The Helimak transport dynamics: low dimensional chaos or coloured noise?

• Main Author: K. Rypdal
• Other Authors: The Pennsylvania State University CiteSeerX Archives
• Format: Text
• Language: English
• Subjects: Norway; Tromsø
• Online Access: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.501.9592; http://epsppd.epfl.ch/Roma/pdf/D5_021.pdf

9037 Tromsø, Norway Recent theoretical developments indicate that the cross-field transport in the Helimak config-uration is mediated by electrostatic flute structures with a fixed perpendicular wave-length [2] and can be modeled as a low-dimensional dynamical system; in the simplest formulation as the Lorenz equations in the diffusionless limit [3]. We investigate this question by analyzing time series of electric potential fluctuations from the edge of the Blaamann device operated in the helimak configuration. Since we work with experimental data, we use time-delay embedding theorem by [1] in an attempt to reconstruct the phase space of an hypothesised low-dymensional dynamical system. Here we transform our scalar data into m-dimensional vectors: xi = (x(ti),x(ti + τ),.,x(ti +(m−1)τ)) , (1) where i=1,.,N and τ is an appropriate time lag. Since the dynamics in the core plasma is mostly influenced by unstable flute convective cells, we analyse edge fluctuations, which reflect the fluctuations in the ensuing anomalous plasma flux. For this purpose we employ the Singular Value Decomposition (SVD) analysis as described in [4]. We present some of the results for the first SVD component, denoted as V1, and the second SVD component, denoted as V2, since they reveal different underlying dynamics. The auto-correlation functions of the V1 and V2 components shown in Fig.1 reveal that the decorrelation time for the V1 component (see Fig. 1b) is larger than the decorrelation time for the V2 component (see Fig. 1a). The standard method for determining the attractor dimension of a dynamical system from a time series of one of its components is the Grassberger-Procaccia (G-P) algorithm [5]. By using this algorithm for the embedding dimensions 2 < m < 7 and time lag τ = 20, we found that the V2 component converges to a correlation dimension of D ≈ 2.5 (see Fig. 2a). On the other hand, the correlation dimension for the V1 component does not converge for 2 < m < 7. It is known, however, that the G-P algorithm can give ...