Xavier Garbet

In the K-epsilon framework, a predator-prey like model determines the plasma turbulent transport. It depends on the underlying plasma turbulence via the growth rate chosen for the turbulent energy, the prey K, and its predator epsilon. Compared to our previous work [1], we propose in this paper modifications of the model to be tested in future simulations. A more appropriate expression of the growth rate is proposed by taking into account the fast dynamics of the parallel electron transport. The stabilising terms that are introduced allow for negative values of the growth rate of interchange coupled to drift wave turbulence. Changes to the K-epsilon model are made to adapt it to handle close to marginal states, then allowing one to address a Landau like bifurcation from negative growth rates, without turbulence, to positive growth rates, with turbulence. The closure using the multi-machine SOL width scaling law is revisited to allow the K-epsilon turbulent transport to depend on the growth rate. This is mandatory in the present model to yield increasing turbulent transport towards the edge and enhanced SOL transport governed by the sheath resistivity. Usual predator-prey limit cycles can be achieved whenever the growth rate of the predator is smaller than that of the prey. The growth rates are determined by a simplified 2D turbulence model taking into account magnetic field inhomogeneity and parallel losses, mostly of electrons. These are computed in Fourier space and must be adapted to plasma coarse grained simulations, in particular for edge-SOL-divertor simulations. A growth rate maximisation procedure then determines the wave vector in terms of the plasma parameters. Although the maximisation results are different for drift wave and interchange instabilities, their spectral properties are not discernable and the two instabilities are shown to be difficult to disentangle. Both facets of turbulence are therefore accounted for in the analytical expressions that are obtained for the growth rates, which are to be implemented in K-epsilon simulations of plasma-wall interaction with consistent turbulent transport.

Accurately predicting plasma behavior based on discharge configurations is essential for the safe and efficient operation of tokamak experiments. While physics-based integrated modeling codes provide valuable insights, their high computational cost limits their applicability for fast scenario design and control optimization. In this study, we propose a transformer-based machine learning model to predict key global plasma parameters on the Tungsten (W) Environment in Steady-State Tokamak (WEST) tokamak, including the normalized beta ( β _n ), toroidal beta ( β _t ), poloidal beta ( β _p ), plasma stored energy ( W mhd ), safety factor at the magnetic axis ( q ₀ ), and safety factor at the 95% flux surface ( q ₉₅ ). The model uses only signals that can be defined before the discharge, such as magnetic coil currents, auxiliary heating power, plasma current reference, and line-averaged plasma density. Trained on 550 discharges from the WEST campaigns, the model demonstrates an average mean square error (MSE) loss of 0.026, an average coefficient of determination R ² of 0.94, and achieves inference times on the order of 0.1 s. These results highlight the potential of data-driven surrogate models for assisting in discharge planning, scenario evaluation, and real-time control of tokamak plasmas.

Comparative modelling of ion temperature gradient (ITG)/trapped electron mode (TEM) turbulence in negative (NT) and positive (PT) triangularity plasma shapes was done using the nonlinear global full-f gyrokinetic particle code JOREK-GK in the realistic X -point tokamak geometry including the Scrape Off Layer (SOL) for TCV and DIII-D parameters. A comparison of JOREK-GK code with the gyrokinetic codes GS2 and GENE was done using NT/PT triangularity TCV L-modes parameters showing good agreement between codes in linear growth rates and clear beneficial effect of NT as compared to PT. Global non-linear modelling of the ITG/TEM saturated turbulence for realistic DIII-D NT pulses was done and compared with numerically constructed PT equilibrium with the same plasma profiles. Existence of longer correlation length of density fluctuations in PT compared to NT was demonstrated. Stronger and more sheared zonal flows are generated via Reynolds stress in NT compared to PT. These factors are stabilizing for TEM/ITG turbulence in NT and lead to smaller heat fluxes and heat conductivities in NT compared to PT configuration. Weak dependence of plasma confinement on collisionality and plasma rotation was found in modelling of DIII-D NT shots similar to the experiment. The confinement scaling with normalized ion gyro-radius ρ * was estimated both for NT and PT. Bohm-like scaling was obtained in both configurations, however with better confinement for NT compared to PT which could be favourable factor for reactor size machines.

Although modern fusion devices consider the use of lithium as a plasma-facing component, its transport mechanism remains under-investigated, being different from those of heavy impurities such as tungsten. For lithium and other light impurities, turbulent transport dominates over neoclassical contributions, motivating a dedicated study on the determination of turbulent diffusion, thermodiffusion, and convective pinch velocity. In this work, we benchmark a new method to extract these coefficients using the global full-f gyrokinetic GYSELA code. In the absence of a transport barrier, the method reproduces results consistent with helium, showing that thermodiffusion is comparable in magnitude to both diffusion and pure convection. Introducing an E×B shear layer to form a transport barrier modifies the radial structure of the transport coefficients. Transport levels decrease in the inner core, while within the barrier, convection becomes dominant, and all fluxes undergo sign reversals. Diffusive and thermodiffusive contributions are also found to partially compensate each other depending on local gradients. Finally, an evaluation of the peaking factor further demonstrates that the presence of a transport barrier significantly mitigates core impurity accumulation.

We present the electromagnetic (EM) extension of the flux-driven full-F global gyrokinetic code GYSELA (for GYrokinetic SEmi-LAgrangian), enabling self-consistent simulations of turbulence and transport in magnetised plasmas beyond the electrostatic limit. A mixed-variable pullback scheme has been implemented and enhanced with a predictor for the non-ideal component of the parallel vector potential, reducing numerical stiffness and preserving conservation properties. The resulting formulation allows stable timestepping with realistic parameters. Verification is performed against theoretical shear Alfv´en wave dispersion and linear benchmarks in the Cyclone Base Case, showing excellent agreement. Furthermore, nonlinear flux-driven electromagnetic ion-temperature-gradient turbulence simulations demonstrate the robustness of the scheme, with conservation of particles, energy, and momentum below 1% error. These developments establish the EM version of GYSELA as a reliable tool for investigating multi-scale electromagnetic plasma dynamics and transport in fusion-relevant regimes.

Gyrokinetic codes are used to simulate transport in tokamak plasmas. In these codes, the distribution functions evolve self consistently with an electromagnetic field. To compute the temporal evolution of the electrostatic potential, a quasi-neutrality equation is solved. In some gyrokinetic codes, the quasi-neutrality solver assumes that the background densities and temperatures are constant in time and on flux surfaces. This assumption, which implicitly uses the so-called δF approach, can break up, in particular at the edge of the plasma which can display large and time evolving poloidal asymmetries.In this paper, a numerical solver of the quasi-neutrality equation accounting for time evolving poloidal asymmetries is presented. This solver is compatible with all electron models (adiabatic, kinetic or hybrid) and written for the long wavelength or the Padé approximations for the polarisation term. The impact of such an improvement is carefully reported on different types of simulations, illustrating when the δF approach forquasi-neutrality is valid and when it fails. A procedure to limit the numerical cost of updating the background profiles in the quasi-neutrality solver is also presented.

Understanding the interaction between turbulence and zonal flows is critical for modeling turbulence transport in fusion plasmas, often described through predator-prey dynamics. However, traditional deterministic models like the Lotka–Volterra equations simplify this interaction and fail to capture the small fluctuations in simulation data. In this study, we develop a neural network model based on stochastic differential equations (SDEs) to represent the predator-prey dynamics using limited data from simulations of the modified Hasegawa–Wakatani system. We extract the drift and diffusion terms via neural networks, incorporating physical constraints and employing the unscented transform to mitigate challenges brought by limited data. The model accurately reproduces key dynamical features, including stagnation phenomena and energy exchange mechanisms, and the state density distribution generated from the model shows a low KL divergence with the simulation data. A parameter scan reveals that zonal flow shearing efficiency decreases with amplitude, and predator-prey oscillations damp in the absence of stochasticity. These findings underscore the value of integrating physical insight into data-driven approaches for complex plasma systems.

The generation and radial structure of zonal flows are studied in competing collisional drift waves and interchange turbulence using the reduced flux-driven nonlinear model Tokam1D. Zonal flows are generated in both the interchange dominated and adiabatic regimes with the former favoring radially structured flows and avalanche transport. The distance to the instability threshold proves to be key, with a more stable radial flow structure emerging near the threshold and increased energy stored in the flows for interchange turbulence. The avalanches are shown to perturb zonal flow structures in drift-wave turbulence and to reactivate them in the interchange regime. Finally, the ExB staircases with radially structured, stable in time zonal flows are proved beneficial for the overall confinement.

We investigate the interplay between ion temperature gradient (ITG) and parallel velocity gradient (PVG) instabilities in cylindrical geometry using a Water-bag model and 5D gyrokinetic simulations with a modified version of the GYSELA code. The Water-bag model provides an analytical dispersion relation, which is compared to linear gyrokinetic simulations. Strong agreement is found between predicted and simulated growth rates and real frequencies, validating GYSELA's applicability to cylindrical systems. The comparison also highlights key parametric dependencies on instability thresholds, including the effects of density profiles, temperature gradients, and velocity shear. Notably, weak temperature gradients are found to stabilize PVG modes, whereas strong temperature gradients tend to destabilize them. Additionally, parallel flow shear is shown to enhance ITG-PVG hybrid modes. These properties are likely to impact the turbulent regime.