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Monday, November 12, 2018

Fundamentals Of Plasma Physics - By "Paul m. Bellan"

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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. 

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 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 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 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
Appendix A: Intuitive method for vector calculus identities
Appendix B: Vector calculus in orthogonal curvilinear coordinates
Appendix C: Frequently used physical constants and formulae

Author Details
"Paul M. Bellan" 

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