Yi-Min Huang

Fast reconnection in high-Lundquist-number plasmas due to the plasmoid Instability

Thin current sheets in systems of large size that exceed a critical value of the Lundquist number are unstable to a super-Alfvenic tearing instability, referred to hereafter as the plasmoid instability. The scaling of the growth rate of the most rapidly growing plasmoid instability with respect to the Lundquist number is shown to follow from the classical dispersion relation for tearing modes. As a result of this instability, the system realizes a nonlinear reconnection rate that appears to be weakly dependent on the Lundquist number, and larger than the Sweet–Parker rate by nearly an order of magnitude (for the range of Lundquist numbers considered). This regime of fast reconnection is realizable in a dynamic and highly unstable thin current sheet, without requiring the current sheet to be turbulent.

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 thick...

Experimental observation and characterization of the magnetorotational instability

Differential rotation occurs in conducting flows in accretion disks and planetary cores. In such systems, the magnetorotational instability can arise from coupling Lorentz and centrifugal forces to cause large radial angular momentum fluxes. We present the first experimental observation of the magnetorotational instability. Our system consists of liquid sodium between differentially rotating spheres, with an imposed coaxial magnetic field. We characterize the observed patterns, dynamics, and torque increases, and establish that this instability can occur from a hydrodynamic turbulent background.

Plasmoid instability in high-Lundquist-number magnetic reconnection

Our understanding of magnetic reconnection in resistive magnetohydrodynamics has gone through a fundamental change in recent years. The conventional wisdom is that magnetic reconnection mediated by resistivity is slow in laminar high Lundquist (S) plasmas, constrained by the scaling of the reconnection rate predicted by Sweet-Parker theory. However, recent studies have shown that when S exceeds a critical value ∼104, the Sweet-Parker current sheet is unstable to a super-Alfvenic plasmoid instability, with a linear growth rate that scales as S1/4. In the fully developed statistical steady state of two-dimensional resistive magnetohydrodynamic simulations, the normalized average reconnection rate is approximately 0.01, nearly independent of S, and the distribution function f(ψ) of plasmoid magnetic flux ψ follows a power law f(ψ)∼ψ−1. When Hall effects are included, the plasmoid instability may trigger onset of Hall reconnection even when the conventional criterion for onset is not satisfied. The rich varie...

Onset of fast reconnection in Hall magnetohydrodynamics mediated by the plasmoid instability

The role of a super-Alfvenic plasmoid instability in the onset of fast reconnection is studied by means of the largest Hall magnetohydrodynamics simulations to date, with system sizes up to 104 ion skin depths (di). It is demonstrated that the plasmoid instability can facilitate the onset of rapid Hall reconnection, in a regime where the onset would otherwise be inaccessible because the Sweet–Parker width is significantly above di. However, the topology of Hall reconnection is not inevitably a single stable X-point. There exists an intermediate regime where the single X-point topology itself exhibits instability, causing the system to alternate between a single X-point geometry and an extended current sheet with multiple X-points produced by the plasmoid instability. Through a series of simulations with various system sizes relative to di, it is shown that system size affects the accessibility of the intermediate regime. The larger the system size is, the easier it is to realize the intermediate regime. A...

Linear plasmoid instability of thin current sheets with shear flow

This paper presents linear analytical and numerical studies of plasmoid instabilities in the presence of shear flow in high-Lundquist-number plasmas. Analysis demonstrates that the stability problem becomes essentially two dimensional as the stabilizing effects of shear flow become more prominent. Scaling results are presented for the two-dimensional instabilities. An approximate criterion is given for the critical aspect ratio of thin current sheets at which the plasmoid instability is triggered.

Reduced magnetohydrodynamic theory of oblique plasmoid instabilities

The three-dimensional nature of plasmoid instabilities is studied using the reduced magnetohydrodynamic equations. For a Harris equilibrium with guide field, represented by Bo=Bpotanh(x/λ)y+Bzoz, a spectrum of modes are unstable at multiple resonant surfaces in the current sheet, rather than just the null surface of the poloidal field Byo(x)=Bpotanh(x/λ), which is the only resonant surface in 2D or in the absence of a guide field. Here, Bpo is the asymptotic value of the equilibrium poloidal field, Bzo is the constant equilibrium guide field, and λ is the current sheet width. Plasmoids on each resonant surface have a unique angle of obliquity θ≡arctan(kz/ky). The resonant surface location for angle θ is xs=λarctanh(μ), where μ=tanθBzo/Bpo and the existence of a resonant surface requires |θ|<arctan(Bpo/Bzo). The most unstable angle is oblique, i.e., θ≠0 and xs≠0, in the constant-ψ regime, but parallel, i.e., θ=0 and xs=0, in the nonconstant-ψ regime. For a fixed angle of obliquity, the most unstable wave...

Distribution of Plasmoids in High-Lundquist-Number Magnetic Reconnection

The distribution function f(ψ) of magnetic flux ψ in plasmoids formed in high-Lundquist-number current sheets is studied by means of an analytic phenomenological model and direct numerical simulations. The distribution function is shown to follow a power law f(ψ)∼ψ(-1), which differs from other recent theoretical predictions. Physical explanations are given for the discrepant predictions of other theoretical models.

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

Hall magnetohydrodynamic reconnection in the plasmoid unstable regime

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