A Quantitative Model of Energy Release and Heating by Time-dependent, Localized Reconnection in a Flare with a Thermal Loop-top X-ray Source

We present a quantitative model of the magnetic energy stored and then released through magnetic reconnection for a flare on 26 Feb 2004. This flare, well observed by RHESSI and TRACE, shows evidence of non-thermal electrons only for a brief, early phase. Throughout the main period of energy release there is a super-hot (T>30 MK) plasma emitting thermal bremsstrahlung atop the flare loops. Our model describes the heating and compression of such a source by localized, transient magnetic reconnection. It is a three-dimensional generalization of the Petschek model whereby Alfven-speed retraction following reconnection drives supersonic inflows parallel to the field lines, which form shocks heating, compressing, and confining a loop-top plasma plug. The confining inflows provide longer life than a freely-expanding or conductively-cooling plasma of similar size and temperature. Superposition of successive transient episodes of localized reconnection across a current sheet produces an apparently persistent, localized source of high-temperature emission. The temperature of the source decreases smoothly on a time scale consistent with observations, far longer than the cooling time of a single plug. Built from a disordered collection of small plugs, the source need not have the coherent jet-like structure predicted by steady-state reconnection models. This new model predicts temperatures and emission measure consistent with the observations of 26 Feb 2004. Furthermore, the total energy released by the flare is found to be roughly consistent with that predicted by the model. Only a small fraction of the energy released appears in the super-hot source at any one time, but roughly a quarter of the flare energy is thermalized by the reconnection shocks over the course of the flare. All energy is presumed to ultimately appear in the lower-temperature T<20 MK, post-flare loops

Entropy Crisis, Ideal Glass Transition and Polymer Melting: Exact Solution on a Husimi Cactus

We introduce an extension of the lattice model of melting of semiflexible polymers originally proposed by Flory. Along with a bending penalty, present in the original model and involving three sites of the lattice, we introduce an interaction energy that corresponds to the presence of a pair of parallel bonds and a second interaction energy associated with the presence of a hairpin turn. Both these new terms represent four-site interactions. The model is solved exactly on a Husimi cactus, which approximates a square lattice. We study the phase diagram of the system as a function of the energies. For a proper choice of the interaction energies, the model exhibits a first-order melting transition between a liquid and a crystalline phase. The continuation of the liquid phase below this temperature gives rise to a supercooled liquid, which turns continuously into a new low-temperature phase, called metastable liquid. This liquid-liquid transition seems to have some features that are characteristic of the critical transition predicted by the mode-coupling theory.Comment: To be published in Physical Review E, 68 (2) (2003

Velocity-force characteristics of an interface driven through a periodic potential

We study the creep dynamics of a two-dimensional interface driven through a periodic potential using dynamical renormalization group methods. We find that the nature of weak-drive transport depends qualitatively on whether the temperature $T$ is above or below the equilibrium roughening transition temperature $T_c$. Above $T_c$, the velocity-force characteristics is Ohmic, with linear mobility exhibiting a jump discontinuity across the transition. For $T \le T_c$, the transport is highly nonlinear, exhibiting an interesting crossover in temperature and weak external force $F$. For intermediate drive, $F>F_*$, we find near $T_c^{-}$ a power-law velocity-force characteristics $v(F)\sim F^\sigma$, with $\sigma-1\propto \tilde{t}$, and well-below $T_c$, $v(F)\sim e^{-(F_*/F)^{2\tilde{t}}}$, with $\tilde{t}=(1-T/T_c)$. In the limit of vanishing drive ($F\ll F_*$) the velocity-force characteristics crosses over to $v(F)\sim e^{-(F_0/F)}$, and is controlled by soliton nucleation.Comment: 18 pages, submitted to Phys. Rev.

Magnetic Reconnection in Extreme Astrophysical Environments

Magnetic reconnection is a basic plasma process of dramatic rearrangement of magnetic topology, often leading to a violent release of magnetic energy. It is important in magnetic fusion and in space and solar physics --- areas that have so far provided the context for most of reconnection research. Importantly, these environments consist just of electrons and ions and the dissipated energy always stays with the plasma. In contrast, in this paper I introduce a new direction of research, motivated by several important problems in high-energy astrophysics --- reconnection in high energy density (HED) radiative plasmas, where radiation pressure and radiative cooling become dominant factors in the pressure and energy balance. I identify the key processes distinguishing HED reconnection: special-relativistic effects; radiative effects (radiative cooling, radiation pressure, and Compton resistivity); and, at the most extreme end, QED effects, including pair creation. I then discuss the main astrophysical applications --- situations with magnetar-strength fields (exceeding the quantum critical field of about 4 x 10^13 G): giant SGR flares and magnetically-powered central engines and jets of GRBs. Here, magnetic energy density is so high that its dissipation heats the plasma to MeV temperatures. Electron-positron pairs are then copiously produced, making the reconnection layer highly collisional and dressing it in a thick pair coat that traps radiation. The pressure is dominated by radiation and pairs. Yet, radiation diffusion across the layer may be faster than the global Alfv\'en transit time; then, radiative cooling governs the thermodynamics and reconnection becomes a radiative transfer problem, greatly affected by the ultra-strong magnetic field. This overall picture is very different from our traditional picture of reconnection and thus represents a new frontier in reconnection research.Comment: Accepted to Space Science Reviews (special issue on magnetic reconnection). Article is based on an invited review talk at the Yosemite-2010 Workshop on Magnetic Reconnection (Yosemite NP, CA, USA; February 8-12, 2010). 30 pages, no figure

An Observational Overview of Solar Flares

We present an overview of solar flares and associated phenomena, drawing upon a wide range of observational data primarily from the RHESSI era. Following an introductory discussion and overview of the status of observational capabilities, the article is split into topical sections which deal with different areas of flare phenomena (footpoints and ribbons, coronal sources, relationship to coronal mass ejections) and their interconnections. We also discuss flare soft X-ray spectroscopy and the energetics of the process. The emphasis is to describe the observations from multiple points of view, while bearing in mind the models that link them to each other and to theory. The present theoretical and observational understanding of solar flares is far from complete, so we conclude with a brief discussion of models, and a list of missing but important observations.Comment: This is an article for a monograph on the physics of solar flares, inspired by RHESSI observations. The individual articles are to appear in Space Science Reviews (2011

Configuration of long chains in equilibrium with rings

The distance R spanned by N monomers of a long chain in chemical equilibrium with other long chains and rings of all sizes varies like R ∼ N1/D with 1/D = ν( n)/Φ(n) where v(n) and Φ(n) are respectively the correlation length critical exponent and the quadratic anisotropy crossover exponent of the O(n) model with n being a statistical preweighting factor associated with a ring.La distance R entre deux monomères séparés par N monomères sur une longue chaîne en équilibre chimique avec d'autres longues chaînes et des anneaux de toutes tailles varie suivant R ∼ N1/ D avec 1/D = ν(n)/Φ(n) où v(n) et Φ( n) sont respectivement l'exposant critique pour la longueur de corrélation et l'exposant de crossover lié à l'anisotropie quadratique pour le modèle O(n) où n est un poids statistique associé à un anneau