Verification of Energetic-Particle-Induced Geodesic Acoustic Mode in Gyrokinetic Particle Simulations

Abstract

The energetic-particle-induced geodesic acoustic mode (EGAM) is studied using gyrokinetic particle simulations in tokamak plasmas. In our simulations, exponentially growing EGAMs are excited by energetic particles with a slowing-down distribution. The frequencies of EGAMs are always below the frequencies of GAMs, which is due to the non-perturbative contribution of energetic particles (EPs). The mode structures of EGAMs are similar to the corresponding mode structures of GAMs. Our gyrokinetic simulations show that a high EP density can enhance the EGAM growth rate, due to high EP free energy, and that EPs' temperature and the pitch angle of the distribution modify the EGAM frequency/growth rate by means of the resonance condition. Kinetic effects of the thermal electrons barely change the EGAM frequency, and have a weak damping effect on the EGAM. Benchmarks between the gyrokinetic particle simulations and a local EGAM dispersion relation exhibit good agreement in terms of EGAM frequency and growth rate.

Energetic particle-induced geodesic acoustic modes on DIII-D

“…The amplitude of the perturbation for this shot is an order of magnitude lower than the inferred electric field perturbation in [5,6]. Despite the limited radial resolution, the electrostatic potential perturbation, obtained by the radial integration of the electric field perturbation, qualitatively agrees with the results shown in reference [33]. The internally peaked nature of the eigenfunction contrasts with typical GAMs [1] and supports identification of the instability as the EP mode found in numerous simulations such as [4,25,32,50].…”

“…For example, the simulations in [30] show clear examples of the appearance of both types of modes in the complex frequency plane with increasing fast-ion density. Fu [4] found a neutral-beam driven EP mode GAM branch with a frequency ∼60% of the GAM frequency; subsequent simulations [31][32][33] obtained similar results. Several properties of the DIII-D data presented in section 5 indicate that the unstable DIII-D mode is the EP branch.…”

Description of global EGAM in the maximum of local frequency during current ramp-up discharges in DIII-D

“…From the imaginary part of the dispersion relation, the linear growth rate can be calculated as , with , leading to where the first term represents the drive given by the EP, which decreases with larger , similar to numerical calculation (Chen et al. 2020) for , while the second term represents the thermal ion Landau damping. It follows from that a necessary condition for instability () is for and it increases up to for , where the additional contribution from the energetic particles easily overcome the Landal damping from thermal ions.…”

Electromagnetic formulations for GTC simulation

“…For energetic particle, we need to consider the particle source term in equilibrium Vlasov equation, and the steady-state slowing-down distribution can be chosen to model f 0EP [14,15],…”