On deterministic nature of the intermittent geodesic acoustic mode observed in L- mode discharge near tokamak edge, Part I Zonal flow driven by ion temperature gradient turbulence

Through a carefully designed numerical experiment, we demonstrate that a transition between two distinct phases of energy concentration in a zonal flow-drift wave system (caviton and instanton) may play a key role in the intermittent excitation of geodesic acoustic mode (GAM) that are observed in tokamaks. The two energy structures - the caviton, a slowly breathing spatial local structure of negative energy, and the instanton, a fine radial structure of short lifetime in rapid propagation, were recently identified in [Y. Z. Zhang, Z. Y. Liu, T. Xie, S. M. Mahajan, and J. Liu, Physics of Plasmas 24, 122304 (2017)]; the preceding work is based on the micro-turbulence associated with ion temperature gradient (ITG) mode, and slab-based phenomenological model of zonal flow. When toroidal effect are introduced into the system, two branches of zonal flow emerge: the torus-modified low frequency zonal flow (TLFZF), and GAM, necessitating a unified exploration of GAM and TLFZF. Indeed, we observe that the transition (decay) from the caviton to instanton is triggered by a rapid zero-crossing of radial group velocity of drift wave and is found to be strongly correlated with the GAM onset; it happens if and only if the intensity of TLFZF is above a certain level. Many features peculiar to intermittent GAMs, observed in real machines, are thus identified in the numerical experiment; the results will be displayed in figures and in a movie. Since one cannot make a foolproof case that the experimentally observed zonal flows must originate in ITG driven micro-turbulence (Appendix A), we have also explored the possibility that this phenomenon could be caused by electron drift waves, instead; the latter will make part II of this work.