arXiv subjects

Xavier Garbet

Publications and source records attributed to Xavier Garbet.

At least 19 recordsLinked to original sources

arXiv2026

Optimal-Transport-Guided Functional Flow Matching for Turbulent Field Generation in Hilbert Space

High-fidelity modeling of turbulent flows requires capturing complex spatiotemporal dynamics and multi-scale intermittency, posing a fundamental challenge for traditional knowledge-based systems. While deep generative models, such as diffusion models and Flow Matching, have shown promising performance, they are fundamentally constrained by their discrete, pixel-based nature. This limitation restricts their applicability in turbulence computing, where data inherently exists in a functional form. To address this gap, we propose Functional Optimal Transport Conditional Flow Matching (FOT-CFM), a generative framework defined directly in infinite-dimensional function space. Unlike conventional approaches defined on fixed grids, FOT-CFM treats physical fields as elements of an infinite-dimensional Hilbert space, and learns resolution-invariant generative dynamics directly at the level of probability measures. By integrating Optimal Transport (OT) theory, we construct deterministic, straight-line probability paths between noise and data measures in Hilbert space. This formulation enables simulation-free training and significantly accelerates the sampling process. We rigorously evaluate the proposed system on a diverse suite of chaotic dynamical systems, including the Navier-Stokes equations, Kolmogorov Flow, and Hasegawa-Wakatani equations, all of which exhibit rich multi-scale turbulent structures. Experimental results demonstrate that FOT-CFM achieves superior fidelity in reproducing high-order turbulent statistics and energy spectra compared to state-of-the-art baselines.

cs.LG↗

arXiv2026

Plasma GraphRAG: Physics-Grounded Parameter Selection for Gyrokinetic Simulations

Accurate parameter selection is fundamental to gyrokinetic plasma simulations, yet current practices rely heavily on manual literature reviews, leading to inefficiencies and inconsistencies. We introduce Plasma GraphRAG, a novel framework that integrates Graph Retrieval-Augmented Generation (GraphRAG) with large language models (LLMs) for automated, physics-grounded parameter range identification. By constructing a domain-specific knowledge graph from curated plasma literature and enabling structured retrieval over graph-anchored entities and relations, Plasma GraphRAG enables LLMs to generate accurate, context-aware recommendations. Extensive evaluations across five metrics, comprehensiveness, diversity, grounding, hallucination, and empowerment, demonstrate that Plasma GraphRAG outperforms vanilla RAG by over $10\%$ in overall quality and reduces hallucination rates by up to $25\%$. {Beyond enhancing simulation reliability, Plasma GraphRAG offers a methodology for accelerating scientific discovery across complex, data-rich domains.

physics.plasm-ph↗

arXiv2026

Machine learning prediction of plasma behavior from discharge configurations on WEST

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 WEST tokamak, including the normalized beta ($\beta_{n}$), toroidal beta ($\beta_{t}$), poloidal beta ($\beta_{p}$), plasma stored energy ($W_{\mathrm{mhd}}$), 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 seconds. These results highlight the potential of data-driven surrogate models for assisting in discharge planning, scenario evaluation, and real-time control of tokamak plasmas.

physics.plasm-ph↗

arXiv2025

Reconstructing High-fidelity Plasma Turbulence with Data-driven Tuning of Diffusion in Low Resolution Grids

Developing physically consistent closure models is a longstanding challenge in simulating plasma turbulence, even in minimal systems such as the two-field Hasegawa-Wakatani (HW) model, which captures essential features of drift-wave turbulence with a reduced set of variables. In this work, we leverage theoretical insights from Direct Interaction Approximation (DIA) to construct a six-term closure structure that captures the dominant turbulent transport processes, including both diffusion and hyper-diffusion. While the mathematical form of the closure is fully prescribed by DIA, the corresponding transport coefficients are learned from data using physics-informed neural networks (PINNs). The resulting Extended HW model with Closure (EHW-C) model reveals several nontrivial features of plasma turbulence: notably, some inferred coefficients become negative in certain regimes, indicating inverse transport, a phenomenon absent in conventional closure models. Moreover, the EHW-C model accurately reproduces the spectral and flux characteristics of high-resolution Direct Numerical Simulations (DNS), while requiring only one-eighth the spatial resolution per direction, yielding a tenfold speed-up. This work demonstrates how theory-guided machine learning can both enhance computational efficiency and uncover emergent transport mechanisms in strongly nonlinear plasma systems.

physics.plasm-ph↗

arXiv2025

The interaction of turbulence, magnetic islands and zonal fields in fluid plasma models with cubic non-linearities

It is shown that magnetic islands generated by pressure-gradient-driven turbulence are common across a wide range of conditions. The interaction among turbulence, magnetic island and other large scale structures (the zonal flow and the zonal current), largely determines the dynamics of the system. Turbulence takes a background role, providing energy to the large-scale structures, without influencing their evolution directly. The growth of the zonal current is linearly related to that of the magnetic island, while the zonal flow has a strongly sheared region where the island has its maximum radial extension. The zonal current is found to slow down the formation of large-scale magnetic islands, while the zonal flow is needed to have the system move its energy to larger and larger scales. The driving instability in the system is the fluid Kinetic Ballooning Mode (KBM) instability at high beta, while the tearing mode is kept stable. The formation of magnetic-island-like structures at the spatial scale of the fluid KBM instability is observed quite early in the non-linear phase for most cases studied, and a slow coalescence process evolves the magnetic structures towards larger and larger scales. Cases that did not show this coalescence process, nor the formation of the small scale island-like structures, were seen to have narrower mode structures for comparable instability growth rates, which was achieved by varying the magnetic shear. The islands often end up exceeding the radial box size late in the non-linear phase, showing unbounded growth. The impact on the pressure profile of turbulence driven magnetic islands is not trivial, showing flattening of the pressure profile only far from the resonance, where the zonal flow is weaker, and the appearance of said flattening is slow, after the island has reached a sufficiently large size, when compared with collisional time scales.

physics.plasm-ph↗

arXiv2025

A high-fidelity surrogate model for the ion temperature gradient (ITG) instability using a small expensive simulation dataset

One of the main challenges in building high-fidelity surrogate models of tokamak turbulence is the substantial demand for high-quality data. Typically, producing high-quality data involves simulating complex physical processes, which requires extensive computing resources. In this work, we propose a fine tuning-based approach to develop the surrogate model that reduces the amount of high-quality data required by 80\%. We demonstrate the effectiveness of this approach by constructing a proof-of-principle ITG surrogate model using datasets generated from two gyrokinetic codes, GKW and GX. GX needs in terms of computing resources are much lighter than GKW. Remarkably, the surrogate models' performance remain nearly the same whether trained on 798 GKW results alone or 159 GKW results plus an additional 11979 GX results. These encouraging outcomes indicate that fine tuning methods can significantly decrease the high-quality data needed to develop the simulation-driven surrogate model. Moreover, the approach presented here has the potential to facilitate surrogate model development for heavy codes and may ultimately pave the way for digital twin systems of tokamaks.

physics.plasm-ph↗

arXiv2024

Zonal fields as catalysts and inhibitors of turbulence-driven magnetic islands

A novel coalescence process is shown to take place in plasma fluid simulations, leading to the formation of large-scale magnetic islands that become dynamically important in the system. The parametric dependence of the process on the plasma $β$ and the background magnetic shear is studied, and the process is broken down at a fundamental level, allowing to clearly identify its causes and dynamics. The formation of magnetic-island-like structures at the spatial scale of the unstable modes is observed quite early in the non-linear phase of the simulation for most cases studied, as the unstable modes change their structure from interchange-like to tearing-like. This is followed by a slow coalescence process that evolves these magnetic structures towards larger and larger scales, adding to the large-scale tearing-like modes that already form by direct coupling of neighbouring unstable modes, but remain sub-dominant without the contribution from the smaller scales through coalescence. The presence of the cubic non-linearities retained in the model is essential in the dynamics of this process. The zonal fields are key actors of the overall process, acting as mediators between the competitive mechanisms from which Turbulence Driven Magnetic Islands can develop. The zonal current is found to slow down the formation of large-scale magnetic islands, acting as an inhibitor, while the zonal flow is needed to allow the system to transfer energy to the larger scales, acting as a catalyst for the island formation process.

physics.plasm-ph↗

arXiv2023

Transition to super-diffusive transport in turbulent plasmas

We investigate the motion of charged particles in a turbulent electrostatic potential using guiding-center theory. By increasing the Larmor radius, the dynamics exhibit close-to-ballistic transport properties. The transition from diffusive to ballistic transport is analyzed using nonlinear dynamics. It is found that twistless invariant tori in the guiding-center dynamics are responsible for this transition, drastically affecting transport properties of charged particles.

physics.plasm-ph↗

arXiv2023

Self-consistent gyrokinetic modelling of turbulent and neoclassical tungsten transport in toroidally rotating plasmas

The effect of toroidal rotation on both turbulent and neoclassical transport of tungsten (W) in tokamaks is investigated using the flux-driven, global, nonlinear 5D gyrokinetic code GYSELA. Nonlinear simulations are carried out with different levels of momentum injection that drive W to the supersonic regime, while the toroidal velocity of the main ions remains in the subsonic regime. The numerical simulations demonstrate that toroidal rotation induces centrifugal forces that cause W to accumulate in the outboard region, generating an in-out poloidal asymmetry. This asymmetry enhances neoclassical inward convection, which can lead to central accumulation of W in cases of strong plasma rotation. The core accumulation of W is mainly driven by inward neoclassical convection. However, as momentum injection continues, roto-diffusion, proportional to the radial gradient of the toroidal velocity, becomes significant and generate outward turbulent flux in the case of ion temperature gradient (ITG) turbulence. Overall, the numerical results from nonlinear GYSELA simulations are in qualitative agreement with the theoretical predictions for impurity transport, as well as experimental observations.

physics.plasm-ph↗

arXiv2022

Transport barrier onset and edge turbulence shortfall in fusion plasmas

Turbulent plasmas notably self-organize to higher energy states upon application of additional free energy sources or modification of edge operating conditions. Mechanisms whereby such bifurcations occur have been actively debated for decades. Enhanced confinement occurs at the plasma edge, where a shortfall of predicted turbulence intensity has been puzzling scientists for decades. We show, from the primitive kinetic equations that both problems are connected and that interplay of confined plasma turbulence with its material boundaries is essential to curing the shortfall of predicted turbulence and to triggering spontaneous transport barrier onset at the plasma edge. Both problems determine access to improved confinement and are central to fusion research. A comprehensive discussion of the underlying mechanisms is proposed. These results, highly relevant to the quest for magnetic fusion may also be generic to many problems in fluids and plasmas where turbulence self-advection is active.

physics.plasm-ph↗

arXiv2022

Full Self-Consistent Vlasov-Maxwell Solution

Full self-consistent stationary Vlasov-Maxwell solutions of magnetically confined plasmas are built for systems with cylindrical symmetries. The stationary solutions are thermodynamic equilibrium solutions. These are obtained by computing the equilibrium distribution function resulting from maximizing the entropy and closing the equations with source terms that are then computed by using the obtained distribution. This leads to a self-consistent problem corresponding to solving a set of two coupled second order non-linear differential equations. Relevant plasma parameters are introduced and a bifurcation leading to an improvement of plasma confinement is shown. Conversely in the improved confinement setting, we exhibit the emergence of a separatrix in the integrable motion of a charged particles.

physics.plasm-ph↗

arXiv2021

Quasilinear gyrokinetic theory: A derivation of QuaLiKiz

In order to predict and analyze turbulent transport in tokamaks, it is important to model transport that arises from microinstabilities. For this task, quasilinear codes have been developed that seek to calculate particle, angular momentum, and heat fluxes both quickly and accurately. In this tutorial, we present a derivation of one such code known as QuaLiKiz, a quasilinear gyrokinetic transport code. The goal of this derivation is to provide a self-contained and complete description of the underlying physics and mathematics of QuaLiKiz from first principles. This work serves both as a comprehensive overview of QuaLiKiz specifically as well as an illustration for deriving quasilinear models in general.

physics.plasm-ph↗

arXiv2019

Influence of toroidal flow on stationary density of collisionless plasmas

Starting from the given passive particle equilibrium particle cylindrical profiles, we built self-consistent stationary conditions of the Maxwell-Vlasov equation at thermodynamic equilibrium with non-flat density profiles. The solutions to the obtained equations are then discussed. It appears that the presence of an azimuthal (poloidal) flow in the plasma can insure radial confinement, while the presence of a longitudinal (toroidal) flow can enhance greatly the confinement. Moreover in the global physically reasonable situation, we find that no unstable point can emerge in the effective integrable Hamiltonian of the individual particles, hinting at some stability of the confinement when considering a toroidal geometry in the large aspect ratio limit.

physics.plasm-ph↗

arXiv2018

Tailoring steep density profile with unstable points

The mesoscopic properties of a plasma in a cylindrical magnetic field are investigated from the view point of test-particle dynamics. When the system has enough time and spatial symmetries, a Hamiltonian of a test particle is completely integrable and can be reduced to a single degree of freedom Hamiltonian for each initial state. The reduced Hamiltonian sometimes has unstable fixed points (saddle points) and associated separatrices. To choose among available dynamically compatible equilibrium states of the one particle density function of these systems we use a maximum entropy principle and discuss how the unstable fixed points affect the density profile or a local pressure gradient, and are able to create a steep profile that improves plasma confinement.

physics.plasm-ph↗

arXiv2016

Study on creation and destruction of transport barriers via effective safety factors for energetic particles

Charged particles with low kinetic energy move along magnetic field lines, but so do not energetic particles. We investigate the topological structure changes in the phase space of energetic particles with respect to the magnetic one. For this study cylindrical magnetic fields with non-monotonic safety factors that induce the magnetic internal transport barrier are considered. We show that the topological structure of the magnetic field line and of the particle trajectories can be quite different. We explain this difference using the concept of effective particle $q$-profile. Using this notion we can investigate the location and existence of resonances for particle orbits that are different from the magnetic ones. These are examined both numerically by integrating an equation of motion and theoretically by use of Alfvén's guiding center theory and by use of the effective reduced Hamiltonian for the integrable unperturbed system. It is clarified that, for the energetic particles, the grad $B$ drift effect shifts the resonances and the drift induced by curvature of the magnetic field line leads to the vanishing of the resonances. As a result, we give two different mechanisms that lead to the creation of transport barriers for energetic particles in the region where the magnetic field line is chaotic.

nlin.CD↗

arXiv2016

Full particle orbit effects in regular and stochastic magnetic fields

We present a numerical study of charged particle motion in a time-independent magnetic field in cylindrical geometry. The magnetic field model consists of an unperturbed reversed-shear helical part and a perturbation consisting of a superposition of modes. Contrary to most of the previous studies, the particle trajectories are computed by directly solving the full Lorentz force equations of motion in a six-dimensional phase space using a sixth-order, implicit, symplectic Gauss-Legendre method. The level of stochasticity in the particle orbits is diagnosed using averaged, effective Poincare sections. It is shown that when only one mode is present the particle orbits can be stochastic even though the magnetic field line orbits are not stochastic. The lack of integrability of the particle orbits in this case is related to separatrix crossing and the breakdown of the global conservation of the magnetic moment. Some perturbation consisting of two modes creates resonance overlapping, leading to Hamiltonian chaos in magnetic field lines. Then, the particle orbits exhibit a nontrivial dynamics depending on their energy and pitch angle. It is shown that the regions where the particle motion is stochastic decrease as the energy increases. The non-monotonicity of the $q$-profile implies the existence of magnetic ITBs which correspond to shearless flux surfaces located in the vicinity of the $q$-profile minimum. It is shown that depending on the energy, these magnetic ITBs might or might not confine particles. That is, magnetic ITBs act as an energy-dependent particle confinement filter. Magnetic field lines in reversed-shear configurations exhibit topological bifurcations due to separatrix reconnection. We show that a similar but more complex scenario appears in the case of particle orbits that depends in a non-trivial way on the energy and pitch angle of the particles.

nlin.CD↗

arXiv2014

Chaotic motion of charged particles in toroidal magnetic configurations

We study the motion of a charged particle in a tokamak magnetic field and discuss its chaotic nature. Contrary to most of recent studies, we do not make any assumption on any constant of the motion and solve numerically the cyclotron gyration using Hamiltonian formalism. We take advantage of a symplectic integrator allowing us to make long-time simulations. First considering an idealized magnetic configuration, we add a non generic perturbation corresponding to a magnetic ripple, breaking one of the invariant of the motion. Chaotic motion is then observed and opens questions about the link between chaos of magnetic field lines and chaos of particle trajectories. Second, we return to a axi-symmetric configuration and tune the safety factor (magnetic configuration) in order to recover chaotic motion. In this last setting with two constants of the motion, the presence of chaos implies that no third global constant exists, we highlight this fact by looking at variations of the first order of the magnetic moment in this chaotic setting. We are facing a mixed phase space with both regular and chaotic regions and point out the difficulties in performing a global reduction such as gyrokinetics.

nlin.CD↗

arXiv2014

Beam-Plasma Instability and Fast Particles: the Lynden-Bell Approach

The beam-plasma instability, i.e. the response of the plasma bulk to the injection of supra thermal charged-particle beams, results to be appropriately characterized by a long-range interaction system. This physical system hosts a number of very interesting phenomena and, in particular, the emergence of long-lived quasi-stationary states. We characterize the self-consistent distribution functions of such out-of-equilibrium states by means of the Lynden-Bell's theory. The prediction of this theory, based on the statistical mechanics of the Vlasov equation, are checked against the outcomes of numerical simulations of the discrete system. Moreover, a phenomenological study of the effective resonance band for the system response is also addressed. A threshold value has been found in the initial spread of beam-particle momenta. This threshold allows to discriminate between the resonant and non-resonant regimes. The analysis of the thermalization of a few percents of the beam population characterized by large initial momenta (with respect to the main part of the beam itself) is also performed and it confirms and deepens the understanding of the physical meaning of the mentioned threshold.

physics.plasm-ph↗