Plasma Instabilities in Large Scale Magnetic Reconnection Associated with Eruptive Solar Coronal Events

Magnetic reconnection is a process responsible for the conversion of magnetic energy into plasma kinetic and thermal energy in laboratory, space, and astrophysical plasmas. The typical time scales of solar dynamic events indicate the existence of fast reconnection. In recent years, there have been significant new developments in reconnection theory that provide alternative and more convincing mechanisms for fast reconnection. One of them is the plasmoid instability. The plasmoid instability takes place in an extended current sheet when the Lundquist number exceeds a critical value (Loureiro et al. 2007, Bhattacharjee et al. 2009). The fragmentation of a current sheet in the high-Lundquist-number regime caused by the plasmoid instability has been proposed as a possible mechanism for fast reconnection scenario by comparing the distribution of plasmoids obtained from the Large Angle and Spectrometric Coronagraph (LASCO) observational data of a coronal mass ejection event with a resistive magnetohydrodynamic simulation of a similar event. The observational data are analyzed using visual inspection, whereas the numerical data are analyzed using both visual inspection and a more precise topological method. Contrasting the observational data with numerical data analyzed with both methods, we identify a major limitation of the visual inspection method, due to the difficulty in resolving smaller plasmoids. This result raises questions about reports of log-normal distributions of plasmoids and other coherent features in the recent literature. Based on nonlinear scaling relations of the plasmoid instability, we infer a lower bound on the current sheet width, assuming the underlying mechanism of current sheet broadening is the resistive diffusion. Supra-arcade downflows (SADs) used to be confused with plasmoids, but unlike plasmoids they are in fact low-emission, elongated, finger-like features usually observed in coronal active regions above post-eruption flare arcades. Observations exhibit downward-moving SADs intertwined with upward-moving spikes. Whereas SADs are dark voids, spikes are brighter, denser structures. Although SADs have been studied intensively during the last decade, the mechanism for the formation of SADs remains unclear. In our three-dimensional resistive MHD simulations, we demonstrate that secondary ballooning/Rayleigh-Taylor instabilities develop in the downstream region of a reconnecting current sheet. The instabilities result in the formation of low-density coherent structures that resemble SADs, and high-density structures that appear to be spike-like. Comparisons between the simulation results and observations suggest that secondary ballooning/Rayleigh-Taylor instabilities of reconnecting current sheets provide a plausible mechanism for SADs and spikes. The first chapter of this thesis is the introduction of the coronal mass ejection, the plasmoid instability, the Rayleigh-Taylor instability and supra-arcade downflows. The second chapter introduces the study of the plasrnoid instability in post-eruption current sheets. The third chapter demonstrates the study of ballooning/Rayleigh-Taylor instabilities as a mechanism for supra-arcade downflows (SADs). The last chapter contains summary and discussion of future works.