Dynamo action in turbulent accretion discs around black holes – I. The fluctuations

The magnetic field in a turbulent accretion disc is decomposed into large-scale, mean and microscale, fluctuating fields. It is shown that a rather strong, mean magnetic field can be generated by turbulent dynamo action on time-scales of order $M^{-2}_t\enspace t_\text k$ in the small Mach number regime $M_\text t\ll 1$. Magnetic fluctuations much more energetic than the mean magnetic field will occur and will ultimately draw their energy from the turbulence. When the mean field is of strength $B_\text c^2/8\pi = (3/4)c_\text u M_\text t^2 P$, where $c_\text u\lesssim 1/2$ and P is the gas pressure, the magnetic fluctuations shut down the turbulence altogether. An explicit expression for the Maxwell stress, arising from these intense fluctuations, is given.