Studies of nonlinear tearing mode reconnection
Author(s)
Loureiro, Nuno Filipe Gomes
Type
Thesis
Abstract
The resistive tearing mode is studied using the equations of reduced-MHD in slab geometry. We carry out a numerical parameter scan by varying the resistivity rJ and the instability parameter .6.'. We focus on the strongly driven regime (large.6.') , for which the evolution consists of five main stage : FKR linear instability , Rutherford's slow nonlinear growth, Sweet-Parker (SP) reconnection, secondary island generation and saturation . Our main contribution is the identification and thorough characterization of this multi-stage evolution with particular emphasis on the last three stages. The first two stages are characterized by an X-point structure. We show that, for sufficiently large .6.', a collapse of the X point occurs once the island width exceeds a certain critical value ~ 1/ .6.' . A current sheet is formed and the Rutherford regime gives way to exponential SP reconnection. The growth rate of the reconnected flux scales as rJ1/ 2 and can exceed the FKR value. After the collapse , SP reconnection continues at a rate that decreases in time due to the gradual depletion of the unreconnected flux. If the aspect ratio of the current sheet is sufficiently large the sheet can itself become tearing -mod e unstable, giving rise to a second island with an 0-point at the center of the sheet and two new X-points located at the end-points of the sheet. As the second island grows, the new X-points collapse, generating two current sheets. Due to the attraction between islands and th symmetry of our configuration, the second island splits into two halves, which coalesce with the original island. Given strong enough initial drive, this process can be repeated before saturation is reached. The nature of the saturated state depends on whether the mode has undergone an X-point collapse . For small .6.', the saturation amplitude is in very good agreement with the theory due to Escande & Ottaviani and Militello & Porcelli. If .6.' is sufficiently large for the X-point collapse to occur, the saturation amplitude increases noticeably and becomes independent of .6.'. Preliminary studies of the effect of finite ion Larmor radius on the mode evolution are described. Most importantly, for the cases when X-point collapse is possible a Petschek-like structure rather than an SP current sheet is formed.
Version
Open Access
Date Awarded
2005
Copyright Statement
Attribution NoDerivatives 4.0 International Licence (CC BY-ND)
Advisor
Haines, Malcolm
Sponsor
Fund acao para a Ciencia e a Tecnologia
Ministe rio da Ciencia
Portugal. Government
Grant Number
SFRH / BD / 2785 / 2000
Publisher Department
Department of Physics
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)