Number Of Plasmoids Research Articles

General theory of the plasmoid instability

A general theory of the onset and development of the plasmoid instability is formulated by means of a principle of least time. The scaling relations for the final aspect ratio, transition time to rapid onset, growth rate, and number of plasmoids are derived and shown to depend on the initial perturbation amplitude (ŵ0), the characteristic rate of current sheet evolution (1/τ), and the Lundquist number (S). They are not simple power laws, and are proportional to Sατβ[ln f(S,τ,ŵ0)]σ. The detailed dynamics of the instability is also elucidated, and shown to comprise of a period of quiescence followed by sudden growth over a short time scale.

Hall magnetohydrodynamic reconnection in the plasmoid unstable regime

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 dη≡SL-1/2LνA/γ, where SL is the Lundquist number, L, the length of the current sheet, νA, the Alfvén speed, and γ, 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 dη is shorter than the ion skin depth di ≡ c/ωpi. Secondary islands grow faster in this Hall MHD regime: the maximum growth rate scales as (di/L)6/13SL7/13νA/L and the number of plasmoids as (di/L)1/13SL11/26, compared to SL1/4νA/L and S3/8, respectively, in resistive MHD.

Scaling laws of resistive magnetohydrodynamic reconnection in the high-Lundquist-number, plasmoid-unstable regime

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 Sc≃4×104. As a result of the plasmoid instability, the system 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 S3/8, 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−1, and the local current densities of current sheets scale as S−1. Heuristic arguments are given in support of theses scaling relations.