Magnetic filamentary structures in the spectrum of kinematic dynamos in plasmas June 8 , 2009

Kinney et al [PPL 1,(1994)] have investigated plasma filamentary structure dynamics. More recently, Wilkin et al [Phys Rev Lett 99:134501,(2007)] have shown that kinetic energy spectrum of magnetic structures in small-scale dynamos, are predominantly fila-mentary. Kirilov et al [PRE (2009)] have shown that use of the boundary values of the mean-field isotropic helical turbulent α 2-dynamo, could determine the morphology of dynamo instability. In this paper, filamentary Frenet frame in diffusive media, displays the existence of kinematic chaotic dynamo in 3D Euclidean space E 3. In 2D, either no dynamo action spectrum is found, in agreement with Cowling anti-dynamo theorem, or slow dynamos [PPL 15,(2008)]. Curvature and diffusion effects are encodded in the matrix representation of α 2-dynamo operator. Instead of principal scalar curvatures κ 1 and κ 2 of the surface of structures, only one scalar curvature κ is needed to determine dynamos spectra. Filament thickness, increases with scalar curvature, as happens in solar physics.