Authors: Drake Osaben (Montana State University), Jiong Qiu, (Montana State University), Dana Longcope (Montana State University)

Flare loops are formed by magnetic reconnection, which restructures magnetic field and converts free magnetic energy into plasma and particle energy. Theoretically, subject to the helicity conservation and rigid boundary conditions during the timescale of a flare, a linear force free magnetic field describes the state of the minimum magnetic energy, which would be the end goal to be achieved by magnetic reconnection, but this has not been tested in observations. On the other hand, flare observations in the past two decades have revealed a phenomenon called the “strong-to-weak shear evolution” — here the observed shear is defined as the complementary of the angle between the polarity inversion line of the photospheric vertical magnetic field and the post-reconnection flare loop (PRFL) projected to the image plane. Does this observation mean that later formed loops are closer to the potential field than earlier formed flare loops? We answer this question using a data-constrained modeling approach applied to an M-class two-ribbon flare SOL20141218T21:40 that exhibits the typical strong-to-weak shear evolution.  A few thousand post-reconnection flare loops observed in EUV images by AIA have been identified during 40 minutes. These loops are anchored at flare ribbons in the lower atmosphere. We model the post-reconnection, force-free, 3D magnetic field with the constraints of the observed PRFLs and their feet, finding that the force-free parameter alpha of these loops decreases with time: flare loops formed earlier and settled at lower altitudes are characterized by larger force-free parameters than those formed later and settled at higher altitudes. Our work illustrates that post-reconnection magnetic field of the studied event is not linear force free, and the nature of the strong-to-weak shear evolution of PRFLs in this event reflects the varying force-free parameter.  (In addition, we note that the shear, as defined in the 2D plane of the image, of a 3D potential magnetic field is not zero.)  We discuss the implication of the magnetic field configuration of post-reconnection flare loops with respect to flare energetics.