Bifurcation Theory of the Transition to Collisionless Ion-temperature-gradient-driven Plasma Turbulence
Authors: R.A. Kolesnikov and J.A. Krommes
Date of PPPL Report: September 2005
Published in: Physics of Plasmas 12, 122302 (Dec 2005) 25 pp.
The collisionless limit of the transition to ion-temperature-gradient-driven plasma turbulence is considered with a dynamical-systems approach. The importance of systematic analysis for understanding the differences in the bifurcations and dynamics of linearly damped and undamped systems is emphasized. A model with ten degrees of freedom is studied as a concrete example. A four-dimensional center manifold (CM) is analyzed, and fixed points of its dynamics are identified and used to predict a "Dimits shift" of the threshold for turbulence due to the excitation of zonal flows. The exact value of that shift in terms of physical parameters is established for the model; the effects of higher-order truncations on the dynamics are noted. Multiple-scale analysis of the CM equations is used to discuss possible effects of modulational instability on scenarios for the transition to turbulence in both collisional and collisionless cases.