1.1: Background

There are two branches to the area of electromagnetics. One is primarily concerned with electromagnetic waves. Typically of interest are guided and propagating waves ranging from radio to optical frequencies. These may propagate through free space, in plasmas or through optical fibers. Although the interaction of electromagnetic waves with media of great variety is of essential interest, and indeed the media modify these waves, it is the electromagnetic wave that is at center stage in this branch. Dynamical phenomena of interest to this branch are typified by times, \(\tau\), shorter than the transit time of an electromagnetic wave propagating over a characteristic length of the "system" being considered. For a characteristic length \(l\) and wave velocity \(c\) (in free space, the velocity of light), this transit time is \(l/c\).

In the chapters that follow, it is the second branch of electromagnetics that plays the major role. In the sense that electromagnetic wave transit times are short compared to times of interest, the electric and magnetic fields are quasistatic: \(\tau >> l/c\). The important dynamical processes relate to conduction phenomena, to the mechanics of ponderable media, and to the two-way interaction created by electromagnetic forces as they elicit a mechanical response that in turn alters the fields.

Because the mechanics can easily upstage the electromagnetics in this second branch, it is likely to be perceived in terms of a few of its many parts. For example, from the electromagnetic point of view there is much in common between issues that arise in the design of a synchronous alternator and of a fusion experiment. But, on the mechanical side, the rotating machine, with its problems of vibration and fatigue, seems to have little in common with the fluid-like plasma continuum. So, the two areas are not generally regarded as being related.

In this text, the same fundamentals bear on a spectrum of applications. Some of these are reviewed in Sec. 1.2. The unity of these widely ranging topics hinges on concepts, principles and techniques that can be traced through the chapters that follow. By way of a preview, Secs. 1.3-1.7 are outlines of these chapters, based on themes designated by the section headings.

Chapters 2 and 3 are concerned with fundamentals. First the laws and approximations are introduced that account for the effect of moving media on electromagnetic fields. Then, the-force densities and associated stress tensors needed to account for the return influence of the fields on the motion are formulated.

Chapter 4 takes up the class of devices and phenomena that can be described by models in which the distributions (or the relative distributions) of both the material motion and of the field sources are constrained. This subject of electromechanical kinematics embraces lumped parameter electromechanics. The emphasis here is on using the field point of view to determine the relationship between the lumped parameters and the physical attributes of devices, and to determine the distribution of stress and force density.

Chapters 5 and 6 retain the mechanical kinematics, but delve into the self-consistent evolution of fields and sources. Motions of charged microscopic and macroscopic particles entrained in moving media are of interest .in their own right, but also underlie the limitations of commonly used conduction constitutive laws. These chapters both introduce basic concepts, such as the Method of Characteristics and temporal and spatial modes, and model practical devices ranging from the electrostatic precipitator to the linear induction machine.

Chapters 7-11 treat interactions of fields and media where not only the field sources are free to evolve in a way that is consistent with the effect of deforming media, but the mechanical systems respond on a continuum basis to the electric and magnetic forces.

Chapter 7 introduces the basic laws and approximations of fluid mechanics. The formulation of laws, deduction of boundary conditions and use of transfer relations is a natural extension of the viewpoint introduced in the context of electromagnetics in Chapter 2.

Chapter 8 is concerned with electromechanical static equilibria and the dynamics resulting from perturbing these equilibria. Illustrated are a range of electromechanical models motivated by Chaps. 5 and 6. It is here that temporal instability first comes to the fore.

Chapter 9 is largely devoted to electromechanical flows. Included is a discussion of flow development, understood in terms of the same physical processes represented by characteristic times in the previous four chapters. Flows that display super- and sub-critical behavior presage causal effects of wave propagation taken up in Chapter 11. The last half of this chapter is an introduction to "direct" thermal-to-electric energy conversion.

Chapter 10 is divided into parts that are each concerned with diffusion processes. Thermal diffusion, together with convective heat transfer, is considered first. Electrical dissipation accompanies almost all electromechanical processes, so that heat transfer often poses an essential limitation on invention and design. Because fields are often used for dielectric or induction heating, this is a subject in its own right. This part begins with examples where the coupling is "one-way" and ends by consider some of the mechanisms for two-way coupling between the thermal and electromechanical subsystems. The second part of this chapter serves as an introduction to electromechanical processes that occur on a spatial scale small enough that molecular diffusion processes come into play. Here introduced is the interplay between electric and mechanical stresses that makes it possible for particles to undergo electrophoresis rather than migrate in an electric field. The concepts introduced in this second part are applicable to physicochemical systems and point to the electromechanics of biological systems.

Chapter 11 brings together models and concepts from Chaps. 5-10, emphasizing streaming interactions, in which ordered kinetic energy is available for participation in the energy conversion process Included are fluid-like continua such as electron beams and plasmas.