Study on the large scale dynamo transition

Using the magnetohydrodynamic (MHD) description, we develop a nonlinear dynamo model that couples the evolution of the large scale magnetic field with turbulent dynamics of the plasma at small scale by electromotive force (e.m.f.) in the induction equation at large scale. The nonlinear behavior of the plasma at small scale is described by using a MHD shell model for velocity field and magnetic field fluctuations.The shell model allow to study this problem in a large parameter regime which characterizes the dynamo phenomenon in many natural systems and which is beyond the power of supercomputers at today. Under specific conditions of the plasma turbulent state, the field fluctuations at small scales are able to trigger the dynamo instability. We study this transition considering the stability curve which shows a strong decrease in the critical magnetic Reynolds number for increasing inverse magnetic Prandlt number $textrm{Pm}^{-1}$ in the range $[10^{-6},1]$ and slows an increase in the range $[1,10^{8}]$. We also obtain hysteretic behavior across the dynamo boundary reveling the subcritical nature of this transition. The system, undergoing this transition, can reach different dynamo regimes, depending on Reynolds numbers of the plasma flow. This shows the critical role that the turbulence plays in the dynamo phenomenon. In particular the model is able to reproduce the dynamical situation in which the large-scale magnetic field jumps between two states which represent the opposite polarities of the magnetic field, reproducing the magnetic reversals as observed in geomagnetic dynamo and in the VKS experiments.