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تسجيل مستخدم جديدFast Magnetic Reconnection: Ideal Tearing and the Hall Effect
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One of the main questions in magnetic reconnection is the origin of triggering behavior with on/off properties that accounts, once it is activated, for the fast magnetic energy conversion to kinetic and thermal energies at the heart of explosive events in astrophysical and laboratory plasmas. Over the past decade progress has been made on the initiation of fast reconnection via the plasmoid instability and what has been called ideal tearing, which sets in once current sheets thin to a critical inverse aspect ratio $(a/L)_c$: as shown by Pucci and Velli (2014), at $(a/L)_c sim S^{-1/3}$ the time scale for the instability to develop becomes of the order of the Alfven time and independent of the Lundquist number (here defined in terms of current sheet length $L$). However, given the large values of $S$ in natural plasmas, this transition might occur for thicknesses of the inner resistive singular layer which are comparable to the ion inertial length $d_i$. When this occurs, Hall currents produce a three-dimensional quadrupole structure of magnetic field, and the dispersive waves introduced by the Hall effect accelerate the instability. Here we present a linear study showing how the ideal tearing mode critical aspect ratio is modified when Hall effects are taken into account, including more general scaling laws of the growth rates in terms of sheet inverse aspect ratio: the critical inverse aspect ratio is amended to $a/L simeq (di/L)^ {0.29} (1/S)^{0.19}$, at which point the instability growth rate becomes Alfvenic and does not depend on either of the (small) parameters $d_i/L, 1/S$. We discuss the implications of this generalized triggering aspect ratio for recently developed phase diagrams of magnetic reconnection.
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Magnetic reconnection is thought to be the dynamical mechanism underlying many explosive phenomena observed both in space and in the laboratory, though the question of how fast magnetic reconnection is triggered in such high Lundquist ($S$) number pl
asmas has remained elusive. It has been well established that reconnection can develop over timescales faster than those predicted traditionally once kinetic scales are reached. It has also been shown that, within the framework of resistive Magnetohydrodynamics (MHD), fast reconnection is achieved for thin enough sheets via the onset of the so-called plasmoid instability. The latter was discovered in studies specifically devoted to the Sweet-Parker current sheet, either as an initial condition or an apparent transient state developing in nonlinear studies. On the other hand, a fast tearing instability can grow on an ideal, i.e., $S$-independent, timescale (dubbed ideal tearing) within current sheets whose aspect ratio scales with the macroscopic Lundquist number as $L/asim S^{1/3}$ -- much smaller than the Sweet-Parker one -- suggesting a new way to approach to the initiation of fast reconnection in collapsing current configurations. Here we present an overview of what we have called ideal tearing in resistive MHD, and discuss how the same reasoning can be extended to other plasma models commonly used that include electron inertia and kinetic effects. We then discuss a scenario for the onset of ideal fast reconnection via collapsing current sheets and describe a quantitative model for the interpretation of the nonlinear evolution of ideally unstable sheets in two dimensions.
We study, by means of MHD simulations, the onset and evolution of fast reconnection via the ideal tearing mode within a collapsing current sheet at high Lundquist numbers ($Sgg10^4$). We first confirm that as the collapse proceeds, fast reconnection
is triggered well before a Sweet-Parker type configuration can form: during the linear stage plasmoids rapidly grow in a few Alfven times when the predicted ideal tearing threshold $S^{-1/3}$ is approached from above; after the linear phase of the initial instability, X-points collapse and reform nonlinearly. We show that these give rise to a hierarchy of tearing events repeating faster and faster on current sheets at ever smaller scales, corresponding to the triggering of ideal tearing at the renormalized Lundquist number. In resistive MHD this process should end with the formation of sub-critical ($S leq10^4$) Sweet Parker sheets at microscopic scales. We present a simple model describing the nonlinear recursive evolution which explains the timescale of the disruption of the initial sheet.
This paper discusses the transition to fast growth of the tearing instability in thin current sheets in the collisionless limit where electron inertia drives the reconnection process. It has been previously suggested that in resistive MHD there is a
natural maximum aspect ratio (ratio of sheet length and breadth to thickness) which may be reached for current sheets with a macroscopic length L, the limit being provided by the fact that the tearing mode growth time becomes of the same order as the Alfv`en time calculated on the macroscopic scale (Pucci and Velli (2014)). For current sheets with a smaller aspect ratio than critical the normalized growth rate tends to zero with increasing Lundquist number S, while for current sheets with an aspect ratio greater than critical the growth rate diverges with S. Here we carry out a similar analysis but with electron inertia as the term violating magnetic flux conservation: previously found scalings of critical current sheet aspect ratios with the Lundquist number are generalized to include the dependence on the ratio $(d_e/L)^2$ where de is the electron skin depth, and it is shown that there are limiting scalings which, as in the resistive case, result in reconnecting modes growing on ideal time scales. Finite Larmor Radius effects are then included and the rescaling argument at the basis of ideal reconnection is proposed to explain secondary fast reconnection regimes naturally appearing in numerical simulations of current sheet evolution.
Works of D. Tsiklauri, T. Haruki, Phys. of Plasmas, 15, 102902 (2008) and D. Tsiklauri and T. Haruki, Phys. of Plasmas, 14, 112905, (2007) are extended by inclusion of the out-of-plane magnetic (guide) field. In particular, magnetic reconnection duri
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Magnetic reconnection, a fundamentally important process in many aspects of astrophysics, is believed to be initiated by the tearing instability of an electric current sheet, a region where magnetic field abruptly changes direction and electric curre
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