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**Description**

This text is based on a course I have taught for many years to first year graduate and senior-level undergraduate students at Caltech. One outcome of this teaching has been the realization that although students typically decide to study plasma physics as a means towards some larger goal, they often conclude that this study has an attraction and charm of its own; in a sense the journey becomes as enjoyable as the destination. This conclusion is shared by me and I feel that a delightful aspect of plasma physics is the frequent transferability of ideas between extremely different applications so, for example, a concept developed in the context of astrophysics might suddenly become relevant to fusion research or vice versa.

**Content:-**

Preface

1.1 History of the term “plasma”

1.2 Brief history of plasma physics

1.3 Plasma parameters

1.4 Examples of plasmas

1.5 Logical framework of plasma physics

1.6 Debye shielding

1.7 Quasi-neutrality

1.8 Small v. large angle collisions in plasmas

1.9 Electron and ion collision frequencies

1.10 Collisions with neutrals

1.11 Simple transport phenomena

1.12 A quantitative perspective

1.13 Assignments

2.1 Phase-space

2.2 Distribution function and Vlasov equation

2.3 Moments of the distribution function

2.4 Two-fluid equations

2.5 Magnetohydrodynamic equations

2.6 Summary of MHD equations

2.7 Sheath physics and Langmuir probe theory

2.8 Assignments

3.1 Motivation

3.2 Hamilton-Lagrange formalism v. Lorentz equation

3.3 Adiabatic invariant of a pendulum

3.4 Extension of WKB method to general adiabatic invariant

3.5 Drift equations

3.6 Relation of Drift Equations to the Double Adiabatic MHD Equations

3.7 Non-adiabatic motion in symmetric geometry

3.8 Motion in small-amplitude oscillatory fields

3.9 Wave-particle energy transfer

3.10 Assignments

**1 Basic concepts**1.1 History of the term “plasma”

1.2 Brief history of plasma physics

1.3 Plasma parameters

1.4 Examples of plasmas

1.5 Logical framework of plasma physics

1.6 Debye shielding

1.7 Quasi-neutrality

1.8 Small v. large angle collisions in plasmas

1.9 Electron and ion collision frequencies

1.10 Collisions with neutrals

1.11 Simple transport phenomena

1.12 A quantitative perspective

1.13 Assignments

**2 Derivation of fluid equations: Vlasov, 2-fluid,MHD**2.1 Phase-space

2.2 Distribution function and Vlasov equation

2.3 Moments of the distribution function

2.4 Two-fluid equations

2.5 Magnetohydrodynamic equations

2.6 Summary of MHD equations

2.7 Sheath physics and Langmuir probe theory

2.8 Assignments

**3 Motion of a single plasma particle**3.1 Motivation

3.2 Hamilton-Lagrange formalism v. Lorentz equation

3.3 Adiabatic invariant of a pendulum

3.4 Extension of WKB method to general adiabatic invariant

3.5 Drift equations

3.6 Relation of Drift Equations to the Double Adiabatic MHD Equations

3.7 Non-adiabatic motion in symmetric geometry

3.8 Motion in small-amplitude oscillatory fields

3.9 Wave-particle energy transfer

3.10 Assignments

**4 Elementary plasma waves**

4.1 General method for analyzing small amplitude waves

4.2 Two-fluid theory of unmagnetized plasma waves

4.3 Low frequency magnetized plasma: Alfvén waves

4.4 Two-fluid model of Alfvén modes

4.5 Assignments

**5 Streaming instabilities and the Landau problem**

5.1 Streaming instabilities

5.2 The Landau problem

5.3 The Penrose criterion

5.4 Assignments

**6 Cold plasma waves in a magnetized plasma**

6.1 Redundancy of Poisson’s equation in electromagnetic mode analysis

6.2 Dielectric tensor

6.3 Dispersion relation expressed as a relation between n2 x and n2z

6.4 A journey through parameter space

6.5 High frequency waves: Altar-Appleton-Hartree dispersion relation

6.6 Group velocity

6.7 Quasi-electrostatic cold plasma waves

6.8 Resonance cones

6.9 Assignments

**7 Waves in inhomogeneous plasmas and wave energy relations**

7.1 Wave propagation in inhomogeneous plasmas

7.2 Geometric optics

7.3 Surface waves - the plasma-filled waveguide

7.4 Plasma wave-energy equation

7.5 Cold-plasma wave energy equation

7.6 Finite-temperature plasma wave energy equation

7.7 Negative energy waves

7.8 Assignments

**8 Vlasov theory of warm electrostatic waves in a magnetized plasma**

8.1 Uniform plasma

8.2 Analysis of the warm plasma electrostatic dispersion relation

8.3 Bernstein waves

8.4 Warm, magnetized, electrostatic dispersion with small, but finite k

8.5 Analysis of linear mode conversion

8.6 Drift waves

8.7 Assignments

**9 MHD equilibria**

9.1 Why use MHD?

9.2 Vacuum magnetic fields

9.3 Force-free fields

9.4 Magnetic pressure and tension

9.5 Magnetic stress tensor

9.6 Flux preservation, energy minimization, and inductance

9.7 Static versus dynamic equilibria

9.8 Static equilibria

9.9 Dynamic equilibria: flows

9.10 Assignments

10.1 The Rayleigh-Taylor instability of hydrodynamics

10.2 MHD Rayleigh-Taylor instability

10.3 The MHD energy principle

10.4 Discussion of the energy principle

10.5 Current-driven instabilities and helicity

10.6 Magnetic helicity

10.7 Qualitative description of free-boundary instabilities

10.8 Analysis of free-boundary instabilities

10.9 Assignments

11.1 Introduction

11.2 Topological interpretation of magnetic helicity

11.3 Woltjer-Taylor relaxation

11.4 Kinking and magnetic helicity

11.5 Assignments

12.1 Introduction

12.2 Water-beading: an analogy to magnetic tearing and reconnection

12.3 Qualitative description of sheet current instability

12.4 Semi-quantitative estimate of the tearing process

12.5 Generalization of tearing to sheared magnetic fields

12.6 Magnetic islands

12.7 Assignments

13.1 Introduction

13.2 Statistical argument for the development of the Fokker-Planck equation

13.3 Electrical resistivity

13.4 Runaway electric field

13.5 Assignments

14.1 Introduction

14.2 Vlasov non-linearity and quasi-linear velocity space diffusion

9.4 Magnetic pressure and tension

9.5 Magnetic stress tensor

9.6 Flux preservation, energy minimization, and inductance

9.7 Static versus dynamic equilibria

9.8 Static equilibria

9.9 Dynamic equilibria: flows

9.10 Assignments

**10 Stability of static MHD equilibria**10.1 The Rayleigh-Taylor instability of hydrodynamics

10.2 MHD Rayleigh-Taylor instability

10.3 The MHD energy principle

10.4 Discussion of the energy principle

10.5 Current-driven instabilities and helicity

10.6 Magnetic helicity

10.7 Qualitative description of free-boundary instabilities

10.8 Analysis of free-boundary instabilities

10.9 Assignments

**11 Magnetic helicity interpreted andWoltjer-Taylor relaxation**11.1 Introduction

11.2 Topological interpretation of magnetic helicity

11.3 Woltjer-Taylor relaxation

11.4 Kinking and magnetic helicity

11.5 Assignments

**12 Magnetic reconnection**12.1 Introduction

12.2 Water-beading: an analogy to magnetic tearing and reconnection

12.3 Qualitative description of sheet current instability

12.4 Semi-quantitative estimate of the tearing process

12.5 Generalization of tearing to sheared magnetic fields

12.6 Magnetic islands

12.7 Assignments

**13 Fokker-Planck theory of collisions**13.1 Introduction

13.2 Statistical argument for the development of the Fokker-Planck equation

13.3 Electrical resistivity

13.4 Runaway electric field

13.5 Assignments

**14 Wave-particle nonlinearities**14.1 Introduction

14.2 Vlasov non-linearity and quasi-linear velocity space diffusion

14.3 Echoes

14.4 Assignments

15.2 Manley-Rowe relations

15.3 Application to waves

15.4 Non-linear dispersion formulation and instability threshold

15.5 Digging a hole in the plasma via ponderomotive force

15.6 Ion acoustic wave solition

14.4 Assignments

**15 Wave-wave nonlinearities**15.2 Manley-Rowe relations

15.3 Application to waves

15.4 Non-linear dispersion formulation and instability threshold

15.5 Digging a hole in the plasma via ponderomotive force

15.6 Ion acoustic wave solition

15.7 Assignments

16.1 Introduction

16.2 Brillouin flow

16.3 Isomorphism to incompressible 2D hydrodynamics

16.4 Near perfect confinement

16.5 Diocotron modes

16.6 Assignments

17 Dusty plasmas

17.1 Introduction

17.2 Electron and ion current flow to a dust grain

17.3 Dust charge

17.4 Dusty plasma parameter space

17.5 Large P limit: dust acoustic waves

17.6 Dust ion acoustic waves

17.7 The strongly coupled regime: crystallization of a dusty plasma

17.8 Assignments

Bibliography and suggested reading

References

Appendix A: Intuitive method for vector calculus identities

Appendix B: Vector calculus in orthogonal curvilinear coordinates

Appendix C: Frequently used physical constants and formulae

Index

**16 Non-neutral plasmas**16.1 Introduction

16.2 Brillouin flow

16.3 Isomorphism to incompressible 2D hydrodynamics

16.4 Near perfect confinement

16.5 Diocotron modes

16.6 Assignments

17 Dusty plasmas

17.1 Introduction

17.2 Electron and ion current flow to a dust grain

17.3 Dust charge

17.4 Dusty plasma parameter space

17.5 Large P limit: dust acoustic waves

17.6 Dust ion acoustic waves

17.7 The strongly coupled regime: crystallization of a dusty plasma

17.8 Assignments

Bibliography and suggested reading

References

Appendix A: Intuitive method for vector calculus identities

Appendix B: Vector calculus in orthogonal curvilinear coordinates

Appendix C: Frequently used physical constants and formulae

Index

**Author Details**

**"Paul M. Bellan"**

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