ASTRA+STRAHL Framework in Tokamak Transport

• ASTRA+STRAHL is a modular framework for simulating tokamak plasma transport, integrating time-dependent main channel evolution with impurity charge-state kinetics.
• It couples ASTRA’s transport of electron/ion profiles with STRAHL’s detailed impurity evolution, employing neoclassical and turbulent submodules for accurate predictions.
• The framework underpins predictive and interpretive studies in SPARC H-modes and disruption scenarios, enhancing operational design through realistic impurity and radiative loss modeling.

The ASTRA+STRAHL framework refers to a tightly coupled suite of one-dimensional (radially resolved) transport solvers used extensively in modern tokamak physics for both predictive and interpretive simulation of plasma core, edge, and impurity transport phenomena. This modular system, particularly as enhanced for studies on SPARC H-mode impurity transport and disruption/re scenario modeling, enables the self-consistent evolution and mutual feedback of main ion/energy/particle profiles, impurity charge-state kinetics, neoclassical and turbulent transport, radiative losses, and specialized perturbations such as massive gas injection. The framework integrates multiple physics modules (e.g., FACIT for neoclassical coefficients, TGLF-SAT2 for turbulent fluxes, neural EPED-based pedestals, NEOART for disruption-phase neoclassics, REGIA for runaway generation), providing interpretable, medium-fidelity transport predictions that are critical for operational scenario design and experimental analysis (Muraca et al., 24 Dec 2025, Linder et al., 2020).

1. Framework Architecture and Data Coupling

The ASTRA+STRAHL framework consists of two primary codes linked on a one-dimensional normalized flux grid:

• ASTRA handles time-dependent integrated transport for main channel quantities: electron/ion temperatures, densities, momentum, poloidal flux, and additional species (e.g., runaway electrons for disruption studies). It advances these profiles using explicit or implicit schemes (Crank–Nicolson) on a radial mesh ($60$ points typical, $0\leq \rho\leq 1$) using local or global physics sources.
• STRAHL resolves the full set of impurity charge-state densities $n_{Z_c}(\rho)$ and associated radiative/atomic processes via solution of 1D advection-diffusion-reaction equations with time-dependent atomic rates (ADAS-retrieved).
• At each main code time step $\Delta t$:
  • ASTRA passes updated background profiles ($n_e$, $T_e$, $T_i$, $q$, geometry, rotational shear) to STRAHL.
  • STRAHL computes impurity evolution (sources, losses), radiated power $P_{\text{rad}}$, and updates neoclassical diffusivities/velocities ($D_{\text{imp}}, V_{\text{imp}}$) by calling neoclassical submodules (FACIT or NEOART).
  • For core turbulence modeling, ASTRA invokes TGLF-SAT2 to recover turbulent diffusivities/velocities ($D_{\text{turb}}, V_{\text{turb}}$) for trace impurities and main ions.
  • The summed coefficients are returned to ASTRA for use in transport updates.
• In disruption modeling (e.g., MGI), ASTRA additionally evolves runaway density $n_{\text{RE}}$ using kinetic closures from REGIA, with partial-ionization corrections provided by STRAHL (Muraca et al., 24 Dec 2025, Linder et al., 2020).

2. Physics Modules: Neoclassical and Turbulent Transport

Neoclassical Transport (FACIT, NEOART)

Both FACIT and NEOART supply local neoclassical fluxes by analytic or semi-analytic formulas derived for arbitrary collisionality and geometry. The impurity flux for species $s$ is

$$\Gamma_s^{\text{nc}} = - D_s^{\text{nc}}\, \frac{\partial n_s}{\partial r} + V_s^{\text{nc}}\, n_s .$$

Here,

$$D_s^{\text{nc}} = \frac{n_i T_i}{m_i\Omega_i^2}\,H_D(\nu_*,Z_s,A_s,M), \quad V_s^{\text{nc}} = \frac{T_i}{m_i \Omega_i r}\,H_V(\nu_*,Z_s,A_s,M),$$

with $\Omega_i$ the ion gyrofrequency, $\nu_*$ the normalized collisionality, and $M$ the Mach number. Parametric dependence is encoded in $H_D, H_V$ (Muraca et al., 24 Dec 2025).

Turbulent Transport (TGLF-SAT2)

TGLF-SAT2 provides mode-resolved linear growth rates and frequencies ($\gamma_k, \omega_k$) and outputs quasi-linear turbulent transport coefficients. The diffusivity for species $s$ is: $$D_{\text{turb},s} = c_s^2 \sum_k \frac{\gamma_k |\delta\phi_k|^2_{\rm sat}}{\gamma_{\text{ref}} n_e^2},$$ with $|\delta\phi_k|^2_{\rm sat}$ from the SAT2 saturation rule. The convective velocity includes thermo-diffusion, rotodiffusion, and gradients: $$V_{\text{turb},s} = D_{\text{turb},s} \left[ C_T \frac{R}{L_T} + C_n \frac{R}{L_n} + C_u \frac{u'_E}{\Omega_i} \right].$$ TGLF is invoked at each step and radius, with coefficients summed to $D_{\text{imp}}=D_{\text{turb}}+D_{\text{neo}}$ (Muraca et al., 24 Dec 2025).

3. Impurity Charge-State Evolution and Radiation

STRAHL advances the full multi-charge-state impurity distribution,

$$\frac{\partial n_{Z_c}}{\partial t} + \nabla \cdot \Gamma_{Z_c} = S^{\rm ion}_{Z_c}(n_e, T_e) + S^{\rm rec}_{Z_c}(n_e, T_e),$$

using atomic rates ($R_{i\to j}$) from ADAS. Impurity sources are set by wall flux or user constraints (e.g., $n_s(r_{\rm ped}) = f_{s,\rm ped} n_e(r_{\rm ped})$), and resulting charge distributions feed back to $Z_{\rm eff}$, total radiated power $P_{\rm rad}$, and modified resistivity profiles in the main transport equations. Multiple neutral species and population advection are supported in MGI simulations, with explicit tracking until ionization (Linder et al., 2020).

4. Specialized Models: Pedestal Height/Width, Runaway Generation

EPED-NN Pedestal Model

A two-hidden-layer feed-forward ANN trained on $\sim$1000$$EPED runs enables rapid prediction of pedestal height ($$p_{\rm ped}=n_{e,\rm ped}T_{e,\rm ped}+n_{i,\rm ped}T_{i,\rm ped}$) and width ($\Delta\psi$$), as a function of shaping and operational parameters including$$I_p, B_t, \kappa, \delta, P_{\rm heat}, \beta_p, Z_{\rm eff}$$(<a href="/papers/2512.21286" title="" rel="nofollow" data-turbo="false" class="assistant-link" x-data x-tooltip.raw="">Muraca et al., 24 Dec 2025</a>).</p> <h3 class='paper-heading' id='regia-runaway-source-module'>REGIA Runaway Source Module</h3> <p>REGIA supplies reduced Dreicer and avalanche source terms for$$n_{\text{RE}}$$, including partial-ionization effects, via analytic or neural-network surrogates. These rates depend on local$$n_e, T_e, Z_{\rm eff}$$(the latter informed by STRAHL), with closed-form and general kinetic models for$$S_D$and$S_{\rm av}$$(<a href="/papers/2003.00725" title="" rel="nofollow" data-turbo="false" class="assistant-link" x-data x-tooltip.raw="">Linder et al., 2020</a>).</p> <h2 class='paper-heading' id='numerical-implementation-and-workflow'>5. Numerical Implementation and Workflow</h2> <ul> <li><strong>Grid and Time-Stepping:</strong> Uniform mesh in$$\rho$or$\psi$($N_r\sim60$); ASTRA steps with Crank–Nicolson and adaptive$\Delta t$$, STRAHL uses vertex-centered finite volume, blending upwind and centered differencing for Peclet number control.</li> <li><strong>Boundary Conditions:</strong> Fixed outer$$n_s$at pedestal (impurity source), Dirichlet for$T_e,T_i$$at edge, symmetry at axis. No inner-wall impurity inflow.</li> <li><strong>Coupling Loop:</strong> At each$$\Delta t$$, update backgrounds (ASTRA), call transport modules, advance impurities/radiation (STRAHL), propagate back$$D_{\text{imp}}, V_{\text{imp}}, P_{\rm rad}$$, iterate to convergence or stationarity.</li> <li><strong>Disruption/Transient Extensions:</strong> In disruptions, when the neutral or impurity front reaches rational surfaces ($$q=2$), time-localized boosts to$D, v$are applied (e.g.,$D_{\max} \sim 100\,{\rm m}^2/{\rm s}$,$v_{\max}\sim-200\,{\rm m}/{\rm s}$$on ms timescales) to mimic magnetic stochasticity (<a href="/papers/2003.00725" title="" rel="nofollow" data-turbo="false" class="assistant-link" x-data x-tooltip.raw="">Linder et al., 2020</a>).</li> </ul> <h2 class='paper-heading' id='sensitivity-and-benchmarking-studies'>6. Sensitivity and Benchmarking Studies</h2> <p>Parametric scans are performed across:</p> <ul> <li>Top-of-pedestal impurity fractions ($$f_{W,\rm ped}, f_{Ar,\rm ped}$), toroidal edge velocity ($v_{\rm tor, ped}$,$M$), and D-T mix ($f_D$,$f_T$$).</li> <li>Monitored outputs include impurity peaking factor$$P_s \equiv n_s(\rho=0)/n_s(\rho=\rho_{\rm ped})$, core density peaking$R/L_n$, fusion gain$Q$, and access to H-mode ($f_{LH}$$).</li> <li>Key findings: Turbulent impurity transport ($$D_{\text{turb}}, V_{\text{turb}}$$) dominates over neoclassical in SPARC H-modes at low$$\nu_*$. Variations in$f_{W,\rm ped}$have$<10\%$effect on$Q$or peaking; changes in$f_{Ar,\rm ped}$$produce competing effects that nearly cancel, rendering$$Q$$insensitive. Rotation has negligible impact below$$v_{\rm tor}<80$ km/s (realistic parameter range) (Muraca et al., 24 Dec 2025).

7. Applications, Modifications, and Required Inputs

The ASTRA+STRAHL framework has been applied to:

• H-mode core-pedestal transport and impurity control in burning plasma scenarios (SPARC, ITER).
• Disruption and runaway electron scenario modeling with massive impurity (e.g., Ar) injection in ASDEX Upgrade.
• Studies of isotope mixing (D-T fuel splits) and impact on core fusion gain, density peaking, and impurity pinches.
• Reproduction of experimental observables: line-averaged density, current decay, RE current plateau, radiation, and SXR diagnostics.

Essential code modifications include: addition of REGIA and neural surrogate modules, parallelization of neoclassical calls, multiple neutral species support, and tightly unified mesh management to avoid interpolation artifacts. Typical input requirements are background profiles (from experiment or scenario design), heating source characteristics, wall impurity influxes, atomic rates, geometry, and turbulence/transport settings (Muraca et al., 24 Dec 2025, Linder et al., 2020).