Nonlinear Dynamics of Linearly Unstable n = 0 Electrostatic Perturbations in Conventional Tokamak Plasmas

The nonlinear dynamics of axisymmetric radially localized oscillations of the electric potential in a tokamak with stationary toroidal plasma rotation is studied. In the linear approximation, these oscillations split into two independent branches: geodesic acoustic modes (GAMs) and low-frequency zonal flows (ZFs). The stability of the latter is determined by the specifics of the plasma equilibrium, and the frequency/growth rate is determined by the stationary rotation velocity. It is shown that the nonlinear dynamics of the electric potential and the associated fluctuations of pressure, density, and velocity of the plasma along the magnetic field within the MHD model have integrals of motion. The evolution of the electric potential and hydrodynamic characteristics of the plasma is calculated for different velocities of stationary plasma rotation and different initial perturbations of the electric field. The regime the initial stage of which corresponds to a linearly unstable ZF is studied in detail. It is shown that, at the nonlinear stage, the potential fluctuations reach amplitude-limited oscillations of both low frequency and GAM. The resulting oscillation spectrum exhibits GAM frequency splitting and intermittency.