Global non-potential models of the solar corona

The solar corona is the source region of many different Earth-affecting phenomena that fall under the collective umbrella of space weather. Despite decades of research, the coronal magnetic field presents many open problems such as the origins of coronal mass ejections, the solar wind structure, or the Open Flux Problem. This thesis applies global non-potential modelling of the corona to investigate several such questions. First, the solar open flux is simulated over long periods of time with helicity condensation. The long-term photospheric magnetic field is modelled with observed Kitt Peak synoptic magnetograms, held fixed for the duration of each Carrington rotation. Helicity condensation contributes a solar cycle dependent enhancement to the open flux, reducing the discrepancy with observations by up to half. Secondly, the limitation of using synoptic magnetograms to model the global solar photosphere is investigated. Synthetic synoptic magnetograms are created using a procedure matching the production of observed synoptic magnetograms. Although potential field extrapolations from a reference model and the synthetic magnetograms are consistent, open flux estimates in non-potential models show that synthetic magnetogram simulations only produce half of the enhancement required to match the reference model. Thirdly, a detection algorithm for sheared arcade and flux rope eruptions is developed that classifies eruptions by the change in field line skew just above the photosphere. Flux rope eruptions outnumber sheared arcade eruptions four or five to one, and eruptions closely follow bipole emergence patterns. Helicity condensation and bipole self-helicity are shown to be positively-correlated with the geoeffectiveness of eruptions. Finally, a new grid for simulating the solar photosphere is introduced that partitions the global sphere into two complementary subdomains. The new grid matches the accuracy of high-resolution single grid simulations while reducing runtime by two orders of magnitude. Extending this grid to the corona promises high-precision, low-runtime global coronal modelling.