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

Abstract

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.

Relation between energetic and standard geodesic acoustic modes

“…Contrary to what was found in the q = 3 case, the threshold values found in the q = 2 case are similar whether FOW effects are taken into account (Ref. 21) or not (present model). This is consistent with Ref.…”

“…It is worth noting that the link between GAMs and EGAMs is thus different according to the value of the safety factor q: for q = 1.6, the EGAM originates from the GAM; while for q = 3, the GAM and the EGAM belong to different mode branches. The existence of two different kinds of EGAMs has also been shown numerically 21 with the gyrokinetic code NEMORB 22,23 .…”

“…The impacts of FLR/FOW effects on EGAMs, together with a detailed comparison of the analytic dispersion relation with gyrokinetic simulations, are analysed in Ref. 21.…”

“…As a matter of fact, simulations taking FOW effects into account made with the gyrokinetic code NEMORB, in the D-D case with parameters q = 2,ū = 2.8, τ k = 1 and T t /T e = 1, indicate 21 that the EGAM excitation threshold is reached at n k /n eq = 5%. With the present analytical model, we find for the same parameters a threshold of n k /n eq = 4%.…”

Implementation of energy transfer technique in ORB5 to study collisionless wave-particle interactions in phase-space

“…where n sp (ψ), T sp (ψ) are species density and temperature profiles along the radial coordinate ψ, which is the poloidal flux. A symmetric two-bumps-on-tail distribution function has been used in this work for the fast species 41,42 . This distribution assumes a flat temperature profile of the fast species:…”