Glossary · Computational EM & Plasma

Alphabetical reference for the PHY653 wiki.

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Adiabatic invariant — Quantity (e.g. \(\mu = mv_\perp^2/2B\)) conserved when fields vary slowly compared to the particle's periodic motion. → Magnetic mirror

A-stability — Unconditional stability for decaying problems; property of implicit schemes like backward Euler. → Backward Euler

Boris pusher — The standard PIC particle mover; a rotate-and-kick form of the implicit leapfrog. → Leapfrog update

CFL (Courant) condition — \(\Delta t \leq \Delta x/(c\sqrt d)\): the time step must not outrun signal propagation on the grid. → CFL

Cloud-in-cell (CIC) — Linear weighting between particles and grid in PIC deposit and interpolation. → PIC method

Curvature drift — Guiding-center drift from bent field lines, ∝ \(v_\parallel^2\), charge-dependent. → Grad-B & curvature

Cyclotron frequency — \(\omega_c = qB/m\); the gyration rate. → Cyclotron motion

Explicit method — Update computed directly from known values; cheap but conditionally stable. → ODE integration

E×B drift — \(\mathbf{v}_E = \mathbf{E}\times\mathbf{B}/B^2\); charge- and mass-independent. → E×B drift

FDTD — Finite-Difference Time-Domain: leapfrogged, staggered-grid solution of Maxwell's curl equations. → FDTD

Fermi acceleration — Energy gain of particles bouncing between converging magnetic mirrors. → Fermi acceleration

Finite difference — Approximating derivatives with difference quotients on a grid. → FDM

Five-point stencil — The 2-D discrete Laplacian coupling a point to its four neighbors. → FDM

Forward Euler — Simplest explicit scheme, first order; gains energy on orbits. → Forward Euler

Gauss–Seidel — Iterative relaxation solver for Poisson/Laplace using freshly updated neighbors. → Poisson solvers

Grad-B drift — Drift from spatial variation of \(|\mathbf{B}|\), ∝ \(v_\perp^2\), charge-dependent. → Grad-B & curvature

Growth rate (\(\gamma\)) — Exponential rate of an instability's linear phase; measured from the slope of \(\ln\mathcal{E}(t)\). → Two-stream instability

Guiding center — The slowly drifting center of a particle's fast gyration. → Guiding center & drifts

Implicit method — The unknown future state appears on both sides of the update; stable but requires a solve. → Backward Euler

Kick–drift–kick (KDK) — Split-step form of leapfrog used in N-body codes. → Leapfrog

Larmor radius — \(r_L = mv_\perp/qB\); the gyration radius. → Cyclotron motion

Leapfrog — Second-order symplectic integrator with staggered position/velocity. → Leapfrog

Lorentz force — \(m\dot{\mathbf{v}} = q(\mathbf{E} + \mathbf{v}\times\mathbf{B})\). → Lorentz force

Loss cone — The pitch-angle region of particles that escape a magnetic mirror. → Magnetic mirror

Magnetic mirror — Field configuration that reflects particles via converging field lines. → Magnetic mirror

Magnetic moment (\(\mu\)) — \(mv_\perp^2/2B\); first adiabatic invariant. → Magnetic mirror

N-body problem — Direct integration of all pairwise interactions; \(\mathcal{O}(N^2)\). → N-body

Order (of a method) — Power \(p\) in the global error \(\mathcal{O}(\Delta t^p)\). → Convergence & error

Particle-in-cell (PIC) — Particles coupled through grid-based field solves; self-consistent kinetic simulation. → PIC method

Phase space — The \((x, v)\) plane; where kinetic plasma dynamics is legible. → Two-stream instability

Poisson equation — \(\nabla^2\phi = -\rho/\varepsilon_0\); electrostatic potential from charge. → Poisson solvers

Polarization drift — Drift from time-varying \(\mathbf{E}\); mass-dependent, carries current. → Guiding center & drifts

Predictor–corrector — Estimate with an explicit step, refine with an implicit-style evaluation. → Backward Euler

Runge–Kutta (RK4) — Multi-stage explicit schemes; RK4 is 4th order with 4 evaluations. → Runge–Kutta

Softening — Regularizing the \(1/r^2\) force at small separations in N-body codes. → N-body

Staggered (Yee) grid — Interleaved E and H storage in space and time for FDTD. → FDTD

Stiff system — Dynamics with fast decaying modes forcing tiny explicit steps; calls for implicit methods. → ODE integration

Symplectic integrator — Scheme preserving phase-space structure; bounded energy error forever. → Leapfrog

Two-stream instability — Exponentially growing electrostatic instability of counter-streaming beams. → Two-stream

Virial theorem — \(2\langle K\rangle = -\langle U\rangle\) for bound gravitational systems. → N-body