The plasmoid instability during asymmetric inflow magnetic reconnection

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 S α τ β [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.The rapid conversion of magnetic energy into plasma particle energy through the process of magnetic reconnection is of great importance in the realm of plasma physics and astrophysics [1][2][3][4]. Sawtooth crashes, magnetospheric substorms, stellar and gamma-ray flares are just a few examples of pheneomena in which magnetic reconnection plays an essential role.In large systems, such as those found in space and astrophysical environments, the potential formation of highly elongated current sheets would result in extremely low reconnection rates, which fail to account for the observed fast energy release rates [5][6][7]. However, such current sheets are subject to a violent linear instability that leads to their breakup, giving rise to a tremendous increase in the reconnection rate that appears to be very weakly dependent on the Lundquist number of the system in the nonlinear regime [8][9][10][11][12][13][14][15][16][17]. This crucial instability, which serves as a trigger of fast reconnection, is the plasmoid instability [2], thus dubbed as it leads to the formation of plasmoids.In the widely studied Sweet-Parker current sheets, which are characterized by an inverse aspect ratio a/L ∼ S −1/2 , Tajima and Shibata [1], as well as Loureiro et al.[18], have found that the growth rate γ and the wavenumber k of the plasmoid instability obey γτ A ∼ S 1/4 and kL ∼ S 3/8 , where τ A is the Alfvénic timescale based on the length of the current sheet. Since the Lundquist number S is extremely large in most space and astrophysical plasmas [19], the linear growth of the instability turns out to be surprisingly fast, and the number of plasmoids produced is also very high. Other notable works have since followed, which have verified and extended the work on the plasmoid instability in different contexts [20][21][22][23][24].Despite the success of the theory, its limitations soon became evident. For sufficiently high growth rates, Sweet-Parker current sheets cannot be attained as current layers are linearly unstable and disrupt before this state is achieved. In order to bypass this limitation, Pucci and Velli [25] conjectured that current sheets break up when γτ A ∼ 1. Later, Uzdensky and Loureiro [26] considered a similar criterion (γτ = 1) as the end-point of the linear stage of the instability, presenting an appealing but heuristic discussion for the case of a current sheet evolving...

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“…This implies that we can approximateγ(â) withγ s (â) in Eq. (14). In the larget * regime, we recover the Sweet-Parker-limit solution.…”

supporting

confidence: 53%

“…However, for the most interesting caset * < τ ln(1 +â 0 S 1/2 ) [30], which occurs for very large S-values, one has to solve Eq. (14). In this caset * τ ln(â 0 /â * ), and, usingâ * â 0 , we obtain a * c a τ 2/3 S −1/3 ln c δâ…”

mentioning

confidence: 87%

General theory of the plasmoid instability

et al. 2016

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“…Paper I; Ni et al 2010;Shen et al 2011;Lynch et al 2016), exhibit nonlinear dynamics and plasmoid-unstable evolution similar to those simulations with higher Lundquist numbers that exceed the more traditional 10 4 threshold (e.g. Furth et al 1963;Biskamp 1986;Huang & Bhattacharjee 2010;Loureiro et al 2012;Murphy et al 2013).…”

Section: Computational Grid Adaptive Mesh Refinement and Numerical Rementioning

confidence: 89%

Formation and Reconnection of Three-dimensional Current Sheets with a Guide Field in the Solar Corona

Edmondson

Lynch

2017

ApJ

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We analyze a series of three-dimensional magnetohydrodynamic numerical simulations of magnetic reconnection in a model solar corona to study the effect of the guide field component on quasi-steady state interchange reconnection in a pseudostreamer arcade configuration. This work extends the analysis of Edmondson et al. (2010b) by quantifying the mass density enhancement coherency scale in the current sheet associated with magnetic island formation during the nonlinear phase of plasmoid-unstable reconnection. We compare the results of four simulations of a zero, weak, moderate, and a strong guide field, B GF /B 0 = {0.0, 0.1, 0.5, 1.0}, to quantify the plasmoid density enhancement's longitudinal and transverse coherency scales as a function of the guide field strength. We derive these coherency scales from autocorrelation and wavelet analyses, and demonstrate how these scales may be used to interpret the density en-

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“…In this subsection, we describe our technique to identify the plasmoids that are self-consistently generated by reconnection, and to follow individual plasmoids over time. As it is customary in magnetohydrodinamic (MHD) simulations (Fermo et al 2010;Loureiro et al 2012;Huang & Bhattacharjee 2012;Murphy et al 2013), the O-points at the center of plasmoids and the X-points in between neighboring plasmoids are identified in a 2D domain as local maxima and minima of the magnetic vector potential A z . Apart from a minus sign, A z also corresponds to the magnetic flux function.…”

Section: Plasmoid Identification and Trackingmentioning

confidence: 99%

Plasmoids in relativistic reconnection, from birth to adulthood: first they grow, then they go

Sironi¹,

Giannios²,

Πετροπούλου³

2016

Mon. Not. R. Astron. Soc.

176

227

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Blobs, or quasi-spherical emission regions containing relativistic particles and magnetic fields, are often assumed ad hoc in emission models of relativistic astrophysical jets, yet their physical origin is still not well understood. Here, we employ a suite of large-scale two-dimensional particle-in-cell simulations in electron-positron plasmas to demonstrate that relativistic magnetic reconnection can naturally account for the formation of quasi-spherical plasmoids filled with high-energy particles and magnetic fields. Our simulations extend to unprecedentedly long temporal and spatial scales, so we can capture the asymptotic physics independently of the initial setup. We characterize the properties of the plasmoids that are continuously generated as a self-consistent by-product of the reconnection process: they are in rough energy equipartition between particles and magnetic fields (with kinetic and magnetic energy densities proportional to the magnetization σ); the upper energy cutoff of the plasmoid particle spectrum is proportional to the plasmoid width w, corresponding to a Larmor radius ∼ 0.2 w; the plasmoids grow in size at ∼ 0.1 of the speed of light (roughly half of the reconnection inflow rate), with most of the growth happening while they are still non-relativistic ("first they grow"); their growth is suppressed once they get accelerated to relativistic speeds by the field line tension, up to a terminal four-velocity ∼ √ σ c ("then they go"). The largest plasmoids, whose typical recurrence interval is ∼ 2.5 L/c, reach a characteristic size w max ∼ 0.2 L independently of the system length L, they have nearly isotropic particle distributions and they contain the highest energy particles, whose Larmor radius is ∼ 0.03 L. The latter can be regarded as the Hillas criterion for relativistic reconnection. We briefly discuss the implications of our results for the high-energy emission from relativistic jets and pulsar winds.

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The plasmoid instability during asymmetric inflow magnetic reconnection

Cited by 24 publications

References 119 publications

General theory of the plasmoid instability

General theory of the plasmoid instability

Formation and Reconnection of Three-dimensional Current Sheets with a Guide Field in the Solar Corona

Plasmoids in relativistic reconnection, from birth to adulthood: first they grow, then they go

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