  The nonlinear dynamics of energetic-particle (EP) driven geodesic acoustic
modes (EGAM) is investigated here. A numerical analysis with the global
gyrokinetic particle-in-cell code ORB5 is performed, and the results are
interpreted with the analytical theory, in close comparison with the theory of
the beam-plasma instability. Only axisymmetric modes are considered, with a
nonlinear dynamics determined by wave-particle interaction. Quadratic scalings
of the saturated electric field with respect to the linear growth rate are
found for the case of interest. The EP bounce frequency is calculated as a
function of the EGAM frequency, and shown not to depend on the value of the
bulk temperature. Near the saturation, we observe a transition from adiabatic
to non-adiabatic dynamics, i.e., the frequency chirping rate becomes comparable
to the resonant EP bounce frequency. The numerical analysis is performed here
with electrostatic simulations with circular flux surfaces, and kinetic effects
of the electrons are neglected.
