Waves and Oscillations in Plasmas

Hans L. Pecseli

• Publisher: CRC Press
• Year: 2020
• Print ISBN: 9781032236421
• eBook ISBN: 9780429953507
• Edition: 2
• Topic: Computer Science
• Subtopic: Computer Science General
• Index: Computer Science

Waves and Oscillations in Plasmas addresses central issues in modern plasma sciences, within the context of general classical physics. The book is working gradually from an introductory to an advanced level. Addressing central issues in modern plasma sciences, including linear and nonlinear wave phenomena, this second edition has been fully updated and includes the latest developments in relevant fluid models as well as kinetic plasma models, including a detailed discussion of, for instance, collisionless Landau damping, linear as well as non-linear. The book is the result of many years of lecturing plasma sciences in Norway, Denmark, Germany, and also at the Unites States of America.

Offering a clear separation of linear and nonlinear models, the book can be tailored for students of varying levels of expertise in plasma physics, in addition to areas as diverse as the space sciences, laboratory experiments, plasma processing, and more.

Features:

• Presents a simple physical interpretation of basic problems is presented where possible
• Supplies a complete summary of classical papers and textbooks placed in the proper context
• Includes worked examples, exercises, and problems with general applicability
  

1

Introduction

1.1What is a plasma?

Plasma physics deals, in its most general form, with studies of the dynamics of charged particles. In principle this includes the motions of single charged particles in a priori given electric and magnetic fields, but the most interesting problems are concerned with collective interactions between many charged particles. In these cases it is the charge and current distributions resulting from all the particles which ultimately set up the electric and magnetic fields, which together with externally imposed fields determine the self-consistent motion of the plasma particles themselves.

1.2Where do we find plasma?

When the author was a PhD student, we proudly stated that more than 99% of matter in the known universe was supposed to be in the plasma state, and therefore this particular state of matter should actually be the most interesting one! Today we have to be somewhat more modest, stating that 99% of visible matter is in the plasma state, but after all, this is still quite something! Even this percentage may appear surprisingly large, but one should bear in mind that, for instance, in our own solar system, the Sun represents by far the largest accumulation of matter, and because of the high temperatures there, the material in the Sun is almost completely ionized.

More recently, it has been realized that studies of the plasma state include topics which have important industrial applications (Lieberman & Lichtenberg 1994, Roth 1995). Discharges become increasingly important for ion production. To increase the reaction rate of chemical processes it is generally advantageous to increase the temperature of the mixture, and as a consequence, a significant part of the constituents can become ionized. Charged dust has been found to be a serious problem in some industrial plants, and simultaneously it was discovered that this particular state also has an important role in a number of natural phenomena as well. Charged dust particles will in many ways behave as super massive ions with positive or negative charge depending on conditions (Shukla & Mamun 2002a, Piel 2010), and this should be easy enough to incorporate in analytical models. By closer inspection it is, however, found that the charges are fluctuating in time, and the average charge on a dust particle will in general depend on its velocity as well as other dynamic conditions. These and related phenomena are being intensely studied, but the field is still “young” and it will not be covered in the present book.

1.3Plasma physics – why bother?

The dynamics of hot plasmas are in many respects similar to those of neutral gases, and in many cases it might be argued that no particular new physical insight is gained by including elements from plasma physics in the analysis. Plasma sciences as an individual discipline cannot be justified by such examples. There are, however, a number of phenomena which are specific and unique for plasmas. The most notable is magneto-hydrodynamics (MHD), with Alfvén waves being an illustrative example. Also the stability properties of hot dilute plasmas as described by kinetic plasma theory are uniquely plasma related. These examples are not just of academic interest: MHD, for instance, is of central importance for our description and understanding of large scale phenomena in the magnetospheres of planets and stars, such as the Sun in our solar system.

While MHD can be considered as a sort of effective “fluid-like” model for describing the dynamics of a plasma, there is another, in a certain sense complementary, so called “kinetic” description of what is called “collisionless” plasmas. In many ways this description has very surprising implications. That analysis attempts to describe the space-time evolution of the velocity distributions of the particles constituting the plasma. It turns out that a new form of wave damping is discovered, collisionless Landau damping, which is present even though the basic dynamic equations are fully time reversible, in complete variance with experience from electrical circuits, for instance.

One major stimulus for the development of plasma sciences in the time following the mid-1950s can be identified as its importance for controlled fusion (Wilhelmsson 2000, Braams & Stott 2002). An interesting (and beautifully illustrated) account of the early U.S. fusion program is given by Bishop (1958). It seems plausible that the energy demands of mankind can be satisfied for all the foreseeable future if we succeed in harnessing fusion processes. Several concepts have been suggested, and practically all of them involve confinement of matter at temperatures of millions of degrees, a state where we can safely assume all particles to be fully ionized, and constituting what we call a plasma.

Fusion plasma physics will not have any pronounced place in the present treatise, but a few illustrative examples in the form of exercises may be in order.

ⓈExercise: Thermonuclear fusion will not be discussed much in the present book, but it seems appropriate as a minimum to present an exercise to illustrate the importance of the topic.

In a deuterium (D) plasma at temperatures ∼100 keV and an ion density of N = 10¹⁴ cm⁻³ we have the following dominating nuclear reactions

D+D→T+p+4.03MeV,	(1.1)

D+D→He3+n+3.27MeV,	(1.2)

where T stands for tritium, He for helium, p for proton and n for neutron. The reactions occur at such a rate that the number of reactions per sec are 12N2I, where I = 2.3 × 10⁻¹⁷ cm³/s for (1.1) and I = 2.8 × 10⁻¹⁷ cm³/s for (1.2). The expressions for the reaction rates are here to be seen simply as given, but intuitively it seems reasonable that they are proportional to the densities N squared, since two atoms must be present in order to have a fusion process. (Usually we would use n for particle density, but in this particular context we want to avoid confusion with the neutron symbol.) If we had fusion of D and T, we expect the product of the respective densities N_D and N_T to enter. The I’s then account for the probability of fusion processes to occur at the given temperature, provided the two atoms are present. How large is the fusion produced power density in the plasma? For how long does the process have to continue in order to produce the amount o...

Table of contents

• Cover
• Half Title
• Series Page
• Title Page
• Copyright Page
• Contents
• Preface to Second revised edition
• 1. Introduction
• 2. Basics of Continuum Models
• 3. Linear Wave Dynamics
• 4. Weakly Nonlinear Waves
• 5. Basics of Electromagnetism
• 6. Plasmas Found in Nature
• 7. Single Particle Motion
• 8. Basic Plasma Parameters
• 9. Experimental Devices
• 10. Magneto-Hydrodynamics by Brute Force
• 11. Plasma as a Mixture of Charged Gases
• 12. Waves in Cold Plasmas
• 13. Electrostatic Waves in Warm Homogeneous and Isotropic Plasmas
• 14. Fluid Models for Nonlinear Electrostatic Waves: Isotropic Case
• 15. Small Amplitude Waves in Anisotropic Warm Plasmas
• 16. Fluid Models for Nonlinear Electrostatic Waves: Magnetized Case
• 17. Linear Drift Waves
• 18. Weakly Nonlinear Electrostatic Drift Waves
• 19. Kinetic Plasma Theory
• 20. Kinetic Description of Electron Plasma Waves
• 21. Kinetic Plasma Sound Waves
• 22. Nonlinear Kinetic Equilibria
• 23. Nonlinear Landau Damping
• 24. Quasi-linear Theory
• A Dimensional Analysis
• B Collisional Cross Sections
• C The Plasma Dispersion Function
• D Mathematical Theorems and Useful Relations
• Bibliography
• Index