arXiv subjects

Philipp Lauber

Publications and source records attributed to Philipp Lauber.

At least 19 recordsLinked to original sources

arXiv2026

Gyrokinetic global simulation of Alfvenic ion temperature gradient mode in reversed magnetic shear

In this work, a systematic study of electromagnetic instabilities driven by the temperature gradient in magnetically confined fusion plasmas with reversed magnetic shear is conducted using gyrokinetic particle-in-cell simulations. An electromagnetic instability arising in the low-beta regime is investigated, where beta=8*pi*nT/B^2 denotes the ratio of plasma pressure to magnetic pressure. Within a reversed shear safety factor (q) profile, when a mode rational surface coincides with the position of zero shear, an instability dominated by only one poloidal harmonic emerges, rather than the conventional ion-temperature-gradient (ITG) mode. Simulation results demonstrate that the instability exhibits pronounced electromagnetic polarization even in the low-beta regime, with a real frequency significantly higher than that of ITG modes, and show that it is destabilized by the temperature gradient and not by the density gradient. This instability can be observed even for a monotonic q profile with weak magnetic shear. Based on a systematic comparison with other typical electrostatic and electromagnetic instabilities, this instability is identified as a weak shear Alfvenic-ion-temperature-gradient (WSAITG) mode, which may provide an explanation for the low-frequency Alfven modes (LFAM) observed in experiments. Wave-particle resonance analysis in phase space reveals that, in contrast to the ITG mode, well-passing particles provide an additional resonant population that drives the WSAITG mode.

physics.plasm-ph↗

arXiv2026

On nonlinear saturation of toroidal Alfv\'en eigenmode due to thermal plasma nonlinearities

The nonlinear saturation of toroidal Alfven eigenmode (TAE) due to thermal plasma nonlinearities is investigated using gyrokinetic particle-in-cell simulations and theoretical analysis. In the single toroidal mode number simulations with zonal fields filtered out, we find that the saturation level of TAE is governed by thermal plasma nonlinearities for gamma_L/omega_n > 0.47%, which has weak dependence on the linear drive gamma_L, i.e., "stiffness" in saturation level. We find that the frequency of TAE decreases as the amplitude of it increases, which is induced by the phase-space zonal structure (PSZS) of thermal plasmas universally existed in particle-in-cell simulations. The saturation of TAE can be finally reached when the mode merges into the continuum. Following this process, the separation of neighboring poloidal harmonics and mode transition to energetic particle modes can be observed. In simulations with zonal fields, zonal fields can essentially counteract the effects of PSZS of thermal plasmas, leading to roughly a factor of 2 enhancement of the TAE saturation level compared to the single toroidal mode number simulation, implying the necessity of including zonal modes in evaluating the saturation level of TAE.

physics.plasm-ph↗

arXiv2025

TRIMEG-GKX: an electromagnetic gyrokinetic particle code with a Piecewise Field-Aligned Finite Element Method for Micro- and Macro-Instability Studies in Tokamak Core Plasmas

The features of the TRIMEG-GKX code are described with emphasis on the exploration using novel/different schemes compared to other gyrokinetic codes, particularly the use of object-oriented programming, filter/buffer-free treatment, and a high-order piecewise field-aligned finite element method. The TRIMEG-GKX code solves the electromagnetic gyrokinetic equation using the particle-in-cell scheme, taking into account multi-species effects and shear Alfv\'en physics. The mixed-variable/pullback scheme has been implemented to enable electromagnetic studies. This code is parallelized using particle decomposition and domain cloning among computing nodes, replacing traditional domain decomposition techniques. The applications to study the micro- and macro-instabilities are demonstrated, including the energetic-particle-driven Alfv\'en eigenmode, ion temperature gradient mode, and kinetic ballooning mode. Good performance is achieved in both ad hoc and experimentally reconstructed equilibria, such as those of the ASDEX Upgrade (AUG), Tokamak \`a configuration variable (TCV), and the Joint European Torus (JET). Future studies of edge physics using the high-order $C^1$ finite element method for triangular meshes in the TRIMEG-C1 code will be built upon the same numerical methods.

physics.plasm-ph↗

arXiv2024

Construction and analysis of guiding center distributions for tokamak plasmas with ambient radial electric field

The contribution of a time-independent toroidally-symmetric radial electric field $E_r$ is implemented in VisualStart [Comp. Phys. Comm. 275 (2022) 108305; arXiv:2111.08224], a code whose purposes include the construction of guiding center (GC) drift orbit databases for the study of plasma instabilities in tokamaks. $E_r$ is important for the thermal part of the velocity distribution and for fast particle resonances in the kHz frequency range. KSTAR, JT-60U and ITER tokamak cases are used as working examples to test our methods and discuss practical issues connected with $E_r$. Two points are worth noting: First, the GC orbit space is sampled in the magnetic midplane as before, and we find that in the presence of $E_r$, midplane-based coordinates are not only equivalent but superior to conventional constants of motion, allowing to attain high numerical accuracy and efficiency with a relatively simple mesh. Second, the periodic parallel acceleration and deceleration of GCs via the mirror force is modulated by $E_r$. Although this parallel electric acceleration averages to zero during a poloidal transit (or bounce) period, it has important consequences, one being the known shift of the trapped-passing boundary. Another consequence is that electric frequency shifts depend on the chosen reference point, so that some care is required when evaluating the $E_r$-dependence of transit frequencies for resonance analyses.

physics.plasm-ph↗

arXiv2024

Landau Damping for Non-Maxwellian Distribution Functions

Landau damping is one of the cornerstones of plasma physics. In the context of the mathematical framework developed by Landau in his original derivation of Landau damping, we examine the solutions of the linear Vlasov-Poisson system for different equilibrium velocity distribution functions, such as the Maxwellian distribution, kappa distributions, and cut-off distributions without and with energy diffusion. Specifically, we focus on the full set of roots that the dispersion relation of the linear Vlasov-Poisson system generally admits, and we wonder if the full structure of solutions might hint at a deeper understanding of the Landau damping phenomenon.

physics.plasm-ph↗

arXiv2024

Piecewise Field-Aligned Finite Element Method for Multi-Mode Nonlinear Particle Simulations in tokamak plasmas

This paper presents a novel approach for simulating plasma instabilities in tokamak plasmas using the piecewise field-aligned finite element method in combination with the particle-in-cell method. Our method traditionally aligns the computational grid but defines the basis functions in piecewise field-aligned coordinates to avoid grid deformation while naturally representing the field-aligned mode structures. This scheme is formulated and implemented numerically. It also applied to the unstructured triangular meshes in principle. We have conducted linear benchmark tests, which agree well with previous results and traditional schemes. Furthermore, multiple-$n$ simulations are also carried out as a proof of principle, demonstrating the efficiency of this scheme in nonlinear turbulence simulations within the framework of the finite element method.

physics.plasm-ph↗

arXiv2024

Gyrokinetic Electromagnetic Particle Simulations in Triangular Meshes with C1 Finite Elements

The triangular mesh-based gyrokinetic scheme enables comprehensive axis-to-edge studies across the entire plasma volume. Our approach employs triangular finite elements with first-derivative continuity (C1), building on previous work to facilitate gyrokinetic simulations. Additionally, we have adopted the mixed variable/pullback scheme for gyrokinetic electromagnetic particle simulations. The filter-free treatment in the poloidal cross-section with triangular meshes introduces unique features and challenges compared to previous treatments using structured meshes. Our implementation has been validated through benchmarks using ITPA-TAE (Toroidicity-induced Alfvén Eigenmode) parameters, showing its capability in moderate to small electron skin depth regimes. Additional examinations using experimental parameters confirm its applicability to realistic plasma conditions.

physics.plasm-ph↗

arXiv2024

Analysis of non-diffusive avalanche transport of energetic particles

The dynamics of energetic particles (EPs) interacting with Alfv\'en eigenmodes (AEs) for the ITER 15MA baseline scenario was described using a reduced 1D model in [Carlevaro et al. PPCF 64, 035010 (2022)], and successfully tested against nonlinear wave-particle simulations. In this paper, we introduce a detailed phase-space and statistical analysis of this case to characterize the emerging EP transport regimes. Deviations from pure diffusive dynamics are quantitatively addressed, indicating the limitations of standard quasi-linear descriptions. The phase space diagnostics introduced allows to describe the emergence of a very complex dynamics of overlapping resonances and substructure formation, reinforcing the evidence of non-diffusive domino-like AEs.

physics.plasm-ph↗

arXiv2024

Energetic particles transport in constants of motion space due to collisions in tokamak plasmas

The spatio-temporal evolution of the energetic particles in the transport time scale in tokamak plasmas is a key issue of the plasmas confinement, especially in burning plasmas. In order to include sources and sinks and collisional slowing down processes, a new solver, ATEP-3D was implemented to simulate the evolution of the EP distribution in the three-dimensional constants of motion (CoM) space. The Fokker-Planck collision operator represented in the CoM space is derived and numerically calculated. The collision coefficients are averaged over the unperturbed orbits to capture the fundamental properties of EPs. ATEP-3D is fully embedded in ITER IMAS framework and combined with the LIGKA/HAGIS codes. The finite volume method and the implicit Crank-Nicholson scheme are adopted due to their optimal numerical properties for transport time scale studies. ATEP-3D allows the analysis of the particle and power balance with the source and sink during the transport process to evaluate the EP confinement properties.

physics.plasm-ph↗

arXiv2024

Ion temperature gradient mode mitigation by energetic particles, mediated by forced-driven zonal flows

In this work, we use the global electromagnetic and electrostatic gyro kinetic approaches to investigate the effects of zonal flows forced-driven by Alfvén modes due to their excitation by energetic particles (EPs), on the dynamics of ITG (Ion temperature gradient) instabilities. The equilibrium of the 92416 JET tokamak shot is considered. The linear and nonlinear Alfvén modes dynamics, as well as the zonal flow dynamics, are investigated and their respective radial structures and saturation levels are reported. ITG dynamics in the presence of the zonal flows excited by these Alfvén modes are also investigated. We find that, the zonal flows forced-driven by Alfvén modes can significantly impact the ITG dynamics. A zonal flow amplitude scan reveals the existence of an inverse relation between the zonal flow amplitude and the ITG growth rate. These results show that, forced-driven zonal flows can be an important indirect part of turbulence mitigation due to the injection of energetic particles.

physics.plasm-ph↗

arXiv2023

Gyrokinetic simulations of neoclassical electron transport and bootstrap current generation in tokamak plasmas in the TRIMEG code

For magnetic confinement fusion in tokamak plasmas, some of the limitations to the particle and energy confinement times are caused by turbulence and collisions between particles in toroidal geometry, which determine the "anomalous" and the neoclassical transport, respectively. In this work, we focus on the implementation of neoclassical physics in the gyrokinetic code TRIMEG, which is a TRIangular MEsh-based Gyrokinetic code that can handle both the closed and open field line geometries of a divertor tokamak. We report on the implementation of a simplified Lorentz collision operator in TRIMEG. Since the code uses an unstructured mesh, a procedure for calculating the flux surface averages of particle and energy fluxes and the bootstrap current is derived without relying on the poloidal coordinate, which is useful also for other simulations in unstructured meshes. With the newly implemented collision operator, we study electron transport and bootstrap current generation for various simplified and realistic geometries. In comparison to neoclassical theory, good agreement is obtained for the large aspect ratio case regarding the particle and energy fluxes as well as the bootstrap current. However, some discrepancies are observed at moderate aspect ratio and for a case with the realistic geometry of the ASDEX Upgrade tokamak. These deviations can be explained by different treatments and approximations in theory and simulation. In this paper, we demonstrate the capability to calculate the electron transport and bootstrap current generation in TRIMEG, which will allow for the self-consistent inclusion of neoclassical effects in gyrokinetic simulations in the future.

physics.plasm-ph↗

arXiv2023

The impact of fusion-born alpha particles on runaway electron dynamics in ITER disruptions

In the event of a tokamak disruption in a D-T plasma, fusion-born alpha particles take several milliseconds longer to thermalise than the background. As the damping rates drop drastically following the several orders of magnitudes drop of temperature, Toroidal Alfven Eigenmodes (TAEs) can be driven by alpha particles in the collapsing plasma before the onset of the current quench. We employ kinetic simulations of the alpha particle distribution and show that the TAEs can reach sufficiently strong saturation amplitudes to cause significant core runaway electron transport in unmitigated ITER disruptions. As the eigenmodes do not extend to the plasma edge, this effect leads to an increase of the runaway electron plateau current. Mitigation via massive material injection however changes the Alfven frequency and can lead to mode suppression. A combination of the TAE-caused core runaway electron transport with other perturbation sources could lead to a drop of runaway current in unmitigated disruptions.

physics.plasm-ph↗

arXiv2022

Energetic particle transport: diffusion vs convection and phase-space barriers

Energetic particle redistribution in the presence of multiple Alfvén eigenmodes is analyzed in [PPCF 58, 014019 (2016)] for the ITER 15MA baseline scenario: non-linear hybrid simulations (within their well known limits) point out that transport can be dominated by avalanches under certain conditions. These phenomena are properly reproduced by the 1D reduced description of [PPCF 64, 035010 (2022)]. Here, using this simplified 1D model, we define the transport character (convective/diffusive) of self-consistent energetic particle redistribution. Transport barriers in phase space are studied using the Lagrangian Coherent Structures technique.

physics.plasm-ph↗

arXiv2022

Full $f$ and $δf$ gyrokinetic particle simulations of Alfvén waves and energetic particle physics

In this work, we focus on the development of the particle-in-cell scheme and the application to the studies of Alfvén waves and energetic particle physics in tokamak plasmas. The $δf$ and full $f$ schemes are formulated on the same footing adopting mixed variables and the pullback scheme for electromagnetic problems. The TRIMEG-GKX code [Lu et al. J. Comput. Phys. 440 (2021) 110384] has been upgraded using cubic spline finite elements and full $f$ and $δf$ schemes. The EP-driven TAE has been simulated for the ITPA-TAE case featured by a small electron skin depth $\sim 1.18\times10^{-3}\;{\rm m}$, which is a challenging parameter regime of electromagnetic simulations, especially for the full $f$ model. The simulation results using the $δf$ scheme are in good agreement with previous work. Excellent performance of the mixed variable/pullback scheme has been observed for both full $f$ and $δf$ schemes. Simulations with mixed full $f$ EPs and $δf$ electrons and thermal ions demonstrate the good features of this novel scheme in mitigating the noise level. The full $f$ scheme is a natural choice for EP physics studies which allows a large variation of EP profiles and distributions in velocity space, providing a powerful tool for kinetic studies using realistic experimental distributions related to intermittent and transient plasma activities.

physics.plasm-ph↗

arXiv2022

Representation and modeling of charged particle distributions in tokamaks

Experimental diagnostics, analysis tools and simulations represent particle distributions in various forms and coordinates. Algorithms to manage these data are needed on platforms like the ITER Integrated Modelling & Analysis Suite (IMAS), performing tasks such as archiving, modeling, conversion and visualization. A method that accomplishes some of the required tasks for distributions of charged particles with arbitrarily large magnetic drifts in axisymmetric tokamak geometry is described here. Given a magnetic configuration, we first construct a database of guiding center orbits, which serves as a basis for representing particle distributions. The orbit database contains the geometric information needed to perform conversions between arbitrary coordinates, modeling tasks, and resonance analyses. Using that database, an imported or newly modeled distribution is mapped to an exact equilibrium, where the dimensionality is reduced to three constants of motion (CoM). The orbit weight is uniquely given when the input is a true distribution: one that measures the number of physical particles per unit of phase space volume. Less ideal inputs, such as distributions estimated without drifts, or models of particle sources, can also be processed. As an application example, we reconstruct the drift-induced features of a distribution of fusion-born alpha particles in a large tokamak, given only a birth profile, which is not a function of the alpha's CoM. Repeated back-and-forth transformations between CoM space and energy-pitch-cylinder coordinates are performed for verification and as a proof of principle for IMAS.

physics.plasm-ph↗

arXiv2022

Gyrokinetic modelling of the Alfvén mode activity in ASDEX Upgrade with an isotropic slowing-down fast-particle distribution

In the present paper, the evolution of the Alfvén modes is studied in a realistic ASDEX Upgrade equilibrium by analysing the results of simulations with the global, electromagnetic, gyrokinetic particle-in-cell code ORB5. The energetic particles are modelled both via the newly implemented isotropic slowing-down and with Maxwellian distribution functions. The comparison of the numerical results shows that modelling the energetic particles with the equivalent Maxwellian rather than with the slowing-down, does not affect the frequency of the driven Alfvén mode, while its growth rate appears to be underestimated with a quantitative difference as large as almost 30 %. Additionally the choice of the isotropic slowing-down allows a better description of the nonlinear modification of the dominant Alfvén mode frequency, while an equivalent Maxwellian underestimates it. A good comparison with the experimental spectrogram is found.

physics.plasm-ph↗

arXiv2022

One dimensional reduced model for ITER relevant energetic particle transport

We set up a mapping procedure able to translate the evolution of the radial profile of fast ions, interacting with Toroidal Alfvén Eigenmodes, into the dynamics of an equivalent one dimensional bump-on-tail system. We apply this mapping technique to reproduce ITER relevant simulations, which clearly outlined deviations from the diffusive quasi-linear (QL) model. Our analysis demonstrates the capability of the one-dimensional beam-plasma dynamics to predict the relevant features of the non-linear hybrid LIGKA/HAGIS simulations. In particular, we clearly identify how the deviation from the QL evolutive profiles is due to the presence of avalanche processes. A detailed analysis regarding the reduced dimensionality is also addressed, by means of phase-space slicing based on constants of motion. In the conclusions, we outline the main criticalities and outcomes of the procedure, which must be satisfactorily addressed to make quantitative prediction on the observed outgoing fluxes in a Tokamak device.

physics.plasm-ph↗

arXiv2022

Energy-selective confinement of fusion-born alpha particles during internal relaxations in a tokamak plasma

Long-pulse operation of a self-sustained fusion reactor using toroidal magnetic containment requires control over the content of alpha particles produced by D-T fusion reactions. On the one hand, MeV-class alpha particles must stay confined to heat the plasma. On the other hand, decelerated helium ash must be expelled before diluting the fusion fuel. Our kinetic-magnetohydrodynamic hybrid simulations of a large tokamak plasma confirm the existence of a parameter window where such energy-selective confinement can be accomplished by exploiting internal relaxation events known as `sawtooth crashes'. The physical picture -- consisting of a synergy between magnetic geometry, optimal crash duration and rapid particle motion -- is completed by clarifying the role played by magnetic drifts. Besides causing asymmetry between co- and counter-going particle populations, magnetic drifts determine the size of the confinement window by dictating where and how much `reconnection' occurs in particle orbit topology.

physics.plasm-ph↗