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A. Biancalani

Publications and source records attributed to A. Biancalani.

At least 19 recordsLinked to original sources

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

Frequency Chirping of Energetic-Particle-Driven Geodesic Acoustic Modes in Tokamaks

A suprathermal population of ions is present in tokamak plasmas due to external heating mechanisms and fusion reactions. These energetic particles (EPs) can drive waves unstable, via inverse Landau damping. An example is the energetic-particle-induced geodesic acoustic mode (EGAMs). In this work, investigate the nonlinear dynamics of EGAMs by means of global gyrokinetic simulations with the particle-in-cell code ORB5. In particular, we study the nonlinear evolution of the frequency, known as "frequency chirping". To investigate the underlying phase-space dynamics, Phase Space Zonal Structure (PSZS) diagnostics are employed. By identifying the resonance energy from the phase-space distribution and reconstructing the corresponding mode frequency, an independent estimate of the frequency evolution is obtained. The reconstructed frequencies show good agreement with those extracted directly from continuous wavelet transform analysis of the electric-field signal, establishing a direct correspondence between observable frequency chirping and the nonlinear evolution of resonant energetic particles in phase space.

physics.plasm-ph

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

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

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

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

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

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

Phase and amplitude evolution in the network of triadic interactions of the Hasegawa-Wakatani system

Hasegawa-Wakatani system, commonly used as a toy model of dissipative drift waves in fusion devices is revisited with considerations of phase and amplitude dynamics of its triadic interactions. It is observed that a single resonant triad can saturate via three way phase locking where the phase differences between dominant modes converge to constant values as individual phases increase in time. This allows the system to have approximately constant amplitude solutions. Non-resonant triads show similar behavior only when one of its legs is a zonal wave number. However when an additional triad, which is a reflection of the original one with respect to the $y$ axis is included, the behavior of the resulting triad pair is shown to be more complex. In particular, it is found that triads involving small radial wave numbers (large scale zonal flows) end up transferring their energy to the subdominant mode which keeps growing exponentially, while those involving larger radial wave numbers (small scale zonal flows) tend to find steady chaotic or limit cycle states (or decay to zero). In order to study the dynamics in a connected network of triads, a network formulation is considered including a pump mode, and a number of zonal and non-zonal subdominant modes as a dynamical system. It was observed that the zonal modes become clearly dominant only when a large number of triads are connected. When the zonal flow becomes dominant as a 'collective mean field', individual interactions between modes become less important, which is consistent with the inhomogeneous wave-kinetic picture. Finally, the results of direct numerical simulation is discussed for the same parameters and various forms of the order parameter are computed. It is observed that nonlinear phase dynamics results in a flattening of the large scale phase velocity as a function of scale in direct numerical simulations.

nlin.CD

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

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

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

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

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

Gyrokinetic investigation of the damping channels of Alfvén modes in ASDEX Upgrade

The linear destabilization and nonlinear saturation of energetic-particle driven Alfvénic instabilities in tokamaks strongly depend on the damping channels. In this work, the collisionless damping mechanisms of Alfvénic modes are investigated within a gyrokinetic framework, by means of global simulations with the particle-in-cell code ORB5, and compared with the eigenvalue code LIGKA and reduced models. In particular, the continuum damping and the Landau damping (of ions and electrons) are considered. The electron Landau damping is found to be dominant on the ion Landau damping for experimentally relevant cases. As an application, the linear and nonlinear dynamics of toroidicity induced Alfvén eigenmodes and energetic-particle driven modes in ASDEX Upgrade is investigated theoretically and compared with experimental measurements.

physics.plasm-ph

ORB5: a global electromagnetic gyrokinetic code using the PIC approach in toroidal geometry

This paper presents the current state of the global gyrokinetic code ORB5 as an update of the previous reference [Jolliet et al., Comp. Phys. Commun. 177 409 (2007)]. The ORB5 code solves the electromagnetic Vlasov-Maxwell system of equations using a PIC scheme and also includes collisions and strong flows. The code assumes multiple gyrokinetic ion species at all wavelengths for the polarization density and drift-kinetic electrons. Variants of the physical model can be selected for electrons such as assuming an adiabatic response or a ``hybrid'' model in which passing electrons are assumed adiabatic and trapped electrons are drift-kinetic. A Fourier filter as well as various control variates and noise reduction techniques enable simulations with good signal-to-noise ratios at a limited numerical cost. They are completed with different momentum and zonal flow-conserving heat sources allowing for temperature-gradient and flux-driven simulations. The code, which runs on both CPUs and GPUs, is well benchmarked against other similar codes and analytical predictions, and shows good scalability up to thousands of nodes.

physics.plasm-ph

Electromagnetic turbulence suppression by energetic particle driven modes

In recent years, a strong reduction of plasma turbulence in the presence of energetic particles has been reported in a number of magnetic confinement experiments and corresponding gyrokinetic simulations. While highly relevant to performance predictions for burning plasmas, an explanation for this primarily nonlinear effect has remained elusive so far. A thorough analysis finds that linearly marginally stable energetic particle driven modes are excited nonlinearly, depleting the energy content of the turbulence and acting as an additional catalyst for energy transfer to zonal modes (the dominant turbulence saturation channel). Respective signatures are found in a number of simulations for different JET and ASDEX Upgrade discharges with reduced transport levels attributed to energetic ion effects.

physics.plasm-ph

Nonlinear velocity redistribution caused by energetic-particle-driven geodesic acoustic modes, mapped with the beam-plasma system

The nonlinear dynamics of energetic particle (EP) driven geodesic acoustic modes (EGAM) in tokamaks is investigated, and compared with the beam-plasma system (BPS). The EGAM is studied with the global gyrokinetic (GK) particle-in-cell code ORB5, treating the thermal ions and EP (in this case, fast ions) as GK and neglecting the kinetic effects of the electrons. The wave-particle nonlinearity only is considered in the EGAM nonlinear dynamics. The BPS is studied with a 1D code where the thermal plasma is treated as a linear dielectric, and the EP (in this case, fast electrons) with an n-body hamiltonian formulation. A one-to-one mapping between the EGAM and the BPS is described. The focus is on understanding and predicting the EP redistribution in phase space. We identify here two distint regimes for the mapping: in the low-drive regime, the BPS mapping with the EGAM is found to be complete, and in the high-drive regime, the EGAM dynamics and the BPS dynamics are found to differ. The transition is described with the presence of a non-negligible frequency chirping, which affects the EGAM but not the BPS, above the identified drive threshold. The difference can be resolved by adding an ad-hoc frequency modification to the BPS model. As a main result, the formula for the prediction of the nonlinear width of the velocity redistribution around the resonance velocity is provided.

physics.plasm-ph