arXiv subjects

A. Bottino

Publications and source records attributed to A. Bottino.

At least 19 recordsLinked to original sources

arXiv2026

Energetic particles, Shafranov shift and finite $β$ effects on TAE, KBM and ITG instabilities in global electromagnetic gyrokinetic simulations

Burning plasma is computationally challenging to simulate due to the multi-scale interactions between energetic particles (EPs), Alfven eigenmodes, and microinstabilities that drive turbulence. Many studies circumvent this difficulty by focusing on a single instability and making the corresponding simplifying assumptions. However, these approximations do not necessarily preserve the global instability spectrum, leading to conflicting results and inconsistencies. In this work, we identify the minimal set of assumptions needed to model a burning plasma self-consistently with the modes and species in the system. Using the global gyrokinetic code ORB5, to systematically evaluate the impact of commonly adopted assumptions on the plasma response. We find it is essential to include Shafranov shift and finite $β$ effects from all magnetically confined species. Otherwise, unphysical electromagnetic modes like internal kinks and kinetic ballooning modes (KBMs) appear to dominate the instability spectrum. The EP contribution to the Shafranov shift is particularly important, stabilizing both the toroidal ion temperature gradient (ITG) and toroidal Alfven eigenmode (TAE) at the longer wavelengths (low toroidal mode numbers). For TAEs, these effects significantly reduce the linear growth rate, which saturates instead of proportionally increasing with EP fraction. In the nonlinear regime ITG-driven heat and particle fluxes are unaffected by the Shafranov shift in self-consistent magnetic equilibria. While the the nonlinear saturation level of the TAE remains unchanged across all cases, unlike for the ITG case Shafranov shift does reduce the TAE-driven EP fluxes.

physics.plasm-ph↗

arXiv2026

Nonlinear oscillations of the amplitude of energetic-particle induced geodesic acoustic modes

Energetic particle induced geodesic acoustic modes (EGAMs) are axisymmetric perturbations of the radial electric field in tokamak plasmas. They are driven unstable by the phase space nonuniformity of a population of energetic particles (EP). In this paper, the nonlinear oscillation in the amplitude of the energetic-particle induced geodesic acoustic modes is studied by means of the gyrokinetic particle-in-cell code ORB5. Similarities are discussed with the beam-plasma instability (BPI), where a Langmuir wave is driven unstable by phase space nonuniformity of a population of energetic electrons. A similar scaling of the nonlinear oscillation frequency as a function of the mode amplitude is found for the EGAMs and for the BPI, confirming that their nonlinear dynamics is strongly determined by the same physical mechanisms. As a product of this study, a novel diagnostics is proposed for the evaluation of the EGAM intensity in tokamak plasmas.

physics.plasm-ph↗

arXiv2026

Nonlinear generation of global zonal structures in gyrokinetic simulations of TCV and ASDEX Upgrade magnetic configurations

In tokamaks, turbulence is responsible not only for the anomalous transport of heat and particles from the core to the edge, which reduces heating efficiency, but also for the generation of zonal structures (ZSs). Examples of ZSs are those with characteristic sound frequency, like the geodesic acoustic modes (GAMs). Developing a theoretical model of ZS is essential, as they contribute to the turbulence saturation and thus indirectly influence transport. In this paper, we investigate the radial structure of ZS in the frequency range of GAMs, by means of numerical simulations using the gyrokinetic particle-in-cell code ORB5. We find that radially extended coherent ZSs (labelled here as global ZSs) are non-linearly generated by the high-n part of the turbulence spectrum (with n being the toroidal mode number) by means of self-consistent simulations. We also reproduce this generation by mimicking the turbulence modes with an antenna, thus isolating the nonlinear generation mechanism.

physics.plasm-ph↗

arXiv2026

Role of Shafranov shift, zonal structures on the behavior of TAEs, AAEs and microinstabilities in the presence of energetic particles

In future nuclear fusion reactors, even a small fraction of fusion-born energetic particles (EP) about 100 times hotter than the thermal bulk species, contributes substantially to the kinetic pressure and therefore affect the MHD equilibrium, mainly via the Shafranov shift. In this work, we perform first-principles numerical simulations using the gyrokinetic, electromagnetic, global code ORB5 to study the effect of a self-consistent finite $β$ equilibrium on the arising Alfvén Eigenmodes (destabilized by EPs), Ion Temperature Gradient (ITG), and Kinetic Ballooning Modes (KBM) microturbulence (destabilized by thermal species). Linearly, we explore the complex interplay between EP fraction, bulk gradients and a self-consistent Shafranov shift on the plasma stability. We choose single toroidal mode numbers to represent the system's instabilities and study the characteristic nonlinear evolutions of TAEs, KBMs and ITGs separately and including the axisymmetric field response to each mode separately. This study focuses on the impact of Shafranov shift equilibrium consistency, as well as the self-generated zonal ${E \times B}$ flows, the saturation levels and resulting heat and particle fluxes. In the ITG cases including the $n=0$ perturbations reduces turbulent fluxes, as expected, however, for the TAE cases including the $n=0$ perturbations is shown to enhance the fluxes. We show for the first time that Axisymmetric Alfvén Eigenmodes (AAEs) play a role in this mechanism.

physics.plasm-ph↗

arXiv2025

Study of the impact of fast ions on core turbulence at rational surfaces via global gyrokinetic simulations

In this work, the interplay between fast ions and safety factor rational surfaces is studied in a turbulent plasma via global nonlinear gyrokinetic simulations. Initially, the fast particles-induced enhancement of shearing structures from turbulence self-interaction is analyzed. Our study takes into account the competition between this mechanism and other fast ions effects, i.e. thermal profiles dilution and quasi-resonant interaction. We find the fast ions-induced reduction of destabilization threshold for the zonal modes to be a very efficient way to suppress turbulence. Indeed, it leads to the formation of regions where turbulent transport is reduced by 90\% of its original value. Furthermore, an $n=m=1$ fishbone is driven unstable inside the plasma and its interaction with turbulence is studied. We find the beat-driven zonal structure generate by this mode to further reduce turbulence when its presence does not drastically flatten the thermal profiles.

physics.plasm-ph↗

arXiv2023

Nonlinear interaction of Alfvénic instabilities and turbulence via the modification of the equilibrium profiles

Nonlinear simulations of Alfvén modes (AM) driven by energetic particles (EP) in the presence of turbulence are performed with the gyrokinetic particle-in-cell code ORB5. The AMs carry a heat flux, and consequently they nonlinearly modify the plasma temperature profiles. The isolated effect of this modification on the dynamics of turbulence is studied, by means of electrostatic simulations. We find that turbulence is reduced when the profiles relaxed by the AM are used, with respect to the simulation where the unperturbed profiles are used. This is an example of indirect interaction of EPs and turbulence. First, an analytic magnetic equilibrium with circular concentric flux surfaces is considered as a simplified example for this study. Then, an application to an experimentally relevant case of ASDEX Upgrade is discussed.

physics.plasm-ph↗

arXiv2023

How accurate are flux-tube (local) gyrokinetic codes in modeling energetic particle effects on core turbulence?

Flux-tube gyrokinetic codes are widely used to simulate drift-wave turbulence in magnetic confinement devices. While a large number of studies show that flux-tube codes provide an excellent approximation for turbulent transport in medium-large devices, it still needs to be determined whether they are sufficient for modeling supra-thermal particle effects on core turbulence. This is called into question given the large temperature of energetic particles (EPs), which makes them hardly confined on a single flux-surface, but also due to the radially broad mode structure of energetic-particle-driven modes. The primary focus of this manuscript is to assess the range of validity of flux-tube codes in modeling fast ion effects by comparing radially global turbulence simulations with flux-tube results at different radial locations for realistic JET parameters using the gyrokinetic code GENE. To extend our study to a broad range of different plasma scenarios, this comparison is made for four different plasma regimes, which differ only by the profile of the ratio between the plasma kinetic and magnetic pressure. The latter is artificially rescaled to address the electrostatic limit and regimes with marginally stable, weakly unstable and strongly unstable fast ion modes. These energetic-particle-driven modes is identified as an AITG/KBAE via linear ORB5 and LIGKA simulations. It is found that the local flux-tube simulations can recover well the global results only in the electrostatic and marginally stable cases. When the AITG/KBAE becomes linearly unstable, the local approximation fails to correctly model the radially broad fast ion mode structure and the consequent global zonal patterns. According to this study, global turbulence simulations are likely required in regimes with linearly unstable AITG/KBAEs. In conditions with different fast ion-driven modes, these results might change.

physics.plasm-ph↗

arXiv2022

Effect of temperature anisotropy on the dynamics of geodesic acoustic modes

In this work, we revisit the linear gyro-kinetic theory of geodesic acoustic modes (GAMs) and derive a general dispersion relation for an arbitrary equilibrium distribution function of ions. A bi-Maxwellian distribution of ions is then used to study the effects of ion temperature anisotropy on GAM frequency and growth rate. We find that ion temperature anisotropy yields sensible modifications to both the GAM frequency and growth rate as both tend to increase with anisotropy and these results are strongly affected by the electron to ion temperature ratio.

physics.plasm-ph↗

arXiv2022

Gyrokinetic particle-in-cell simulations of electromagnetic turbulence in the presence of fast particles and global modes

Global simulations of electromagnetic turbulence, collisionless tearing modes, and Alfven Eigenmodes in the presence of fast particles are carried out using the gyrokinetic particle-in-cell codes ORB5 (E. Lanti et al, Comp. Phys. Comm., ${\bf 251}$, 107072 (2020)) and EUTERPE (V. Kornilov et al, Phys. Plasmas, ${\bf 11}$, 3196 (2004)) in tokamak and stellarator geometries. Computational feasibility of simulating such complex coupled systems is demonstrated.

physics.plasm-ph↗

arXiv2022

Multi-scale analysis of global electromagnetic instabilities in ITER Pre-Fusion-Power Operation plasmas

Global electromagnetic gyrokinetic simulations are performed with the Particle-in-Cell code ORB5 for an ITER Pre-Fusion-Power-Operation (PFPO) plasma scenario, with half-field (2.65 T) and half-current (7.5 MA). We report on a 'multi-scale' analysis of the discharge, considering eigenmodes and instabilies across three scale-lengths. Although the scenario will nominally have neutral beam heating with particles injected with 1 MeV, Alfvén eigenmodes are investigated in the absence of such source, and Reversed Shear (RSAE), Toroidal (TAE) and Elliptical (EAE) Alfvén eigenmodes are found with weak damping for moderately low toroidal mode numbers ($10 \leq n \leq 35$). At higher toroidal mode numbers ($40 \leq n \leq 70$), unstable Alfvénic modes have been observed close to rational surfaces and are labelled as Beta-induced Alfvén eigenmodes (BAE)/Alfvénic Ion Temperature Gradient (AITG) modes, since their frequency is associated with the BAE gap and they are driven by the bulk plasma on the Alfvénic continuum. These modes are unstable in the absence of energetic particles, and adding a species of energetic particles (with an isotropic 1 MeV slowing down distribution) has negligible impact on their growth rate. At higher toroidal mode numbers ($150 \lessapprox n < 220$), low frequency microscale instabilities are observed.

physics.plasm-ph↗

arXiv2021

Gyrokinetic investigation of the nonlinear interaction of Alfvén instabilities and energetic-particle driven geodesic acoustic modes

This paper presents a study of the interaction between Alfvén modes and zonal structures, considering a realistic ASDEX Upgrade equilibrium. The results of gyrokinetic simulations with the global, electromagnetic, particle-in-cell code ORB5 are presented, where the modes are driven unstable by energetic particles with a bump-on-tail equilibrium distribution function, with radial density gradient. Two regimes have been observed: at low energetic particles concentration, the Alfvén mode saturates at much higher level in presence of zonal structures; on the other hand at high energetic particles concentration the difference is less pronounced. The former regime is characterized by the zonal structure (identified as an energetic particle driven geodesic acoustic mode), being more unstable than the Alfvén mode. In the latter regime the Alfvén mode is more unstable than the zonal structure. The theoretical explanation is given in terms of a 3-wave coupling of the energetic particle driven geodesic acoustic mode and Alfvén mode, mediated by the curvature-pressure coupling term of the energetic particles.

physics.plasm-ph↗

arXiv2020

Global linear and nonlinear gyrokinetic modelling of Alfvén eigenmodes in ITER

Linear and nonlinear modelling of Alfvénic instabilities, most notably toroidal Alfvén eigenmodes (TAEs), obtained by using the global nonlinear electromagnetic gyrokinetic model of the code ORB5 are presented for the 15 MA scenario of the ITER tokamak. Linear simulations show that elliptic Alfvén eigenmodes and odd-parity TAEs are only weakly damped but not excited by alpha particles, whose drive favours even-parity TAEs. Low mode number TAEs are found to be global, requiring global treatment. Nonlinearly, even with double the nominal EP density, single mode simulations lead to saturation with negligible EP transport however multi-mode simulations predict that with double the nominal EP density, enhanced saturation and significant EP redistribution will occur.

physics.plasm-ph↗

arXiv2020

Gyrokinetic investigation of Alfvén instabilities in the presence of turbulence

The nonlinear dynamics of beta-induced Alfvén Eigenmodes (BAE) driven by energetic particles (EP) in the presence of ion-temperature-gradient (ITG) turbulence is investigated, by means of selfconsistent global gyrokinetic simulations and analytical theory. A tokamak magnetic equilibrium with large aspect ratio and reversed shear is considered. A previous study of this configuration has shown that the electron species plays an important role in determining the nonlinear saturation level of a BAE in the absence of turbulence [A. Biancalani, et al., J. Plasma Phys. (2020)]. Here, we extend the study to a turbulent plasma. The EPs are found modify the heat fluxes by introducing energy at the large spatial scales, mainly at the toroidal mode number of the dominant BAE and its harmonics. In this regime, BAEs are found to carry a strong electron heat flux. The feed-back of the global relaxation of the temperature profiles induced by the BAE, and on the turbulence dynamics, is also discussed.

physics.plasm-ph↗

arXiv2020

Development and testing of an unstructured mesh method for whole plasma gyrokinetic simulations in realistic tokamak geometry

In this work, we have formulated and implemented a mixed unstructured mesh-based finite element (FE)-Fourier decomposition scheme for gyrokinetic simulations in realistic tokamak geometry. An efficient particle positioning (particle-triangle mapping) scheme for the charge deposition and field scattering using an intermediate grid as the search index for triangles has been implemented and a significant speed-up by a factor of $\sim30$ is observed as compared with the brute force scheme for a medium-size simulation. The TRIMEG (TRIangular MEsh based Gyrokinetic) code has been developed. As an application, the ion temperature gradient (ITG) mode is simulated using the simplified gyrokinetic Vlasov-Poisson model. Our simulation and that using the ORB5 code for the DIII-D Cyclone case show reasonable agreement. As an additional application, ITG simulations using an ASDEX Upgrade equilibrium have been performed with density and temperature gradient profiles similar to the Cyclone case. Capabilities of the TRIMEG code for simulations with realistic experimental equilibria in the plasma core and in the whole plasma volume with open field lines are demonstrated.

physics.plasm-ph↗

arXiv2020

Nonlinear gyrokinetic PIC simulations in stellarators with the code EUTERPE

In this work, the first nonlinear particle-in-cell simulations carried out in a stellarator with the global gyrokinetic code EUTERPE using realistic plasma parameters are reported. Several studies are conducted with the aim of enabling reliable nonlinear simulations in stellarators with this code. First, EUTERPE is benchmarked against ORB5 in both linear and nonlinear settings in a tokamak configuration. Next, the use of noise control and stabilization tools, a Krook-type collision operator, markers weight smoothing and heating sources is investigated. It is studied in detail how these tools influence the linear growth rate of instabilities in both tokamak and stellarator geometries and their influence on the linear zonal flow evolution in a stellarator. Then, it is studied how these tools allow improving the quality of the results in a set of nonlinear simulations of electrostatic turbulence in a stellarator configuration. Finally, these tools are applied to a W7-X magnetic configuration using experimental plasma parameters.

physics.plasm-ph↗

arXiv2020

Nonlinear dynamics of energetic-particle driven geodesic acoustic modes in ASDEX Upgrade

Turbulence in tokamaks generates radially sheared zonal flows. Their oscillatory counterparts, geodesic acoustic modes (GAMs), appear due to the action of the magnetic field curvature. The GAMs can be driven unstable by an anisotropic energetic particle (EP) population leading to the formation of global radial structures, called EGAMs. The EGAMs can redistribute EP energy to the bulk plasma through collisionless wave-particle interaction. In such a way, the EGAMs might contribute to the plasma heating. Thus, investigation of EGAM properties, especially in the velocity space, is necessary for precise understanding of the transport phenomena in tokamak plasmas. In this work, the nonlinear dynamics of EGAMs without considering the mode interaction with the turbulence is investigated with the help of a Mode-Particle-Resonance (MPR) diagnostic implemented in the global gyrokinetic particle-in-cell code ORB5. An ASDEX Upgrade discharge is chosen as a reference case for this investigation due to its rich EP nonlinear dynamics. An experimentally relevant magnetic field configuration, thermal species profiles and an EP density profile are taken for EGAM chirping modelling and its comparison with available empirical data. The same magnetic configuration is used to explore energy transfer by the mode from the energetic particles to the thermal plasma including kinetic electron effects. For a given EGAM level the plasma heating by the mode can be significantly enhanced by varying the EP parameters. Electron dynamics decreases the EGAM saturation amplitude and consequently reduces the plasma heating, even though the mode transfers its energy to thermal ions much more than to electrons.

physics.plasm-ph↗

arXiv2019

Gyrokinetic investigation of Alfvén instabilities in the presence of turbulence

The global and electromagnetic gyrokinetic particle-in-cell code ORB5 is employed to investigate the self-consistent interactions between Alfvén modes (AM) and ion temperature gradient (ITG) turbulence in a magnetically confined plasma. Here, an axisymmetric magnetic equilibrium with reversed shear and large aspect ratio is considered. An AM with toroidal mode number n=5 is driven unstable by introducing a population of suprathermal ions. Once the AM saturates in the presence of the fully developed turbulence, the ion heat flux is dominated by the AM and its main harmonics. ITG-induced transport is found to also be enhanced in the presence of the unstable AM.

physics.plasm-ph↗

arXiv2019

Effect of the electron redistribution on the nonlinear saturation of Alfvén eigenmodes and the excitation of zonal flows

Numerical simulations of Alfvén modes (AM) driven by energetic particles are performed with the GK global PIC code ORB5. A reversed shear equilibrium magnetic field is adopted. A simplified configuration with circular flux surfaces and large aspect ratio is considered. The nonlinear saturation of beta-induced Alfvén eigenmodes (BAE) is investigated. The roles of the wave-particle nonlinearity of the different species, i.e. thermal ions, electrons, and energetic ions are described, in particular for their role in the saturation of the BAE and the generation of zonal flows. The nonlinear redistribution of the electron population is found to be important in increasing the BAE saturation level and the zonal flow amplitude.

physics.plasm-ph↗