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In order to bridge the gap between heliospheric and solar observations of coronal mass ejections (CMEs), one of the key steps is to improve the understanding of their corresponding magnetic structures like the magnetic flux ropes (MFRs). But it remains a challenge to confirm the existence of a coherent MFR before or upon the CME eruption on the Sun and to quantitatively characterize the CME-MFR due to the lack of direct magnetic field measurements in the corona. In this study, we investigate MFR structures originating from two active regions (ARs), AR 11719 and AR 12158, and estimate their magnetic properties quantitatively. We perform nonlinear force-free field extrapolations with preprocessed photospheric vector magnetograms. In addition, remote-sensing observations are employed to find indirect evidence of MFRs on the Sun and to analyze the time evolution of magnetic reconnection flux associated with the flare ribbons during the eruption. A coherent “preexisting” MFR structure prior to the flare eruption is identified quantitatively for one event from the combined analysis of the extrapolation and observation. Then the characteristics of MFRs for two events on the Sun before and during the eruption forming the CME-MFR, including the axial magnetic flux, field line twist, and reconnection flux, are estimated and compared with the corresponding in situ modeling results. We find that the magnetic reconnection associated with the accompanying flares for both events injects a significant amount of flux into the erupted CME-MFRs.

Onestrongmagnetic cloud (MC) with a magnetic field magnitude reaching ∼40 nT at 1 au during 2012 June 16–17 is examined in association with a preexisting magnetic flux rope (MFR) identified on the Sun. The MC is characterized by a quasi-three-dimensional (3D) flux rope model based on in situ measurements from the Wind spacecraft. The contents of the magnetic flux and other parameters are quantified. In addition, a correlative study with the corresponding measurements of the same structure crossed by the Venus Express (VEX) spacecraft at a heliocentric distance of 0.7 au and with an angular separation of ∼6° in longitude is performed to validate the MC modeling results. The spatial variation between the Wind and VEX magnetic field measurements is attributed to the 3D configuration of the structure appearing as a knotted bundle of flux. A comparison of the magnetic flux contents between the MC and the preexisting MFR on the Sun indicates that the 3D reconnection process accompanying an M1.9 flare may correspond to the magnetic reconnection between the field lines of the preexisting MFR rooted in the opposite polarity footpoints. Such a process reduces the amount of the axial magnetic flux in the erupted flux rope, by approximately 50%, in this case.

Magnetic reconnection in naturally occurring and laboratory settings often begins locally and elongates, or spreads, in the direction perpendicular to the plane of reconnection. Previous work has largely focused on current sheets with a uniform thickness, for which the predicted spreading speed for anti‐parallel reconnection is the local speed of the current carriers. We derive a scaling theory of three‐dimensional (3D) spreading of collisionless anti‐parallel reconnection in a current sheet with its thickness varying in the out‐of‐plane direction, both for spreading from a thinner to thicker region and a thicker to thinner region. We derive an expression for calculating the time it takes for spreading to occur for a current sheet with a given profile of its thickness. A key result is that when reconnection spreads from a thinner to a thicker region, the spreading speed in the thicker region is slower than both the Alfvén speed and the speed of the local current carriers by a factor of the ratio of thin to thick current sheet thicknesses. This is important because magnetospheric and solar observations have previously measured the spreading speed to be slower than previously predicted, so the present mechanism might explain this feature. We confirm the theory via a parametric study using 3D two‐fluid numerical simulations. We use the prediction to calculate the time scale for reconnection spreading in Earth's magnetotail during geomagnetic activity. The results are also potentially important for understanding reconnection spreading in solar flares and the dayside magnetopause of Earth and other planets.

We develop an optimization approach to model the magnetic field configuration of magnetic clouds, based on a linear force‐free formulation in three dimensions. Such a solution, dubbed the Freidberg solution, is kin to the axisymmetric Lundquist solution, but with more general “helical symmetry.” The merit of our approach is demonstrated via its application to two case studies of in situ measured magnetic clouds. Both yield results of reducedχ² ≈ 1. Case 1 shows a winding flux rope configuration with one major polarity. Case 2 exhibits a double‐helix configuration with two flux bundles winding around each other and rooted on regions of mixed polarities. This study demonstrates the three‐dimensional complexity of the magnetic cloud structures.