Two-fluid magnetic island dynamics in slab geometry: II - Islands interacting with resistive walls or static external resonant magnetic perturbations

The dynamics of a propagating magnetic island interacting with a resistive wall or a static external magnetic perturbation is investigated using two-fluid, drift-MHD theory in slab geometry. In both cases, the island equation of motion is found to take exactly the same form as that predicted by single-fluid MHD theory. Three separate ion polarization terms are found in the Rutherford island width evolution equation. The first is the drift-MHD polarization term for an isolated island, and is completely unaffected by interaction with a wall or magnetic perturbation. Next, there is the polarization term due to interaction with a wall or magnetic perturbation which is predicted by single-fluid MHD theory. Finally, there is a hybrid of the other two polarization terms. The sign of this term depends on many factors. However, under normal conditions, it is stabilizing if the unperturbed island propagates in the ion diamagnetic direction (in the lab. frame), and destabilizing if it propagates in the electron diamagnetic direction

Phase Diagrams of Forced Magnetic Reconnection in Taylor's Model

Recent progress in the understanding of how externally driven magnetic reconnection evolves is organized in terms of parameter space diagrams. These diagrams are constructed using four pivotal dimensionless parameters: the Lundquist number $S$, the magnetic Prandtl number $P_m$, the amplitude of the boundary perturbation $\hat \Psi_0$, and the perturbation wave number $\hat k$. This new representation highlights the parameters regions of a given system in which the magnetic reconnection process is expected to be distinguished by a specific evolution. Contrary to previously proposed phase diagrams, the diagrams introduced here take into account the dynamical evolution of the reconnection process and are able to predict slow or fast reconnection regimes for the same values of $S$ and $P_m$, depending on the parameters that characterize the external drive, never considered so far. These features are important to understand the onset and evolution of magnetic reconnection in diverse physical systemsComment: Comments: 13 pages, 2015 Workshop "Complex plasma phenomena in the laboratory and in the universe

Formation of Plasmoid Chains in Fusion Relevant Plasmas

The formation of plasmoid chains is explored for the first time within the context of the Taylor problem, in which magnetic reconnection is driven by a small amplitude boundary perturbation in a tearing-stable slab plasma equilibrium. Numerical simulations of a magnetohydrodynamical model of the plasma show that for very small plasma resistivity and viscosity, the linear inertial phase is followed by a nonlinear Sweet-Parker evolution, which gives way to a faster reconnection regime characterized by a chain of plasmoids instead of a slower Rutherford phase

Extended theory of the Taylor problem in the plasmoid-unstable regime

A fundamental problem of forced magnetic reconnection has been solved taking into account the plasmoid instability of thin reconnecting current sheets. In this problem, the reconnection is driven by a small amplitude boundary perturbation in a tearing-stable slab plasma equilibrium. It is shown that the evolution of the magnetic reconnection process depends on the external source perturbation and the microscopic plasma parameters. Small perturbations lead to a slow nonlinear Rutherford evolution, whereas larger perturbations can lead to either a stable Sweet-Parker-like phase or a plasmoid phase. An expression for the threshold perturbation amplitude required to trigger the plasmoid phase is derived, as well as an analytical expression for the reconnection rate in the plasmoid-dominated regime. Visco-resistive magnetohydrodynamic simulations complement the analytical calculations. The plasmoid formation plays a crucial role in allowing fast reconnection in a magnetohydrodynamical plasma, and the presented results suggest that it may occur and have profound consequences even if the plasma is tearing-stable.Comment: Accepted for publication in Physics of Plasma

The algebra of supertraces for 2+1 super de Sitter gravity

The algebra of the observables for 2+1 super de Sitter gravity, for one genus of the spatial surface is calculated. The algebra turns out to be an infinite Lie algebra subject to non-linear constraints. The constraints are solved explicitly in terms of five independent complex supertraces. These variables are the true degrees of freedom of the system and their quantized algebra generates a new structure which is referred to as a 'central extension' of the quantum algebra SU(2)q

Gyro-induced acceleration of magnetic reconnection

The linear and nonlinear evolution of magnetic reconnection in collisionless high-temperature plasmas with a strong guide field is analyzed on the basis of a two-dimensional gyrofluid model. The linear growth rate of the reconnecting instability is compared to analytical calculations over the whole spectrum of linearly unstable wave numbers. In the strongly unstable regime (large \Delta '), the nonlinear evolution of the reconnecting instability is found to undergo two distinctive acceleration phases separated by a stall phase in which the instantaneous growth rate decreases. The first acceleration phase is caused by the formation of strong electric fields close to the X-point due to ion gyration, while the second acceleration phase is driven by the development of an open Petschek-like configuration due to both ion and electron temperature effects. Furthermore, the maximum instantaneous growth rate is found to increase dramatically over its linear value for decreasing diffusion layers. This is a consequence of the fact that the peak instantaneous growth rate becomes weakly dependent on the microscopic plasma parameters if the diffusion region thickness is sufficiently smaller than the equilibrium magnetic field scale length. When this condition is satisfied, the peak reconnection rate asymptotes to a constant value.Comment: Accepted for publication on Physics of Plasma

Two-fluid magnetic island dynamics in slab geometry: I - Isolated islands

A set of reduced, 2-D, two-fluid, drift-MHD equations is derived. Using these equations, a complete and fully self-consistent solution is obtained for an isolated magnetic island propagating through a slab plasma with uniform but different ion and electron fluid velocities. The ion and electron fluid flow profiles around the island are uniquely determined, and are everywhere continuous. Moreover, the island phase-velocity is uniquely specified by the condition that there be zero net electromagnetic force acting on the island. Finally, the ion polarization current correction to the Rutherford island width evolution equation is evaluated, and found to be stabilizing provided that the anomalous perpendicular ion viscosity significantly exceeds the anomalous perpendicular electron viscosity

Quantization of Space and Time in 3 and in 4 Space-time Dimensions

The fact that in Minkowski space, space and time are both quantized does not have to be introduced as a new postulate in physics, but can actually be derived by combining certain features of General Relativity and Quantum Mechanics. This is demonstrated first in a model where particles behave as point defects in 2 space dimensions and 1 time, and then in the real world having 3+1 dimensions. The mechanisms in these two cases are quite different, but the outcomes are similar: space and time form a (non-cummutative) lattice. These notes are short since most of the material discussed in these lectures is based on two earlier papers by the same author (gr-qc/9601014 and gr-qc/9607022), but the exposition given in the end is new.Comment: Lectures held at the NATO Advanced Study Institute on ``Quantum Fields and Quantum Space Time", Carg\`ese, July 22 -- August 3, 1996. 16 pages Plain TeX, 6 Figure

The Framework of Plasma Physics

Plasma physics is a necessary part of our understanding of stellar and galactic structure. It determines the magnetospheric environment of the earth and other planets; it forms the research frontier in such areas as nuclear fusion, advanced accelerators, and high power lasers; and its applications to various industrial processes (such as computer chip manufacture) are rapidly increasing. It is thus a subject with a long list of scientific and technological applications. This book provides the scientific background for understanding such applications, but it emphasizes something else: the intrinsic scientific interest of the plasma state. It attempts to develop an understanding of this state, and of plasma behavior, as thoroughly and systematically as possible. The book was written with the graduate student in mind, but most of the material would also fit into an upper-level undergraduate course