Geodesic modes driven by untrapped resonances of NB energetic ions in tokamaks

Abstract

Geodesic modes are typically excited by a minor concentration of energetic ions, but unstable mode frequencies are substantially different from Geodesic Acoustic Modes (GAMs) and are named EGAM (Energetic particle GAM). The EGAM instability driven by Neutral Beam Injection (NBI) has been observed in DIII-D tokamak experiments. The problem of the geodesic mode instability is analytically studied using a full drift kinetic equation. To analyze the instability condition, an ionization NBI location is assumed to be on the high field side of tokamaks. A minority NBI ion distribution is modeled by an energetic ion tail in the untrapped-passing region that remains between a magnetic axis and the trapped NBI boundary. The EGAM instability condition is defined by the parallel NBI ion velocity v||≈(1.2−1.5)ωR0q0 that has to be above the effective EGAM phase velocity. In this case, the EGAM frequency is ≈50% below the standard stable GAM frequency, which is reduced by a small concentration of energetic NBI ions. Qualitative comparison of the developed geodesic mode theory with NBI heating experiments in the midregion of the tokamak plasma is discussed.

Geodesic acoustic modes in magnetic confinement devices

“…A general expression for the EP response including passing and trapped particles was given in [45], but the specific influence of trapped particles was not studied. Elfimov has considered the effects of EP and GAM destabilization in the analytical theory by integrating the DKE over the exact ion trajectories using the Jacobi function representation for trapped and passing particles [202][203][204]. The instability criteria was determined for a specific EP distribution which has a maximum at the trapped and un-trapped boundary and with high energy tail of several hundred keV.…”

“…Another result here [202,203] is the modification of the neoclassical polarization factor by the EPs. Using a similar approach, Elfimov [204] also considers the EGAMs destabilization due to un-trapped resonances of NB energetic ions with v (1.2-1.5)ωR 0 q. Such EGAMs have a maximum growth rate in the frequency range near the slowing-down transit frequency, cf [198].…”

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

“…2006; Lakhin & Sorokina 2014; Qu et al. 2017; de Souza, Elfimov & Galvão 2018; Elfimov, Galvão & Gorelenkov 2019). The method applied to a real case scenario, with simulated profiles explaining the frequency and marginal stability point of oscillation during ramp-up discharges, with quantitative experimental correlation.…”