Radial propagation of geodesic acoustic modes in up-down asymmetric magnetic geometries

The energy approach to the analysis of the propagation of geodesic acoustic modes presented in the work of Hager and Hallatschek [Phys. Plasmas 16, 072503 (2009)] is generalized to up-down asymmetric magnetic geometries including a model for single-null configuration. By removing the neoclassical cancellation effects, up-down asymmetry can trigger a nonvanishing group velocity at zero radial wavenumber. A theoretical insight in this effect is provided by analytical calculations combined with numerical gyrokinetic and two-fluid studies. Thereby, an useful estimate of the group velocity at zero radial wavenumber is derived within a two-fluid framework.