  The nonlinear dynamics of energetic particle (EP) driven geodesic acoustic
modes (EGAM) in tokamaks is investigated, and compared with the beam-plasma
system (BPS). The EGAM is studied with the global gyrokinetic (GK)
particle-in-cell code ORB5, treating the thermal ions and EP (in this case,
fast ions) as GK and neglecting the kinetic effects of the electrons. The
wave-particle nonlinearity only is considered in the EGAM nonlinear dynamics.
The BPS is studied with a 1D code where the thermal plasma is treated as a
linear dielectric, and the EP (in this case, fast electrons) with an n-body
hamiltonian formulation. A one-to-one mapping between the EGAM and the BPS is
described. The focus is on understanding and predicting the EP redistribution
in phase space. We identify here two distint regimes for the mapping: in the
low-drive regime, the BPS mapping with the EGAM is found to be complete, and in
the high-drive regime, the EGAM dynamics and the BPS dynamics are found to
differ. The transition is described with the presence of a non-negligible
frequency chirping, which affects the EGAM but not the BPS, above the
identified drive threshold. The difference can be resolved by adding an ad-hoc
frequency modification to the BPS model. As a main result, the formula for the
prediction of the nonlinear width of the velocity redistribution around the
resonance velocity is provided.
