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Self-organization in continuous systems is associated with dissipative processes. In particular, for magnetized plasmas, it is known as magnetic relaxation, where the magnetic energy is converted into heat and kinetic energy of flow through the process of magnetic reconnection. An example of such a system is the solar corona, where reconnection manifests as solar transients like flares and jets. Consequently, toward investigation of plasma relaxation in solar transients, we utilize a novel approach of data-constrained MHD simulation for an observed solar flare. The selected active region NOAA 12253 hosts a GOES M1.3 class flare. The investigation of extrapolated coronal magnetic field in conjunction with the spatiotemporal evolution of the flare reveals a hyperbolic flux tube (HFT), overlying the observed brightenings. MHD simulation is carried out with the EULAG-MHD numerical model to explore the corresponding reconnection dynamics. The overall simulation shows signatures of relaxation. For a detailed analysis, we consider three distinct sub-volumes. We analyze the magnetic field line dynamics along with time evolution of physically relevant quantities like magnetic energy, current density, twist, and gradients in magnetic field. In the terminal state, none of the sub-volumes are seen to reach a force-free state, thus remaining in non-equilibrium, suggesting the possibility of further relaxation. We conclude that the extent of relaxation depends on the efficacy and duration of reconnection, and hence, on the energetics and time span of the flare.

Magnetic flux ropes (MFRs) play an important role in high-energetic events like solar flares and coronal mass ejections in the solar atmosphere. Importantly, solar observations suggest an association of some flaring events with quadrupolar magnetic configurations. However, the formation and subsequent evolution of MFRs in such magnetic configurations still need to be fully understood. In this paper, we present idealized magnetohydrodynamics (MHD) simulations of MFR formation in a quadrupolar magnetic configuration. A suitable initial magnetic field having a quadrupolar configuration is constructed by modifying a three-dimensional (3D) linear force-free magnetic field. The initial magnetic field contains neutral lines, which consist of X-type null points. The simulated dynamics initially demonstrate the oppositely directed magnetic field lines located across the polarity inversion lines (PILs) moving towards each other, resulting in magnetic reconnections. Due to these reconnections, four highly twisted MFRs form over the PILs. With time, the foot points of the MFRs move towards the X-type neutral lines and reconnect, generating complex magnetic structures around the neutral lines, thus making the MFR topology more complex in the quadrupolar configuration than those formed in bipolar loop systems. Further evolution reveals the non-uniform rise of the MFRs. Importantly, the simulations indicate that the pre-existing X-type null points in magnetic configurations can be crucial to the evolution of the MFRs and may lead to the observed brightenings during the onset of some flaring events in the quadrupolar configurations., Comment: 18 pages, 9 figures

We present a novel Hall magnetohydrodynamics (HMHD) numerical simulation of a three-dimensional (3D) magnetic flux rope (MFR) -- generated by magnetic reconnections from an initial 3D bipolar sheared field. Magnetic reconnections during the HMHD evolution are compared with the MHD. In both simulations, the MFRs generate as a consequence of the magnetic reconnection at null points which has not been realized in contemporary simulations. Interestingly, the evolution is faster and more intricate in the HMHD simulation. Repetitive development of the twisted magnetic field lines (MFL) in the vicinity of 3D nulls (reconnection site) is unique to the HMHD evolution of the MFR. The dynamical evolution of magnetic field lines around the reconnection site being affected by the Hall forcing, correspondingly affects the large-scale structures., Comment: Accepted for publication in Physica Scripta