Response to “Comment on ‘Scaling of asymmetric magnetic reconnection: General theory and collisional simulations’ ” [Phys. Plasmas 16, 034701 (2009)]

Cassak, P. A.; Shay, M. A.

doi:10.1063/1.3083264

Cited by 6 publications

(9 citation statements)

References 9 publications

(9 reference statements)

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“…Direct numerical simulations of reconnection processes concur with observations in displaying ubiquitous evidence for plasmoid formation. Plasmoids have been reported in numerical simulations using various physical models, ranging from kinetic [29][30][31][32][33] to Hall-MHD [34,35] and to single fluid MHD [36][37][38][39][40][41][42][43][44][45][46][47][48][49]. Plasmoid formation has also been reported in numerical simulations of reconnection in relativistic plasmas, both resistive [50] and kinetic [51][52][53][54].…”

Section: Introductionmentioning

confidence: 99%

Plasmoid and Kelvin-Helmholtz instabilities in Sweet-Parker current sheets

2013

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A two-dimensional (2D) linear theory of the instability of Sweet-Parker (SP) current sheets is developed in the framework of reduced magnetohydrodynamics. A local analysis is performed taking into account the dependence of a generic equilibrium profile on the outflow coordinate. The plasmoid instability [Loureiro et al., Phys. Plasmas 14, 100703 (2007)] is recovered, i.e., current sheets are unstable to the formation of a large-wave-number chain of plasmoids (k(max)L(CS)~S(3/8), where k(max) is the wave number of fastest growing mode, S=L(CS)V(A)/η is the Lundquist number, L(CS) is the length of the sheet, V(A) is the Alfvén speed, and η is the plasma resistivity), which grows super Alfvénically fast (γ(max)τ(A)~S(1/4), where γ(max) is the maximum growth rate, and τ(A)=L(CS)/V(A)). For typical background profiles, the growth rate and the wave number are found to increase in the outflow direction. This is due to the presence of another mode, the Kelvin-Helmholtz (KH) instability, which is triggered at the periphery of the layer, where the outflow velocity exceeds the Alfvén speed associated with the upstream magnetic field. The KH instability grows even faster than the plasmoid instability γ(max)τ(A)~k(max)L(CS)~S(1/2). The effect of viscosity (ν) on the plasmoid instability is also addressed. In the limit of large magnetic Prandtl numbers Pm=ν/η, it is found that γ(max)~S(1/4)Pm(-5/8) and k(max)L(CS)~S(3/8)Pm(-3/16), leading to the prediction that the critical Lundquist number for plasmoid instability in the Pm>>1 regime is S(crit)~10(4)Pm(1/2). These results are verified via direct numerical simulation of the linearized equations, using an analytical 2D SP equilibrium solution.

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Section: Introductionmentioning

confidence: 99%

Plasmoid and Kelvin-Helmholtz instabilities in Sweet-Parker current sheets

2013

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“…The basic conceptual underpinnings of the modern understanding of resistive reconnection can be summarised in three points: (i) generic X-point configurations are unstable and collapse into current layers [5,6]; (ii) the structure of resistive current layers is well described by the Sweet-Parker (SP) model [7]: if B 0 is the upstream magnetic field, V A = B 0 / √ 4πρ is the Alfvén speed (ρ the plasma density), L the length of the layer, η the magnetic diffusivity, and S ≡ V A L/η the Lundquist number, then the layer thickness is δ ∼ L/ √ S, the outflow velocity is V A , and the reconnection rate is cE ∼ V A B 0 / √ S -"slow" because it depends on S, which is very large in most natural systems; (iii) when S exceeds a critical value S c ∼ 10 4 , the SP layers are linearly unstable [8] and break up into secondary islands, or plasmoids [9]. This fact has emerged as a defining feature of numerical simulations of reconnection as they have broken through the S c barrier [6,[9][10][11][12][13][14][15][16]. It seems that high-S reconnection generically occurs via a chain of plasmoids, born, growing, coalescing, and being ejected in a stochastic fashion [17,18].…”

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confidence: 99%

Fast Magnetic Reconnection in the Plasmoid-Dominated Regime

2010

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A conceptual model of resistive magnetic reconnection via a stochastic plasmoid chain is proposed. The global reconnection rate is shown to be independent of the Lundquist number. The distribution of fluxes in the plasmoids is shown to be an inverse square law. It is argued that there is a finite probability of emergence of abnormally large plasmoids, which can disrupt the chain (and may be responsible for observable large abrupt events in solar flares and sawtooth crashes). A criterion for the transition from magnetohydrodynamic to collisionless regime is provided.PACS numbers: 52.35. Vd, 94.30.cp, 96.60.Iv, 52.35.Py Introduction. Magnetic reconnection is the process of topological rearrangement of magnetic field, resulting in a conversion of magnetic energy into various forms of plasma energy [1]. It is believed to cause solar flares and has been studied in tokamaks [2], dedicated laboratory experiments [3] and measured in situ in the Earth's magnetosphere [4]. The basic conceptual underpinnings of the modern understanding of resistive reconnection can be summarised in three points: (i) generic X-point configurations are unstable and collapse into current layers [5,6]; (ii) the structure of resistive current layers is well described by the Sweet-Parker (SP) model [7]: if B 0 is the upstream magnetic field, V A = B 0 / √ 4πρ is the Alfvén speed (ρ the plasma density), L the length of the layer, η the magnetic diffusivity, and S ≡ V A L/η the Lundquist number, then the layer thickness is δ ∼ L/ √ S, the outflow velocity is V A , and the reconnection rate is cE ∼ V A B 0 / √ S -"slow" because it depends on S, which is very large in most natural systems; (iii) when S exceeds a critical value S c ∼ 10 4 , the SP layers are linearly unstable [8] and break up into secondary islands, or plasmoids [9]. This fact has emerged as a defining feature of numerical simulations of reconnection as they have broken through the S c barrier [6,[9][10][11][12][13][14][15][16]. It seems that high-S reconnection generically occurs via a chain of plasmoids, born, growing, coalescing, and being ejected in a stochastic fashion [17,18]. Importantly, recent numerical evidence [11,[13][14][15][16] suggests that plasmoid reconnection is "fast", i.e., independent of S.

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“…In addition to increasing the reconnection rate, secondary islands hasten the transition to Hall reconnection [26,34]. When a secondary island forms, the fragmented current sheet is shorter, so its Sweet-Parker thickness is smaller [25,26]. When the layer reaches ion gyroscales [35,36], Hall reconnection begins abruptly [15,26,[37][38][39].…”

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confidence: 99%

“…Islands arise when δ/L SP ∼ 0.01, which gives δ ∼ 2.0 since L SP ∼ 200. It has been shown [25,26] that if N X-lines are present, δ decreases by a factor of N 1/2 . For a single secondary island (N = 2), the layer shrinks to δ ∼ 2.0/2 1/2 ∼ 1.4.…”

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confidence: 99%

Comparison of Secondary Islands in Collisional Reconnection to Hall Reconnection

Shepherd

Cassak

2010

Phys. Rev. Lett.

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Large-scale resistive Hall-magnetohydrodynamic simulations of the transition from Sweet-Parker (collisional) to Hall (collisionless) magnetic reconnection are presented; the first to separate secondary islands from collisionless effects. Three main results are described. There exists a regime with secondary islands but without collisionless effects, and the reconnection rate is faster than Sweet-Parker, but significantly slower than Hall reconnection. This implies that secondary islands do not cause the fastest reconnection rates. The onset of Hall reconnection ejects secondary islands from the vicinity of the X line, implying that energy is released more rapidly during Hall reconnection. Coronal applications are discussed.

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Response to “Comment on ‘Scaling of asymmetric magnetic reconnection: General theory and collisional simulations’ ” [Phys. Plasmas 16, 034701 (2009)]

Cited by 6 publications

References 9 publications

Plasmoid and Kelvin-Helmholtz instabilities in Sweet-Parker current sheets

Plasmoid and Kelvin-Helmholtz instabilities in Sweet-Parker current sheets

Fast Magnetic Reconnection in the Plasmoid-Dominated Regime

Comparison of Secondary Islands in Collisional Reconnection to Hall Reconnection

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