The nonlinear dispersion relation of geodesic acoustic modes

The energy input and frequency shift of geodesic acoustic modes (GAMs) due to turbulence in tokamak edge plasmas are investigated in numerical two-fluid turbulence studies. Surprisingly, the turbulent GAM dispersion relation is qualitatively equivalent to the linear GAM dispersion but can have drastically enhanced group velocities. As a consequence radially broad (∼ cm) GAM eigenmodes may form. Those may lead to experimentally observable deviations from the expected scaling of the GAM frequency with the square root of the plasma temperature. In up-down asymmetric geometry, the energy input due to turbulent transport may favor the excitation of GAMs with one particular sign of the radial phase velocity relative to the magnetic drifts. Including the radial gradient of the GAM frequency may lead to periodic bursts of the GAM and the turbulence intensity.