Nonlinear dynamics of geodesic-acoustic-mode packets

The dynamics of finite-amplitude, undamped geodesic-acoustic-mode (GAM) packets is shown to be well described by a nonlinear Schrodinger equation. The GAM is supposed to be generated through an appropriate initial perturbation, and its coupling with other possible modes in the plasma is disregarded. However, the nonlinear modifications of the dispersion properties of the plasma due to the GAM itself are retained. A theoretical approach based on the variational method is shown to compare successfully with the nonlinear particle-in-cell simulations. Typical nonlinear phenomena, as known, e.g., from nonlinear optics, like nonlinear phase shift, nonlinear phase-front shape, and wave breaking are analyzed. Depending on the electron-to-ion temperature ratio and hence on the dispersion regime (normal or anomalous), synergy or competition between dispersive and nonlinear packet broadening takes place. In the latter regime, the existence of "GAM solitons " is reported.