Relation between energetic and standard geodesic acoustic modes

Abstract

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.

Modelling third harmonic ion cyclotron acceleration of deuterium beams for JET fusion product studies experiments

“…In particular, NBI+ICRH accelerated ions are found to have a strong stabilizing effect. However, sawtooth crashes still occur, especially due to tornado modes induced by fast ions [54]. This sawtooth stabilization by fast ions is a major issue for ITER, which should have significant population of fusion-born alpha particles.…”

“…The study reported here, fully detailed in [54], aims at demonstrating the stabilization effect of third harmonic NBI+ICRH heated deuterium ions within the Porcelli model [55]. This model assumes that a sawtooth remains stable as long as the potential energy functional δŴ is positive:…”

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

“…This model would allow one to explain some features of energetic modes observed in experiments, such as the modification of the frequency. This model is also suitable to analyse the nature of the energetic-particle driven GAM with respect to the standard GAM [15] and for verification of gyrokinetic codes when the distribution function departs from a Maxwellian. It also allows us to provide a simple expression of the GAM frequency modified by energetic particles in the fluid limit.…”

“…The interested reader is encouraged to go through Ref. [15], where the theoretical dispersion relation is fully exploited in that direction, showing clearly the link between the energetic and the standard geodesic acoustic modes. Why the nature changes depending on the safety factor could be qualitatively explained by considering that the resonance occurs at the transit frequency, namely ω t = v /qR ≈ v res /qR, where v res is the velocity of particles having a higher free energy from the point of view of the interaction with the mode, i.e.…”

Geodesic acoustic modes in a fluid model of tokamak plasma: the effects of finite beta and collisionality

“…They are usually classified as an m = n = 0 perturbation in potential coupled with an m = 1, n = 0 perturbation in density or pressure, where m and n are the poloidal and the toroidal mode numbers respectively. GAMs are linearly damped unless fast particles are present [5][6][7][8][9][10][11]. Otherwise they are excited by nonlinear processes like turbulent reynolds stresses [12][13][14][15][16][17][18], poloidally asymmetric particle fluxes [19] and heat fluxes [20].…”