Critical phenomenon, crisis and transition to spatiotemporal chaos in plasmas

Abstract

In a driven/damped drift-wave system a steady wave induces nonlinear variation of the dispersion of a perturbation wave (PW). Competition between the nonlinear dispersion with self-nonlinearity of the PW results in rich wave dynamic behaviors. In particular, a steady wave at the negative tangency slope of a hysteresis becomes unstable due to a saddle instability. It is found that such saddle steady wave (SSW) plays an important role in the discontinuous transition from a spatially coherent state to spatiotemporal chaos (STC). The transition is caused by a crisis due to a collision of the PW attactor to an unstable orbit of the SSW. In the time evolution, it is a ‘pattern resonance’ of the realized wave with the virtual SSW that triggers the crisis. The transition also displays as a critical phenomenon in parameter space, which is related to the change in the symmetry property of the motion of master mode (k = 1) of the PW with respect to that of SSW. In the spatially coherent state the former is trapped by the SSW partial wave, while in the STC it can become free from the latter, its trajectory crosses two unstable orbits of the SSW frequently, causing very turbulent behavior.