# GDBS Physics Glossary

Symbol-to-definition reference for the physics terms and quantities used across the GDBS PRO modules, each with a primary-source citation. 32 terms across 4 modules.

## Fluids

### Falkner-Skan boundary layer  -  FS

Wedge-flow generalization of Blasius. β=0 → flat plate; β=1 → stagnation; β=-0.1988 → marginal separation.

`f''' + f·f'' + β(1 - f'²) = 0`

Source: [Falkner & Skan 1931](https://doi.org/10.1080/14786443109461870)

### Taylor-Green vortex  -  TGV

Analytic 3D Navier-Stokes solution. Kinetic energy decays as exp(-4νt) for k=1. Canonical CFD verification.

Source: [Taylor & Green 1937](https://doi.org/10.1098/rspa.1937.0036)

## General

### GeoNum drift  -  drift

First-class uncertainty tracking. drift < 1.0 shade means floating-point operation stayed within zone precision.

Source: [GDBS GeoNum v2.0](#docs:geonum)

### GeoNum precision tier  -  tier

Zone tessellation depth: 2048 (full) → 1024 → 512 → 256. Trade speed for accuracy.

Source: [GDBS GeoNum v2.0](#docs:geonum)

## Plasma

### Bootstrap current  -  j_BS

Neoclassical pressure-driven toroidal current. Dominates the off-axis current in advanced tokamaks; the difference between Q=10 and Q=2 ITER.

`⟨j_BS·B⟩ = -F·(L31·p_e'/p_e + L32·T_e'/T_e + α·T_i'/T_e)`

Source: [Sauter, Angioni, Lin-Liu 1999](https://doi.org/10.1063/1.873240)

### Edge safety factor  -  q_95

Safety factor at the 95% flux surface — practical edge value. ITER design point: q_95 = 3.

`q evaluated at ψ_n = 0.95`

Source: [ITER Physics Basis 1999](https://doi.org/10.1088/0029-5515/39/12/301)

### Elongation  -  κ

Ratio of plasma height to width. κ > 1 boosts β_N and current capacity but raises vertical instability.

`κ = b/a (semi-axes)`

Source: [Freidberg 2014](https://www.cambridge.org/9781107006256)

### FRC kinetic parameter  -  s*

R_s/δ_i — separation between kinetic (s* < 5) and MHD (s* >> 5) regimes. Higher s* approaches tilt-unstable.

`s* = R_s / δ_ion`

Source: [Belova et al. 2003](https://doi.org/10.1063/1.1574018)

### FRC tilt instability  -  n=1 tilt

External kink-like mode that flips the FRC end-over-end. Dominant FRC failure mode without kinetic stabilization.

Source: [Belova et al. 2003](https://doi.org/10.1063/1.1574018)

### Fusion gain  -  Q

Ratio of fusion power output to auxiliary heating input. Q=1 = breakeven; Q=10 = ITER target; Q=∞ = ignition.

`Q = P_fusion / P_aux`

Source: [ITER Physics Basis 1999](https://doi.org/10.1088/0029-5515/39/12/302)

### Grad-Shafranov equation  -  Δ*ψ

Axisymmetric MHD equilibrium PDE. Δ*ψ = -μ₀R²p'(ψ) - F(ψ)F'(ψ). Soloviev gives closed-form solution.

Source: [Grad-Rubin 1958, Shafranov 1966](https://doi.org/10.1088/0741-3335/30/10/001)

### Greenwald density limit  -  n_GW

Empirical density limit. Operation above this triggers MARFEs and disruptions.

`n_GW = I_p / (π · a²)  [10²⁰ m⁻³]`

Source: [Greenwald 2002](https://doi.org/10.1088/0741-3335/44/8/201)

### H-mode enhancement factor  -  H_98

τ_E / τ_IPB98. H_98=1 baseline L-mode; H>1 = enhanced regime; H=1.0–1.4 typical for fusion-relevant designs.

Source: [ITER Physics Basis 1999](https://doi.org/10.1088/0029-5515/39/12/302)

### IPB98(y,2) confinement scaling  -  τ_IPB98

Gold-standard tokamak energy-confinement-time scaling. Sets the τ_E target for any new device.

`τ_E = 0.0562·I^0.93·B^0.15·n^0.41·P^-0.69·R^1.97·ε^0.58·κ^0.78·M^0.19`

Source: [ITER Physics Basis 1999, Ch. 2](https://doi.org/10.1088/0029-5515/39/12/302)

### Magnetic shear  -  s

Normalized radial gradient of q. Shear stabilizes ballooning; reversed shear opens second-stability access.

`s = (r/q) · dq/dr`

Source: [Connor, Hastie, Taylor 1979](https://doi.org/10.1098/rspa.1979.0010)

### Mercier number  -  D_M

Local interchange stability criterion. D_M < 1/4 for stability. Magnetic well stabilizes; pressure destabilizes.

`D_M = D_well + D_shear + D_current`

Source: [Mercier 1962, Greene-Johnson 1962](https://doi.org/10.1063/1.1706652)

### Neoclassical tearing mode  -  NTM

Magnetic island driven by missing bootstrap current inside the island; growth threshold depends on β_p and seed island width.

Source: [Sauter et al. 1997](https://doi.org/10.1063/1.872270)

### Normalized beta  -  β_N

Plasma pressure normalized to magnetic field and current. Troyon limit ≈ 3.5 sets the ideal-MHD stability boundary.

`β_N = β · a · B₀ / I_p  [%·m·T/MA]`

Source: [Troyon et al. 1984](https://doi.org/10.1088/0741-3335/26/1A/305)

### Normalized ion gyroradius  -  ρ*

FLR parameter. ρ* > 0.1 means strong finite-Larmor-radius stabilization of tilt mode.

`ρ* = ρ_i / R_s`

Source: [Steinhauer 2011](https://doi.org/10.1063/1.3613676)

### Peeling-ballooning mode  -  P-B

Coupled ELM precursor — edge current drives peeling, edge pressure drives ballooning. Sets pedestal-height limit.

Source: [Snyder, Wilson 2002](https://doi.org/10.1063/1.1449463)

### Poloidal beta  -  β_p

Ratio of plasma kinetic pressure to poloidal magnetic pressure. Drives Shafranov shift and bootstrap current.

`β_p = 2μ₀⟨p⟩/B_p²`

Source: [Wesson 2004 §3.6](https://global.oup.com/academic/product/tokamaks-9780198509226)

### Pressure gradient parameter  -  α

Normalized pressure gradient drives ballooning modes. First-stability ceiling: α ~ s + small.

`α = -2μ₀·q²·R·dp/dr / B²`

Source: [Connor, Hastie, Taylor 1979](https://doi.org/10.1098/rspa.1979.0010)

### Rotational transform  -  ι

Stellarator analog of 1/q. Average iota and shear set magnetic surface quality.

`ι = 1/q`

Source: [Helander 2014, Rep. Prog. Phys.](https://doi.org/10.1088/0034-4885/77/8/087001)

### Safety factor  -  q

Number of toroidal turns of a field line per poloidal turn. q < 1 is sawtooth-prone; q = m/n rational surfaces host modes.

`q(r) = r B_t / (R B_p)`

Source: [Wesson 2004 §3.2](https://global.oup.com/academic/product/tokamaks-9780198509226)

### Shafranov shift  -  Δ

Outward shift of magnetic axis at finite β. Δ/a → 0.5 sets equilibrium β limit.

`Δ/a ≈ β_p · ε`

Source: [Shafranov 1966](https://doi.org/10.1088/0741-3335/30/10/001)

### Soloviev equilibrium  -  Soloviev

Analytic closed-form Grad-Shafranov solution. Benchmark anchor for any numerical equilibrium solver.

Source: [Soloviev 1968](http://jetp.ras.ru/cgi-bin/dn/e_026_02_0400.pdf)

### Tearing parameter  -  Δ'

Discontinuity in the radial logarithmic derivative of perturbed flux at a rational surface. Δ' > 0 → classically tearing-unstable.

Source: [Furth, Killeen, Rosenbluth 1963](https://doi.org/10.1063/1.1706761)

### Toroidal beta  -  β_t

Ratio of plasma kinetic pressure to toroidal magnetic pressure. Drives ideal-MHD limits.

`β_t = 2μ₀⟨p⟩/B₀²`

Source: [Wesson 2004 §3.6](https://global.oup.com/academic/product/tokamaks-9780198509226)

### Triangularity  -  δ

D-shape parameter. Positive δ (D-shape) raises β limits; negative δ (reverse-D) suppresses ELMs.

`δ = (R_geo - R_top)/a`

Source: [Camenen et al. 2007](https://doi.org/10.1088/0029-5515/47/7/021)

### Troyon β limit  -  Troyon

Empirical ideal-MHD β limit. β_N ≤ 3.5 for unshaped tokamaks; up to 6+ for advanced scenarios.

`β_max = g · I_p/(a · B₀), g ≈ 2.8-3.5`

Source: [Troyon et al. 1984](https://doi.org/10.1088/0741-3335/26/1A/305)

## Quantum

### H₂ Kolos-Wolniewicz reference  -  H₂ K-W

Gold-standard variational H₂ ground state. E = -1.17448 Eh at R_eq = 1.401 bohr.

Source: [Kolos & Wolniewicz 1968](https://doi.org/10.1063/1.1669836)

### Hartree-Fock method  -  HF

Mean-field self-consistent solution to the many-electron Schrödinger equation. Reference for Clementi-Roetti atomic energies.

Source: [Clementi & Roetti 1974](https://doi.org/10.1016/S0092-640X(74)80016-1)