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*
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Lecture 17 (10/24/17): General Particle Drifts*
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Lecture 18 (10/26/17):
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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):
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Lecture 21 (11/07/17): Plasma Waves & Instabilities*
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Lecture 22 (11/09/17): Gravitational Instability
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Lecture 23 (11/14/17): Double Adiabatic Equations*
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Lecture 24 (11/16/17):
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Lecture 25 (11/21/17):
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Lecture 26 (11/28/17):
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Lecture 27 (11/30/17):
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* indicates that I was physically present for the lecture