Fully kinetic PiC simulations of current sheet instabilities for the Solar corona

The plasma of the Solar corona is practically collisionless. This imposes an important role of waves and micro-turbulent interactions with particles for plasma transport, dissipation, stability, etc, since binary particles collisions are inefficient. As a result the Solar corona is also a natural laboratory for testing basic plasma turbulent phenomena. Current sheets (CS), through which magnetic energy can be released, are ubiquitous in this environment. Different from many other plasmas, the presence of large guide magnetic fields plays a crucial role in the corona. In general, CS are prone to a large number of macro and micro-instabilities, the more the thinner they become. CS can lead to or are formed as consequence of magnetic reconnection. This is a fundamental physical process in the Universe that converts magnetic into other forms of energy which goes along with change of the magnetic connectivity. In this context, we aim towards an appropriate characterization of the influence of the guide magnetic field on the instabilities of and magnetic reconnection through CS, for which in coronal plasmas small scale kinetic effects are essential. In order to investigate the essential nonlinear properties, we use fully kinetic Particle-in-Cell (PIC) numerical simulations to adequately describe the collisionless solar coronal plasma. The kinetic approach is necessary to properly describe coupling of scales in collisionless magnetic reconnection and to provide, in the end, macroscopic transport properties appropriately describing the coronal plasma. In order to validate our methods, we also analyze the limits cases of zero (antiparallel configuration) and infinite guide fields (gyrokinetic theory) for comparison. In the case of antiparallel Harris CS, we find several instabilities driven by temperature anisotropy which might be numerically induced when more realistic parameters (high mass ratios) are used in PIC simulations. We reveal that they may mimic real collisional physical processes, and we show how they can be efficiently avoided by choosing appropriate numerical parameters, such as the shape functions (interpolation schemes). Next, we analyze the instabilities of Harris CS in the presence of small guide fields. We develop methods to calculate spatial and temporal derivatives, as well as averages, for a proper calculation of the mechanisms supporting the reconnected electric field. Our methods, more accurate than previously used ones, reveals the appearance of additional terms in the mean field generalized Ohm's law at the edge of the magnetic islands, arising from the interaction with electromagnetic fluctuations. Our findings reveal cross-field streaming and pressure gradient driven instabilities, causing plasma heating, particle acceleration and turbulence. In the third and last part, we analyze instabilities of force free CS in the presence of large guide fields, which we compare with the results of gyrokinetic simulations. For beta_i=0.01, we find that gyrokinetic simulations model sufficiently well the regions close to the reconnection X point for guide fields b_g>5, and practically everywhere for b_g>30. But only a fully kinetic PIC simulation can reveal, e.g., the physics of secondary magnetic islands for moderate guide fields b_g>5, where macro and micro instabilities driven by shear flow and streamings generate magnetic fields, particle heating and acceleration besides of high frequency electromagnetic fluctuations. For beta_i~1, the applicability of gyrokinetic simulation is much less restricted, in the sense that the convergence to the PIC simulations results requires even lower guide fields. Our results have important implications for understanding the role of current sheet instabilities in the solar corona and their macroscopic consequences for the overall dynamics and energy conversion processes. This also applies for astrophysical collisionless plasmas, as well as laboratory plasmas and nuclear fusion facilities on Earth.