Glossary¶
Terms from fusion plasma physics and control theory used in scpn-control.
A¶
Alpha heating — Self-heating of plasma by 3.52 MeV alpha particles produced in D-T fusion reactions. Becomes the dominant heat source when Q > 5. MW. core.integrated_transport_solver
Anomalous transport — Cross-field particle and heat transport driven by turbulent fluctuations, exceeding neoclassical predictions by 1-2 orders of magnitude. Modelled with gyro-Bohm scaling in scpn-control. m^2/s. core.gyrokinetic_transport
Anti-windup — Controller modification preventing integral wind-up when actuator saturation occurs. The super-twisting SMC and PI controllers in scpn-control clamp the integrator state. control.sliding_mode_vertical
Aspect ratio (A) — R0/a, the ratio of major to minor radius. ITER: 3.1, SPARC: 3.25. Dimensionless. core.tokamak_config
B¶
Ballooning mode — Pressure-driven MHD instability localised on the outboard (bad curvature) side of a tokamak. The infinite-n ideal ballooning criterion sets the critical pressure gradient. core.ballooning_solver
Beta (beta_N, beta_p, beta_t) — Ratio of plasma kinetic pressure to magnetic pressure. beta_t = 2 mu_0
/ B0^2 (toroidal), beta_p = 2 mu_0
/ B_pol^2 (poloidal), beta_N = beta_t / (Ip/aB0) (normalised, Troyon). Dimensionless; beta_N in % MA/m/T. core.stability_mhd
Bootstrap current — Self-generated toroidal current driven by trapped-particle pressure gradients in the banana regime. Modelled by the Sauter formula (Phys. Plasmas 6, 2834, 1999). A/m^2. core.integrated_transport_solver
Bremsstrahlung — Electromagnetic radiation from electron-ion Coulomb collisions. Scales as n_e^2 Z_eff T_e^{1/2}. A net power loss in the energy balance. MW/m^3. core.integrated_transport_solver
Burning plasma — A plasma where alpha heating exceeds external heating, i.e. Q > 5. The primary target of ITER and SPARC.
C¶
Confinement time (tau_E) — Energy confinement time: ratio of stored energy to total heating power minus dW/dt. Characterises how well the plasma retains energy. s. core.scaling_laws
Controllability — A state x is controllable if there exists an input sequence driving the system from x to the origin. Checked via the rank of [B, AB, ..., A^{n-1}B]. control.h_infinity_controller
Critical gradient — The temperature gradient threshold above which turbulent transport sharply increases (stiff transport). The critical-gradient model approximates ITG/TEM-driven chi as max(0, gradient - gradient_crit). core.neural_transport
Current diffusion — Resistive evolution of the current profile (q profile) on the skin time. Solved by a 1D diffusion equation in the normalised poloidal flux coordinate. core.current_diffusion
Current drive — Non-inductive methods of sustaining plasma current: NBI, ECCD, LHCD, bootstrap. Required for steady-state tokamak operation. A. core.current_drive
D¶
DARE (Discrete Algebraic Riccati Equation) — The matrix equation X = A^T X A - A^T X B (R + B^T X B)^{-1} B^T X A + Q, solved to obtain LQR/H-infinity gains for a sampled-data plant. control.h_infinity_controller
D-K iteration — Iterative mu-synthesis algorithm alternating between D-scale fitting and H-infinity controller synthesis to achieve robust performance against structured uncertainty. control.mu_synthesis
Detachment — Divertor operating regime where the plasma cools and recombines before reaching the target plates, reducing peak heat flux. core.sol_model
Disruption — Abrupt loss of plasma confinement, causing rapid thermal and current quenches. Generates large halo currents and mechanical loads. The primary off-normal event in tokamak operation. control.disruption_predictor
Divertor — Magnetic geometry that directs scrape-off-layer flux to dedicated target plates for power exhaust and impurity control. core.sol_model
E¶
ECCD (Electron Cyclotron Current Drive) — Current driven by asymmetric electron heating at electron cyclotron resonance. Used for NTM stabilisation by depositing current at the rational surface. A. core.current_drive
ELM (Edge Localised Mode) — Repetitive MHD instability at the H-mode pedestal, expelling 5-15% of stored energy per burst. Type-I ELMs are peeling-ballooning driven. core.stability_mhd
Elongation (kappa) — Vertical elongation of the plasma cross-section: ratio of vertical to horizontal extent. ITER: 1.7, SPARC: 1.97. Increases beta limits but requires active vertical stabilisation. Dimensionless. core.tokamak_config
Energy confinement scaling (IPB98y,2) — ITER Physics Basis scaling law tau_E = C I_p^{0.93} B^{0.15} n^{0.41} P^{-0.69} ... derived from multi-machine regression. s. core.scaling_laws
F¶
Fault detection and isolation (FDI) — Real-time detection of actuator or sensor failures and reconfiguration of the control system to maintain stability. control.fault_tolerant_control
Flux coordinates — Coordinate system (psi, theta_p, phi) aligned to magnetic flux surfaces. Eliminates the magnetic field's cross-surface component, simplifying transport equations. core.fusion_kernel
Flux surface — A toroidal surface of constant poloidal flux psi on which magnetic field lines lie. Equilibrium profiles (p, q, J) are flux functions. core.fusion_kernel
Free-boundary equilibrium — Grad-Shafranov solution where the plasma boundary is self-consistently determined by external coil currents, not imposed. core.fusion_kernel
G¶
Gain margin — The factor by which loop gain can increase before the closed-loop system goes unstable. Measured in dB. H-infinity synthesis guarantees >= 6 dB. control.h_infinity_controller
Grad-Shafranov equation — The elliptic PDE for axisymmetric toroidal equilibrium: Delta psi = -mu_0 R^2 p'(psi) - F F'(psi), where Delta is the toroidal Laplacian operator. Solved by Picard iteration. core.fusion_kernel
Greenwald limit — Empirical density limit n_G = I_p / (pi a^2) [10^20 m^-3]. Exceeding it triggers disruptions. 10^20 m^-3. core.scaling_laws
Gyrokinetic transport — First-principles turbulent transport modelling based on the gyrokinetic Vlasov equation. Approximated in scpn-control via critical-gradient and QLKNN-10D surrogate models. core.gyrokinetic_transport
H¶
H-mode (High confinement mode) — Operating regime with an edge transport barrier (pedestal), achieving ~2x the L-mode confinement time. Accessed by exceeding a power threshold. core.fusion_kernel
H-infinity control — Robust control synthesis minimising the worst-case disturbance-to-performance transfer function norm. Solved via two continuous Riccati equations, then discretised by ZOH. control.h_infinity_controller
Halo current — Current flowing through open field lines and the vessel wall during vertical displacement events. Generates large electromagnetic forces. A. control.halo_re_physics
I¶
ITER — International Thermonuclear Experimental Reactor. R0=6.2 m, B0=5.3 T, Ip=15 MA, target Q=10. The reference configuration in scpn-control. core.tokamak_config
Island width — Half-width of a magnetic island at a rational surface, governed by the Modified Rutherford Equation. Controls NTM stability. m. core.ntm_dynamics
Isoflux — Shape control strategy where external coil currents are adjusted to match the poloidal flux at target control points on the desired plasma boundary. control.tokamak_flight_sim
K¶
Kink mode — Current-driven MHD instability. External kinks limit q_edge > 2; internal kinks (m=1, n=1) trigger sawteeth when q_axis < 1. core.stability_mhd
Kuramoto model — Coupled oscillator model: d theta_i/dt = omega_i + (K/N) sum_j sin(theta_j - theta_i). Exhibits a synchronisation phase transition at critical coupling K_c. phase.kuramoto
L¶
L-mode (Low confinement mode) — Standard tokamak operating regime without an edge transport barrier. Confinement time follows the L-mode scaling. core.fusion_kernel
Lagrangian PPO — Proximal Policy Optimisation with Lagrangian constraint enforcement for safe reinforcement learning. Maintains a Lagrange multiplier for each safety constraint (e.g. beta_N < Troyon limit). control.safe_rl_controller
Lawson criterion — Condition for ignition: n tau_E T > ~3 x 10^21 m^-3 s keV for D-T. Defines the minimum triple product for net energy gain.
LIF neuron (Leaky Integrate-and-Fire) — Neuron model: dv/dt = -v/tau + I. Fires when v crosses threshold, then resets. Used as the transition-firing element in the SPN-to-SNN compilation. scpn.compiler
Lyapunov stability — A system is Lyapunov stable if trajectories starting near an equilibrium remain near it. The Lyapunov guard in scpn-control monitors V(theta) = 1 - R(t) and triggers alerts when dV/dt > 0. phase.lyapunov_guard
M¶
MHD (Magnetohydrodynamics) — Fluid description of plasma. Ideal MHD governs kink, ballooning, and peeling modes; resistive MHD governs tearing and NTM. core.stability_mhd
MPC (Model Predictive Control) — Receding-horizon optimal control: solve a finite-horizon optimisation at each time step using a plant model, apply the first control action, repeat. control.fusion_sota_mpc
Modified Rutherford Equation (MRE) — ODE governing NTM island width evolution: dw/dt = eta/(mu_0 r_s) [Delta'(w) + Delta_bs(w) + Delta_ECCD(w)]. Predicts when islands grow or shrink. core.ntm_dynamics
Mu-synthesis (mu-synthesis) — Robust control framework that accounts for structured (parametric) uncertainty. Uses D-K iteration to minimise the structured singular value mu. control.mu_synthesis
N¶
NBI (Neutral Beam Injection) — Heating and current drive method injecting high-energy neutral atoms (50-500 keV) into the plasma. MW. core.current_drive
NTM (Neoclassical Tearing Mode) — Resistive MHD instability at rational surfaces (q = m/n) sustained by a bootstrap current deficit inside the island. core.ntm_dynamics
Neural transport — Machine-learning surrogate for turbulent transport coefficients. The critical-gradient model and QLKNN-10D input space are implemented. core.neural_transport
O¶
Observability — A state x is observable if it can be determined from output measurements over a finite interval. Dual of controllability. control.state_estimator
Ohmic heating — Resistive heating from the plasma current: P_ohm = eta J^2. Dominates at low temperature; diminishes as T_e^{3/2} (Spitzer resistivity). MW/m^3. core.integrated_transport_solver
Order parameter (R) — Kuramoto order parameter: R exp(i psi) = (1/N) sum_j exp(i theta_j). R=0 is incoherence, R=1 is full synchrony. Dimensionless. phase.kuramoto
P¶
PAC (Phase-Amplitude Coupling) — Cross-frequency coupling where the phase of a low-frequency oscillation modulates the amplitude of a high-frequency one. Used for SNN closed-loop modulation. control.advanced_soc_fusion_learning
Pedestal — The steep gradient region at the plasma edge in H-mode. Pedestal height and width set the boundary condition for core transport. keV. core.pedestal
Picard iteration — Fixed-point iteration for solving the GS equation: psi^{k+1} = G(psi^k) with under-relaxation. core.fusion_kernel
Plasma current (Ip) — Total toroidal current in the plasma, providing the poloidal magnetic field. ITER: 15 MA, SPARC: 8.7 MA. MA. core.tokamak_config
Poloidal — The short way around the torus (in the R-Z plane). Poloidal magnetic field B_pol confines plasma vertically. core.fusion_kernel
PPO (Proximal Policy Optimisation) — Policy gradient RL algorithm with clipped surrogate objective. The default RL agent in TokamakEnv. control.gym_tokamak_env
Q¶
Q factor — Fusion gain: Q = P_fusion / P_external. Q=1 is breakeven, Q=10 is the ITER target, Q=infinity is ignition.
q (safety factor) — q = d phi / d theta_p, the number of toroidal transits per poloidal transit of a field line. q < 1 at the axis triggers sawteeth; q < 2 at the edge triggers kinks. Dimensionless. core.fusion_kernel
R¶
Resistive wall mode (RWM) — External kink stabilised only by eddy currents in the resistive wall. Grows on the wall time constant (~10 ms). Requires active feedback. control.rwm_feedback
Riccati equation — Matrix equation arising in LQR and H-infinity synthesis. Continuous: A^T X + X A - X B R^{-1} B^T X + Q = 0. Solved by scipy.linalg.solve_continuous_are. control.h_infinity_controller
S¶
Safety factor (q) — See q (safety factor).
Sawtooth — Periodic relaxation oscillation when q_axis < 1, caused by the internal kink mode. Flattens the core temperature profile. core.sawtooth
Scrape-off layer (SOL) — Open-field-line region outside the last closed flux surface, connecting to the divertor or limiter. Carries the exhaust power. core.sol_model
SNN (Spiking Neural Network) — Neural network operating on discrete spike events. The FusionCompiler maps SPN transitions to LIF neurons with bitstream-encoded weights. scpn.compiler
SPN (Stochastic Petri Net) — Bipartite graph (places, transitions) with stochastic firing rules. Marking vector m(t) encodes the system state; transition firing updates m via the incidence matrix. scpn.structure
Sliding-mode control — Robust nonlinear control driving the state to a sliding surface s=0. The super-twisting algorithm provides chattering-free second-order convergence. control.sliding_mode_vertical
SPARC — Compact high-field tokamak (R0=1.85 m, B0=12.2 T, Ip=8.7 MA). Target Q > 2 with HTS magnets. Creely et al., J. Plasma Phys. 86 (2020). core.tokamak_config
Super-twisting algorithm — Second-order sliding mode: u = -alpha |s|^{1/2} sign(s) + v, dv/dt = -beta sign(s). Finite-time convergence, continuous control signal. control.sliding_mode_vertical
T¶
Tearing mode — Resistive MHD instability that reconnects magnetic field lines at rational surfaces, forming magnetic islands. Degrades confinement. core.ntm_dynamics
Tokamak — Toroidal magnetic confinement device with a strong toroidal field and a plasma current providing the poloidal field. The dominant fusion concept.
Toroidal — The long way around the torus (the phi direction). Toroidal magnetic field B_phi is the dominant confining field.
Transport — Particle, heat, and momentum fluxes across magnetic surfaces. Neoclassical transport is the irreducible minimum; anomalous (turbulent) transport dominates in practice. m^2/s. core.integrated_transport_solver
Triangularity (delta) — Triangular shaping of the plasma cross-section. Positive delta stabilises ballooning modes. ITER: 0.33, SPARC: 0.54. Dimensionless. core.tokamak_config
Troyon limit — Empirical stability limit: beta_N < g_Troyon, with g_Troyon ~ 2.8 for conventional profiles. Exceeding it triggers MHD instabilities. % MA/m/T. core.stability_mhd
U¶
UPDE (Unified Phase Dynamics Equation) — Coupled Kuramoto system across SCPN layers: d theta_n/dt = omega_n + sum_m K_nm sin(theta_m - theta_n) + zeta sin(Psi - theta_n). Governs inter-layer synchronisation. phase.upde
V¶
VDE (Vertical Displacement Event) — Loss of vertical position control, causing the plasma to move vertically until it contacts the wall. Generates halo currents and large forces. control.sliding_mode_vertical
Vertical stability — Elongated plasmas are vertically unstable with a growth rate gamma proportional to sqrt(kappa - 1). Requires active feedback with sub-millisecond response. control.h_infinity_controller
Vessel model — Lumped-element model of the vacuum vessel and passive conductors. Provides the eddy current response needed for vertical stability control design. core.vessel_model
Z¶
Z_eff (Effective charge) — Ion-charge-weighted average: Z_eff = sum(n_i Z_i^2) / n_e. Increases Bremsstrahlung and resistivity. Typical range 1.2-3.0. Dimensionless. core.integrated_transport_solver