We show in this paper that geodesic acoustic modes (GAMs) can be efficiently excited by a population of fast ions even when Landau damping on thermal ions is accounted for. We report in particular fully kinetic calculations of the GAM dispersion relation and its complete solution. Written under a variational form, the quasi-neutrality condition, together with the kinetic Vlasov equation, leads to the density of exchanged energy between particles and the mode. In particular, a linear threshold for the GAMs excitation is derived. Two examples of fast ion distribution have been discussed analytically. It turns out that particles with high perpendicular energy compared to the parallel resonance energy are most responsible for the excitation of the mode. Subsequent numerical simulations of circular plasmas using GYSELA code have been carried out. In particular, the linear kinetic threshold has been reproduced during the excitation phase, and a nonlinear saturation has been observed. Analysis in the phase space of the evolution of the equilibrium distribution function is presented and the saturation level quantified.

Abstract

This paper addresses non-linear gyrokinetic simulations of ion temperature gradient (ITG) turbulence in tokamak plasmas. The electrostatic Gysela code is one of the few international 5D gyrokinetic codes able to perform global, full-f and flux-driven simulations. Its has also the numerical originality of being based on a semi-Lagrangian (SL) method. This reference paper for the Gysela code presents a complete description of its multi-ion species version including: (i) numerical scheme, (ii) high level of parallelism up to 500k cores and (iii) conservation law properties.

The impact on turbulent transport of geodesic acoustic modes excited by energetic particles is evidenced for the first time in flux-driven 5D gyrokinetic simulations using the Gysela code. Energetic geodesic acoustic modes (EGAMs) are excited in a regime with a transport barrier in the outer radial region. The interaction between EGAMs and turbulence is such that turbulent transport can be enhanced in the presence of EGAMs, with the subsequent destruction of the transport barrier. This scenario could be particularly critical in those plasmas, such as burning plasmas, exhibiting a rich population of suprathermal particles capable of exciting energetic modes.Understanding turbulent transport is crucial in numerous plasma physics frameworks, ranging from plasma laboratories such as nuclear fusion devices 1 to astrophysical systems such as the solar tachocline 2 or the atmospheres 3 . In this letter, we focus on the turbulent transport in toroidal nuclear fusion devices (tokamaks), where accurate predictions are essential on the route towards the steady-state production of energy. Together with turbulence, energetic particles (EPs) constitute a ubiquitous component of current and future tokamaks, due to both nuclear reactions and heating systems. EPs are characterized by energies larger than the thermal energy. Whereas the impact of turbulence on EP transport has been analyzed and found to be weak 4 , the effect of EPs on turbulence has not been much studied so far (see e.g. Ref. 5) and represents the aim of our study. This analysis is done via the excitation by EPs of a class of modes naturally existing in tokamaks: the geodesic acoustic modes (GAMs) 6 , which are the oscillatory component of large scale E × B zonal flows. The EP-driven GAMs are called EGAMs. These modes have been predicted theoretically 7,8 , observed experimentally 9,10 and reported very recently numerically in the absence of turbulence 11 in gyrokinetic simulations with the 5D Gysela code 12 . The motivation of the present work relies upon fluid simulations where the turbulence level was controlled by GAMs in the core/edge transitional regime 13 . In addition, experimental evidence of the role of GAMs in the edgeturbulence suppression has been reported for the first time during the analysis of the L-H transition in the AS-DEX Upgrade tokamak 14 . However, in the context of core-turbulence suppression, the role of GAMs is less evident for several reasons. First, these modes are Landau damped in the core plasma. Second, since they are nonlinearly generated by turbulence, their external control a) Electronic mail:david.zarzoso-fernandez@polytechnique.org; Current address: Max-Planck-Institut für Plasmaphysik, EU-RATOM Association, Boltzmannstr. 2, Garching D-85748, Germany has proven difficult. Last, their frequency ω GAM is close to the characteristic turbulence frequency ω turb , which means that the shearing rate provided by GAMs might be large compared to the autocorrelation time. In that respect, theoretical predictions of the shearing effect ...

Abstract. 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.

Geodesic Acoustic Modes (GAMs) are electrostatic, axisymmetric modes which are non-linearly excited by turbulence. They can also be excited linearly by fast-particles; they are then called Energetic-particle-driven GAMs (EGAMs). Do GAMs and EGAMs belong to the same mode branch? Through a linear, analytical model, in which the fast particles are represented by a Maxwellian bump-on-tail distribution function, we find that the answer depends on several parameters. For low values of the safety factor q and for high values of the fast ion energy, the EGAM originates from the GAM. On the contrary, for high values of q and for low values of the fast ion energy, the GAM is not the mode which becomes unstable when fast particles are added: the EGAM then originates from a distinct mode, which is strongly damped in the absence of fast particles. The impact of other parameters is further explored: ratio of the ion temperature to the electron temperature, width of the fast particle distribution, mass and charge of the fast ions. The ratio between the EGAM and the GAM frequencies was found in experiments (DIII-D) and in non-linear numerical simulations (code GYSELA) to be close to 1/2: the present analytical study allows one to recover this ratio.

This paper compares the confinement in JET low and high triangularity hybrid and baseline ELMy H-mode regimes in a large database of 112 plasmas and identifies the location and source for the enhanced confinement factors in the hybrid plasmas. JET hybrid plasmas feature enhanced performance, and typically have b N~2 .5-3, H 98 < 1.5 compared to baseline H-mode plasmas, which typically have b N~1 .5-2, H 98 ~1. The higher global pressure achieved in hybrid plasmas is obtained through a tight coupling of the core and pedestal pressures. The confinement in hybrid plasmas is therefore strongly linked to the obtainable pedestal confinement. A comparison of the EPED1 predictive pedestal model with the experimental pedestal pressures shows good agreement of the model predictions with the measured data, offering a possible explanation for the tight link between global and pedestal pressure through the stabilising effect of high b on the pedestal MHD stability. The electron kinetic profiles do not show a net profile peaking of the electron pressure, although the electron density and temperature show respectively decreasing and increasing trends with collisionality. Hence the confinement benefit from the electron profile peaking as reported in previous studies [most recently in M. Maslov et al., Nucl. Fusion 49] is not confirmed by the current study. Both low and high triangularity hybrid plasmas feature T i /T e > 1 across the entire profile leading to a confinement benefit through the ions. Additional performance is obtained in the low triangularity hybrid plasmas through increased ion temperature profile peaking at low collisionality.

This is a report about a comparison of collisionless simulations on global modes (i.e. low poloidal mode number) with gyrokinetic code NEMORB against analytical theory and other codes. Only axisymmetric modes, i.e. with toroidal mode number n=0, are considered, and flat equilibrium profiles. Benchmarks are performed for GAMs against local analytical theory. In the presence of energetic ions, local benchmarks of NEMORB are performed against semilagrangian gyrokinetic code GYSELA. The models of adiabatic vs trapped-kinetic-vs fully-kinetic-electrons and of electrostatic vs electromagnetic at very low beta are compared. Scalings of Alfvén modes are also presented.