A. Biancalani

Kinetic structures of shear Alfvén and acoustic wave spectra in burning plasmas

We present a general theoretical framework for discussing the physics of low frequency fluctuation spectra of shear Alfven and acoustic waves in toroidal plasmas of fusion interest. This framework helps identifying the relevant dynamics and, thus, interpreting experimental observations. We also discuss the roles of such general theoretical framework for verification and validation of numerical simulation codes vs. analytic predictions and experimental results.

Experimental turbulence studies for gyro-kinetic code validation using advanced microwave diagnostics

For a comprehensive comparison with theoretical models and advanced numerical turbulence simulations, a large spectrum of fluctuation parameters was measured on the devices ASDEX Upgrade, TCV, and Tore-Supra. Radial profiles of scale-resolved turbulence levels in H-mode discharges are measured and compared with GENE simulations in the transition range from ion-temperature-gradient to trapped-electron-mode turbulence. Correlation reflectometry is used to study the microscopic structure of turbulence and GAMs in discharges where poloidal flow damping was varied by means of variations of the shape of the poloidal plasma cross-section and collisionality. Full-wave codes and synthetic diagnostics are applied for the interpretation of the data.

Numerical validation of the electromagnetic gyrokinetic code NEMORB on global axisymmetric modes

In this paper, we report on a comparison of collisionless simulations on global modes (i.e. low poloidal mode number) with the gyrokinetic particle-in-cell code NEMORB against analytical theory and the gyrokinetic semilagrangian code GYSELA. Only axisymmetric modes, i.e. with toroidal mode number n = 0, are considered, and flat equilibrium profiles. Benchmarks are performed for geodesic acoustic modes against local analytical theory. In the presence of energetic ions, benchmarks of NEMORB are performed against GYSELA. The models of adiabatic versus trapped-kinetic versus fully kinetic-electrons and of electrostatic versus electromagnetic at very low beta are compared. Scalings of Alfven modes are also presented.

Analytic dispersion relation of energetic particle driven geodesic acoustic modes and simulations with NEMORB

Recent progress regarding the excitation of energetic-particle driven geodesic acoustic modes (EGAMs) in particle-in-cell simulations is presented in this paper. The exact dispersion relation with adiabatic electrons is derived and solved. The origin of the so-called EGAM is briefly analysed and we show that its nature changes, at least, with the safety factor. A simple expression for the GAM frequency modified in the presence of a small concentration of energetic particles is given in the fluid limit. We show that gyrokinetic simulations with Nemorb in the presence of adiabatic electrons are able to reproduce the analytic predictions. Also, different energy channels are analysed by means of dedicated energy diagnostics characterizing the wave-particle interaction. Finite Larmor radius and finite orbit width effects are studied regarding the excitation of geodesic acoustic modes, showing that these effects are likely to be negligible for sufficiently high concentration of energetic particles, but significant when approaching the threshold of excitation.

Active Magnetic Experiment: a magnetic bubble in the ionospheric stream

A space plasma experiment is discussed which consists of a magnetized plasma bubble interacting with the ambient (ionospheric) plasma. The magnetized plasma inside the magnetized bubble is either tied to the dipole magnetic field generated inside the satellite or is inflated by a particle outflow from the satellite. The parameters of the bubble are discussed in relation to the parameters of the ambient plasma and the plasma regimes and phenomena that can be investigated are indicated.

2D continuous spectrum of shear Alfvén waves in the presence of a magnetic island

The radial structure of the continuous spectrum of shear Alfven modes is calculated in the presence of a magnetic island in tokamak plasmas. Modes with the same helicity as the magnetic island are considered in a slab model approximation. In this framework, with an appropriate rotation of the coordinates the problem reduces to two dimensions. Geometrical effects due to the shape of the flux surfaces cross-section are retained to all orders. On the other hand, we neglect toroidal couplings but fully take into account curvature effects responsible for the beta-induced gap in the low-frequency part of the continuous spectrum. New continuum accumulation points are found at the O-point of the magnetic island. The beta-induced Alfven eigenmodes (BAE) continuum accumulation point is found to be positioned at the separatrix flux surface. The most remarkable result is the modification of the BAE continuum accumulation point frequency, due to the presence of the magnetic island.

Comparison of experiment and models of geodesic acoustic mode frequency and amplitude geometric scaling in ASDEX Upgrade

In a set of dedicated ASDEX Upgrade shape-scan experiments, the influence of plasma geometry on the frequency and amplitude behaviour of the geodesic acoustic mode (GAM), measured by Doppler reflectometry, is studied. In both limiter and divertor configurations, the plasma elongation was varied between circular and highly elongated states (). Also, the edge safety factor was scanned between 3 < q < 5. The GAM frequency and amplitude are used to test several models (heuristic, fluid and gyrokinetic based), which incorporate various plasma geometry effects. The experimentally observed effect of decreasing with increasing κ is predicted by most models. Other geometric factors, such as inverse aspect ratio e and Shafranov shift gradient are also seen to be influential in determining a reliable lower boundary. The GAM amplitude is found to vary with boundary elongation and safety factor q. The collisional damping is compared to multiple models for the collisionless damping. Collisional damping appears to play a stronger role in the divertor configuration, while collisional and collisionless damping both may contribute to the GAM amplitude in the limiter configuration.

Linear gyrokinetic particle-in-cell simulations of Alfvén instabilities in tokamaks

The linear dynamics of Alfven modes in tokamaks is investigated here by means of the global gyrokineticparticle-in-cell code ORB5, within the NEMORB project. The model equations are shown and the local shear Alfven wave dispersion relation is derived, recovering the continuous spectrum in the incompressible ideal MHD limit. A verification and benchmark analysis is performed for continuum modes in a cylinder and for toroidicity-induced Alfven Eigenmodes. Modes in a reversed-shear equilibrium are also investigated, and the dependence of the spatial structure in the poloidal plane on the equilibrium parameters is described. In particular, a phase-shift in the poloidal angle is found to be present for modes whose frequency touches the continuum, whereas a radial symmetry is found to be characteristic of modes in the continuum gap.

Combined action of phase-mixing and Landau damping causing strong decay of geodesic acoustic modes

We report evidence of a new mechanism able to damp very efficiently geodesic acoustic mode (GAM) in the presence of a nonuniform temperature profile in a toroidally confined plasma. This represents a particular case of a general mechanism that we have found and that can be observed whenever the phase-mixing acts in the presence of a damping effect that depends on the wave number k r . Here, in particular, the combined effect of the Landau and continuum damping is found to quickly redistribute the GAM energy in phase-space, due to the synergy of the finite orbit width of the passing ions and the cascade in wave number given by the phase-mixing. This damping mechanism is investigated analytically and numerically by means of global gyrokinetic simulations. When realistic parameter values of plasmas at the edge of a tokamak are used, damping rates up to 2 orders of magnitude higher than the Landau damping alone are obtained. We find in particular that, for temperature and density profiles characteristic of the high confinement mode, the so-called H-mode, the GAM decay time becomes comparable to or lower than the nonlinear drive time, consistently with experimental observations (Conway G. D. et al., Phys. Rev. Lett. , 106 (2011) 065001).

Nonlinear interplay of Alfvén instabilities and energetic particles in tokamaks

The confinement of energetic particles (EP) is crucial for an efficient heating of tokamak plasmas. Plasma instabilities such as Alfven Eigenmodes (AE) can redistribute the EP population making the plasma heating less effective, and leading to additional loads on the walls. The nonlinear dynamics of toroidicity induced AE (TAE) is investigated by means of the global gyrokinetic particle-in-cell code ORB5, within the NEMORB project. The nonperturbative nonlinear interplay of TAEs and EP due to the wave-particle nonlinearity is studied. In particular, we focus on the nonlinear modification of the frequency, growth rate and radial structure of the TAE, depending on the evolution of the EP distribution in phase space. For the ITPA benchmark case, we find that the frequency increases when the growth rate decreases, and the mode shrinks radially. This nonlinear evolution is found to be correctly reproduced by means of a quasilinear model, namely a model where the linear effects of the nonlinearly modified EP distribution function are retained.