Magnetic Fields in Proto-Neutron Stars and in Accretion Discs Around Neutron Stars

Themain characters of this thesis are themagnetic field, the plasma velocity field, the turbulentmagnetic resistivity and the numerical codes. They act on two different stages and on two different levels and occasionaly there are other bit players, e.g. the α-effect, the quenching, the differential rotation, themagnetic streamfunction, themagnetic Reynolds number, the Interactive Data Language and even ZEUS. All of them are led by the same invisible hand with the purpose of understanding better the intricate topic of the magnetic field - plasma relation. The two stages of the scene could not be more different, in one case everything is done in less than a minute inside a proto-neutron star soon after a supernova explosion, in the other case there is no time evolution at all and an equilibrium configuration is looked for inside a disc ofmatter spiraling around a neutron star. Nevertheless the same set of equations can describe the behaviour of the characters on both stages, this set is composed of the equations of the electromagnetic field plus the fluid equations. However knowing that the answers to all of your questions are written inside only one book, does not mean that you are able to read that book ... It is at this moment that the numerical codes come into the scene, offering you a way of translating the book in a language that you know. Unfortunately they like playing tricks and you cannot trust their translations unless you take many precautions every time. Eventually, after the equations have been solved, comes the art of interpreting the results; a task that might seem quite simple in comparison with the difficulties overcome on the path to get there, but that requires a deep knowledge of what has already been done and a good intuition about what can possibly happen later on. We do not presume to have made big leaps forward in the process of understanding the behaviour of the magnetic field in the cases considered here, nonetheless thanks to our simplified models we were able to grasp the fundamental aspects of the phenomena being considered, to gain some insights and to propose new falsifiable ideas. At the same time we have also developed new tools for making our models more elaborate and realistic. Therefore we expect to find even more characters in the future Chapters of this analysis, but that is another story, and will be told another time.