Resonant amplification of zonal flow driven by the negative mass instability in tokamak plasma

We investigate the formation of Bernstein-Greene-Kruskal-type E×B staircase equilibrium in the presence of energetic ions. We show that such staircase solutions, which display crucial kinetic features and which propagate like coherent electrostatic structures, represent saturated states of negative mass instability. An energy transfer from these staircase structures and zonal flows takes place, which becomes resonant in the presence of a global phase synchronization process. This zonal flow amplification occurs as a bifurcation process and leads to the formation of an internal transport barrier, which is crucial for suppressing ion-temperature-gradient turbulence. We discuss numerical experiments in support of this scenario, which have been performed with a reduced model (referred to as "particle-mode" model) based on a double gyro-average over both the fast cyclotron phase and the bounce (or transit) phases.