MHD relaxation of fossil magnetic fields in stellar interiors

The understanding of fossil fields origin, topology, and stability is one of the corner stones of the stellar magnetism theory. On one hand, since they survive on secular time scales, they may modify the structure and the evolution of their host stars. On the other hand, they must have a complex stable structure since it has been demonstrated that the simplest purely poloidal or toroidal fields are unstable on dynamical time scales. In this context, the only stable stellar configurations found today are those resulting from numerical simulations by Braithwaite and collaborators who studied the evolution of an initial stochastic magnetic field, which relaxes with a selective decay of magnetic helicity and energy, on mixed stable configurations (poloidal and toroidal) that seem to be in equilibrium and then diffuse. In this talk, we report the semi-analytical investigation of such an equilibrium field in the axisymmetric case. We use variational methods, which describe selective decay of magnetic helicity and energy during MHD relaxation, and we identify a supplementary invariant due to the stable stratification of stellar radiation zones. This leads to states that generalize force-free Taylor's relaxation states studied in plasma laboratory experiments that become non force-free in the stellar case. Moreover, astrophysical applications are presented and the stability of obtained configurations is studied.

Self-organization, anomalous resistance and anomalous heating in magnetized plasmas

The nonlinear dynamics and structure of plasmas with tightly twisted magnetic field lines have been studied using a toroidal plasma device. Stepwise magnetohydrodynamic (MHD) relaxation occurs, resulting in a discontinuous change in the pitch of magnetic field lines. This discrete nature of the pitch stems from the instability of kink (torsional) modes. The MHD relaxation stabilizes kink modes by selecting (self-organizing) appropriate pitches. The self-organized state displays the characteristic of a ‘dissipative structure’ in that it is accompanied by enhanced energy dissipation; the global resistance of the plasma current is substantially enhanced. The magnetic energy, which is generated by the internal plasma current, first changes into fluctuation energy through the kink instability, and then it goes mainly to ion thermal energy through viscous dissipation of the fluctuating flow. The viscosity dissipates the fluctuation energy with conservation of helicity. The self-organization of the stabilized magnetic field is characterized by the preferential conservation of the helicity.