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Journal Articles Physical Review Letters Year : 2008

Time window for magnetic reconnection in plasma configurations with velocity shear

Abstract

It is shown that the rate of magnetic field line reconnection can be clocked by the evolution of the large scale processes that are responsible for the formation of the current layers where reconnection can take place. In unsteady plasma configurations, such as those produced by the onset of the Kelvin-Helmholtz instability in a plasma with a velocity shear, qualitatively different magnetic structures are produced depending on how fast the reconnection process develops on the external clock set by the evolving large scale configuration. PACS numbers: 52.35.Vd, 52.35.Mw, 52.65.Kj, 52.35.Py Fast magnetic field line reconnection is believed to be a crucial phenomenon in low collisionality or collision-less plasmas, as expected to occur on time scales that do not exceed by large factors the dynamical plasma time scales as determined within the ideal magnetohy-drodynamic (MHD) description. When current layers are formed that have widths of order of the ion skin depth d i ≡ c/ω pi , with ω pi the ion plasma frequency, ions inside these current layers decouple their motion from the evolution of the magnetic field. Per se this decoupling is not sufficient to allow for magnetic reconnection which requires electron decoupling. This latter occurs inside a thinner region that, depending on the plasma parameters , has a width determined either by a non-vanishing resistivity or by kinetic effects, or, as is the two fluids model description adopted here, by electron inertia effects. The large spatial separation between these two decoupling regions allows magnetic reconnection to grow at a faster rate [1-5]. In a magnetized plasma streaming with a nonuniform velocity, the Kelvin-Helmholtz (K-H) instability plays a major role in mixing different plasma regions and in stretching the magnetic field lines leading to the formation of layers with a sheared magnetic field where magnetic field line reconnection can take place. A relevant example is provided by the formation of a mixing layer between the Earth's magnetosphere and the solar wind at low latitudes during northward periods recently investigated in Ref. [6] (see also references therein). In the considered configuration, in the presence of a magnetic field nearly perpendicular to the plane defined by the velocity field and its inhomogeneity direction, velocity shear drives a K-H instability which advects and distorts the magnetic field configuration. If the Alfvén velocity associated to the in-plane magnetic field is sufficiently weak with respect to the variation of the fluid velocity in the plasma, the K-H instability generates fully rolled-up vortices which advect the magnetic field lines into a complex configuration, causing the formation of current layers. Since the plasma dynamics is essentially driven by the vortex motion, the reconnection events that are produced in these layers are usually denoted as Vortex Induced Reconnection (VIR) [7-11]. Pairing of the vortices generated by the K-H instability is a well know phenomenon in two-dimensional hy-drodynamics [12, 13]. On the other hand, the role of the magnetic field on vortex dynamics has been studied essentially in the limit of only one vortex, the largest one contained in the simulation box. It has been shown that, even if the magnetic field is weak and unable to prevent the formation of the KH vortex, nevertheless the VIR process eventually leads to vortex disruption [9, 10, 14]. On the contrary, in this letter we investigate the development of magnetic reconnection during the vortex pairing process and show that completely different large scale magnetic structures are produced depending on how fast the reconnection process develops on the time scale set by the pairing process. We consider a configuration with a value of the plasma β parameter (ratio of plasma pressure over total magnetic field pressure) of order unity and show that in this regime the Hall term in Ohm's law, corresponding to the decoupling of electrons and ions inside the current layers, allows magnetic reconnection to occur on time scales fast enough to compete with the pairing process. In our simulations, the conditions for magnetic reconnection are provided, in an initially uniform in-plane magnetic field, by the motion of the K-H vortices that grow and pair in the initially imposed shear velocity field. We observe that VIR does not destroy the vortices before they coalesce, in agreement with multiple vortices study in a homogeneous plasma [8]. We find that if the Hall term is removed from Ohm's law, the development of reconnection, and thus eventually of the K-H vortices, is qualitatively, not only quantitatively, different. This result provides a clear cut example of the feedback between large and small scale physics, as the necessary conditions for reconnection to occur are produced by the large scale vortex motion, but the specific physical processes that make reconnection act faster or slower determine eventually the evolution of the entire system and the final magnetic field structure. We consider a 2D description of the system, with the inhomogeneity direction along x, the periodic direction along y, and z an ignorable coordinate. We adopt a
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Dates and versions

hal-02315150 , version 1 (14-10-2019)

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  • HAL Id : hal-02315150 , version 1

Cite

Matteo Faganello, F. Califano, F. Pegoraro. Time window for magnetic reconnection in plasma configurations with velocity shear. Physical Review Letters, 2008. ⟨hal-02315150⟩
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