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In the second test simulation, two bipolar active regions are inserted along the equator with no over- lying polar field. These regions were emerged such that the polarities allow a similar coronal field set up to that of the breakout model, but now with all of the magnetic flux originated within the active regions. Figure 3.5 shows an image of the radial surface field showing the initial set up of the simu- lation, where two bipolar active regions emerge along the equator. The orientation of the polarities is such that the orientation of the bipoles is the same in each case. Figure 3.6 shows an orthographic plot, viewed from the south pole region, showing field lines plotted throughout the corona. This shows that the coronal field topology is similar to that of the breakout model.

Two different tests are then carried out in order to calculate the height at which the orientation of the field lines change over the central region of the flux (taken atθ = 90◦,φ = 180◦) and at which radial height the location of the coronal null occurred. The first simulation involves holding the size of the inner polarities constant and increasing the size of the outer polarity from a peak strength of 1 Gauss

Figure 3.5: Image showing the radial surface field distribution in the second test simulation. Two magnetic bipoles have been inserted along the equator with zero tilt angle. This is a setup similar to the surface configuration of the breakout model as it is also a quadrapolar field configuration. In the image red indicates positive flux and blue indicates negative flux.

up to 200 Gauss. The second simulation involves holding the strength of the outer polarities constant and varying the peak strength of the inner polarities from 1 to 200 Gauss. Figure 3.7 shows a plot of the height of the field reversal within the simulation, demonstrating the location of the null points. The dotted line indicates the height change when the strength of the outer polarities is held constant, the solid line indicates the height change when the inner polarities strength is held constant. In these simulations, the non changing bipole is held constant at a strength of approximately 20 Gauss. Clearly both simulations produce different, but expected, behaviour within the magnetic field. When the size of the outer bipole is held constant and the inner bipole is very weak, the overlying field from the outer bipole restricts the field from the inner bipole from reaching out into the solar corona. This means that the height of the change in orientation of the magnetic field is low down. As the size of the inner bipole increases, the field lines reach higher into the solar corona. This means that the height at which the angle change occurs (and hence null point will form) is higher in the corona. Eventually, as the size of the inner bipole becomes much greater than the size of the outer bipole the magnetic field from the inner regions extend out through the corona and pass out beyond 2.5R_⊙. This means that the field reversal between the two regions of flux is no longer picked up as the flux from the inner polarity reaches beyond the outer boundary of the model.

Figure 3.6: Image showing an orthographic plot and field lines of the set up of the second simulation. The extrapolated coronal field shows a configuration similar to the coronal field set up within the initial configuration of the breakout model.

Conversely, when the size of the inner bipole is held constant and the size of the outer bipole is varied we see the opposite effect. As the size of the outer bipole starts very weak, the field from the inner bipole dominates and reaches out beyond the outer boundary of the simulation. As the size of the outer bipole increases, the amount of magnetic flux from the inner bipole connecting to the outer bipole increases. This means that the height of the change in orientation between the two regions of flux decreases as the amount of flux from the outer magnetic bipole increases and compresses the flux from the inner bipole. This happens very rapidly as the outer bipole strength builds up.

This method provides a good starting point for looking for nulls within the field configurations. these simple field configurations are done to provide a first estimate as to the location of the coronal null point. However, the method is very simplified and ideal for use on highly symmetric cases. In general, actual solar magnetic field configurations are much more complex, so this technique would not work.

Figure 3.7: Plot showing the height in solar radii of the field line orientation change when (a) the inner bipole strength is held constant and the outer bipole strength is increased (solid line) and (b) the outer bipole strength is held constant and the inner bipole strength is increased (dashed line).

A much more rigorous technique will be needed for use throughout our main simulations.