Octupolar out-of-plane magnetic field structure generation during magnetic reconnection

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Magnetic Reconnection is is a topic or great interest in the field of astro-plasma physics due to its role in solar eruptions and energrtic events in the geomagnetic tail of teh earth (see Figure 1). While field lines are normally 'frozen' into plasmas, and thus prevented from touching or crossing another, in a reconnection event two field lines touch and form two new field lines. Thus there is change in the toplogy of teh field lines. As a result of this, energy stored up in the maggnetic field can be released rapidly leading to particle aacceleration.

Figure 1:

In the collisionless plasma regime, i.e. when particles are acted on only by the overall electromagnetic field rather than that of individual charges, magnetic reconnection has an observational signature, known as the Hall magnetic field. This quadrupolar magnetic field that forms over the point where the seperatrices of the reconnectring field lines cross, i.e. the X-point. If we consider magnetic field-lines in a plane, moving horizontally towards and vertically away from the X-point, the Hall magnetic field manifests iself as four regions of magnetic field intensity, pointing in and out of the plane. The out-of plane field has been observed in several simulational studies using both tearing-mode scenarios and X-point collapse (see Ref. pritch and Ref . Tsik respectively) and it was phtysically observed in space craf missions in the geomagnetic tail (see ref. eastwood) as well as in laboratory experiments (see Ref. MRX)

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The regions of out-of-plane field intensity in the Hall fiel are produced as ions and electrons decouple from the reconnecting field lines. Since ions are heavier, they decouple sooner, while electrons remain frozen in, leading to current loops as shown in Figure 2. More precisely, as explained in Ref. Uze)))), after ions decouple and cease to move with teh field lines, coupled electrons are pulled towards and away from the X-point to conserve charge neutrality as the spacing of field lines near the X-point contracts and expands during reconnection. Thus, the Hall field is mostly caused by electron motion.

In Ref. GVDP the discovery of a related effect, leading to an additional four regions of opposite magnetic polarity in the out-of-plane magnetic field, is presented. Here, the resulting overall magnetic field has an octupolar structure, which could be of similar observational significance and a potential avenue for further experimental investigation. We shall refer to the central quadrupolar magnetic field structure as quadrupolar components and to the additional regions of magnetic polarity as octupolar components.

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The reconnection setup used in this study is that of X-point collapse, first introduced by Dungey in 1953 [dungey], as one of the earliest analysis of magnetic reconnection, pre-dating the tearing-mode. As shown in Figire 3, this setup is made up of parabolic field lines, with field strenth decreasing towards the centre. Compressing the field in the X-direction leads to an out-of-plane current and thus a Lorentz force, dragging field lines towards the X-point, increasing the initial asymmetry, and the field collapses (see also Ref. priest). While this setup is distinctly different from the well-studied tearing-mode instability, after a Harris type current sheet is disrupted by the tearing instability and magnetic islands and X-points start to form, there are few distinguishable differences between the two approaches.

As in previous studies of reconnection, a distinct out-of-plane quadrupolar magnetic field was observed early in the simulation. However, after the peak in the reconnection rate, four further regions of magnetic polarity emerged, resulting in an octupolar magnetic field. This was tested with both open and closed boundary conditions imposed on fields and particles (see Figure 4) as well as for increasing system sizes (4 to 16 ion inertial lengths) and the effect was persistent.

Figure 4: from Ref. Gvdp, showing the evolution out-of-plane magnetic field during X-point collapse reconnection over time for a domain size of 8 ion inertial lengths. Panel a) to c) show the evolution for closed boundary conditions while panels d) to f) show that for open boundary conditions.

From Ref. gvdp: showing the out-of-plane magnetic field in the lower left quarter of the domain, obtained by breaking down Ampere's law into individual current components and integrating over the simulation domain. Panel b) and c) show electron and ion contributions respectively while panel a) represents their combined contribution, effectively representing the lower left quarter of panel b) in figure 4.

The cause of the additional areas of magnetic polarity were investigated by investigating individual contributions to the out-of-plane magnetic field from ion and electron currents seperately (see Figure 5). As expected, it was shown that the inner quadrupolar field was the result of electron motion. However, as shown in panel c) of Figure 5, the octupolar components are the result of ion currents. This can be explained by the decoupled motion of the ions, while electrons are frozen into the magnetic field except close to the X-point. The resulting charge imbalance leads to electrons moving along the field lines to restore charge neutrality. This explains the lower electron contribution to the ouy-of-plane field in panel b) of Figure 5, which seperates the octupolar components from the edge of the domain.

In the collisionless plasma regime, magnetic field lines in a suitable set-up can reconnect through a mechanism called Hall reconnection, as first proposed by B. Sonnerup in 1979 [1], is a mode of reconnection relying on the decoupling of ions and electrons in a diffusion region. In other words, it is mode of reconnection in the collisionle and is of great interest in the study of magnetic recon- nection as it presents an alternative to the the Petschek model, which relies on an anomalous resistivity [2].

An observational consequence of Hall reconnection is the associated quadrupolar out-of-plane magnetic field, induced by currents resulting from the decoupling i.e. the Hall currents, first demonstrated in a study by Tere- sawa in 1983 [4]. From 1994, the effect was further shown to occur in numerical Hybrid simulations [5–7] and later in a full Particle In Cell (PIC) numerical simulation in 2001 [8].

By be- ing an observational signature of magnetic reconnection, the quadrupolar field has thus been of great interest in recent spacecraft missions, including Polar [10] in 2002 and Cluster [11] in 2005, which both observed individual magnetic poles in the magnetotail of the Earth. Sub- sequently, a full quadrupolar pattern was observed in a multi-spacecraft Cluster mission in 2007 [12]. The exper- imental evidence of the full quadrupolar structure was found at the MRX facility in 2004 [13].

Magnetic Hall reconnection, as first proposed by B. Sonnerup in 1979 [1], is a mode of reconnection relying on the decoupling of ions and electrons in a diffusion region and is of great interest in the study of magnetic recon- nection as it presents an alternative to the the Petschek model, which relies on an anomalous resistivity [2].