Phase diagrams of forced magnetic reconnection in Taylor’s model

Abstract

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 perturbationΨ 0 , and the perturbation wave numberk. This new representation highlights the parameter 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, which have not been considered until now. These features are crucial to understanding the onset and evolution of magnetic reconnection in diverse physical systems.

Perspectives on magnetic reconnection

“…That is, reconnection sets in slowly, and, when it does, it is a slow reconnection. Alternative reconnection scenarios for the Taylor-Hahm-Kulsrud problem are reviewed in [37]. It is found that fast reconnection occurs if the boundary perturbation amplitude is large enough that the current sheet breaks up into plasmoids, due to an instability discussed in §4f.…”

Visco-resistive plasmoid instability

“…i.e., the critical Lundquist number for the stability of the sheet increases with increasing plasma viscosity due to the reduction of the outflow velocity [31,62]. In particular, in the limit P m ≪ 1 we get S c ≈ ǫ −2 c [7, 10], whereas in the limit P m ≫ 1 it follows that S c ≈ ǫ −2 c P 1/2 m , which agrees with the condition proposed by Loureiro et al [17].…”

Variational formulation of relaxed and multi-region relaxed magnetohydrodynamics

“…(2013), Comisso et al. (2015 a , b ). Low-order resonant structures within the plasma that are excited, Boozer & Pomphrey (2010), White (2013) by geometric change resist the formation of magnetic islands by developing shielding current sheets. A long diffusion (possibly anomalous) time scale on which plasma and magnetic flux leak and mix between subregions through weak spots in the current sheets , violating the mass and flux isolation of the subregions assumed in MRxMHD and also violating entropy conservation.…”

“…(2013), Comisso et al. (2015 a , b ). Low-order resonant structures within the plasma that are excited, Boozer & Pomphrey (2010), White (2013) by geometric change resist the formation of magnetic islands by developing shielding current sheets.…”

“…Physically, this corresponds to the assumption of confinement within a perfectly conducting wall (but not necessarily a rigid wall if one wishes to model, for example, the response to an externally imposed perturbation by switching on boundary ripple, Hahm & Kulsrud (1985), Dewar et al. (2013), Comisso, Grasso & Waelbroeck (2015 a , b )). In this paper, we assume for simplicity that the wall has no gaps, so that the wall completely shields the plasma from penetration of externally generated magnetic fluxes, but this restriction is not essential for a Lagrangian formulation to be possible, Dewar (1978), Hosking & Dewar (2015), and would need to be lifted if one wished to consider Ohmic current drive or helicity injection.…”