GENE-Tango Framework for Fusion Plasma Modeling

• GENE–Tango is a computational framework that couples the global gyrokinetic turbulence code GENE with the 1D transport solver Tango to self-consistently capture microturbulence and macroscopic profile evolution.
• The iterative methodology integrates short-time turbulent flux calculations with transport equations, significantly reducing computational cost while accurately representing key physics such as kinetic electrons, collisions, toroidal rotation, and electromagnetic effects.
• Experimental validation on ASDEX Upgrade discharges demonstrated that incorporating electromagnetic stabilization and realistic geometry yields accurate predictions of ion temperature peaking and transport phenomena.

The GENE–Tango framework refers to a computational method for multiscale, high-fidelity prediction of fusion plasma behavior, achieved by coupling the global gyrokinetic turbulence code GENE with the 1D transport solver Tango. It is designed to self-consistently resolve the interplay between microturbulence (on microsecond timescales) and the evolution of macroscopic plasma profiles (on millisecond–second timescales), incorporating experimental realism via kinetic electrons, collisions, toroidal rotation, and electromagnetic effects. This framework significantly expands the predictive capabilities of plasma modeling for current experiments and next-generation devices by reducing the computational expense associated with direct, long-timescale gyrokinetic simulations, while capturing crucial profile formation dynamics and detailed turbulence-driven transport (Siena et al., 2022, Siena et al., 11 Jun 2024).

1. Coupling Methodology and Mathematical Foundations

GENE–Tango is architected as an iterative, multi-timescale feedback loop operating between the microphysical (turbulence) and macroscopic (transport) levels. GENE performs global nonlinear gyrokinetic simulations with fixed background profiles, calculating time-averaged turbulent fluxes of heat and particles:

$$\overline{Q}_s = \Big\langle \int \frac{1}{2} m_s v^2 \delta f_{1,s} (\mathbf{v}_{E \times B} \cdot \nabla x) d^3v \Big\rangle_S,$$

$$\overline{\Gamma}_s = \Big\langle \int \delta f_{1,s} (\mathbf{v}_{E \times B} \cdot \nabla x) d^3v \Big\rangle_S,$$

where the integral is over species-dependent perturbed distribution functions and spatial volumes.

Tango evolves macroscopic profiles (density $n_s$, pressure $p_s$) according to the 1D transport equations:

$$\frac{\partial n_s}{\partial t} + \frac{1}{V'} \frac{\partial}{\partial x} (V' \overline{\Gamma}_s) = S_n,$$

$$\frac{3}{2} \frac{\partial p_s}{\partial t} + \frac{1}{V'} \frac{\partial}{\partial x} (V' \overline{Q}_s) = S_{i,e} + \text{collisional terms},$$

where $V'$ is the volume derivative, and $S_n$, $S_{i,e}$ are source terms.

Transport coefficients are extracted from GENE’s turbulent fluxes via the LoDestro method, decomposing total flux into diffusive and convective (pinch) contributions:

$$\overline{Q}_{m,l} = -D_{m,l-1}^p \partial_x p_{m,l} + c_{m,l-1}^p p_{m,l},$$

with $D$ (diffusivity) and $c$ (pinch) calculated from the previous iteration.

Each iteration: GENE produces turbulence fluxes from fixed profiles, Tango updates profiles to achieve flux-source balance, then profiles are re-initialized in GENE. This continues until consistent, steady-state equilibrium is achieved.

2. Physical Realism and Advanced Physics

GENE–Tango's predictive skill arises from its inclusion of experimental physics missing from reduced or local models:

• Kinetic Electrons: Full kinetic electron treatment, not the adiabatic limit, is used. This enables accurate resolution of ITG/TEM and electron-scale instabilities necessary for experimental profile matching and correctly reproducing cross-species turbulence interplay (Siena et al., 2022, Siena et al., 11 Jun 2024).
• Collisions: Linearized Landau–Boltzmann operator with energy/momentum conserving terms regulates fluxes and profile shapes, especially balancing outward diffusive and inward convective components in density evolution.
• Toroidal Rotation: Incorporated as an $E\times B$ phase factor on the perturbed distribution function $$f_1 \rightarrow f_1 \exp[-i\omega_{E\times B}\Delta t]$$, with $\omega_{E\times B}$ computed from toroidal velocity and other normalized quantities. Rotation acts to shear turbulence, reducing transport and improving outer-region profile agreement (Siena et al., 2022).
• Electromagnetic Effects: Full electromagnetic fluctuations (e.g., parallel component $A_{1,\parallel}$) allow inclusion of finite-$\beta$ and magnetic perturbations. These are essential to capturing turbulence suppression in critical radial zones, with electromagnetic stabilization being responsible for on-axis ion temperature peaking observed in experiment.
• Realistic Geometry: GENE global runs in realistic shaped magnetic configurations, resolving major/minor radius and poloidal/toroidal field effects.

Retaining all of these effects is vital for obtaining experimentally matched profile peaking, profile gradients, and the correct turbulence suppression phenomena—especially as new instabilities (e.g., submarginal MHD) or stiff transport responses are strongly geometry- and physics-dependent.

3. Numerical Results and Experimental Validation

The framework was validated on ASDEX Upgrade discharges:

• Discharge #13151 ($t=1.35$ s): GENE–Tango produced temperature profiles that agreed within 5–7% of earlier local (GENE–Trinity) models. Slight differences were attributed to global, finite-radii and finite-size effects.
• Discharge #31555 ($t=1.45$ s): Notable for strong peaking of the ion temperature profile not reproducible by reduced models (e.g., TGLF–ASTRA). GENE–Tango, when run with full electromagnetic effects, correctly recovered the core temperature peaking by capturing local turbulence suppression in $\rho_\text{tor}\sim 0.2$–$0.35$. Purely electrostatic simulations, even with rotation, did not reproduce this peaking, confirming the centrality of electromagnetic stabilization (Siena et al., 2022).
• Impact of Collisions and Rotation: Collisions controlled profile shape by mediating the inward/outward flux balance, while rotation contributed to turbulence stabilization.

These studies demonstrate the capability for first-principles frameworks to reproduce features missed by reduced models, such as sub-regions of transport reduction leading to strong peaking or strong stiffness.

4. Computational Efficiency and Scaling

A core strength of GENE–Tango is its exploitation of timescale separation between turbulence and profile evolution:

• Microscale (turbulence): $\sim$ microseconds;
• Transport scale (profile evolution): $\sim$ milliseconds–seconds.

Instead of direct, ultra-long-time gyrokinetic runs, GENE–Tango iterates on short ($\sim$6–12 ms simulation time per iteration) turbulence runs, passing averaged fluxes to the transport solver. This produces two main scaling improvements:

Device/Setup	Standard Gyrokinetic Cost	GENE–Tango Speedup
ASDEX Upgrade	$\sim 10^2$ more	$>100\times$
ITER extrapolation	$\sim 10^3$ more	$>200\times$ (potentially $600\times$ if requiring full convergence)

This performance, scaling as $\sim (1/\rho_*)^2$–$(1/\rho_*)^3$, renders first-principles ITER modeling feasible on contemporary supercomputers (Siena et al., 2022).

5. Consequences for Predictive Fusion Modeling

GENE–Tango’s ability to couple high-fidelity turbulence physics to macroscopic transport yields several key implications:

• Enhanced Scenario Design: Enables reliable predictions of core and edge profile evolution for advanced scenarios, capturing effects missed by reduced models (e.g., electromagnetic stabilization, strong profile peaking) that may affect global confinement scaling and performance optimization.
• Realism for Reactor Projections: Supports design studies and performance forecasting for next-generation reactors (e.g., ITER), providing confidence in modeled operating regimes by integrating experimental physics, thereby reducing uncertainties in high-consequence regime selection and operational limits.
• Accessibility: Due to computational efficiency, GENE–Tango can be deployed routinely for multi-parameter scans, scenario optimization, or uncertainty quantification essential for future experiment planning and regulatory submissions.
• Basis for Further Extensions: The framework forms the foundation for even broader coupled models (e.g., with neoclassical, energetic particle, or impurity modules) and for integration into whole-device modeling campaigns.

6. Limitations and Outlook

While GENE–Tango overcomes the most prohibitive computational bottlenecks of direct gyrokinetic modeling, several challenges and frontiers remain:

• Boundary Condition Sensitivity: Achieving steady-state agreement requires careful handling of profile boundary conditions, especially as transport barriers or pedestal dynamics are not resolved in global runs limited to core domains.
• Physics Completeness: Some phenomena—such as fast particle–induced Alfvénic instabilities or neutral/impurity interactions—are not natively included but may become imperative for reactor-grade scenarios.
• Experimental Coupling: Further improvement in integrating real-time experimental diagnostics and source profiles will enhance predictive power and validation cycles.
• Cross-Device Consistency: Validation across additional devices (DIII-D, JET, W7-X, stellarators) is underway to confirm generality and to stress-test the model under a wider set of operational regimes (Siena et al., 11 Jun 2024, Fernando et al., 11 Mar 2025).

In summary, the GENE–Tango framework enables comprehensive, computationally efficient, and experimentally realistic modeling of multiscale plasma transport, standing as a pivotal capability for predictive fusion science and engineering.