Curvature and folding dynamo effects in turbulent plasmas and ABC flux tubes

Abstract

Investigation of the eigenvalue spectra of dynamo solutions, has been proved fundamental for the knowledge of dynamo physics. Earlier, curvature-folding relation on dynamos in Riemannian spaces has been investigated [PPL 2008]. Here, analytical solutions representing general turbulent dynamo filaments are obtained in resistive plasmas. Turbulent diffusivity with vanishing kinetic helicity yields a fast mode for a steady dynamo eigenvalue. The magnetic field lays down on a local frame 2 plane along the filaments embedded in a 3D plasma. Curvature effects plays the role of folding in fast magnetic dynamos. In the present examples, plasma equipartition between normal and binormal components of the magnetic field components is considered. In the opposite case, oscillatory, purely imaginary, branches of the spectrum are found in dynamo manifold. Degenerate eigenvalues, are obtained when the dynamo growth rate coincides with the filaments curvature. Spectra of dynamo obtained are similar to the fast dynamo solution obtained by Arnold on a compact torus. Dynamo experiments making use of this kind of solution have been investigated by Shukurov et al [Phys Rev E, 2008] with Perm liquid sodium experiments on a circular torus implications. Another example of dynamo plasma is given by the Arnold-Beltrami-Childress [ABC] twisted magnetic flux tubes with stagnation points.