Destabilization of geodesic acoustic-like mode in the presence of a poloidally inhomogeneous heat sources in tokamak plasmas

The effects of poloidally inhomogeneous heat sources are investigated through a gyrokinetic formula in collisionless toroidal plasmas. The gyrokinetic dispersion relation is newly derived assuming that equilibrium parallel heat flows are generated to remove the injected poloidally nonuniform heat source. The dispersion relation is numerically solved using both inboard and outboard heat sources. For the inboard source injection, both Stringer spin-up (SSU) and geodesic acoustic mode (GAM) can be driven. For the case of outboard source injection, a heat source-driven geodesic acoustic mode (so-called, Q-GAM) is newly found, which features a frequency around half of the standard GAM frequency. It originates from a strongly damped Landau pole when there is no source injection. However, once the heat source intensity is larger than a certain threshold, it becomes unstable while maintaining its frequency. The parametric dependencies of the Q-GAM frequency and source threshold are carried out, and an empirical equation for the source, the threshold is also derived. The Q-GAM frequency is similar to that of EGAM driven by the energetic particles because the main driving terms have the similar structures in poloidal, radial, and parallel velocity coordinates, giving the similar response function of the perturbed parallel pressure to the potential.