Fundamentals of Plasma Physics

Citation

Bittencourt, J. A. (2004). Fundamentals of Plasma Physics (3rd ed.). Springer.

Chapter Summary

The book has 22 chapters and runs to about 680 pages. It starts from the motion of single charged particles, builds up kinetic theory and the fluid (magnetohydrodynamic) description of a plasma, spends a long middle stretch on waves, and closes with collisions and transport. It is organised around theory rather than devices or experiments.

Chapter 1: Introduction

Sets the scene with sections on the occurrence of plasmas in nature and on the theoretical ways of describing plasma phenomena, which prepares the choice between particle, kinetic and fluid models used later.

Chapters 2–4: Charged Particle Motion in Constant and Uniform Electromagnetic Fields; Charged Particle Motion in Nonuniform Magnetostatic Fields; Charged Particle Motion in Time-Varying Electromagnetic Fields

The single-particle part. Chapter 2 treats uniform electrostatic and magnetostatic fields. Chapter 3 moves to nonuniform magnetic fields with a first-order approximation of the equation of motion, including gradient drift and curvature drift. Chapter 4 adds time-varying fields and ends with a summary of guiding-centre drifts.

Chapters 5–7: Elements of Plasma Kinetic Theory; Average Values and Macroscopic Variables; The Equilibrium State

The statistical foundation: the kinetic equation with a relaxation model for the collision term, then the moments of the distribution function (pressure tensor and higher moments), then the Maxwell–Boltzmann equilibrium and the degree of ionization in equilibrium.

Chapters 8–9: Macroscopic Transport Equations; Macroscopic Equations for a Conducting Fluid

Moment equations, including momentum conservation and the cold-plasma model, lead to the electrodynamic equations of a conducting fluid and a simplified set of magnetohydrodynamic equations.

Chapters 10–11: Plasma Conductivity and Diffusion; Some Basic Plasma Phenomena

Chapter 10 covers conductivity and mobility (including a linearized Langevin equation and AC conductivity) and diffusion in magnetic fields and in a fully ionized plasma. Chapter 11 turns to basic phenomena such as Debye shielding derived from the Vlasov equation, and a section on the plasma probe.

Chapters 12–13: Simple Applications of Magnetohydrodynamics; The Pinch Effect

Magnetic viscosity and Reynolds number, the freezing of field lines into the plasma, magnetic pressure and confinement in a magnetic field. Chapter 13 applies this to the equilibrium pinch, the Bennett pinch, a dynamic model, and the sausage and kink instabilities.

Chapters 14–15: Electromagnetic Waves in Free Space; Magnetohydrodynamic Waves

Chapter 14 reviews plane and harmonic waves, polarization, energy flow, wave packets and group velocity as groundwork. Chapter 15 treats magnetohydrodynamic wave propagation, including propagation perpendicular to the magnetic field and the effect of the displacement current.

Chapters 16–19: Waves in Cold Plasmas; Waves in Warm Plasmas; Waves in Hot Isotropic Plasmas; Waves in Hot Magnetized Plasmas

Four chapters take the wave problem in order of increasing physical detail: cold plasmas (isotropic electron plasmas, then magnetized plasmas with propagation parallel and at arbitrary angles to the field, and special wave phenomena), warm plasmas, hot isotropic plasmas (electrostatic longitudinal and transverse waves), and hot magnetized plasmas.

Chapters 20–22: Particle Interactions in Plasmas; The Boltzmann and the Fokker–Planck Equations; Transport Processes in Plasmas

The closing chapters return to collisions: binary collision dynamics and cross sections, the Boltzmann equation with the H function, the Fokker–Planck equation, and finally electric conductivity in a magnetized plasma, free diffusion and heat flow. Appendices follow.

Key Concepts

• Guiding-centre drifts: the slow motion of a charged particle's gyration centre in nonuniform or time-varying fields (gradient and curvature drift are named in the contents).
• Kinetic description and moments: working from a distribution function and its moments to obtain macroscopic variables such as the pressure tensor.
• Collision term and Fokker–Planck equation: the treatment of collisions, from a relaxation model to the Boltzmann and Fokker–Planck equations.
• Magnetohydrodynamics: the conducting-fluid description, including field-line freezing and magnetic pressure.
• Debye shielding: screening of charge in a plasma, derived from the Vlasov equation.
• Pinch equilibrium and instabilities: the equilibrium and Bennett pinch, with sausage and kink instabilities.
• Wave propagation in cold, warm and hot plasmas: dispersion of waves with increasing complexity of the plasma model, with and without a background magnetic field.

Critical Analysis

Strengths

• Derivations written out. The publisher's description says the emphasis is on clarity rather than formality, that the mathematics is set out in great detail with the steps normally left to the reader carried out, and that physical interpretations are given wherever possible.
• Problems with guidance. According to the same description, the problems are an integral part of the text and most are designed with intermediate steps and answers, which suits independent study; the description presents the book as suitable for self-learning and self-paced courses.
• A single line of development. The contents move from single particles to kinetic theory, fluid equations, waves and collision-based transport, so the fluid and wave chapters can be traced back to their kinetic origin.
• Extensive wave coverage. Six of the 22 chapters (14–19) concern waves, ordered by model, which gives a clear progression for a course on plasma waves.

Limitations

• Theory-centred. The chapter list contains no chapter on experimental methods or on a particular application area; devices and diagnostics appear only as sections (the pinch, the plasma probe).
• Length and pace. At about 680 pages with detailed derivations, the book is more than a one-semester course can cover in full, and selection is needed.
• Date. The book is from 2004, so developments since then are outside it.

Where It Fits in the Course

Within the electromagnetism course, Bittencourt is a specialist text: it applies Maxwell's equations and charged-particle dynamics to ionized gases rather than teaching electromagnetism itself. It is best read after a standard electrodynamics text such as Griffiths's Introduction to Electrodynamics (an advanced-undergraduate course in the theory) and, for the wave chapters, alongside Jackson's Classical Electrodynamics, the graduate treatment of fields, wave propagation and radiation. Purcell and Morin's Electricity and Magnetism and the OpenStax University Physics Volume 2 are first courses, and Fleisch's A Student's Guide to Maxwell's Equations is a short companion to the four equations; all three come before this book.

How to Use This Book

The book suits a graduate student or an advanced undergraduate who wants a first systematic course in plasma physics and is comfortable with electromagnetism, statistical mechanics, vector calculus and differential equations (the prerequisites given on the site).

A practical plan: read Chapters 1–4 for particle orbits; Chapters 5–9 for the kinetic-to-fluid chain, which everything later depends on; then choose a path. For magnetic confinement, continue with Chapters 10–13. For waves, read Chapter 14 quickly, then Chapters 15–16 and, if time allows, Chapters 17–19. Chapters 20–22 are for readers who need collisions and transport in depth. Work the problems as they come, using the intermediate steps and answers they provide, and treat the cold-plasma wave chapter as the first target if only one wave chapter can be read.