Theory and Applications of Non-Relativistic and Relativistic Turbulent Reconnection

Realistic astrophysical environments are turbulent due to the extremely high Reynolds numbers. Therefore, the theories of reconnection intended for describing astrophysical reconnection should not ignore the effects of turbulence on magnetic reconnection. Turbulence is known to change the nature of many physical processes dramatically and in this review we claim that magnetic reconnection is not an exception. We stress that not only astrophysical turbulence is ubiquitous, but also magnetic reconnection itself induces turbulence. Thus turbulence must be accounted for in any realistic astrophysical reconnection setup. We argue that due to the similarities of MHD turbulence in relativistic and non-relativistic cases the theory of magnetic reconnection developed for the non-relativistic case can be extended to the relativistic case and we provide numerical simulations that support this conjecture. We also provide quantitative comparisons of the theoretical predictions and results of numerical experiments, including the situations when turbulent reconnection is self-driven, i.e. the turbulence in the system is generated by the reconnection process itself. We show how turbulent reconnection entails the violation of magnetic flux freezing, the conclusion that has really far reaching consequences for many realistically turbulent astrophysical environments. In addition, we consider observational testing of turbulent reconnection as well as numerous implications of the theory. The former includes the Sun and solar wind reconnection, while the latter include the process of reconnection diffusion induced by turbulent reconnection, the acceleration of energetic particles, bursts of turbulent reconnection related to black hole sources as well as gamma ray bursts. Finally, we explain why turbulent reconnection cannot be explained by turbulent resistivity or derived through the mean field approach.Comment: 66 pages, 24 figures, a chapter of the book "Magnetic Reconnection - Concepts and Applications", editors W. Gonzalez, E. N. Parke

Scaling Theory of 3D Magnetic Reconnection X-Line Spreading

Magnetic reconnection is fundamental process in plasmas that converts magnetic energy into kinetic and thermal energy via a change in magnetic topology. Magnetic reconnection is known to mediate eruptive solar flares, geomagnetic substorms that create the Northern lights, heating and particle acceleration in controlled fusion devices, and is thought to be an important process in numerous settings in high-energy astrophysics. Classical models of reconnection are two-dimensional (2D), but naturally occurring reconnection is three-dimensional (3D), and a manifestation of the 3D nature is that the x-line where the magnetic field topology changes has a finite extent in the direction normal to the plane of reconnection. The x-line can also elongate or spread over time, and this trait has been observed in the laboratory, Earth\u27s magnetosphere, and is thought to be related to the elongation of chromospheric ribbons during solar flares. This dissertation presents a first‐principles scaling theory of the three-dimensional spreading of quasi-2D magnetic reconnection of finite extent in the out of plane direction. This theory addresses systems with or without an out of plane (guide) magnetic field, with or without Hall physics, in current sheets with thicknesses that are both uniform and non‐uniform in the out of plane direction. The theory reproduces known spreading speeds and directions with and without guide fields, unifying previous knowledge in a single theory, along with new results: (1) Reconnection spreads in a particular direction if an x‐line is induced at the interface between reconnecting and non‐reconnecting regions, which is controlled by the out of plane gradient of the electric field in the outflow direction. (2) The theory explains why anti‐parallel reconnection in resistive‐magnetohydrodynamics does not spread. (3) Numerical simulations of anti-parallel reconnection initiated with a pressure pulse instead of a magnetic perturbation suggest magnetosonic waves do not play a role in the propagation of quasi-2D anti-parallel reconnection, as had previously been speculated. (4) In current sheets of non‐uniform thickness, when anti-parallel reconnection spreads from a thinner to a thicker region of a current sheet, the spreading speed is both sub‐Alfv\\u27enic and slower than the speed of the local current carriers predicted for a uniform current sheet of equivalent local thickness; this is due to the initial reconnecting magnetic field being effectively reduced. We confirm these results using 3D two‐fluid and resistive‐magnetohydrodynamics simulations. The result can be used to predict the time scale of reconnection spreading in Earth\u27s magnetotail, where the near Earth cross‐tail current sheet has a thickness that varies along the dawn‐dusk direction. It is also potentially important for understanding observations of two‐ribbon solar flares and dayside magnetopause reconnection in which reconnection spreads at sub‐Alfv\\u27enic and sub‐current carrier speeds

Fast Magnetic Reconnection and Spontaneous Stochasticity

Magnetic field-lines in astrophysical plasmas are expected to be frozen-in at scales larger than the ion gyroradius. The rapid reconnection of magnetic flux structures with dimensions vastly larger than the gyroradius requires a breakdown in the standard Alfv\'en flux-freezing law. We attribute this breakdown to ubiquitous MHD plasma turbulence with power-law scaling ranges of velocity and magnetic energy spectra. Lagrangian particle trajectories in such environments become "spontaneously stochastic", so that infinitely-many magnetic field-lines are advected to each point and must be averaged to obtain the resultant magnetic field. The relative distance between initial magnetic field lines which arrive to the same final point depends upon the properties of two-particle turbulent dispersion. We develop predictions based on the phenomenological Goldreich & Sridhar theory of strong MHD turbulence and on weak MHD turbulence theory. We recover the predictions of the Lazarian & Vishniac theory for the reconnection rate of large-scale magnetic structures. Lazarian & Vishniac also invoked "spontaneous stochasticity", but of the field-lines rather than of the Lagrangian trajectories. More recent theories of fast magnetic reconnection appeal to microscopic plasma processes that lead to additional terms in the generalized Ohm's law, such as the collisionless Hall term. We estimate quantitatively the effect of such processes on the inertial-range turbulence dynamics and find them to be negligible in most astrophysical environments. For example, the predictions of the Lazarian-Vishniac theory are unchanged in Hall MHD turbulence with an extended inertial range, whenever the ion skin depth $\delta_i$ is much smaller than the turbulent integral length or injection-scale $L_i.$Comment: 31 pages, 5 figure

Computational methods and software systems for dynamics and control of large space structures

Two key areas of crucial importance to the computer-based simulation of large space structures are discussed. The first area involves multibody dynamics (MBD) of flexible space structures, with applications directed to deployment, construction, and maneuvering. The second area deals with advanced software systems, with emphasis on parallel processing. The latest research thrust in the second area involves massively parallel computers