Glossary · Computational Plasma Simulation
Alphabetical reference for the PHY653B wiki.
BGK operator — Single-relaxation-time collision model, \(\mathcal{C} = -(f - f^{\rm eq})/\tau\). Crude but conservative and cheap; the entire collision model of LBM. → Collision operators
Boris pusher — The standard particle mover: half electric kick, exact magnetic rotation, half electric kick. Conserves energy in a static \(\mathbf{B}\) to round-off. → Boris pusher
Bounce frequency — \(\omega_B = \sqrt{kE}\), the oscillation rate of a particle trapped in a wave trough. Trapping arrests damping when \(\omega_B \gtrsim |\gamma|\). → Nonlinear trapping
Brio–Wu — The standard MHD shock tube; a single discontinuity decaying into fast rarefactions, a compound wave, a contact and a slow shock. → Godunov MHD
Cat's eye — The closed island of trapped orbits that forms at the resonant velocity in phase space during nonlinear trapping. → Nonlinear trapping
Chapman–Enskog expansion — Systematic expansion of \(f\) about local equilibrium in the Knudsen number; derives transport coefficients rather than asserting them. Gives \(\nu = c_s^2(\tau - \tfrac12)\) for LBM. → Chapman–Enskog
CIC (cloud-in-cell) — First-order shape function, the PIC workhorse. → Shape functions
Closure — An asserted relation for a high moment that truncates the otherwise infinite moment hierarchy. A physical assumption, not an algebraic step. → Closure problem
Compound wave — A shock attached to a rarefaction; a purely MHD structure with no gas-dynamic analogue, appearing in Brio–Wu. → Godunov MHD
Constrained transport (CT) — Staggered discretisation (\(\mathbf{B}\) on faces, \(\mathbf{E}\) on edges) that preserves \(\nabla\cdot\mathbf{B} = 0\) to round-off by construction. → Divergence constraint
D2Q9 — The nine-velocity two-dimensional lattice; the abscissae and weights of the third-order Gauss–Hermite quadrature, giving \(c_s^2 = 1/3\). → D2Q9 lattice
de Vahl Davis — The differentially heated square cavity, the standard natural-convection benchmark with tabulated Nusselt numbers. → Thermal LBM
Gauss–Hermite quadrature — The quadrature rule underlying the LBM velocity set; exact for polynomial moments up to a given order. → D2Q9 lattice
Grid heating — Spurious numerical heating when \(\Delta x > \lambda_D\); the plasma warms until \(\lambda_D\) matches \(\Delta x\). Stable, smooth, and completely wrong. → PIC noise and heating
Guo forcing — Second-order-accurate body-force term for LBM that correctly accounts for the discrete time step. → LBM widget
Gyro-average — Averaging over gyrophase, replacing a particle by a charged ring; in Fourier space, multiplication by \(J_0(k_\perp\rho)\). → Gyrokinetic ordering
Gyrokinetic ordering — \(\omega/\Omega_c \sim k_\parallel/k_\perp \sim \delta f/f \sim \varepsilon\) with \(k_\perp\rho_i \sim 1\); removes gyration while keeping FLR physics. → Gyrokinetic ordering
HLLD — Five-wave approximate Riemann solver, the modern default for MHD. → Godunov MHD
ITG mode — Ion-temperature-gradient instability, the dominant turbulence drive in the tokamak core. → Zonal flows
Landau collision operator — The correct Fokker–Planck operator for Coulomb collisions; conservative, and the most expensive object in computational plasma physics. → Collision operators
Manufactured solution — An invented solution substituted into the operator to generate a source term, giving an exact solution to verify against. → MMS
Marker — A sample point of \(f\) in PIC. Not a physical particle. → Shape functions
Observed order of accuracy — \(p_{\rm obs} = \ln(E_{2h}/E_h)/\ln 2\); the measured convergence rate, and the single most informative verification test. → Verification and validation
Orszag–Tang vortex — 2-D MHD test with smooth initial data developing a network of interacting shocks. → Godunov MHD
Phase mixing — The shearing of a perturbation into ever-finer velocity-space filaments; what Landau damping physically is. → Recurrence
Polarisation density — The difference between gyro-averaged and true density in gyrokinetics; the analogue of a dielectric response. → Gyrokinetic ordering
Profile stiffness — Transport rising so steeply above the ITG threshold that the temperature gradient is pinned near critical. → Zonal flows
Rayleigh number, critical — \(Ra_c = 1707.76\), the onset of Rayleigh–Bénard convection; a sharp threshold sensitive to the entire coupled solver. → Thermal LBM
Recurrence time — \(T_R = 2\pi/(k\Delta v)\); the time at which discrete velocities rephase and a "damped" wave revives. → Recurrence
Riemann problem — The exact evolution of a single initial discontinuity; the flux calculation at the heart of Godunov schemes. → Godunov MHD
Self-force — Spurious force of a marker on itself, caused by mismatched deposit and interpolate shape functions. → Shape functions
Semi-Lagrangian — Scheme that traces characteristics backwards to a departure point and interpolates; no CFL restriction. → Semi-Lagrangian solver
Strang splitting — Symmetric operator splitting \(\mathcal{A}_{h/2}\mathcal{B}_h\mathcal{A}_{h/2}\), second-order accurate for essentially no extra cost. → Semi-Lagrangian solver
Synthetic diagnostic — Application of an instrument's response to simulation output, so that like is compared with like. → Numerical diagnostics
Validation — Am I solving the right equations? Requires data from the world. → Verification and validation
Verification — Am I solving the equations right? A pure mathematics question, answered by a convergence rate. → Verification and validation
Weibel instability — Electromagnetic instability driven purely by temperature anisotropy; the standard EM PIC benchmark. → Weibel instability
Zonal flow — Axisymmetric sheared \(\mathbf{E}\times\mathbf{B}\) flow with \(k_\theta = k_\parallel = 0\); generated by turbulence and suppressing it. → Zonal flows