The Double Beltrami model of coronal mass ejections
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Coronal mass ejections (CMEs) are the most powerful events on the Sun and have important effects on Earth (geomagnetic storms), but their initiation is still not well understood. I show that the general class of Double Beltrami states, which are the lowest energy equilibria of Hall magnetohydrodynamics, can have characteristics similar to those of CME source regions in the solar corona and are capable of undergoing a catastrophe that can supply enough kinetic energy to create a CME. I then compare this Double Beltrami model of CMEs with observations. First, I show that the qualitative evolution of the DB state is consistent with that of a CME. Second, I carry out a detailed quantitative study of the expansion of the field during the quasi-equilibrium stage leading up to the catastrophe using LASCO C1 CME data, confirming the model prediction of an expansion of a factor of 1-2 in the height of the CME leading edge before major acceleration begins. Finally, I use the assumption that DB states are randomly chosen from the allowed phase space of coronal structures to predict the CME rate from the rate at which DB states appear. Taking each active region as having a corresponding DB state and using observational constraints to estimate that the state is replaced every 60 minutes by emerging loops results in a CME rate of 19.5 per day, which is in reasonable agreement with the actual rate of 6 per day at solar maximum (systematic uncertainties may be responsible for the differences that do exist). Future work for the dissertation will involve improvements leading up to a full simulation of the DB model including heat transfer, and the application of the model to stars and accretion disks.