Plasma Physics

Orbits, Fluids, Waves and Collisions in an Ionised Gas in 15 chapters — from “What makes an ionised gas a plasma: shielding, the plasma parameter and the natural frequencies” to “Transport across and along the field: ambipolar, classical, neoclassical and anomalous”.

Chapters

  1. What makes an ionised gas a plasma: shielding, the plasma parameter and the natural frequencies
    • Saha ionisation
    • Debye shielding
    • Quasineutrality and the plasma parameter
    • The plasma frequency
    • Cyclotron frequency and Larmor radius
    • Collision frequency estimate
    • The plasma regimes map
    • Problems
  2. One particle in given fields: gyration and the guiding-centre drifts
    • Gyromotion and magnetic moment
    • The E cross B drift
    • General force drift and gravity
    • Guiding-centre ordering
    • Grad-B drift and curvature drift
    • Polarisation drift
    • Drift currents and the ring current
    • Problems
  3. Slow changes and what survives them: adiabatic invariants, mirrors and trapped orbits
    • Adiabatic invariance
    • The magnetic moment invariant
    • Mirror force and reflection
    • The loss cone
    • The longitudinal invariant and the hierarchy
    • Rotational transform and banana orbits
    • Problems
  4. From particles to fluids: the distribution function, its moments and the two-fluid model
    • The distribution function and its moments
    • Liouville's theorem and the kinetic equation
    • Continuity and momentum from velocity moments
    • The pressure tensor in a magnetic field
    • The closure problem
    • The two-fluid equations
    • Diamagnetic drift and Boltzmann electrons
    • Problems
  5. Magnetohydrodynamics: Ohm's law for a moving plasma, frozen flux and magnetic pressure
    • Single-fluid variables and momentum
    • The generalised Ohm's law
    • The ideal MHD equations and their limits
    • The induction equation and frozen-in flux
    • Resistive diffusion of the field
    • Magnetic pressure and tension
    • Alfven speed and Lundquist number
    • Problems
  6. Holding a plasma still: pinches, flux surfaces and the Grad-Shafranov equation
    • Force balance and isobaric surfaces
    • Theta and z pinches
    • Flux surfaces and the safety factor
    • Toroidal force balance
    • The Grad-Shafranov equation
    • The Solov'ev equilibrium
    • Confinement configurations compared
    • Problems
  7. Whether it stays held: the energy principle, interchange, kink and tearing
    • Linearised MHD and force operator
    • The Rayleigh quotient and self-adjointness
    • The energy principle
    • Rayleigh-Taylor and interchange instability
    • Pinch modes and the Kruskal-Shafranov limit
    • Shear stabilisation and the beta limit
    • Tearing modes and magnetic islands
    • Problems
  8. Plasma oscillations and light in an unmagnetised plasma
    • The plasma dielectric response
    • The cold plasma dielectric
    • Electromagnetic wave cutoff and dispersion
    • Critical density and reflection
    • Plasma interferometry and the dispersion measure
    • Problems
  9. Cold magnetised plasma waves: the dielectric tensor, cutoffs, resonances and the CMA diagram
    • The cold magnetised dielectric tensor
    • The cold-plasma dispersion relation
    • Parallel R and L waves
    • The whistler mode and Faraday rotation
    • Perpendicular O and X modes
    • The low-frequency limit
    • Cutoffs and resonances on the CMA diagram
    • Problems
  10. Waves that need pressure or tension: Langmuir, ion-acoustic, Alfven and magnetosonic
    • The Bohm-Gross wave
    • The ion-acoustic wave
    • The Bohm criterion at a wall
    • Electrostatic magnetised waves
    • Linear MHD and the shear Alfven wave
    • Magnetosonic waves and Friedrichs diagrams
    • Problems
  11. Waves in a non-uniform plasma: rays, reflection, mode conversion and radiofrequency heating
    • The WKB approximation
    • Ray tracing
    • Cutoff reflection and reflectometry
    • Resonance absorption
    • Mode conversion and tunnelling
    • RF heating schemes and accessibility
    • Problems
  12. The Vlasov equation and Landau damping
    • The linearised Vlasov-Poisson system
    • Analytic functions and continuation
    • The Landau initial-value problem
    • Kinetic dielectric and weak damping
    • The plasma dispersion function
    • The Landau damping mechanism
    • Ion-acoustic Landau damping and particle trapping
    • Problems
  13. Hot plasmas and free energy: beam instabilities, cyclotron damping and Bernstein waves
    • The Penrose criterion
    • The two-stream instability
    • The bump-on-tail and the quasilinear plateau
    • Current-driven instabilities and anomalous resistivity
    • Helical orbits and the hot magnetised response
    • Cyclotron damping and Bernstein waves
    • Firehose and mirror anisotropy instabilities
    • Problems
  14. Coulomb collisions: the Coulomb logarithm, the Fokker-Planck equation and Spitzer resistivity
    • The binary Coulomb collision
    • Coulomb logarithm cutoffs
    • The Fokker-Planck equation
    • The Landau collision operator
    • The collision-time hierarchy and fast ions
    • Spitzer resistivity
    • Runaway electrons
    • Current drive
    • Problems
  15. Transport across and along the field: ambipolar, classical, neoclassical and anomalous
    • Diffusion and mobility
    • Ambipolar diffusion
    • Classical cross-field diffusion and heat flow
    • Bohm diffusion and neoclassical transport
    • The bootstrap current
    • Drift waves and anomalous transport
    • Confinement scaling and the H-mode
    • Problems