Introduction

Chapter Outline Head

1.1 Introduction   2

1.2 Plasmas   5

1.3 System of Units   8

1.3.1 The Gaussian System   9

1.3.2 The SI System   9

1.3.3 Maxwell's Equations and Lorentz Force on a Unit Charge q   9

1.4 Characteristic Lengths and Times in a Plasma   10

1.5 Scattering of Electromagnetic Radiation by a Plasma   11

1.6 Radiation by a Moving Charge   12

1.7 Acceleration of a Charge by an Electromagnetic Wave   14

1.7.1 Low-Velocity Charge (v/c 1) with No Other Forces Acting   15

1.7.2 High-Velocity Charge with No Other Forces Acting   18

1.7.3 Low-Velocity Charge (v/c 1) with Additional Forces Acting   19

1.7.4 High-Velocity Charge with Applied Magnetic Fields   19

1.8 General Restrictions Applied to Calculations in This Book   20

1.8.1 Macroscopic Interaction of Radiation with a Plasma   20

1.8.2 General Restrictions   21

1.8.3 Noncollective and Collective Spectra   23

Problems   24

Solutions to Odd Problems   25

1.1 INTRODUCTION

It is well known that electromagnetic radiation is emitted by an accelerating charge. An important example of this phenomenon occurs when acceleration is induced by an electromagnetic wave. This interaction, when the incident radiation is of sufficiently low frequency ? that ?? is much less than mec2, the rest energy of the charge, is generally referred to as Thomson scattering.1 It is the extension of the theory to include the simultaneous scattering from a large number of free positive and negative charges, that is, a plasma, and the experimental application of scattering that are the topics discussed in this book.

For a single charge, the angular distribution of intensity, the frequency, and the phase of the scattered radiation depend on the orbit of that charge relative to the observer. Equally, for a large group of charges, the scattered spectrum is related to the orbits of all those charges, or rather in practice, to some average taken over the probable behavior of the group. Anticipating the results derived below, we find that from the spectrum of radiation scattered from a plasma, we may in principle determine the electron and ion temperature, the ionization state, densities the ionization state, the direction and magnitude of a magnetic field in the plasma, and in general, information about all the fluctuations (waves, instabilities) within the plasma. In reality, we are of course limited by the radiation sources available to us; the cross section for scattering is so small that measurements on laboratory plasmas were limited until the advent of high-power lasers. The first measurements were by the scattering of radio waves from the ionosphere in the late 1950s. The history of the subject is discussed briefly in Appendix E.

CHAPTER 1

The purpose of this introductory chapter is to remind the reader of some basic properties of a plasma and of the interaction of radiation with a plasma. The conditions under which radiation will penetrate a plasma are established. The discussion is then restricted to situations where the radiation is primarily transmitted. In this situation, we can reasonably deal with the interaction of each charge in the plasma taken independently. The response of a single charge to radiation is then evaluated. The scattered power is found to be inversely proportional to the mass of a charge, and thus, we can see immediately that the scattering is essentially only from the electrons.

Finally, the problem of adding up the scattered waves from the large number of electrons in the scattering volume is discussed in general terms. The scattered spectrum is found to have two parts. The first is the spectrum that would be obtained if there were no charge interactions, the "noncollective spectrum." The second is a result of these interactions (collective effects).

CHAPTER 2

In this chapter, a general relationship is derived between the scattered power spectrum and the fluctuations in plasma density. The spectral density function S(k, ?) is introduced.

CHAPTER 3

The general scattered spectrum for an unmagnetized quasi-equilibrium plasma is derived. The effect of collisions on the result is determined.

CHAPTER 4

A derivation is given of the noncollective spectrum for a plasma, including a steady magnetic field. The application of the results is discussed.

CHAPTER 5

The results of the general scattered spectrum (Chapter 3) in the collective regime are analyzed, and their experimental applications are discussed. These are illustrated by reference to some of the significant experimental work in the field.

CHAPTER 6

The constraints and problems that arise in the application of scattering as a diagnostic technique are discussed.

CHAPTER 7

The characteristic performance of various dispersion elements, image dissectors, and detectors is reviewed.

CHAPTER 8

Some interesting applications of scattering are discussed to illustrate the use of Thomson scattering.

CHAPTER 9

Industrial plasmas, scattering from energetic ions, and fusion plasmas are discussed.

CHAPTER 10

A derivation is given of the general scattering spectrum for a magnetized plasma, and the application of the results is discussed.

CHAPTER 11

The use of hard x-rays (high energy photons) is discussed for probing warmdense matter and dense plasmas. Recent applications in the Compton and plasmon scattering regime are presented.

CHAPTER 12

Work on the scattering from unstable plasmas is reviewed, e.g., the scattering from enhanced fluctuations driven by plasma wave turbulence or laser-plasma interaction.

APPENDIX A

A brief review is given of relevant mathematical techniques.

APPENDIX B

The kinetic theory of plasmas is reviewed.

APPENDIX C

A derivation of the general dispersion relation for a hot, magnetized uniform plasma is presented.

APPENDIX D

A brief discussion of computational techniques used to calculate the Thomson scattering spectrum is given. A simple computational method for solving for the scattering spectrum is presented.

APPENDIX E

A historical review of work on the scattering of radiation from plasmas is given.

APPENDIX F

This appendix contains a list of physical constants and significant formulas. The latter includes a list of the various scattered spectra obtained under different approximations.

1.2 PLASMAS

A plasma is an assembly of free electrons and positive ions, which is essentially neutral. Thus, while locally there may be a charge imbalance, in the assembly as a whole, there are to a very good approximation equal number of electrons and positive ions. The term "plasma" was used by Langmuir (1928) as a description of the ionized state found in an arc discharge. For gases at temperatures2 >1 eV (11,600 K), there are many particles in the high-energy tail of the distribution function with sufficient energy to ionize, and consequently large numbers of free charges. The ideal plasma state may be characterized by the following ordering of characteristic scale lengths:

c«n-1/3«?De«?c,Lp,

  (1.2.1)

where rc = q2/?T is the distance at which the potential and kinetic energies are equal when two like charges q approach each other; n-1/3 is the average interparticle separation; n is the number density of charges; ?De, the "Debye length," is the characteristic distance over which the potential of a charge is shielded by neighboring charges; ?c is the mean collision length, c=1/4prc2n for simple 90° Rutherford scattering; and Lp is a representative dimension of the plasma.

The key features...