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

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) ω R 0 q 0 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.