Mean-field dynamo as a quantumlike modulational instability

Abstract: Presented here is a novel formulation of the mean-field dynamo as a modulational instability of magnetohydrodynamic (MHD) turbulence. This formulation, termed mean-field wave kinetics (MFWK), is based on the Weyl symbol calculus and allows describing the interaction between the mean fields (magnetic field and fluid velocity) and turbulence without requiring scale separation that is commonly assumed in literature. The turbulence is described by the Wigner--Moyal equation for the spectrum of the two-point correlation matrix (Wigner matrix) of magnetic-field and velocity fluctuations and depicts the turbulence as an effective plasma of quantumlike particles that interact via the mean fields. Eddy--eddy interactions, which serve as `collisions' in this effective plasma, are modeled within the standard minimal tau approximation to aid comparison with existing theories. Using MFWK, the nonlocal electromotive force is calculated for generic turbulence from first principles, modulo the limitations of MFWK. This result is then used to study, both analytically and numerically, the modulational modes of MHD turbulence, which appear as linear instabilities of said effective quantumlike plasma of fluctuations. The standard $\alpha^2$-dynamo and other known results are reproduced as a special cases. A new dynamo effect is predicted that is driven by correlations between the turbulent flow velocity and the turbulent current.