Fourth state of matter: ionised gas with collective electromagnetic interactions. Debye shielding, plasma oscillations, magnetohydrodynamics (MHD), kinetic theory (Vlasov), confinement, Alfvén waves, Landau damping.
Plasma Physics
Plasma (ionised gas)
Macroscopically neutral ionised gas exhibiting collective electromagnetic behaviour. Characterised by density n_e, temperature T_e, and…
Debye length λ_D
Screening length for static charges in a plasma: λ_D = √(ε₀ k_B T / n e²). Collective effects dominate at scales ≫ λ_D.
Plasma frequency ω_p
Natural oscillation frequency of electron-density perturbations in a plasma: ω_p = √(n_e e² / ε₀ m_e).
Debye shielding
Exponential screening of a test charge's potential by the surrounding plasma over a distance ~λ_D: φ(r) = (q/4πε₀r) e^{−r/λ_D}.
Vlasov equation
Collisionless Boltzmann equation for the phase-space density f(x, v, t): ∂_t f + v·∇_x f + (F/m)·∇_v f = 0. Backbone of kinetic plasma…
Magnetohydrodynamics (MHD)
Fluid description of a conducting plasma coupling Navier–Stokes to Maxwell's equations: ρ Dv/Dt = J×B − ∇p, ∂_t B = ∇×(v×B) + η ∇²B.
Alfvén wave
Transverse electromagnetic wave in a magnetised plasma propagating along B with speed v_A = B/√(μ₀ρ). Low-frequency building block of MHD…
Landau damping
Collisionless damping of plasma waves by resonant particles (v ≈ ω/k) even without dissipation. Hallmark of Vlasov dynamics; purely…
Magnetic plasma confinement
Engineering/theoretical programme to confine hot plasma for fusion by shaping B (tokamak, stellarator). Performance measured by the Lawson…
Saha ionisation equation
Thermal-equilibrium ratio of successive ionisation states in a plasma: n_{i+1} n_e / n_i = (2π m_e k_B T/h²)^{3/2} · 2 g_{i+1}/g_i ·…
Tokamak magnetic confinement
Toroidal + poloidal B-fields wind on nested flux surfaces; plasma current provides poloidal. ITER (500 MW, Q=10, 2035).…
Inertial confinement fusion
Laser/ion-beam compression of DT capsule to ~1000× solid density. NIF achieved ignition Q>1 in Dec 2022. Polar-direct + indirect (hohlraum)…
Magnetic reconnection
Topological rearrangement of B-field lines in finite resistivity; converts magnetic → kinetic/thermal energy. Solar flares, CMEs,…
Dusty plasmas & Coulomb crystals
Charged microparticles in ionized gas form ordered structures. Plasma crystals (Melzer-Homann-Piel 1994). Astrophysical relevance…
Debye length & screening
λ_D = √(ε₀k_BT/ne²); Coulomb potential exponentially screened beyond λ_D; quasineutrality holds on scales ≫ λ_D.
Plasma parameter Λ = n λ_D³
Λ ≫ 1 defines weakly coupled plasma with collective behaviour; Λ<1 → strongly-coupled (Coulomb crystal, WDM).
Alfvén and MHD waves
Shear Alfvén, fast/slow magnetosonic; v_A = B/√(μ₀ρ); dispersion ω = k_∥ v_A; observed in solar corona, magnetosphere.
Guiding-center drift theory
For slowly varying fields: E×B drift, grad-B drift, curvature drift; adiabatic invariants μ, J; basis of gyrokinetics.
Gyrokinetic equation
Average over gyromotion; reduces 6D Vlasov to 5D; basis of GENE, GYRO simulations of tokamak turbulence.
Landau damping
Damping of Langmuir waves without collisions via resonant v = ω/k particles; Penrose criterion for instability.
Stellarator optimized fields
Non-axisymmetric 3D coils provide rotational transform; W7-X quasi-isodynamic optimization suppresses neoclassical losses.
Bohm diffusion
Anomalous plasma transport D_B = k_BT/(16eB); orders of magnitude above neoclassical; driven by turbulence.
Drift-wave turbulence
Pressure-gradient driven modes with k_⊥ ρ_s ~ 1; ITG, TEM, ETG branches; dominant transport channel in tokamak core.
MHD kink and tearing modes
External kink m=1/n=1 limits q>2 in tokamak; internal kink sawteeth; tearing mode neoclassical seed.
Dusty (complex) plasma & Coulomb crystals
Micron dust grains charged to 10³-10⁴ e; strongly coupled; form lattices; laboratory analog of condensed matter, with individual particle…
Astrophysical jet launching
Blandford–Znajek from spinning BH magnetosphere; Blandford–Payne from disk; magnetic tower collimation; AGN jets > kpc long.
Parker spiral solar wind
Supersonic flow from sonic point at ~ few R_⊙; magnetic field wound into Archimedean spiral; heliospheric current sheet.
Ionosphere–magnetosphere coupling
Van Allen belts; ring current; magnetotail reconnection drives aurora; space weather disrupts GPS, power grids.
Laser-wakefield acceleration
Ultrashort laser pulse drives plasma wave; accelerating gradients ~100 GV/m; multi-GeV electrons in cm; compact FELs.
Runaway electrons (Dreicer, avalanche)
E > E_D decouples fast electrons from collisions → MeV runaway beams; major tokamak disruption threat; avalanche amplification.