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

Abstract

Turbulence in tokamaks generates radially sheared zonal flows (ZFs). Their oscillatory counterparts, geodesic acoustic modes (GAMs), appear due to the action of the magnetic field curvature. The GAMs can also be driven unstable by an anisotropic energetic particle (EP) population leading to the formation of global radial structures, called EGAMs. The EGAMs might play the role of an intermediate agent between the EPs and thermal plasma, by redistributing 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 is investigated with the help of a Mode-Particle-Resonance (MPR) diagnostic recently implemented in the global gyrokinetic (GK) particle-in-cell code ORB5. This enables to investigate the relative importance and the evolution of the resonances responsible for the ion and electron Landau damping, and of the EP drive. An ASDEX Upgrade discharge is chosen as a reference case for this investigation due to its rich EP nonlinear dynamics.

Linear dispersion relation of geodesic acoustic modes driven by trapped and circulating energetic particles

“…When the thermal ion Landau damping is taken into account (Zarzoso et al 2012) the excitation of the mode is possible when the energetic particle (EP) drive exceeds the damping (Biancalani et al 2017a). Through the ion Landau damping, EGAMs become a channel for redirection of the EP beam energy into thermal energy of the bulk (Sasaki, Itoh & Itoh 2011;Novikau et al 2020). The nonlinear dynamics and mode saturation due to redistribution of particles in velocity space (Biancalani et al 2017a;Zarzoso et al 2012) have also been studied, as well as the non-adiabatic chirping due to particle trapping (Biancalani et al 2017a).…”

“…Through the ion Landau damping, EGAMs become a channel for redirection of the EP beam energy into thermal energy of the bulk (Sasaki, Itoh & Itoh 2011; Novikau et al. 2020). The nonlinear dynamics and mode saturation due to redistribution of particles in velocity space (Biancalani et al.…”

Gyrokinetic modelling of anisotropic energetic particle driven instabilities in tokamak plasmas

“…[15] in reference to experimental observations in Large Helical Device [16]. The mechanism of wave-particle energy exchange works with opposite contributions for EPs (giving energy to the mode, exciting it) and thermal ions (absorbing energy from it, damping it), therefore EGAMs are shown to be an effective means to transfer energy from high energy species to colder ones [9,17]. Experimental evidence showed that EGAM's frequency is about 50% of the usual GAM frequency [10].…”

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

“…The equilibrium quasi neutrality is fulfilled by keeping constant the radial electron density profile and varying the EPs concentration, together with the deuterium concentration, satisfying: n e = i Z i n i (being n the density profile of the i-th species). The bulk plasma species (electrons and deuterium) have Maxwellian distribution functions, while the EPs have a double bump-on-tail distribution function (as in [23], [24], [29], [34]), because an anisotropy in velocity is needed to drive unstable EGAMs, [15]:…”