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    About this atlas

    This atlas was assembled with AI assistance from selected Oxford MMathPhys plasma-physics courses and Princeton/PPPL graduate teaching materials, with additional topics in plasma theory.

    It is a personal synthesis, not an official syllabus. The map focuses on theoretical plasma physics; topic titles follow the English source catalogue.

    In my personal version, each star records the level I have reached in that topic. Here the levels are fixed examples for illustration.

    Oxford MMathPhys courses · Princeton / PPPL courses

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    The complete topic list is available without JavaScript or WebGL. Topic titles retain the English wording of the source map.

    This atlas was assembled with AI assistance from selected Oxford MMathPhys plasma-physics courses and Princeton/PPPL graduate teaching materials, with additional topics in plasma theory.

    It is a personal synthesis, not an official syllabus. The map focuses on theoretical plasma physics; topic titles follow the English source catalogue.

    In my personal version, each star records the level I have reached in that topic. Here the levels are fixed examples for illustration.

    Oxford MMathPhys courses · Princeton / PPPL courses

    A · Fundamentals of plasma physics (9)
    1. A.01 Plasma parameters and orders of magnitude: λ_D, ω_p, ρ, ν and β in fusion plasmas
    2. A.02 Two-fluid theory: moment equations, closures and the generalised Ohm's law
    3. A.03 Diamagnetic drift and current; magnetisation; guiding-centre and fluid flows
    4. A.04 Drift waves in the two-fluid model; diamagnetic frequency ω*
    5. A.05 Fusion: Lawson criterion, triple product and magnetic configurations
    6. A.06 Magnetic mirrors: loss cone, trapping and ambipolar potential
    7. A.07 Sheaths and the Bohm criterion
    8. A.08 Plasma oscillations in the cold-fluid model
    9. A.09 Self-consistent beams and currents; Child–Langmuir law
    B · Kinetic theory of gases (13)
    1. B.01 Length and time scales; Boltzmann–Grad limit; Boltzmann and Vlasov regimes
    2. B.02 N-particle Hamiltonian mechanics; Poisson brackets
    3. B.03 Liouville's theorem and the N-particle distribution
    4. B.04 Reduced s-particle distributions
    5. B.05 BBGKY hierarchy; mean-field closure and the Vlasov equation
    6. B.06 Boltzmann equation: binary collisions, collision kernel and power-law potentials
    7. B.07 Properties of the Boltzmann operator; collisional invariants
    8. B.08 Boltzmann's inequality and the Maxwell–Boltzmann distribution
    9. B.09 H-theorem
    10. B.10 Relative entropy
    11. B.11 Linearised operator: spectrum, collision frequency and the BGK model
    12. B.12 Hydrodynamics from moments; Euler equations
    13. B.13 Multiple-scale Chapman–Enskog expansion; viscosity and thermal conductivity
    C · Plasma kinetics and linear theory (14)
    1. C.01 Quasineutrality, weak coupling and Debye shielding
    2. C.02 Microscopic and macroscopic fields; averaged Maxwell equations
    3. C.03 Vlasov–Landau equation; introduction to the collision operator
    4. C.04 Plasma frequency; slow equilibrium and fast fluctuations; hierarchy of approximations
    5. C.05 Vlasov–Poisson as an initial-value problem: Laplace transform and dielectric function
    6. C.06 Landau prescription; weak-damping and slow-growth limits
    7. C.07 Langmuir waves; Landau damping and kinetic instabilities; physical interpretation
    8. C.08 Hot and cold beams; bump-on-tail and two-stream instabilities
    9. C.09 Ion-acoustic waves: damping and instability; ion Langmuir waves
    10. C.10 Plasma dispersion function Z: properties, series and asymptotic expansions
    11. C.11 Transverse waves and the Weibel instability
    12. C.12 Nyquist method; stability of monotonic distributions; Penrose criterion
    13. C.13 Beam-, current- and anisotropy-driven instabilities; Buneman instability
    14. C.14 Landau contour and analytic continuation
    D · Free energy, phase mixing and quasilinear theory (9)
    1. D.01 Energy conservation and heating
    2. D.02 Entropy and free energy; stability
    3. D.03 Structure of δf: ballistic response and phase mixing
    4. D.04 Role of collisions and irreversibility; Case–van Kampen modes
    5. D.05 Free energy of damped waves; fluctuation–dissipation relation
    6. D.06 Quasilinear theory: general framework and conservation laws
    7. D.07 Bump-on-tail QLT: plateau, spectrum, resonant particles and heating of the thermal bulk
    8. D.08 QLT of Weibel and ion–electron streaming instabilities; stochastic acceleration; driven plasmas
    9. D.09 Quasiparticle kinetics: QLT in terms of plasmons
    E · Collisions (13)
    1. E.01 Klimontovich description; self-consistent field and collisions
    2. E.02 General form of the collision integral; two-particle correlations
    3. E.03 Quasilinear collision integral
    4. E.04 Stoßzahlansatz and the Balescu–Lenard operator
    5. E.05 H-theorem and thermal equilibrium
    6. E.06 Landau operator; divergences and the Coulomb logarithm
    7. E.07 Fokker–Planck operator: conservation laws, H-theorem and solutions
    8. E.08 Estimates of collision frequencies; multispecies operator
    9. E.09 Electron–ion collisions: friction and Spitzer resistivity
    10. E.10 Runaway electrons
    11. E.11 Ion–electron collisions: diffusion, slowing down and energy exchange
    12. E.12 Linearised operator: Landau form, isotropy and self-adjointness; model operators
    13. E.13 Stochastic processes: random walks, Langevin equation and master equation
    F · Collisional transport and Braginskii theory (8)
    1. F.01 Fluid equations from kinetic theory; momentum and heat fluxes
    2. F.02 Collisional expansion for electrons
    3. F.03 Parallel electron transport: friction, current and heat flux
    4. F.04 Onsager thermodynamics; variational principle and entropy production
    5. F.05 Perpendicular electron transport; magnetic-field transport
    6. F.06 Ion heat fluxes; magnetothermal instability
    7. F.07 Braginskii stress: parallel and perpendicular viscosity
    8. F.08 Classical transport in collisional plasmas: applications
    G · Magnetohydrodynamics (25)
    1. G.01 MHD equations: mass, momentum, magnetic forces and Maxwell stress
    2. G.02 Induction; magnetic Reynolds number; Lundquist's theorem and flux freezing
    3. G.03 Field amplification; energy conservation; virial theorem
    4. G.04 Lagrangian MHD; stochastic Lundquist theorem
    5. G.05 MHD from kinetic equations and particle drifts
    6. G.06 Small-scale dynamo: Zeldovich and Kazantsev; anti-dynamo theorem
    7. G.07 MHD waves: Alfvén and magnetosonic waves; anisotropic propagation; high-β limit
    8. G.08 Subsonic ordering; incompressible MHD; Elsasser variables; cross-helicity
    9. G.09 Reduced MHD: Alfvénic and compressive perturbations
    10. G.10 MHD turbulence: Iroshnikov–Kraichnan, Goldreich–Sridhar and critical balance
    11. G.11 Static and cylindrical equilibria; force-free fields
    12. G.12 Magnetic helicity; Taylor relaxation; relaxed pinch
    13. G.13 Decay of MHD turbulence; Parker problem
    14. G.14 Energy principle and evaluation of δW
    15. G.15 Interchange instability; Schwarzschild criterion; Rayleigh–Taylor instability
    16. G.16 Pinch instabilities: sausage and kink modes
    17. G.17 Instabilities in rotating and stratified fluids: Kelvin–Helmholtz and MRI
    18. G.18 MHD discontinuities and shocks
    19. G.19 Electron MHD and Hall MHD
    20. G.20 Reconnection: X-point collapse
    21. G.21 Sweet–Parker current sheet
    22. G.22 Tearing mode: outer and inner solutions, dispersion relation, FKR and Coppi limits
    23. G.23 Nonlinear tearing, plasmoids and fast reconnection
    24. G.24 Ambipolar and viscous damping of Alfvén waves in a partially ionised plasma
    25. G.25 Non-Newtonian fluid dynamics: Stokes flow, suspensions and viscoelasticity
    H · Particle motion and strongly magnetised kinetics (14)
    1. H.01 Uniform, time-independent fields: gyromotion and E×B drift
    2. H.02 Magnetised particles in general fields: ∇B, curvature and polarisation drifts
    3. H.03 Magnetic moment and adiabatic invariance; guiding-centre equations
    4. H.04 Magnetic mirrors and trapping; longitudinal invariant
    5. H.05 Kinetics in the fluid frame; moment equations in a magnetised plasma
    6. H.06 Ideal Ohm's law; magnetised limit; gyrotropic plasma and pressure anisotropy
    7. H.07 Firehose instability
    8. H.08 Gyroaveraged kinetic equation; magnetic moment; parallel electric field
    9. H.09 High-flow and low-flow drift kinetics
    10. H.10 Drift kinetics from particle motion: perturbation theory and Jacobian
    11. H.11 Kinetic MHD: Alfvén waves, compressive modes and magnetosonic waves
    12. H.12 Mirror instability; Barnes damping; magnetic pumping
    13. H.13 Origin of pressure anisotropy; CGL equations and double adiabaticity
    14. H.14 Energy principle and free energy in kinetic MHD
    I · Waves in magnetised plasmas (13)
    1. I.01 Wave equation, dielectric tensor and cold-plasma dispersion relation
    2. I.02 Parallel propagation: R and L waves, whistlers and ion-cyclotron waves
    3. I.03 Perpendicular propagation: O and X waves, hybrid resonances
    4. I.04 Cutoffs, resonances, CMA diagram and polarisation
    5. I.05 WKB approximation for cold-plasma waves; ray tracing; amplitude equation
    6. I.06 Wave action, energy and momentum
    7. I.07 Cutoffs and resonances in an inhomogeneous plasma; mode conversion
    8. I.08 Warm-fluid waves
    9. I.09 Hot-plasma waves: dielectric and conductivity tensors; Bessel functions
    10. I.10 Dispersion relation for Maxwellian distributions; cold-plasma limit
    11. I.11 Landau and cyclotron damping; transit-time magnetic pumping
    12. I.12 Bernstein waves; waves in the hybrid-frequency ranges
    13. I.13 Kinetic Alfvén wave and the gyrokinetic limit of plasma waves
    J · Electrostatic drift kinetics, ITG and transport (10)
    1. J.01 Electrostatic drift kinetics; Boltzmann electrons
    2. J.02 Kinetic drift waves
    3. J.03 Fluid ITG: mechanism and threshold
    4. J.04 Kinetic slab ITG: dispersion relation involving Z, stability boundary and ηi
    5. J.05 Nature of the electrostatic limit
    6. J.06 Interchange instability in a drift-kinetic z-pinch
    7. J.07 Free energy in electrostatic drift kinetics
    8. J.08 Nonlinear ITG equations; turbulent diffusion; mixing-length estimates
    9. J.09 Energy injection, cascade and outer scale
    10. J.10 Parallel coherence and Barnes scaling: critical balance in ITG turbulence
    K · Gyrokinetics (15)
    1. K.01 Scale separation; fluctuation and transport time scales; gyro-Bohm scaling
    2. K.02 Turbulence averaging; Vlasov–Maxwell–Landau equations; quasineutrality
    3. K.03 Gyrokinetic ordering
    4. K.04 Gyrokinetic variables; gyroaverages at fixed R and fixed r
    5. K.05 Vlasov equation in gyrokinetic variables: guiding-centre velocity and gyrokinetic potential χ
    6. K.06 Gyroaveraged drifts (E×B, ∇B and curvature); evolution of ε and μ
    7. K.07 Zeroth order: gyrotropic F0, entropy production and a Maxwellian whose parameters are flux functions
    8. K.08 Boltzmann response and the function h; equilibrium currents
    9. K.09 Derivation of the gyrokinetic equation
    10. K.10 Field equations: quasineutrality, parallel and perpendicular Ampère's law, pressure balance
    11. K.11 Free-energy conservation: injection and dissipation
    12. K.12 Gyrokinetic heating
    13. K.13 Gyrokinetics in Fourier space; Bessel function J0
    14. K.14 Multiscale gyrokinetics for rotating plasmas; flows and transport
    15. K.15 Formal foundations: Lie transforms and variational formulation
    L · Toroidal geometry (10)
    1. L.01 Why a torus: equilibrium, field lines and magnetic surfaces
    2. L.02 Flux surfaces; poloidal and toroidal fluxes; flux functions
    3. L.03 Flux-surface averaging and its properties
    4. L.04 Axisymmetric field B = I∇ζ + ∇ψ×∇ζ; equilibrium currents
    5. L.05 Flux coordinates; straight-field-line coordinates; Hamada and Boozer coordinates
    6. L.06 Safety factor q, magnetic shear and rational surfaces
    7. L.07 Field-aligned coordinates; flux tube; twist-and-shift boundary condition
    8. L.08 Metric, Jacobian and operators in curvilinear coordinates; field-line curvature
    9. L.09 Local geometry models: circular large-aspect-ratio, s-α and Miller equilibria
    10. L.10 Hamiltonian structure of field lines; stellarators
    M · Toroidal orbits, neoclassical theory and flows (10)
    1. M.01 Passing and trapped orbits; trapped-particle fraction
    2. M.02 Transit and bounce frequencies; banana-orbit width
    3. M.03 Invariants: energy, μ and canonical toroidal momentum
    4. M.04 Bounce averages; drift kinetics in toroidal geometry
    5. M.05 Classical and neoclassical transport: banana, plateau and Pfirsch–Schlüter regimes
    6. M.06 Bootstrap current; Ware pinch
    7. M.07 Poloidal flows and their damping; neoclassical rotation
    8. M.08 Neoclassical polarisation and the Rosenbluth–Hinton residual
    9. M.09 Geodesic acoustic modes: fluid model and kinetic damping
    10. M.10 Stringer rotation and the Stringer–Winsor force
    N · Toroidal MHD (8)
    1. N.01 Grad–Shafranov equation; Solov'ev solution
    2. N.02 Large-aspect-ratio equilibrium; Shafranov shift; βp
    3. N.03 Equilibrium currents in a torus: diamagnetic and Pfirsch–Schlüter currents
    4. N.04 Energy principle in toroidal geometry; Suydam and Mercier criteria
    5. N.05 Tokamak kink modes; Kruskal–Shafranov criterion
    6. N.06 Ballooning modes; s-α diagram
    7. N.07 Magnetic islands; tokamak tearing and an introduction to neoclassical tearing modes
    8. N.08 β and density limits; operating context
    O · Toroidal and electromagnetic microinstabilities (11)
    1. O.01 Gyrokinetic slab ETG: Laplace transform and dispersion relation
    2. O.02 Curvature-driven instabilities; gyrokinetic z-pinch
    3. O.03 Modified adiabatic response; ITG and ETG; role of zonal flows
    4. O.04 Ballooning representation and flux-tube boundary conditions
    5. O.05 Toroidal ITG: magnetic-drift resonance, threshold and ballooning structure
    6. O.06 Trapped-electron modes (TEM)
    7. O.07 Electromagnetic gyrokinetics with gradients: β, A∥ and δB∥
    8. O.08 Kinetic ballooning modes and electromagnetic ITG
    9. O.09 Microtearing
    10. O.10 Drift kinetics as a limit of gyrokinetics; FLR effects on instabilities
    11. O.11 Effects of flow shear on instabilities
    P · Turbulence and zonal flows (11)
    1. P.01 Hydrodynamic turbulence: K41, the four-fifths law and intermittency
    2. P.02 Weak wave turbulence
    3. P.03 Fluid models of drift-wave turbulence: Hasegawa–Mima and Hasegawa–Wakatani
    4. P.04 Zonal-flow generation: Reynolds stress, modulational instability and wave kinetics
    5. P.05 Secondary and tertiary instabilities: Rogers–Dorland–Kotschenreuther and Plunk
    6. P.06 Dimits shift and regimes dominated by zonal flows
    7. P.07 Suppression of turbulence by flow shear
    8. P.08 Gyrokinetic turbulence: kinetic cascades and the entropy cascade
    9. P.09 Critical balance in ITG turbulence
    10. P.10 Toroidal secondary modes: model, mechanism and dispersion relation
    11. P.11 Statistical theories of turbulence: closures and fluctuation–dissipation
    Q · Mathematical methods (9)
    1. Q.01 Fourier and Laplace transforms; analytic continuation; complex-contour integrals
    2. Q.02 Special functions: Bessel functions, Z and Γ0
    3. Q.03 Power series and Frobenius solutions; asymptotic behaviour of ODEs
    4. Q.04 Asymptotic evaluation of integrals: Laplace, stationary-phase and saddle-point methods
    5. Q.05 WKB, turning points, Stokes diagrams and phase integrals
    6. Q.06 Boundary layers and matched asymptotic expansions
    7. Q.07 Multiple scales and averaging methods
    8. Q.08 Hamiltonian mechanics: action–angle variables, adiabatic invariants and Lie transforms
    9. Q.09 Vector and tensor calculus; vector identities; curvilinear coordinates
    R · Self-gravitating systems (6)
    1. R.01 Mean-field theory for self-gravitating systems; negative heat capacity
    2. R.02 Two-body relaxation and evaporation
    3. R.03 Action–angle variables; Eddington inversion; isochrone potential
    4. R.04 Linear response of homogeneous systems; Jeans instability
    5. R.05 Balescu–Lenard and Fokker–Planck equations for stellar systems; Rostoker's principle
    6. R.06 Application: the tepid disc; kinetic blocking
    S · Advanced kinetic theory (7)
    1. S.01 Weak turbulence: three-wave and four-wave interactions; Langmuir–sound turbulence
    2. S.02 Langmuir turbulence; Zakharov equations; condensate and collapse
    3. S.03 Nonlinear stability and thermodynamics of collisionless plasmas: Fowler, Kruskal–Oberman and Gardner
    4. S.04 Statistical mechanics of collisionless plasmas: Lynden-Bell and multi-waterbag models
    5. S.05 Collisionless collision integrals: Kadomtsev–Pogutse and hyperkinetic theories
    6. S.06 Phase-space turbulence: plasma echoes, cascades and Adkins–Nastac theory
    7. S.07 Nonlinear Landau damping; BGK solutions; phase-space holes