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Figure 5.11: Time slices along the length of the separator which has been normalised such that it lies between 0.0 ≤z∗ ≤1.0 showing contours of (a) (∇ ×v)z = ωz and (b)

(∇ ×B)z =jz and the discriminant of the component of (c)vand (d)Bperpendicular to

the separator. The end of phase I and start of phase II is highlighted by the black dashed line and symbols “I” and “II”.

the separator, which is the location of the peak reconnection, we now examine the residual forces in the system during the reconnection experiment (Sect. 5.4) before investigating the nature of the waves which are launched due to the reconnection (Sect. 5.5).

5.4

Effects of residual forces during the reconnection exper-

iment

In Chapts. 3 and 4, we examined the magnitude and direction of the residual total force along the length, through the depth and across the width of the MHS equilibrium separator current layer and found that the very small residual total force acted to make the current layer longer, wider and thinner.

Throughout the reconnection experiment, the total force along the separator continues to act outwards towards the null points, but the magnitude of the total force decreases through phase I to a value of ∼ 0.02 (Fig. 5.12). During phase II this peak value does not change although the position along the separator, from which the total force acts outwards, varies slightly from z∗ = 0.56, att= 0tf, toz∗ = 0.62 in phase II.

The decrease in the magnitude of the residual forces directed along the separator occurs due to the dissipation of the separator current during the reconnection and the subsequent

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Figure 5.12: Time slice of the total force plotted along the z∗-axis. Note that time is plotted on a log scale. The white dashed line and symbols “I” and “II” indicate where phase I ends and phase II begins.

loss of force balance at the separator. These residual forces cause the nulls to move a little away from each other, along thez-axis, during the experiment, as was detailed in Sect. 5.3. In perpendicular cuts across the z-axis (at z = 0.4) the magnitude of the total force initially decreases due to the loss of current about the separator (Figs. 5.13a to 5.13c). However, as phase I continues, the total force about the separator intensifies (Figs. 5.13d to 5.13f). This indicates that the residual forces start to build up again during phase I when the reconnection rate is slowing. This is linked to the plasma trying to regain force balance (i.e., rebuild the current layer) at the separator. However, due to the resistive nature of the system about the separator, current is immediately dissipated as soon as it gets above|j|= 10 and so the current layer is never reformed.

This behaviour is clarified by the arrows on the plots in Fig. 5.13. These arrows indicate the direction of thexand y-components of the total force in this plane atz= 0.4 and show that there is a strong component of the total force pointing outwards from the separator into the cusp regions or, in other words, the total force is still trying to widen the current layer (Figs. 5.13d to 5.13i). Also, arrows are observed to be pointing in towards the separator from the other two flux domains, i.e., outwith the cusps, which highlights that the total force is still acting to make the current layer thinner in cuts perpendicular to the separator. This behaviour of the total force has been seen before in 2D X-point reconnection [Fuentes-Fern´andez et al., 2012]. In this work the total force was observed to be directed in towards the X-point outwith the cusp regions formed by the separatrices of the nulls, and was directed outwards away from the X-point in the cusp regions.

A circular motion is witnessed about the two strong regions of total force in Figs. 5.13d to 5.13f. The total force appears to be acting from the limits of the current layer (width ways) into the centre of the current layer where it is being squeezed thinner.

Figs. 5.14 and 5.15 show the magnitude of the total force on surfaces which go through the depth and across the width of the current layer from the lower to the upper null, respectively. Therefore, the two surfaces are not straight planes, but twist along the length of the separator, as the current layer itself twists. On top of these contours are arrows which show the direction of the total force in these planes. These arrows are coloured orange whered <0 andw <0 and are coloured black whered >0 andw >0 so that the direction of the arrows is clear. The strength of the total force through the

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Figure 5.13: Contours of the total force in the plane perpendicular to the separator at

z = 0.4 at (a) t = 0tf, (b) t= 0.02tf, (c) t= 0.04tf, (d) t = 0.06tf, (e) t = 0.08tf, (f)

t= 0.1tf, (g)t= 0.3tf, (h)t= 0.54tf and (i)t= 0.61tf. Black arrows, normalised to the

maximum value on the colour bar, display the direction of the total force in the plane (x

and y-components of the total force).

depth is weak and so the arrows here, pointing in towards the separator at l = 0.0, are small (Fig. 5.14). Fig. 5.15 shows the total force plotted across the width of the current layer. The total force is stronger here than it is through the depth of the current layer and the arrows indicate that the total force is acting outwards away from the separator as expected from the contours in Fig. 5.13.

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Figure 5.14: Contours of the total force through the depth,d, of the current layer plotted along the length of the separator at (a) t = 0tf, (b) t = 0.02tf, (c) t = 0.04tf, (d)

t= 0.06tf, (e) t= 0.08tf, (f) t= 0.1tf, (g) t= 0.3tf, (h) t = 0.54tf and (i) t = 0.61tf.

Arrows, normalised to the maximum value on the colour bar, display the direction of the total force in this plane. The arrows are coloured orange/black wheredis less than/greater than 0.

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Figure 5.15: Contours of the total force across the width, w, of the current layer plotted along the length of the separator at (a) t = 0tf, (b) t = 0.02tf, (c) t = 0.04tf, (d)

t= 0.06tf, (e) t= 0.08tf, (f) t= 0.1tf, (g) t= 0.3tf, (h) t = 0.54tf and (i) t = 0.61tf.

Arrows, normalised to the maximum value on the colour bar, display the direction of the total force in this plane. The arrows are coloured orange/black wherewis less than/greater than 0.