The auroras in the polar sky are not only a beautiful consequence of cosmic particles interacting with the Earths magnetosphere. They are also an indicator that astrophysical objects like our planet can have large scale magnetic fields. It is more standard to consider the gravitational interaction at astrophysical length-scales. However, the complex dynamic inside planets and stars can lead to the generation of large scale magnetic field. The dynamo theory is able to give an insight on the mechanism behind this phenomenon. The underlying idea is that turbulent motion in the inner core of some planets and stars can couple with small scale magnetic fields to generate a large scale magnetic fields.
At the heart of todays solar magnetic field evolution models lies the α-dynamo description. α-dynamos are based on the mechanism that velocity fields and magnetic fields of small wave-number can interact and generate a large scale magnetic field. The analysis of the α-effect has vastly been studied in what is called the diffusive regime. The dimensionless parameter used to define the diffusive regime is called the magnetic Reynolds number : Rm = U l /η (U, l and η are the rms velocity, the length scale and the magnetic diffusity respectively). Even though the α-effect is well understood in the low Rm diffusive regime, a clear description of the effect at high Rm is still an open question.
In order to understand the dynamics happening at large Rm, massive simulations modeling the α-effect have been carried out using mean field theories. However, this mean field approximation leads to some contradictions when looking at simplified models. Using Floquet theory, we are able to prove that even in the simplified case of kinematic dynamos, the α-effect does not follow all of the mean field predictions especially as the Rm crosses the small scale dynamo threshold. My presentation will retrace the state of the art on the domain, discuss the existing models and present the recent results published in Fate of Alpha Dynamos at Large Rm, Alexandre Cameron and Alexandros Alexakis, PRL.