Development of tearing instability in a current sheet forming by sheared incompressible flow

Tolman, Elizabeth A.; Loureiro, Nuno; Uzdensky, Dmitri

doi:10.1017/s002237781800017x

Cited by 16 publications

(23 citation statements)

References 47 publications

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“…We first establish that pressure anisotropy is produced during CS formation. For that, we adopt a simple local model for CS formation based on a one-dimensional generalization of the Chapman–Kendall solution (Chapman & Kendall 1963; Tolman, Loureiro & Uzdensky 2018, §2). A sheared magnetic field is frozen into an incompressible, time-independent fluid velocity , where and are constants describing the strengths of the reconnecting and guide components of , respectively, and is the characteristic CS-formation time scale.…”

Section: Prerequisitesmentioning

confidence: 99%

Onset of magnetic reconnection in a collisionless, high- plasma

Alt

Kunz

2019

J. Plasma Phys.

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In a magnetized, collisionless plasma, the magnetic moment of the constituent particles is an adiabatic invariant. An increase in the magnetic-field strength in such a plasma thus leads to an increase in the thermal pressure perpendicular to the field lines. Above a β-dependent threshold (where β is the ratio of thermal to magnetic pressure), this pressure anisotropy drives the mirror instability, producing strong distortions in the field lines on ion-Larmor scales. The impact of this instability on magnetic reconnection is investigated using a simple analytical model for the formation of a current sheet (CS) and the associated production of pressure anisotropy. The difficulty in maintaining an isotropic, Maxwellian particle distribution during the formation and subsequent thinning of a CS in a collisionless plasma, coupled with the low threshold for the mirror instability in a high-β plasma, imply that the geometry of reconnecting magnetic fields can differ radically from the standard Harris-sheet profile often used in simulations of collisionless reconnection. As a result, depending on the rate of CS formation and the initial CS thickness, tearing modes whose growth rates and wavenumbers are boosted by this difference may disrupt the mirror-infested CS before standard tearing modes can develop. A quantitative theory is developed to illustrate this process, which may find application in the tearing-mediated disruption of kinetic magnetorotational "channel" modes. †

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Section: Prerequisitesmentioning

confidence: 99%

Onset of magnetic reconnection in a collisionless, high- plasma

Alt

Kunz

2019

J. Plasma Phys.

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“…This can occur if the current sheet is broken up into smaller pieces due to the formation of plasmoids as a result of the tearing instability. A stationary reconnecting current sheet is unstable to a fast tearing instability, or plasmoid instability above a critical value of the Lundquist number that is typically quoted as S S c = 10 4 (Loureiro et al 2007), leading to a reconnection rate of order 10 −2 v A (Samtaney et al 2009;Bhattacharjee et al 2009;Uzdensky et al 2010;Loureiro et al 2012;Huang & Bhattacharjee 2013;Murphy et al 2013;Comisso et al 2016;Comisso et al 2017;Tolman et al 2018). Special relativistic resistive magnetohydrodynamic (SRRMHD) simulations have confirmed this critical value of the Lundquist number in relativistic plasmas with a uniform resistivity Zenitani et al 2010;Zanotti & Dumbser 2011;Takamoto 2013;Baty & Pétri 2013;Pétri et al 2014;Del Zanna et al 2016;Papini et al 2018).…”

Section: Introductionmentioning

confidence: 99%

Relativistic resistive magnetohydrodynamic reconnection and plasmoid formation in merging flux tubes

Ripperda

Porth

Sironi

et al. 2019

Monthly Notices of the Royal Astronomical Society

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We apply the general relativistic resistive magnetohydrodynamics code BHAC to perform a 2D study of the formation and evolution of a reconnection layer in between two merging magnetic flux tubes in Minkowski spacetime. Small-scale effects in the regime of low resistivity most relevant for dilute astrophysical plasmas are resolved with very high accuracy due to the extreme resolutions obtained with adaptive mesh refinement. Numerical convergence in the highly nonlinear plasmoid-dominated regime is confirmed for a sweep of resolutions. We employ both uniform resistivity and nonuniform resistivity based on the local, instantaneous current density. For uniform resistivity we find Sweet-Parker reconnection, from η = 10 −2 down to η = 10 −4 , for a reference case of magnetisation σ = 3.33 and plasma-β = 0.1. For uniform resistivity η = 5 × 10 −5 the tearing mode is recovered, resulting in the formation of secondary plasmoids. The plasmoid instability enhances the reconnection rate to v rec ∼ 0.03c compared to v rec ∼ 0.01c for η = 10 −4 . For non-uniform resistivity with a base level η 0 = 10 −4 and an enhanced current-dependent resistivity in the current sheet, we find an increased reconnection rate of v rec ∼ 0.1c. The influence of the magnetisation σ and the plasma-β is analysed for cases with uniform resistivity η = 5 × 10 −5 and η = 10 −4 in a range 0.5 ≤ σ ≤ 10 and 0.01 ≤ β ≤ 1 in regimes that are applicable for black hole accretion disks and jets. The plasmoid instability is triggered for Lundquist numbers larger than a critical value of S c ≈ 8000.

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“…Because of its perceived importance – from determining the reconnection rate in MHD plasmas to its possible role in the reconnection onset (Pucci & Velli 2014; Comisso et al. 2016; Uzdensky & Loureiro 2016; Tolman, Loureiro & Uzdensky 2018) and in the energy partition (Loureiro et al. 2012; Numata & Loureiro 2015) and particle acceleration and plasma heating (Drake et al.…”

Section: Introductionmentioning

confidence: 99%

“…Magnetic reconnection is a fundamental plasma physics phenomenon, relevant to laboratory, space and astrophysical systems (Biskamp 2000;Zweibel & Yamada 2009;Uzdensky 2011). It involves a rapid topological rearrangement of the magnetic field, leading to efficient magnetic energy conversion and dissipation.…”

Section: Introductionmentioning

confidence: 99%

Plasmoid instability in the semi-collisional regime

Bhat

Loureiro

2018

J. Plasma Phys.

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We investigate analytically and numerically the semi-collisional regime of the plasmoid instability, defined by the inequality $\unicode[STIX]{x1D6FF}_{\text{SP}}\gg \unicode[STIX]{x1D70C}_{s}\gg \unicode[STIX]{x1D6FF}_{\text{in}}$, where $\unicode[STIX]{x1D6FF}_{\text{SP}}$ is the width of a Sweet–Parker current sheet, $\unicode[STIX]{x1D70C}_{s}$ is the ion sound Larmor radius and $\unicode[STIX]{x1D6FF}_{\text{in}}$ is the width of the boundary layer that arises in the plasmoid instability analysis. Theoretically, this regime is predicted to exist if the Lundquist number $S$ and the length of the current sheet $L$ are such that $(L/\unicode[STIX]{x1D70C}_{s})^{14/9}<S<(L/\unicode[STIX]{x1D70C}_{s})^{2}$ (for a sinusoidal-like magnetic configuration; for a Harris-type sheet the lower bound is replaced with $(L/\unicode[STIX]{x1D70C}_{s})^{8/5}$). These bounds are validated numerically by means of simulations using a reduced gyrokinetic model (Zocco & Schekochihin, Phys. Plasmas, vol. 18 (10), 2011, 102309) conducted with the code Viriato. Importantly, this regime is conjectured to allow for plasmoid formation at relatively low, experimentally accessible, values of the Lundquist number. Our simulations obtain plasmoid instability at values of $S$ as low as ${\sim}250$. The simulations do not prescribe a Sweet–Parker sheet; rather, one is formed self-consistently during the nonlinear evolution of the initial tearing mode configuration. This proves that this regime of the plasmoid instability is realizable, at least at the relatively low values of the Lundquist number that are accessible to current dedicated experiments.

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Development of tearing instability in a current sheet forming by sheared incompressible flow

Cited by 16 publications

References 47 publications

Onset of magnetic reconnection in a collisionless, high- plasma

Onset of magnetic reconnection in a collisionless, high- plasma

Relativistic resistive magnetohydrodynamic reconnection and plasmoid formation in merging flux tubes

Plasmoid instability in the semi-collisional regime

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