An analysis of reconnection dynamics in an eruptive flare model

This dissertation develops a one-dimensional, analytic model for current sheets that form during solar flares. The model uses a method developed by B. V. Somov & V. S. Titov for Petschek-type reconnection. The first part of this dissertation provides a detailed analysis of the Somov-Titov model, its assumptions, strengths and weaknesses. We consider the role of both the diffusion region and nonuniform resistivity in the generation of Petschek-type solutions. The second part of this dissertation extends the averaging method to the dynamics of an asymmetric current sheet during a solar flare. We determine the location of the x-line and the distribution of incoming Poynting flux into upward and downward directed reconnection jets. We find that, except at the very beginning of a flare when the current sheet is most symmetric, the x-line is generally located near the lower tip of the sheet. We predict that it should be low enough in the corona to be observed by X-ray and EUV telescopes. We find that in most cases the majority of incoming flux exits the current sheet through the upward jet, in contrast to previous studies that assumed as much as 50% of the incoming flux is directed into the downward jet and flare ribbons. In the third part, we integrate thermal conduction into the Somov-Titov framework using a slow-shock model that includes conduction, and allows us to describe the thermal halo that surrounds the current sheet because of heat flow across the current sheet boundary. We find that thermal conduction has a significant effect on the fast-mode mach number of the reconnection outflow, producing mach numbers as high as 7 for solar-flare conditions, three times greater than previously calculated. We conclude that these termination shocks are considerably more efficient at producing particle acceleration than previously thought since the efficiency of particle acceleration at shocks increases dramatically with Mach number. We compare this model with numerical simulations by T. Yokoyama & K. Shibata and find good agreement

Microcanonical entropy inflection points: Key to systematic understanding of transitions in finite systems

We introduce a systematic classification method for the analogs of phase transitions in finite systems. This completely general analysis, which is applicable to any physical system and extends towards the thermodynamic limit, is based on the microcanonical entropy and its energetic derivative, the inverse caloric temperature. Inflection points of this quantity signal cooperative activity and thus serve as distinct indicators of transitions. We demonstrate the power of this method through application to the long-standing problem of liquid-solid transitions in elastic, flexible homopolymers.Comment: 4 pages, 3 figure