Growth rate distribution and intermittency in kinematic turbulent dynamos : which moment predicts the dynamo onset?

We consider the generation of magnetic field by a turbulent flow. For the linear induction equation (i.e. the kinematic dynamo problem), we show that the statistical moments of the magnetic field display multiscaling and in particular moments of different order turn unstable for different values of the control parameter. On a canonical example, we map the problem onto the calculation of the injected power by a time correlated fluctuating force acting on a Brownian particle. We are then able to calculate analytically the growth rate of the moments of the magnetic field and explain the origin of this intermittency. We finally show that the onset for the nonlinear problem is predicted by the linear onset of the moment of order 0 + (i.e. the logarithm of the magnetic field)