Random Attractors and ELMs

In order to predict ELM scaling to larger devices and to design a control system it is important to be able to distinguish between different low dimensional models for Type I ELMs. We consider the possibility that the ELMs are influenced by noise from the tokamak core. The first step in nonlinear time series analysisis is to distinguish a linear stochastic system from a nonlinear deterministic system. We have constructed a second order nonlinear system with noise that contributes in a fundamental way, causing the system to occupy a region of its state space far from any attractor of the underlying deterministic system, and this phrandom attractor behaves much like a chaotic deterministic attractor. This type of behavior, which is nonlinear but involves stochasticity in a fundamental way, appears not to have been observed in previous nonlinear dynamical studies. For this system, the dynamics consists of a series of large localized bursts separated by quiescent time intervals, and both the burst amplitudes and intervals appear to be chaotic, similar to ELMs in tokamaks. We have found that there is a strong nonlinear correlation between the burst amplitudes and the succeeding time intervals, but the time intervals are decorrelated from the succeeding burst amplitudes. We will show experimental results from a nonlinear circuit having some of these characteristics.