 1996a) to be the fundamental physical entities. Steady conditions often can be treated using the E, j paradigm, but the dynamics of time-dependent systems becomes difficult, if not impossible, because of the inability to express Newton's equation in terms of E and j in a tractable form. That is to say, E and j are proxies for B and v, but too remote from B and v to handle the momentum equation. So it is not possible to construct a workable set of dynamical field equations in terms of j and E from the equations of Newton and Maxwell. The generalized Ohm's law is often employed, but Ohm's law does not control the large-scale dynamics. The tail does not wag the dog. This inadequacy has led to fantasy to complement the limited equations available in the E, j paradigm, attributing the leading dynamical role to an electric field E with unphysical properties. Magnetospheric physics has suffered severely from this misdirection, and we will come back to the specific aspects of the misunderstanding at appropriate places in these conversations.

The essential point is that we live in a magnetohydrodynamic universe in which the magnetic field B is responsible for the remarkable behavior of the gas velocity v, and vice versa. Then we must recognize that the large-scale magnetic stresses in the interlaced field line topologies created by the plasma motions have the peculiar property of causing the field gradients to increase without bound. The resulting thin layers of intense field shear and high current density "eat up" the magnetic fields at prodigious rates. The effect is commonly called rapid reconnection of the magnetic field because the field lines are cut and rejoined across the intense shear layer, and it is a universal consequence of the large-scale field line topology. Rapid reconnection is evidently responsible for such phenomena as the solar flare, the million degree temperature of the solar X-ray corona, and the terrestrial aurora. So the MHD universe is far more active and interesting than a purely HD universe, with the magnetic activity of the Sun an outstanding example. R. W. Leighton remarked many years ago that if it were not for magnetic fields, the Sun would be as uninteresting as most astronomers seem to think it is. The activity of the Sun is the model, then, for the unresolved activity of other stars.

The conversation is intended to complement, rather than replace, the familiar textbook development of electromagnetic theory and of HD and MHD. It is assumed that the reader is already familiar with the conventional development of electromagnetic theory, and it is to be hoped that the reader has the patience to follow the conversation when it briefly reiterates some of that familiar boilerplate, because the basics are necessarily the same, even as we provide a different emphasis.

There will be some new twists to the development along with the boilerplate. For instance, we show that the Biot-Savart integral form of Ampere's law implies Maxwell's equation. This will-o'-the-wisp is rediscovered every decade or so, but never seems to get into the standard textbooks. It has amusing implications for the early controversy over Maxwell's equation. Then we point out the singular properties of the Maxwell stress tensor in arbitrary equilibrium field topologies.

We show that the familiar equations of hydrodynamics are required by the principles of conservation of particles, momentum, and energy in the large-scale bulk flow of the plasma. These are valid principles regardless of the presence or absence of interparticle collisions and magnetic fields. As already noted, HD is valid so long as there are enough particles to provide a statistically well-defined fluid density, contrary to what one sometimes reads in the literature about the relatively collisionless plasma. We show, too, that the familiar equations of magnetohydrodynamics are inescapable unless there are so few free electrons and ions that the gas is an effective electrical insulator. The air that we breathe is an example, and only upon reaching the ionosphere does MHD become effective.

In particular, the conversation emphasizes the principle-Occam's razor-that the theoretical concepts should contain no unnecessary embellishments. So we prune away concepts and notation that are not vital to the experimental physics, and we note in particular that physical reality is made up of the manner in which things are experimentally perceived to be. This seemingly trivial point is commonly violated by the vocabulary of magnetic induction, and it leads us into conflict with a variety of customs and...