Transport and Stability¶
SCPN-Fusion-Core couples the equilibrium solver with 1.5D radial transport, multiple stability analysis tools, and AI-based turbulence surrogates.
1.5D Radial Transport¶
The integrated transport solver (integrated_transport_solver.py)
solves the coupled energy and particle diffusion equations on the
normalised radial coordinate \(\rho\):
where \(D\) is the particle diffusion coefficient, \(\chi\) is the thermal diffusivity, \(V'(\rho)\) is the flux-surface volume derivative, and \(S_n\) is the particle source.
The anomalous transport coefficients \(D\) and \(\chi\) are derived from the turbulence oracle (see below) or from prescribed scaling laws.
Auxiliary Heating Source Normalisation¶
The auxiliary-heating source in TransportSolver.evolve_profiles is
power-normalised in physical units:
input auxiliary power \(P_\mathrm{aux}\) [MW] is converted to W,
a radial deposition shape is volume-normalised with \(dV(\rho)\),
volumetric power density is mapped to temperature source terms using \(\frac{3}{2} n \frac{dT}{dt} = P\).
This enforces an explicit MW->keV/s consistency path and provides
per-step telemetry in _last_aux_heating_balance with target and
reconstructed injected powers for ion/electron channels.
A reproducible benchmark lane for this contract is available at:
validation/benchmark_transport_power_balance.py.
IPB98(y,2) Confinement Scaling¶
The global energy confinement time is cross-checked against the IPB98(y,2) scaling law (ITER Physics Basis, Nuclear Fusion 39, 1999):
where \(I_p\) is in MA, \(B_T\) in T, \(\bar{n}_{e,19}\) in \(10^{19}\,\text{m}^{-3}\), \(P_\text{loss}\) in MW, \(R\) in m, \(\kappa\) is the elongation, \(\varepsilon = a/R\) is the inverse aspect ratio, and \(M\) is the effective ion mass in amu.
The uncertainty quantification follows the Bayesian regression framework of Verdoolaege et al. (Nuclear Fusion 61, 2021) using the 20-shot ITPA H-mode confinement database.
RF Heating Models¶
The rf_heating module simulates auxiliary heating deposition profiles
using simplified ray-tracing:
- ICRH – Ion Cyclotron Resonance Heating
Power is deposited at the ion cyclotron resonance layer \(\omega = n \omega_{ci}\) where \(\omega_{ci} = eB / m_i\).
- ECRH – Electron Cyclotron Resonance Heating
Power deposited at the electron cyclotron resonance \(\omega = n \omega_{ce}\) where \(\omega_{ce} = eB / m_e\).
- LHCD – Lower Hybrid Current Drive
Non-inductive current drive via lower-hybrid wave absorption.
Turbulence Models¶
FNO Turbulence Suppressor¶
The Fourier Neural Operator (FNO) turbulence model
(fno_turbulence_suppressor.py) provides real-time spectral
turbulence prediction using 12 Fourier modes. The FNO architecture
(Li et al. 2021) learns the solution operator of the turbulence PDE
directly in Fourier space:
where \(\mathcal{F}\) is the Fourier transform, \(R_l\) is a learnable spectral filter, and \(\sigma\) is a nonlinear activation.
Multi-regime training data is generated from a modified Hasegawa-Wakatani model with regime-dependent parameters (ITG, TEM, ETG).
Turbulence Oracle¶
The turbulence oracle (turbulence_oracle.py) predicts the dominant
instability regime (ITG, TEM, or ETG) from local plasma parameters and
provides anomalous transport coefficient estimates for the transport
solver.
MHD Stability¶
Sawtooth Oscillations¶
The mhd_sawtooth module models sawtooth crash dynamics using a
modified Kadomtsev reconnection model (Kadomtsev 1975). The sawtooth
period is estimated from the resistive evolution of the \(q = 1\)
surface, and the crash amplitude is computed from the flux reconnection
geometry.
Hall-MHD Effects¶
The hall_mhd_discovery module incorporates two-fluid Hall-MHD
effects (Huba, NRL Plasma Formulary 2019) that become significant
in compact, high-field tokamaks where the ion skin depth
\(d_i = c/\omega_{pi}\) is comparable to the equilibrium scale
length. Hall-MHD modifications include:
Whistler-wave dispersion at frequencies above \(\omega_{ci}\)
Hall-term correction to the magnetic induction equation: \(\partial \mathbf{B}/\partial t = \nabla \times [(\mathbf{v} - d_i \mathbf{J}/ne) \times \mathbf{B}]\)
Modified reconnection rates relevant to sawtooth crash timing
Stability Analysis¶
The stability_analyzer module provides:
Nyquist stability analysis for closed-loop feedback systems
Lyapunov stability margins for nonlinear dynamics
Vertical stability index (decay index \(n = -R/B_z \cdot \partial B_z/\partial R\)) for positional control
Beta limits (\(\beta_N\) Troyon limit, \(\beta_p\) critical)
Self-Organised Criticality (Legacy Research Lane)¶
The sandpile_fusion_reactor module is retained as a legacy SOC
research lane for reproducibility and exploratory avalanche studies.
It is not part of the release-gated transport validation path (which is
based on Gyro-Bohm + Chang-Hinton + EPED-like boundary scaling).
Fusion Ignition and Burn Physics¶
The fusion_ignition_sim module computes the Lawson criterion and
ignition margins using the Bosch-Hale D-T fusion reactivity
parametrisation:
where \(\theta\), \(\xi\), and \(C_1\) are fit parameters (Bosch & Hale, Nuclear Fusion 32, 1992).
The ignition condition \(Q \to \infty\) requires that alpha-particle heating alone sustains the plasma temperature:
where \(E_\alpha = 3.52\,\text{MeV}\) per fusion event.
Warm Dense Matter EOS¶
The wdm_engine module provides a reduced equation-of-state model
for warm dense matter conditions relevant to inertial confinement
scenarios and pellet ablation physics.