Cio-cio-san no Yūutsu: memoirs of magnetogenesis and Turbulent Dynamo Theory

Master Thesis


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University of Cape Town

The origins of cosmic magnetic fields are not as yet well understood. In this dissertation we investigate, via direct numerical simulation, the temporal evolution and behaviour of magnetic fields that are generated from absolute zero initial conditions via a thermal battery term in the Induction Equations (i.e. the Magnetogenesis problem), whilst making use of the Ideal- and Chaplygin Gas equations of state, in turn, to model the relationship between pressure and density. The dependence of the onset of dynamo action on various values of the magnetic Reynolds- and Prandtl numbers for the cases of the Roberts Flow kinematic dynamo and a flow that, in turn, incorporates both a non-helical and helical forcing function that introduces turbulence into the system is also considered via direct numerical simulation. For the purposes of the simulation work conducted, we make use of the PENCIL CODE, which is a high-order finite-difference Magnetohydrodynamical code capable of performing simulation runs in parallel using the Message Passing Interface (MPI) system for parallel processing. Theoretical results relevant to the simulations conducted are partially recovered and discussed in detail. These include, and are not limited to, the emergence of the thermal battery term in the General Ohm's Law as a consequence of the two-fluid approximation of a plasma, derivation of the Induction Equations incorporating the aforementioned battery term, introduction and discussion of the Chaplygin Gas and its place in the field of Cosmology, energetics governing the flow of kinetic- and magnetic energy during the dynamo process, the Zel'dovich stretch-twist-fold dynamo as an example of both a fast dynamo and a cornerstone underlying the operation of all dynamos and, finally, the Kazantsev Theory for small-scale, turbulent dynamos. For our magnetogenesis simulations, it is found that the magnetic fields produced undergo two distinct growth phases (the first, classified as an initial """"upshoot"""" that is possibly due to the battery term and the second, classified as an exponential growth phase), as well as two distinct phases of decay in strength, which is attributed to the effects of magnetic diffusion. This behaviour is observed for fields generated using both the Ideal- and Chaplygin Gas equations of state in turn and it is noted that the Chaplygin Gas equation of state produces magnetic fields that are of comparable strength to those produced by the Ideal Gas equation of state. Dynamo action simulations confirm the existence of a critical magnetic Reynolds number, beyond which, an initial prescribed magnetic field will grow exponentially in strength. In the case of the forced turbulence simulations, it is noted that the use of a helical forcing function greatly lowers the value of the critical magnetic Reynolds number required for the onset of guaranteed dynamo action and also produces stronger magnetic fields when compared to University of Cape Town the cases that used a non-helical forcing function. In both cases of the forced turbulence, the magnetic field is observed to saturate when its kinematic (i.e. exponential growth) phase is complete, provided that the magnetic Reynolds number is above the aforementioned critical threshold. Results of the magnetogenesis simulations are also investigated for dynamo action, and it is concluded that a type of """"kinematic dynamo"""" phase was most probably present when these fields underwent the observed phase of exponential growth.