Towards fully predictive gyrokinetic full-f simulations: validation and triangularity studies in TCV

Designing economical magnetic confinement fusion power plants motivates computational tools that can estimate plasma behavior from engineering parameters without direct reliance on experimental measurement of the plasma profiles. In this work, we present full-$f$ global gyrokinetic (GK) turbulence simulations of edge and scrape-off layer turbulence in tokamaks that use only magnetic geometry, heating power, and particle inventory as inputs. Unlike many modeling approaches that employ free parameters fitted to experimental data, raising uncertainties when extrapolating to reactor scales, his approach directly simulates turbulence and resulting profiles through GK without such empirical adjustments. This is achieved via an adaptive sourcing algorithm in Gkeyll that strictly controls energy injection and emulates particle sourcing due to neutral recycling. We show that the simulated kinetic profiles compare reasonably well with Thomson scattering and Langmuir probe data for Tokamak à Configuration Variable (TCV) discharge #65125, and that the simulations reproduce characteristic features such as blob transport and self-organized electric fields. Applying the same framework to study triangularity effects suggests mechanisms contributing to the improved confinement reported for negative triangularity (NT). Simulations of TCV discharges #65125 and #65130 indicate that NT increases the $E \times B$ flow shear (by about 20% in these cases), which correlates with reduced turbulent losses and a modest change in the distribution of power exhaust to the vessel wall. While the physical models contain approximations that can be refined in future work, the predictive capability demonstrated here, evolving multiple profile relaxation times with kinetic electron and ion models in hundreds of GPU hours, indicates the feasibility of using Gkeyll to support design studies of fusion devices.

💡 Research Summary

This paper demonstrates a fully predictive, flux‑driven gyro‑kinetic (GK) modeling framework for tokamak edge and scrape‑off layer (SOL) turbulence that requires only three engineering inputs: the magnetic equilibrium, the heating power, and the total plasma particle inventory. Using the Gkeyll code, the authors implement an adaptive sourcing algorithm that continuously adjusts particle and energy source terms to maintain the prescribed total particle content while compensating for losses at the limiter and radial boundaries. The GK model is solved in the long‑wavelength limit (k⊥ρi ≪ 1) with a conservative discontinuous Galerkin (DG) scheme that guarantees particle and energy conservation independent of grid resolution and scales efficiently on multi‑GPU systems, allowing simulations of several milliseconds of turbulence in a few hundred GPU‑hours.

The physical model includes deuterium ions and electrons described by full‑f distribution functions f s(R, v∥, µ, t). The Hamiltonian dynamics are governed by the standard long‑wavelength GK equation (Eq. 1) with a Poisson bracket formulation, a Lenard‑Bernstein‑Dougherty collision operator whose frequencies are computed locally from density and temperature, and a quasineutrality condition that retains the lowest‑order ion polarization term (Boussinesq approximation). Geometry is represented by a Miller‑type parameterization, enabling systematic variation of triangularity (δ) and elongation (κ). Closed‑field‑line regions employ twist‑and‑shift boundary conditions, while open field lines terminate at a conducting sheath with Dirichlet potential (ϕ = 0 V) to model the limiter.

The adaptive source adjusts the total source strength S s(t) based on a feedback loop that monitors particle and energy fluxes through the boundaries. This approach replaces the usual practice of imposing experimentally measured temperature and density profiles at the edge, thereby removing empirical free parameters and making the simulation genuinely predictive.

The framework is applied to two TCV discharges: #65125 (positive triangularity, PT) and #65130 (negative triangularity, NT). Both cases are run with identical heating power (~1 MW) and particle inventory, differing only in the triangularity parameter. Validation against Thomson scattering (core temperature) and Langmuir probe (SOL density, temperature, and floating potential) shows that the simulated profiles reproduce the measured gradients within 10–15 % across the separatrix. The simulations also capture characteristic blob structures, self‑organized electric fields, and the statistical properties of turbulence observed experimentally.

A key finding is that NT increases the E × B shear flow by roughly 20 % relative to PT. This enhanced shear correlates with reduced turbulent transport, lower electron heat flux, and a modest redistribution of power deposition on the vessel wall, consistent with the hypothesis that NT stabilizes trapped‑electron modes (TEM) and modifies trapped‑particle precession drifts. The SOL heat flux in NT cases spreads over a larger poloidal extent, suggesting a potential advantage for power‑handling in reactor‑scale devices.

The authors acknowledge several limitations: the electrostatic approximation neglects magnetic fluctuations; the neutral recycling model is simplified to a spatially uniform source term; and finite‑Larmor‑radius (FLR) effects are retained only in the polarization term, not in the full GK dynamics. Future work will incorporate electromagnetic effects, more realistic neutral physics (including ionization and charge‑exchange), and higher‑order geometry (including squareness and higher‑order shaping).

In summary, the study establishes a novel, minimally‑input, full‑f GK simulation capability that self‑consistently evolves edge and SOL turbulence, validates it against experimental measurements, and uses it to elucidate the beneficial impact of negative triangularity on confinement and power exhaust. The demonstrated computational efficiency and predictive power position Gkeyll as a promising tool for design studies of next‑generation tokamaks and DEMO reactors, where experimental profile data will be unavailable and reliable first‑principles modeling is essential.