Generalized magnetic helicity, large-scale magnetic field, and dynamo saturation

Dynamo effect allows the creation of large-scale magnetic fields through a purely mechanical driving. The efficiency of the process is much higher if the driving is helical. This effect has long been postulated to saturate when the self-generated large-scale magnetic field grows above a certain threshold. On the other hand, some numerical results show an apparent suppression of the dynamo effect in the presence of a strong, large-scale, externally supported magnetic field. Here, it is shown that the overall behavior in these extreme cases, as well as in intermediate cases, can be understood in terms of: (i) conservation of a generalized form of magnetic helicity; and (ii) a proper separation of scales. These results lend additional perspective to the sometimes difficult issue of the relationship between the physics of externally supported and locally supported mean magnetic fields. In particular, it is shown that: (a) the externally supported component has a predominant role in quenching dynamo action; (b) the electromotive force tends to be aligned to the sum of both components, that is to the total large-scale magnetic field.