The linear properties of the geodesic acoustic modes (GAM) in tokamaks are investigated by means of the comparison of analytical theory and gyrokinetic numerical simulations. The dependence on the value of the safety factor, finite-orbit-width of the ions in relation to the radial mode width, magnetic-flux-surface shaping, and electron/ion mass ratio are considered. Nonuniformities in the plasma profiles (such as density, temperature, or safety factor), electro-magnetic effects, collisions and presence of minority species are neglected. Also, only linear simulations are considered, focusing on the local dynamics. We use three different gyrokinetic codes: the lagrangian (particle-in-cell) code ORB5, the eulerian code GENE and semi-lagrangian code GYSELA. One of the main aims of this paper is to provide a detailed comparison of the numerical results and analytical theory, in the regimes where this is possible. This helps understanding better the behavior of the linear GAM dynamics in these different regimes, the behavior of the codes, which is crucial in the view of a future work where more physics is present, and the regimes of validity of each specific analytical dispersion relation. 1 theories derived so far treat the m = 0 component of the electrons as adiabatic (whereas the m=0 component of the electron density perturbation is imposed to zero). We will refer to this model for treating the electrons as "adiabatic". The importance of having an analytical description is twofold. On the one hand, it allows a direct understanding of the physical mechanisms leading to the each different effect under investigation. On the other hand, it allows a detailed linear verification process of the numerical tools, which is at the basis of the development of gyrokinetic codes aimed at a rigorous turbulence investigation.Many numerical investigations of the linear GAM dynamics and comparison with analytical theory or benchmark among codes have been carried out in the last few decades, most of which treating the electrons as adiabatic. As a non-extensive list of example, we mention here simulations performed with the gyrokinetic codes GTC [20,21], ORB5 [22] (where the effect of the elongation was studied), TEMPEST [16] (where the effect of high-order terms of the finite ion orbit width was studied), GYRO [23] (where the effect of finite orbit width and the application to the radial velocity in the large-q limit was studied), GYSELA [24], ELMFIRE [25], and GENE with GKW [26]. In particular, a first verification of ORB5 against analytical theories, for circular geometries and low values of k r ρ i , was started in Ref. [27]. A numerical study of the effect of kinetic electrons in circular plasmas has been described in Ref. [28].In this paper, we aim at performing a comprehensive cross-code verification and benchmark of several gyrokinetic codes, in different regimes. We perform numerical simulations with three different gyrokinetic codes, adopting equivalent physical models for the dynamics of the ions (which is the most basic ...

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 (1.1 < κ < 1.8). Also, the edge safety factor was scanned between 3 < q < 5. The GAM frequency ω GAM 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 ω GAM with increasing κ is predicted by most models. Other geometric factors, such as inverse aspect ratio and Shafranov shift gradient ∆ are also seen to be influential in determining a reliable lower ω GAM boundary. The GAM amplitude is found to vary with boundary elongation κ b 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.

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 kr. 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 phasemixing. 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.

For electricity producing tokamak fusion reactors like EU-DEMO, it is prudent to choose a plasma scenario close to the ITER baseline, where the largest amount of experimental evidence is available. Nevertheless, there are some aspects in which ITER and EU-DEMO have to differ, as the simple exercise of up-scaling from ITER to a larger device is constrained both by physical nonlinearities and by technological limits. In this work, relevant differences between ITER and the current EU-DEMO baseline in terms of plasma scenario are discussed. Firstly, EU-DEMO is assumed to operate with a very large amount of radiative power originating both from the scrape-off layer and, markedly, from the core. This radiation level is obtained by means of seeded impurities, whose presence significantly affects many aspects of the scenario itself, especially in terms of transient control. Secondly, because of the need of breeding tritium, the EU-DEMO wall is less robust than the ITER one. This implies that every offnormal interruption of the plasma discharge, for example in presence of a divertor reattachment, cannot rely on fastshutdown procedures finally triggering a loss of plasma control at high current, but other strategies need to be developed. Thirdly, the ITER method for the control of the so-called sawteeth (ST) has been shown to be too expensive in terms of auxiliary power requirements, thus other solutions have to be explored. Finally, the problem of actively mitigating, or suppressing, the Edge Localised Modes (ELMs) has recently increased the interest on naturally ELM-free regimes (like QH-mode, I-mode, and also negative triangularity) for EU-DEMO, thus increasing the needs for ELM mitigation or suppression with respect to the approach adopted in ITER.