Strange Attractors in Drift Wave Turbulence
Author: Jerome L.V. Lewandowski
Date of PPPL Report: September 2003
Published in: the Canadian Journal of Physics 81: 1331-1341 (2003)
There are growing experimental, numerical and theoretical evidences that the anomalous transport observed in tokamaks and stellarators is caused by slow, drift-type modes (such as trapped electron modes and ion-temperature gradient-driven modes). Although typical collision frequencies in hot, magnetized fusion plasmas can be quite low in absolute values, collisional effects are nevertheless important since they act as dissipative sinks. As it is well known, dissipative systems with many (strictly speaking more than two) degrees of freedom are often chaotic and may evolve towards a so-called attractor.
This paper shows that strange attractors in collisional, electrostatic drift wave turbulence with kinetic electrons can exist and that their fractal dimension are actually quite small; this result suggests the presence of deterministic dynamics with few key variables but displaying chaotic behavior (because of the fractal dimensionality of the attractor). Another important conclusion is that our observation of a low-dimensional attractor for this specific model of drift wave turbulence has been achieved using an accurate scheme for kinetic electrons (splitting scheme). In the presence of kinetic electrons, standard schemes (e.g., df scheme) fail to resolve the underlying dynamics of the system, that is the fractal dimension cannot be measured.