Authors: Wen He (UAH), Qiang Hu (UAH), Jiong Qiu (MSU)

Along with the development of high-resolution observations from multiple points either in remote-sensing or in-situ measurements, investigations of solar eruptions go deeper into different physical processes. Such investigations also motivate the characterization of the corresponding magnetic flux ropes (MFRs), which are generally considered to be the core magnetic structure of various eruption phenomena like coronal mass ejections (CMEs). For the purpose to bridge the gap between erupted MFRs on the Sun and their interplanetary counterparts, a quantitative description of MFRs in different stages is desired. However, it remains a challenge to confirm the existence of a coherent MFR before or upon the CME eruption in the solar source region due to the lack of direct measurement of the vector magnetic field. In this study, we utilize the nonlinear-fore-free field extrapolation method with preprocessed photospheric vector magnetograms from SDO/HMI to study the three-dimensional coronal magnetic field before and after the eruption of two solar eruption events from two active regions (ARs), AR 11719 and AR 12443. After the extrapolation results are evaluated through a series of metrics, the reconstructed magnetic topology will be analyzed and compared with remote-sensing observations to find evidence of MFRs on the sun. And we also analyze the evolution of MFRs via the time evolution of magnetic reconnection flux associated with flare ribbons during the eruption. Then the magnetic properties of MFRs on the sun will be summarized and further compared with the corresponding in-situ modeling results of the magnetic clouds observed at 1 au.