Lecture Notes from PHYS761 - Plasma Physics I, as taught by Dr. James Drake in the Fall, 2017 semester. Lecture 1 (08/29/17): Introduction - What is a Plasma? - Basic Parameters & Units - The Plasma Parameter - Maxwell-Boltzmann Distributions Lecture 2 (08/31/17): Shielding, Waves, and Ionization - The Plasma Parameter - Distribution Functions - Debye Shielding - Plasma Waves -> Nonlinearity -> Thermal Motion - Ionization -> Derivation of the Saha Equation Lecture 3 (09/05/17): Ionization & Collisions* - Ionization Equations - Notes on the Saha Eq. from ASTR601 (Miller, F'16) - Coronal Equilibrium Model - Collision Rates in Full Ionized Plasma -> Simple-Minded Estimate - Electrons Scattering Off of Ions -> Large-angle scattering -> Small-angle scattering Lecture 4 (09/07/17): Energy Exchange & Liouville's Equation - Fractional Ionization in Dilute Plasmas (Coronal Model) - Electron-Ion Collision Rate - Other Collisions: -> Electron-electron -> Ion-ion (momentum scattering) - Energy Exchange [rate] - Liouville's Equation - The Vlasov Equation (Collisionless Boltzmann Eq.) Lecture 5 (09/12/17): Collisions in the Boltzmann Equation* - Liouville's Equation - Collisionless Boltzman Equation - Collisions in the Boltzmann Equation - The Collision Operator - Fokker-Planck Equation -> Plasma Drag - Landau Form of the Collision Operator Lecture 6 (09/14/17): The Krook Model & Fluid Equations - Adding Collisions to the Boltzmann Equation - The Krook Model - Characteristics of the Vlasov Equation - The Fluid Equations - Zero Moment -> Continuity Equation - First Moment -> Pressure Tensor -> Fluid Momentum Equation Lecture 7 (09/19/17): Collisions & the Pressure Tensor - Deriving the Fluid Equations from the Vlasov Eq. - Closure with Collisions - Second Moment -> Energy Equation - Adiabatic Limit - Electrostatic Waves in a Warm Plasma - Kinetic Theory Lecture 8 (09/21/17): Kinetic & Fluid Theories - Kinetic Theory of Electrostatic Waves -> Perturbed distribution function -> Dielectric functions for a warm plasma - Thermal Corrections - Plasma Wave Dispersion: Kinetic Theory - Fluid Model -> Plasma Wave Dispersion: Fluid Theory - Landau Damping Lecture 9 (09/26/17): Landau Damping* - Kinetic Dispersion Relation - Deriving the Damping Expression -> Fourier & Laplace Transforms - Im{w} > 0 vs. Im{w} < 0 -> Natural Mode & Free-Streaming Particles - Math Aside: Residue Theorem - How to handle Im{w_o}~=0 -> Reduced Distribution Function - Expression for Landau Damping - Plasma Dispersion Function Lecture 10 (09/28/17): Wave Energy - Damping of Plasma Waves - Plasma Dispersion Function (ES Waves) -> Cold vs. Warm Plasma - Derivation of the Rate of Change in Plasma Energy, W-dot_P -> Application of Linear Theory - Full Rate of Change in (W-dot_P + W-dot_E) Total Energy - Wave Energy: Electrostatic Waves Lecture 11 (10/03/17): Adding in Electromagnetic Waves - Wave Energy (ES Waves) - Electromagnetic Waves -> Transverse Waves - Dispersion Relation for EM Waves in a Plasma -> Propagation vs. Reflection - General Dielectric Function - General Dispersion Relation Lecture 12 (10/05/17): Wave Energy & Momentum - General Dispersion Relation - Wave Energy & Momentum - Energy Density in a General Wave -> Rate of change of energy in an EM wave -> Work put into an EM wave - Momentum Density -> Rate of momentum transfer: particle to wave -> EM wave momentum - Group Velocity & Power Flux Lecture 13 (10/10/17): Fluctuations & Interactions* - Energy Density & Energy Flux, EM Waves - Thermal Fluctuations - Derivation of fluctuation level eq. -> Aside: Properties of F(x,v,t) - Resonance as fluctuation source - Wave-Particle Interactions - Resonant Interactions: Narrow Wave Spectrum -> Particle trapping - Resonant Interactions: Broad Wave Spectrum Lecture 14 (10/12/17): Quasilinear Theory - Wave-Particle Interactions -> Narrow vs. Broad wave spectra - Quasilinear Treatment of Wave-Particle Interactions - Linear Theory to obtain Growth Rate of Instability - Quasilinear Theory -> Diffusion Coefficient as a complete set of quasilinear equations - Conservation of Particles: Number Density - Conservation of Momentum: Momentum Density - Conservation of Energy: Energy Density Lecture 15 (10/17/17): Evolution of Quasilinear Systems* - Quasilinear Equations for Bump-on-Tail Instability - System Evolution -> Qualitative & Steady-State - Energy Spectra of Waves - Finding the Phase Speed Boundaries - Resonant vs. Non-Resonant Diffusion Lecture 16 (10/19/17): Particle Orbits in Magnetic Fields* - Lecture 17 (10/24/17): General Particle Drifts* - Lecture 18 (10/26/17): - Lecture 19 (10/31/17): The Magnetohydrodynamics Equations* - Ordering of Equations - Lowest Order MHD (Rank 1) - Symmetry Properties of the Collision Operator - Derivation of the Continuity Equation - Derivation of the Momentum Equation - Derivation of the Pressure/Energy Equation - First Order MHD (Rank 1 & Rank \epsilon) - Ideal MHD Equilibria -> Example cases, e.g., \Theta- and z-pinches Lecture 20 (11/02/17): - Lecture 21 (11/07/17): Plasma Waves & Instabilities* - Lecture 22 (11/09/17): Gravitational Instability - Lecture 23 (11/14/17): Double Adiabatic Equations* - Lecture 24 (11/16/17): - Lecture 25 (11/21/17): - Lecture 26 (11/28/17): - Lecture 27 (11/30/17): - * indicates that I was physically present for the lecture