Plasma Physics

1. Plasma Dynamics
   1. Kinetic Theory of Plasmas
      1. Introduction to kinetic theory
         1. Liouville's theorem
         2. Distribution functions
      2. Vlasov equation
         1. Collisionless plasmas
         2. Application in plasma simulations
      3. Boltzmann equation
         1. Inclusion of collisions
         2. Relaxation time approximation
      4. Fokker-Planck equation
         1. Diffusion processes in velocity space
         2. Applications in space plasmas
   2. Magnetohydrodynamics (MHD)
      1. Basic principles
         1. Single-fluid approximation
         2. Importance in plasma confinement
      2. MHD equations
         1. Continuity equation
         2. Momentum equation
         3. Induction equation
         4. Energy equation
      3. Ideal vs. resistive MHD
         1. Conductivity considerations
         2. Magnetic reconnection
      4. MHD stability
         1. Rayleigh-Taylor instability in plasmas
         2. Tearing mode instability
         3. Kink instability
   3. Fluid Models
      1. Two-Fluid Model
         1. Separate treatment of ions and electrons
         2. Applications in space and astrophysical plasmas
         3. Implications for wave propagation
      2. Single-Fluid Model
         1. Assumptions for plasma unification
         2. Quasineutrality condition
         3. Applicability in denser plasmas
   4. Particle-in-Cell (PIC) Simulations
      1. Principles of PIC simulations
         1. Computational particles
         2. Gridded field solutions
      2. PIC algorithm
         1. Charge assignment
         2. Field computation
         3. Particle push
      3. Applications of PIC
         1. Modeling of plasma sheaths
         2. Investigation of micro-instabilities
         3. Simulation of laser-plasma interactions
   5. Advanced Plasma Dynamics
      1. Nonlinear plasma dynamics
         1. Wave-wave interactions
         2. Formation of solitons
      2. Chaos and turbulence in plasmas
         1. Route to chaos
         2. Turbulent transport
      3. Plasma instabilities
         1. Drift instabilities
         2. Electrostatic and electromagnetic instabilities
      4. Computational fluid dynamics in plasma studies
         1. Numerical techniques
         2. Impacts on stability analysis
         3. Role in fusion plasma analysis
   6. Multi-Scale Aspects of Plasma Dynamics
      1. Coupling different scales
         1. Micro and macro-scale interactions
         2. Importance in fusion devices
      2. Hierarchical modeling techniques
         1. Multi-fluid models
         2. Hybrid modeling approaches
      3. Implications of scale separation
         1. Role in astrophysical plasmas
         2. Influence on transport processes
   7. Applications and Impact of Plasma Dynamics
      1. Plasma control in fusion devices
         1. Role of plasma dynamics in containment strategies
         2. Impact on fusion energy gain
      2. Space weather prediction
         1. Influence of solar plasma dynamics
         2. Contributions to magnetospheric studies
      3. Industrial applications
         1. Plasma processes in manufacturing
         2. Contributions to advanced propulsion systems