Alignment and Structure in MHD Dynamos

Abstract

Magnetic fields are ubiquitous within astrophysical settings. There is strong evidence to suggest that some of these magnetic fields, for example the Sun’s, are maintained through a dynamo process whereby energy is exchanged between a flow and a magnetic field. Magnetohydrodynamics (MHD) is the branch of mathematics where this interaction is studied. The initial amplification of a weak seed field is often modelled using the kinematic dynamo approximation where the flow is not influenced by the magnetic field. This approximation to the early behaviour of a nonlinear dynamo problem, where the magnetic field grows exponentially during a kinematic phase and then saturates into a nonlinear regime, has the benefit of being far less computationally intensive.In this thesis, I examine three different topics within MHD dynamos. First, I examine how measuring alignment of the flow and magnetic field during a kinematic dynamo can reveal changes to the magnetic field structure. This I show to be useful both within individual simulations and when comparing magnetic fields within parameter studies. Secondly, I examine nonlinear dynamos where the flow and magnetic field are strongly aligned and have almost identical energies. I reproduce, and give an explanation for, a previously unexplained behaviour. Furthermore, I show that aligned flow and magnetic fields can exist for increasingly complex forcings and as such the aligned state is remark-ably robust. Finally, I consider a number of different nonlinear dynamos for a family of forcings with different magnetic field structures during their kinematic phase. Using Minkowski Functions to quantify the structures, I show that, where the magnetic field becomes sufficiently strong, the magnetic fields become (or remain) ribbon-like in the nonlinear regime. As such, the influence that stagnation points in the flow have on the magnetic field structure is less than in the kinematic dynamo equivalent.