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

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Journal Article: Publisher's Accepted Manuscript
Journal Name:
Physics of Plasmas
Additional Journal Information:
Journal Volume: 22; Journal Issue: 4; Related Information: CHORUS Timestamp: 2016-12-26 04:27:33; Journal ID: ISSN 1070-664X
American Institute of Physics
Country of Publication:
United States

Citation Formats

Comisso, L., Grasso, D., and Waelbroeck, F. L.. Extended theory of the Taylor problem in the plasmoid-unstable regime. United States: N. p., 2015. Web. doi:10.1063/1.4918331.
Comisso, L., Grasso, D., & Waelbroeck, F. L.. Extended theory of the Taylor problem in the plasmoid-unstable regime. United States. doi:10.1063/1.4918331.
Comisso, L., Grasso, D., and Waelbroeck, F. L.. 2015. "Extended theory of the Taylor problem in the plasmoid-unstable regime". United States. doi:10.1063/1.4918331.
title = {Extended theory of the Taylor problem in the plasmoid-unstable regime},
author = {Comisso, L. and Grasso, D. and Waelbroeck, F. L.},
abstractNote = {},
doi = {10.1063/1.4918331},
journal = {Physics of Plasmas},
number = 4,
volume = 22,
place = {United States},
year = 2015,
month = 4

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record at 10.1063/1.4918331

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Cited by: 20works
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  • 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 ismore » 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.« less
  • The Sweet-Parker layer in a system that exceeds a critical value of the Lundquist number (S) is unstable to the plasmoid instability. In this paper, a numerical scaling study has been done with an island coalescing system driven by a low level of random noise. In the early stage, a primary Sweet-Parker layer forms between the two coalescing islands. The primary Sweet-Parker layer breaks into multiple plasmoids and even thinner current sheets through multiple levels of cascading if the Lundquist number is greater than a critical value S{sub c}approx =4x10{sup 4}. As a result of the plasmoid instability, the systemmore » realizes a fast nonlinear reconnection rate that is nearly independent of S, and is only weakly dependent on the level of noise. The number of plasmoids in the linear regime is found to scales as S{sup 3/8}, as predicted by an earlier asymptotic analysis [N. F. Loureiro et al., Phys. Plasmas 14, 100703 (2007)]. In the nonlinear regime, the number of plasmoids follows a steeper scaling, and is proportional to S. The thickness and length of current sheets are found to scale as S{sup -1}, and the local current densities of current sheets scale as S{sup -1}. Heuristic arguments are given in support of theses scaling relations.« less
  • A set of reduced Hall magnetohydrodynamic (MHD) equations are used to evaluate the stability of large aspect ratio current sheets to the formation of plasmoids (secondary islands). Reconnection is driven by resistivity in this analysis, which occurs at the resistive skin depth d{sub {eta}}{identical_to}S{sub L}{sup -1/2}{radical}(L{nu}{sub A}/{gamma}), where S{sub L} is the Lundquist number, L, the length of the current sheet, {nu}{sub A,} the Alfven speed, and {gamma}, the growth rate. Modifications to a recent resistive MHD analysis [N. F. Loureiro et al., Phys. Plasmas 14, 100703 (2007)] arise when collisions are sufficiently weak that d{sub {eta}} is shorter thanmore » the ion skin depth d{sub i}{identical_to}c/{omega}{sub pi}. Secondary islands grow faster in this Hall MHD regime: the maximum growth rate scales as (d{sub i}/L){sup 6/13}S{sub L}{sup 7/13}{nu}{sub A}/L and the number of plasmoids as (d{sub i}/L){sup 1/13}S{sub L}{sup 11/26}, compared to S{sub L}{sup 1/4}{nu}{sub A}/L and S{sup 3/8}, respectively, in resistive MHD.« less
  • We present an analytic approach to the problem of predicting the widths of fingers in a Hele-Shaw cell. Our analysis is based on the WKB technique developed recently for dealing with the effects of surface tension in the problem of dendritic solidification. We find that the relation between the dimensionless width lambda and the dimensionless group of parameters containing the surface tension,, has the form lambda-(1/2) 2/3/ in the limit of small
  • The Hahm–Kulsrud (HK) [T. S. Hahm and R. M. Kulsrud, Phys. Fluids 28, 2412 (1985)] solutions for a magnetically sheared plasma slab driven by a resonant periodic boundary perturbation illustrate fully shielded (current sheet) and fully reconnected (magnetic island) responses. On the global scale, reconnection involves solving a magnetohydrodynamic (MHD) equilibrium problem. In systems with a continuous symmetry, such MHD equilibria are typically found by solving the Grad–Shafranov equation, and in slab geometry the elliptic operator in this equation is the 2-D Laplacian. Thus, assuming appropriate pressure and poloidal current profiles, a conformal mapping method can be used to transformmore » one solution into another with different boundary conditions, giving a continuous sequence of solutions in the form of partially reconnected magnetic islands (plasmoids) separated by Syrovatsky current sheets. The two HK solutions appear as special cases.« less