The Nonlinear α ‐ Ω Dynamo

The kinematic dynamo is limited by “alpha‐quenching”, in which the local accumulation of magnetic helicity in small scale structures turns off the dynamo process well before the large scale field reaches equipartition with the small scale turbulence. In disk systems the shearing of the radial component of the magnetic field allows continued algebraic growth, albeit with steadily decreasing radial domain sizes. Continued exponential growth, and saturation at more realistic levels, depends on the small scale magnetic helicity current. I will discuss how this works for α ‐ Ω dynamos, concentrating in particular on systems where the turbulence is driven by the magnetorotational instability, so that the small scale turbulence and the large scale magnetic energy density are always close to equipartition. This leads to strong large scale magnetic fields in accretion disks, and possibly in galactic disks as well.