Stretching magnetic fields by dynamo plasmas in Riemannian knotted tubes

Abstract

Recently Shukurov et al [Phys Rev E 72, 025302 (2008)], made use of non-orthogonal curvilinear coordinate system on a dynamo Moebius strip flow, to investigate the effect of stretching by a turbulent liquid sodium flow. In plasma physics, Chui and Moffatt [Proc Roy Soc A 451,609,(1995)] (CM), considered non-orthogonal coordinates to investigate knotted magnetic flux tube Riemann metric. Here it is shown that, in the unstretching knotted tubes, dynamo action cannot be supported. Turbulence there, is generated by suddenly braking of torus rotation. Here, use of CM metric, shows that stretching of magnetic knots, by ideal plasmas, may support dynamo action. Investigation on the stretching in plasma dynamos, showed that in diffusive media [Phys Plasma \textbf{15},122106,(2008)], unstretching unknotted tubes do not support fast dynamo action. Non-orthogonal coordinates in flux tubes of non-constant circular section, of positive growth rate, leads to tube shrinking to a constant value. As tube shrinks, curvature grows enhancing dynamo action.