arXiv subjects

B. J. Frei

Publications and source records attributed to B. J. Frei.

13 recordsLinked to original sources

arXiv2026

First-Principles Explanation of the Drift Configuration Dependence of the Radial Electric Field and High-Confinement Access in Tokamaks

The origin of the difference in the high-confinement (H-mode) power threshold between favorable and unfavorable drift configurations in tokamaks, experimentally linked to a deeper radial electric field (Er) well in the former, remains unresolved. Using first-principles gyrokinetic simulations of edge and scrape-off-layer turbulence in ASDEX Upgrade, we show that turbulence-driven poloidal flows generate this deeper Er well in the favorable configuration through enhanced nonlinear turbulence-mean flow energy transfer. This transfer is significantly weaker in the unfavorable case, yielding a shallower Er well, while turbulence intensity is simultaneously higher. Within the turbulence-flow shear suppression paradigm, the combination of stronger shear and reduced turbulence facilitates H-mode access in the favorable configuration. These results provide the first validated, self-consistent full-f gyrokinetic explanation of how drift configuration controls the nonlinear dynamics of profiles, Er, flows, and turbulence, thereby setting the H-mode power threshold.

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arXiv2026

Pre L-H Transition Radial Electric Field and Transport Validations of Edge and Scrape-off Layer Gyrokinetic Simulations at ASDEX Upgrade

This work presents a stepwise validation of the evolution of the radial electric field (Er) and heat transport during the pre L-H transition phase using full-f gyrokinetic simulations of the edge and scrape-off layer in the ASDEX Upgrade (AUG) tokamak, including X-point geometry. Several L-mode time slices up to the L-H transition from a dedicated hydrogen discharge, featuring stepwise increases in ECRH input power, are selected [N. Bonanomi \textit{et al.}, Phys. Plasmas 31, 072302 (2024)] and simulated with the \texttt{GENE-X} code. As the edge boundary conditions are progressively increased between the time slices, particle and heat fluxes rise, and the radial electric field Er well deepens. A detailed validation of the Er profiles and of the Er well depth shows excellent agreement with experimental measurements at the successive time slices approaching the L-H transition. A force balance decomposition identifies turbulence-driven poloidal flows as the dominant contribution within the Er well. Edge turbulence is governed by a competition between electron drift waves and trapped-electron modes. The introduction of an edge density source, modeling neutral gas ionization, is shown to be essential to reproduce experimentally relevant density profiles, Er, and edge ion heat fluxes, which are dominated by both turbulent and diamagnetic contributions. This stepwise validation constitutes an important milestone toward predictive, first-principles gyrokinetic simulations of the L-H transition power threshold.

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arXiv2025

Turbulence and Transport in Spectrally Accelerated full-f Gyrokinetic Simulations

We investigate edge and scrape-off layer (SOL) turbulence and transport using the spectrally accelerated full-f gyrokinetic (GK) code GENE-X, recently introduced in [B. J. Frei et al., arXiv:2411.09232 (2024)]. Extending previous work on the TCV-X21 scenario, we show that the velocity-space spectral approach not only reproduces outboard midplane profiles but also captures key features of trapped electron mode (TEM)-driven turbulence and transport, including fluctuation spectra, turbulent fluxes, phase shifts, and power crossing the separatrix, in close agreement with grid-based results. This agreement remains robust when increasing spectral resolutions. We further analyze the radial force balance (accurately satisfied) and the structure of the radial electric fields and poloidal flows in the edge and SOL. Finally, we contrast our results with Braginskii-like fluid models, which inherently neglect TEMs. These results confirm the spectral full-f GENE-X approach as an efficient and first-principles tool for predicting edge and SOL turbulence.

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arXiv2024

Spectrally Accelerated Edge and Scrape-Off Layer Gyrokinetic Turbulence Simulations

This paper presents the first gyrokinetic (GK) simulations of edge and scrape-off layer (SOL) turbulence accelerated by a velocity-space spectral approach in the full-f GK code GENE-X. Building upon the original grid velocity-space discretization, we derive and implement a new spectral formulation and verify the numerical implementation using the method of manufactured solution. We conduct a series of spectral turbulence simulations focusing on the TCV-X21 reference case [Oliveira D. S. et al., Nucl. Fusion 62, 096001 (2022)] and compare these results with previously validated grid simulations [Ulbl P. et al., Phys. Plasmas 30, 107986 (2023)]. The spectral approach reproduces the outboard midplane (OMP) profiles (density, temperature, and radial electric field), dominated by trapped electron mode (TEM) turbulence, with excellent agreement and significantly lower velocity-space resolution. Thus, the spectral approach reduces the computational cost by at least an order of magnitude, achieving a speed-up of approximately 50 for the TCV-X21 case. This enables high-fidelity GK simulations to be performed within a few days on modern CPU-based supercomputers for medium-sized devices and establishes GENE-X as a powerful tool for studying edge and SOL turbulence, moving towards reactor-relevant devices like ITER.

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arXiv2024

Full-F Turbulent Simulation in a Linear Device using a Gyro-Moment Approach

Simulations of plasma turbulence in a linear plasma device configuration are presented. These simulations are based on a simplified version of the gyrokinetic (GK) model proposed by B. J. Frei et al. [J. Plasma Phys. 86, 905860205 (2020)] where the full-F distribution function is expanded on a velocity-space polynomial basis allowing us to reduce its evolution to the solution of an arbitrary number of fluid-like equations for the expansion coefficients, denoted as the gyro-moments (GM). By focusing on the electrostatic and neglecting finite Larmor radius effects, a full-F GM hierarchy equation is derived to evolve the ion dynamics, which includes a nonlinear Dougherty collision operator, localized sources, and Bohm sheath boundary conditions. An electron fluid Braginskii model is used to evolve the electron dynamics, coupled to the full-F ion GM hierarchy equation via a vorticity equation where the Boussinesq approximation is used. A set of full-F turbulent simulations are then performed using the parameters of the LArge Plasma Device (LAPD) experiments with different numbers of ion GMs and different values of collisionality. The ion distribution function is analyzed illustrating the convergence properties of the GM approach. In particular, we show that higher-order GMs are damped by collisions in the high-collisional regime relevant to LAPD experiments. The GM results are then compared with those from two-fluid Braginskii simulations, finding qualitative agreement in the time-averaged profiles and statistical turbulent properties.

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arXiv2023

Gyrokinetic moment-based simulations of the Dimits shift

We present a convergence study of the gyromoment (GM) approach, which is based on projecting the gyrokinetic distribution function onto a Hermite-Laguerre polynomial basis, focused on the cyclone base case (CBC) (Lin et al. 1999) and Dimits shift (Dimits et al. 2000) as benchmarks. We report that the GM approach converges more rapidly in capturing the nonlinear dynamics of the CBC than the continuum GENE code (Jenko et al. 2000) when comparing the number of points representing the velocity space. Increasing the velocity dissipation improves the convergence properties of the GM approach, albeit yielding a slightly larger saturated heat flux. By varying the temperature equilibrium gradient, we show that GM approach successfully reproduces the Dimits shift (Dimits et al. 2000) and effectively captures its width, which is in contrast to the gyrofluid framework. In the collisional regime, the convergence properties of the GM approach improve and a good agreement with previous global PIC results on transport is obtained (Lin et al. 1999). Finally, we report that the choice of collision model has a minimal impact both on the ITG growth rate and on the nonlinear saturated heat flux, at tokamak-relevant collisionality.

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arXiv2023

Gyrokinetic simulations of plasma turbulence in a Z-pinch using a moment based approach and advanced collision operators

The first nonlinear gyrokinetic simulations obtained using a moment approach based on the Hermite-Laguerre decomposition of the distribution function are presented, implementing advanced models for the collision operator. Turbulence in a \modif{two-dimensional} Z-pinch is considered within a flux tube configuration. In the collisionless regime, our gyromoment approach shows very good agreement with nonlinear simulations carried out with the continuum gyrokinetic code GENE, even with fewer gyromoments than required for the convergence of the linear growth rate. By using advanced linear collision operators, the role of collisions in setting the level of turbulent transport is then analyzed. The choice of collision operator model is shown to have a crucial impact when turbulence is quenched by the presence of zonal flows. The convergence properties of the gyromoment approach improve when collisions are included.

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arXiv2022

Moment-Based Approach to the Flux-Tube linear Gyrokinetic Model

This work reports on the development and numerical implementation of the linear electromagnetic gyrokinetic (GK) model in a tokamak flux-tube geometry using a moment approach based on the expansion of the perturbed distribution function on a velocity-space Hermite-Laguerre polynomials basis. A hierarchy of equations of the expansion coefficients, referred to as the gyro-moments (GM), is derived. We verify the numerical implementation of the GM hierarchy in the collisionless limit by performing a comparison with the continuum GK code GENE, recovering the linear properties of the ion-temperature gradient, trapped electron, kinetic ballooning, and microtearing modes, as well as the collisionless damping of zonal flows. The present investigation reveals the ability of the GM approach to describe fine velocity-space scale structures appearing near the trapped and passing boundary and kinetic effects associated with parallel and perpendicular particle drifts. In addition, the effects of collisions are studied using advanced collision operators, including the GK Coulomb collision operator. The main findings are that the number of GMs necessary for convergence decreases with plasma collisionality and is lower for pressure gradient-driven modes, such as in H-mode pedestal regions, compared to instabilities driven by trapped particles and magnetic gradient drifts often found in the core. The accuracy of approximations often used to model collisions (relative to the GK Coulomb operator) is studied, showing differences between collision operator models that increase with collisionality and electron temperature gradient in the case of TEM. The present linear analysis demonstrates that the GM approach efficiently describes the plasma dynamics for typical parameters of the tokamak boundary, ranging from the low-collisionality banana H-mode to the high-collisionality Pfirsch-Schlüter conditions.

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arXiv2022

Numerical Implementation of the Improved Sugama Collision Operator Using a Moment Approach

The numerical implementation of the linearized gyrokinetic (GK) and drift-kinetic (DK) improved Sugama (IS) collision operators, recently introduced by Sugama et al. [Phys. Plasmas 26, 102108 (2019)], is reported. The IS collision operator extends the validity of the widely-used original Sugama (OS) operator [Sugama et al., Phys. Plasmas 16, 112503 (2009)] to the Pfirsch-Schlüter collisionality regime. Using a Hermite-Laguerre velocity-space decomposition of the perturbed gyrocenter distribution function that we refer to as the gyro-moment approach, the IS collision operator is written in a form of algebraic coefficients that depend on the mass and temperature ratios of the colliding species and perpendicular wavenumber. A comparison between the IS, OS, and Coulomb collision operators is performed, showing that the IS collision operator is able to approximate the Coulomb collision operator in the case of trapped electron mode (TEM) in H-mode pedestal conditions better than the OS operator. In addition, the IS operator leads to a level of zonal flow (ZF) residual which has an intermediate value between the Coulomb and the OS collision operators. The IS operator is also shown to predict a parallel electrical conductivity that approaches the one of the Coulomb operator within less than 1%, while the OS operator can underestimate the parallel electron current by at least 10%. Finally, closed analytical formulae of the lowest-order gyro-moments of the IS, OS, and Coulomb operators are given that are ready to use to describe collisional effects in reduced gyro-moment fluid models.

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arXiv2022

Development of Advanced Linearized Gyrokinetic Collision Operators Using a Moment Approach

The derivation and numerical implementation of a linearized version of the gyrokinetic (GK) Coulomb collision operator (Jorge R. et al., J. Plasma Phys. 85, 905850604 (2019)) and of the widely-used linearized GK Sugama collision operator (Sugama H. et al., Phys. Plasmas 16, 112503 (2009)) is reported. An approach based on a Hermite-Laguerre moment expansion of the perturbed gyrocenter distribution function is used, referred to as gyro-moment expansion. This approach allows considering arbitrary perpendicular wavenumber and expressing the two linearized GK operators as a linear combination of gyro-moments where the expansion coefficients are given by closed analytical expressions that depend on the perpendicular wavenumber and on the temperature and mass ratios of the colliding species. The drift-kinetic (DK) limits of the GK linearized Coulomb and Sugama operators are also obtained. Comparisons between the gyro-moment approach with the GK continuum code GENE are reported focusing on the ion-temperature-gradient (ITG) instability and zonal flow (ZF) damping, finding an excellent agreement. In particular, we demonstrate that the GK linearized Sugama yields a stronger collisional damping of the ZF residual compared to the GK linearized Coulomb. Finally, we show that the numerical efficiency of the gyro-moment approach increases with collisionality, a desired property for boundary plasma applications.

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arXiv2022

Local Gyrokinetic Collisional Theory of the Ion-Temperature Gradient Mode

We present a study of the linear properties of ion temperature gradient (ITG) modes with collisions modelled by the linearized gyrokinetic (GK) Coulomb collision operator (Frei et al. 2021) in the local limit. The study is based on a Hermite-Laguerre polynomial expansion of the perturbed ion distribution function applied to the linearized GK Boltzmann equation, yielding a hierarchy of coupled equations for the expansion coefficients, referred to as gyro-moments. We explore analytically the collisionless and high-collisional limits of the gyro-moment hierarchy. Parameter scans revealing the dependence of the ITG growth rate on the collisionality are reported, showing strong damping at small scales as the collisionality increases. These properties are compared with the predictions based on the Sugama, the momentum-conserving pitch-angle scattering, the Hirshman- Sigmar-Clarke, and the Daugherty collision operators. The importance of finite Larmor radius (FLR) terms in the collision operators is pointed out by the appearance of a short wavelength (SW) ITG branch when collisional FLR terms are neglected, this branch being completely suppressed by collisional FLR effects. We demonstrate that energy diffusion is important at high collisionality and small scale lengths and that, among the collision operators considered in this work, the GK Sugama collision operator yields, in general, the smallest deviation on the ITG growth rate compared to the GK Coulomb collision operator. Convergence studies of the gyro-moment method are reported.

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arXiv2020

A gyrokinetic model for the plasma periphery of tokamak devices

A gyrokinetic model is presented that can properly describe strong flows, large and small amplitude electromagnetic fluctuations occurring on scale lengths ranging from the electron Larmor radius to the equilibrium perpendicular pressure gradient scale length, and large deviations from thermal equilibrium. The formulation of the gyrokinetic model is based on a second order description of the single charged particle dynamics, derived from Lie perturbation theory, where the fast particle gyromotion is decoupled from the slow drifts, assuming that the ratio of the ion sound Larmor radius to the perpendicular equilibrium pressure scale length is small. The collective behavior of the plasma is obtained by a gyrokinetic Boltzmann equation that describes the evolution of the gyroaveraged distribution function and includes a non-linear gyrokinetic Dougherty collision operator. The gyrokinetic model is then developed into a set of coupled fluid equations referred to as the gyrokinetic moment hierarchy. To obtain this hierarchy, the gyroaveraged distribution function is expanded onto a velocity-space Hermite-Laguerre polynomial basis and the gyrokinetic equation is projected onto the same basis, obtaining the spatial and temporal evolution of the Hermite-Laguerre expansion coefficients. The Hermite-Laguerre projection is performed accurately at arbitrary perpendicular wavenumber values. Finally, the self-consistent evolution of the electromagnetic fields is described by a set of gyrokinetic Maxwell's equations derived from a variational principle, with the velocity integrals of the gyroaveraged distribution function explicitly evaluated.

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arXiv2019

Nonlinear Gyrokinetic Coulomb Collision Operator

A gyrokinetic Coulomb collision operator is derived, which is particularly useful to describe the plasma dynamics at the periphery region of magnetic confinement fusion devices. The derived operator is able to describe collisions occurring in distribution functions arbitrarily far from equilibrium with variations on spatial scales at and below the particle Larmor radius. A multipole expansion of the Rosenbluth potentials is used in order to derive the dependence of the full Coulomb collision operator on the particle gyroangle. The full Coulomb collision operator is then expressed in gyrocentre phase-space coordinates, and a closed formula for its gyroaverage in terms of the moments of the gyrocenter distribution function in a form ready to be numerically implemented is provided. Furthermore, the collision operator is projected onto a Hermite-Laguerre velocity space polynomial basis and expansions in the small electron-to-ion mass ratio are provided.

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