Fully kinetic description of the linear excitation and nonlinear saturation of fast-ion-driven geodesic acoustic mode instability

Abstract

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.

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

“…A shifted Maxwellian distribution function in parallel velocity is adopted as distribution function for EP. The dispersion relation derived in this framework leads to the well-known frequency of GAMs in the limit of no energetic particles [11,5]. Second, we show results of numerical simulations of EGAMs performed with NEMORB, in the framework of an electrostatic linear collisionless model with electrons treated adiabatically, and verify that the code gives the expected results when going towards the analytic limit.…”

“…[5] to obtain the kinetic dispersion relation in the long wavelength limit, namely k ⊥ ρ i ≪ 1, where k ⊥ is the perpendicular wave vector of the mode and ρ i is the ion Larmor radius. With respect to the calculations of Ref.…”

“…With respect to the calculations of Ref. [5], energetic particles are included and modelled by a double shifted Maxwellian …”

“…The EGAMs are axisymmetric modes and therefore driven mainly by the positiveness of the slope of the distribution function of ions at a certain position in velocity space, namely at v = qRω EGAM [5]. This is the reason why EGAMs must be described kinetically.…”

“…The excitation of geodesic acoustic modes by energetic particles (EGAMs) has been predicted analytically [1,2] and observed in both experiments [3,4] and simulations [5]. There has been an increasing interest in these modes mainly due to the rather optimistic possibility of using them as an external knob to suppress turbulence [3].…”