Glossary

The vocabulary of closed magnetic confinement, defined the way the family's repositories use it.

Flux surface

A nested toroidal surface that a magnetic field line covers; particles stream along field lines and so stay on the surface. Closed-field devices confine by keeping these surfaces inside the vessel.

Major radius \(R_0\), minor radius \(a\), aspect ratio \(A\)

Distance from the torus axis to the plasma centre; half-width of the plasma cross-section; their ratio. Below about 2 the tokamak is called spherical.

Elongation \(\kappa\), triangularity \(\delta\)

Vertical stretch and D-shape of the cross-section. The volume \(2\pi^2 R_0 a^2\kappa\) is exact for an ellipse and ignores \(\delta\).

Toroidal and poloidal field

Field along the torus, and around its cross-section. A tokamak's toroidal field comes from external coils and falls as \(1/R\); its poloidal field comes from the plasma current.

Safety factor \(q\)

Toroidal turns per poloidal turn of a field line. Above unity in a tokamak, below unity in a reversed-field pinch; the cylindrical estimate \(q_{\mathrm{cyl}} = 5a^2B_t(1+\kappa^2)/(2R_0I_p)\) is a consistency instrument.

Greenwald density limit

\(n_G = I_p/(\pi a^2)\) in \(10^{20}\,\mathrm{m^{-3}}\) with \(I_p\) in MA (Greenwald 2002, eq. 1.3); an empirical operational limit, not a prediction of disruption.

Normalised current \(I_N\)

\(I_p/(aB_t)\) in MA per metre-tesla; Peng & Strickler 1985 print a ceiling of about 7 for the spherical torus.

Rotational transform

The twist of the field lines, \(1/q\); in a stellarator it is made by external three-dimensional coils, so no plasma current is needed.

Field period

The number of times a stellarator's coil geometry repeats around the torus.

Taylor state, relaxation

The minimum-energy state at fixed helicity, \(\nabla\times\mathbf{B} = \mu\mathbf{B}\) with constant \(\mu\); a driven plasma relaxes toward it through fluctuations (the dynamo).

Bessel-function model

The Taylor state of a cylinder: \(B_\phi = B_0J_0(\mu r)\), \(B_\theta = B_0J_1(\mu r)\). Real reversed-field pinches depart from it.

Pinch parameter \(\Theta\), reversal parameter \(F\)

\(B_\theta(a)/\langle B_\phi\rangle\) and \(B_\phi(a)/\langle B_\phi\rangle\). The model reverses at \(\Theta_{\mathrm{rev}} = j_{0,1}/2 = 1.2024\ldots\) and is defined below \(j_{1,1}/2 = 1.9158\ldots\)

\(j_{0,1}\), \(j_{1,1}\)

The first zeros of \(J_0\) and \(J_1\): 2.404825… and 3.831705… (NIST DLMF 10.21), supplied by the shared kernel library.

Flux conserver

The conducting vessel of a spheromak, whose shape alone fixes the lowest relaxed state.

Taylor eigenvalue \(\lambda_{\mathrm{fc}}\)

\(\sqrt{(j_{1,1}/R)^2 + (\pi/L)^2}\) for a right circular conserver; 9.9 m⁻¹ for SSPX (Wood 2005). Inversely proportional to size at fixed shape.

Helicity injection, \(\lambda_{\mathrm{gun}}\)

Formation and sustainment of a spheromak by a magnetised coaxial gun; \(\mu_0 I_{\mathrm{gun}}/\psi_{\mathrm{gun}}\) is its figure of merit, and its ratio to \(\lambda_{\mathrm{fc}}\) gives hollow, peaked or relaxed profiles.

Compact toroid

A toroidal plasma with no material structure through its centre: the spheromak (with toroidal field) and the FRC (without).

Separatrix, \(x_s\), elongation \(E\)

In an FRC, the surface dividing closed from open field lines; its radius over the coil radius; its length over its diameter.

Kinetic-scale parameter \(S^*\)

Separatrix radius over ion skin depth. The empirical bound \(S^*/E < 3.5\) orders operating points; it does not claim stability.

Advisory band

A frequency range a core's diagnostics are declared against (RFP 1–500 kHz, spheromak 1–200 kHz); findings are reported, never clamped.

Composed, not restated

The tokamak core's rule: a level-0 record reads a limit from the object that owns it, so one number has one source of truth.

Evidence maturity

One of six states per capability — architecture_only, computational_prototype, benchmark_validated, external_code_parity, experiment_correlated, control_research_ready. None means machine-ready, safety-certified or reactor-ready.