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Preface | |
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Basic concepts | |
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History of the term "plasma" | |
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Brief history of plasma physics | |
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Plasma parameters | |
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Examples of plasmas | |
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Logical framework of plasma physics | |
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Debye shielding | |
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Quasi-neutrality | |
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Small- vs. large-angle collisions in plasmas | |
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Electron and ion collision frequencies | |
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Collisions with neutrals | |
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Simple transport phenomena | |
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A quantitative perspective | |
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Assignments | |
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The Vlasov, two-fluid, and MHD models of plasma dynamics | |
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Overview | |
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Phase-space | |
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Distribution function and Vlasov equation | |
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Moments of the distribution function | |
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Two-fluid equations | |
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Magnetohydrodynamic equations | |
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Summary of MHD equations | |
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Classical transport | |
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Sheath physics and Langmuir probe theory | |
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Assignments | |
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Motion of a single plasma particle | |
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Motivation | |
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Hamilton-Lagrange formalism vs. Lorentz equation | |
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Adiabatic invariant of a pendulum | |
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Extension of WKB method to general adiabatic invariant | |
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Drift equations | |
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Relation of drift equations to the double adiabatic MHD equations | |
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Non-adiabatic motion in symmetric geometry | |
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Particle motion in small-amplitude oscillatory fields | |
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Wave-particle energy transfer | |
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Assignments | |
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Elementary plasma waves | |
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General method for analyzing small-amplitude waves | |
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Two-fluid theory of unmagnetized plasma waves | |
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Low-frequency magnetized plasma: Alfven waves | |
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Two-fluid model of Alfven modes | |
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Assignments | |
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Streaming instabilities and the Landau problem | |
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Overview | |
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Streaming instabilities | |
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The Landau problem | |
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The Penrose criterion | |
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Assignments | |
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Cold plasma waves in a magnetized plasma | |
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Overview | |
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Redundancy of Poisson's equation in electromagnetic mode analysis | |
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Dielectric tensor | |
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Dispersion relation expressed as a relation between n<sub>x</sub><sup>2</sup> and n<sub>z</sub><sup>2</sup> | |
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A journey through parameter space | |
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High-frequency waves: Altar-Appleton-Hartree dispersion relation | |
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Group velocity | |
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Quasi-electrostatic cold plasma waves | |
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Resonance cones | |
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Assignments | |
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Waves in inhomogeneous plasmas and wave-energy relations | |
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Wave propagation in inhomogeneous plasmas | |
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Geometric optics | |
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Surface waves - the plasma-filled waveguide | |
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Plasma wave-energy equation | |
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Cold plasma wave-energy equation | |
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Finite-temperature plasma wave-energy equation | |
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Negative energy waves | |
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Assignments | |
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Vlasov theory of warm electrostatic waves in a magnetized plasma | |
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Solving the Vlasov equation by tracking each particle's history | |
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Analysis of the warm plasma electrostatic dispersion relation | |
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Bernstein waves | |
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Finite k<sub></sub> dispersion: linear mode conversion | |
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Analysis of linear mode conversion | |
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Drift waves | |
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Assignments | |
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MHD equilibria | |
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Why use MHD? | |
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Vacuum magnetic fields | |
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Force-free fields | |
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Magnetic pressure and tension | |
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Magnetic stress tensor | |
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Flux preservation, energy minimization, and inductance | |
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Static versus dynamic equilibria | |
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Static equilibria | |
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Dynamic equilibria: flows | |
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Assignments | |
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Stability of static MHD equilibria | |
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Introduction | |
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The Rayleigh-Taylor instability of hydrodynamics | |
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MHD Rayleigh-Taylor instability | |
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The MHD energy principle | |
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Discussion of the energy principle | |
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Current-driven instabilities and helicity | |
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Magnetic helicity | |
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Characterization of free-boundary instabilities | |
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Analysis of free-boundary instabilities | |
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Assignments | |
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Magnetic helicity interpreted and Woltjer-Taylor relaxation | |
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Introduction | |
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Topological interpretation of magnetic helicity | |
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Woltjer-Taylor relaxation | |
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Kinking and magnetic helicity | |
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Assignments | |
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Magnetic reconnection | |
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Introduction | |
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Water-beading: an analogy to magnetic reconnection | |
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Qualitative description of sheet current instability | |
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Semi-quantitative estimate of the tearing process | |
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Generalization of tearing to sheared magnetic fields | |
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Magnetic islands | |
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Assignments | |
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Fokker-Planck theory of collisions | |
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Introduction | |
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Statistical argument for the development of the Fokker-Planck equation | |
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Electrical resistivity | |
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Runaway electric field | |
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Assignments | |
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Wave-particle nonlinearities | |
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Introduction | |
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Vlasov nonlinearity and quasi-linear velocity space diffusion | |
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Echoes | |
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Assignments | |
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Wave-wave nonlinearities | |
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Introduction | |
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Manley-Rowe relations | |
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Application to waves | |
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Instability onset via nonlinear dispersion method | |
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Digging a density hole via ponderomotive force | |
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Ion acoustic wave soliton | |
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Assignments | |
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Non-neutral plasmas | |
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Introduction | |
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Brillouin flow | |
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Isomorphism to incompressible 2-D hydrodynamics | |
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Near-perfect confinement | |
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Diocotron modes | |
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Assignments | |
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Dusty plasmas | |
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Introduction | |
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Electron and ion current flow to a dust grain | |
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Dust charge | |
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Dusty plasma parameter space | |
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Large P limit: dust acoustic waves | |
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Dust ion acoustic waves | |
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The strongly coupled regime: crystallization of a dusty plasma | |
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Assignments | |
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Appendices | |
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Intuitive method for vector calculus identities | |
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Vector calculus in orthogonal curvilinear coordinates | |
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Frequently used physical constants and formulae | |
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Bibliography and suggested reading | |
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References | |
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Index | |