Dynamo action with flow shear and magnetic shear

Dynamo action is a fundamental mechanism that explains ubiquitous magnetic fields in a variety of systems, including astrophysical, geophysical and laboratory plasmas. In this contribution, we provide an analytical theory of dynamo ($\alpha$ and $\beta$ effects) in 3D forced helical MHD turbulence [1]. By non-perturbatively incorporating the effect of shear, we show that the $\alpha$ and $\beta$ effects are enhanced by a weak shear while strongly suppressed by strong shear. In particular, for strong shear, the $\beta$ effect is shown to be much more strongly suppressed than the $\alpha$ effect with the scalings $\alpha \propto A^{-5/3}$ and $\beta \propto A^{-7/3}$, respectively ($A$ is the strength of the shear). The quenching of the $\alpha$ and $\beta$ effect by shear has recently been confirmed in a numerical experiment [2]. One of the interesting implications of these results is that the dynamo efficiency, conventionally measured by the dynamo number $D$, depends more strongly on the shear than conventionally assumed. Specifically, $D$ scales as $A^{4}$ rather than $A$. Incorporating a shear in the magnetic field, we then discuss its effect on the stability. Magnetic shear is shown to destabilize when it is stronger than flow shear. On the other hand, a weak magnetic shear compared to flow shear weakens the stabilizing effect of flow shear, thereby leading to a stronger turbulence than in the case without magnetic shear. \\[0pt] [1] N. Leprovost and E. Kim, Astrophys J Lett. v696, L125 (2009); Phys. Rev. Lett., v100, 144502 (2008) \\[0pt] [2] D. Mitra et al, Astron \& Astrophys, v495, 1 (2009)