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 (S ≫ 10 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 Alfvén 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 ≤ 10 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.
We study the linear and nonlinear evolution of the tearing instability on thin current sheets by means of twodimensional numerical simulations, within the framework of compressible, resistive MHD. In particular we analyze the behavior of current sheets whose inverse aspect ratio scales with the Lundquist number S as S 1 3-. This scaling has been recently recognized to yield the threshold separating fast, ideal reconnection, with an evolution and growth that are independent of S provided this is high enough, as it should be natural having the ideal case as a limit for S ¥. Our simulations confirm that the tearing instability growth rate can be as fast aswhere A t is the ideal Alfvénic time set by the macroscopic scales, for our least diffusive case with S 10 7 = . The expected instability dispersion relation and eigenmodes are also retrieved in the linear regime, for the values of S explored here. Moreover, in the nonlinear stage of the simulations we observe secondary events obeying the same critical scaling with S, here calculated on the local, much smaller lengths, leading to increasingly faster reconnection. These findings strongly support the idea that in a fully dynamic regime, as soon as current sheets develop, thin, and reach this critical threshold in their aspect ratio, the tearing mode is able to trigger plasmoid formation and reconnection on the local (ideal) Alfvénic timescales, as required to explain the explosive flaring activity often observed in solar and astrophysical plasmas.
Modes and manifestations of the explosive activity in the Earth’s magnetotail, as well as its onset mechanisms and key pre-onset conditions are reviewed. Two mechanisms for the generation of the pre-onset current sheet are discussed, namely magnetic flux addition to the tail lobes, or other high-latitude perturbations, and magnetic flux evacuation from the near-Earth tail associated with dayside reconnection. Reconnection onset may require stretching and thinning of the sheet down to electron scales. It may also start in thicker sheets in regions with a tailward gradient of the equatorial magnetic field ; in this case it begins as an ideal-MHD instability followed by the generation of bursty bulk flows and dipolarization fronts. Indeed, remote sensing and global MHD modeling show the formation of tail regions with increased , prone to magnetic reconnection, ballooning/interchange and flapping instabilities. While interchange instability may also develop in such thicker sheets, it may grow more slowly compared to tearing and cause secondary reconnection locally in the dawn-dusk direction. Post-onset transients include bursty flows and dipolarization fronts, micro-instabilities of lower-hybrid-drift and whistler waves, as well as damped global flux tube oscillations in the near-Earth region. They convert the stretched tail magnetic field energy into bulk plasma acceleration and collisionless heating, excitation of a broad spectrum of plasma waves, and collisional dissipation in the ionosphere. Collisionless heating involves ion reflection from fronts, Fermi, betatron as well as other, non-adiabatic, mechanisms. Ionospheric manifestations of some of these magnetotail phenomena are discussed. Explosive plasma phenomena observed in the laboratory, the solar corona and solar wind are also discussed.
This paper studies the growth rate of reconnection instabilities in thin current sheets in the presence of both resistivity and viscosity. In a previous paper, Pucci and Velli (2014), it was argued that at sufficiently high Lundquist number S it is impossible to form current sheets with aspect ratios L/a which scale as L/a ∼ S α with α > 1/3 because the growth rate of the tearing mode would then diverge in the ideal limit S → ∞. Here we extend their analysis to include the effects of viscosity, (always present in numerical simulations along with resistivity) and which may play a role in the solar corona and other astrophysical environments. A finite Prandtl number allows current sheets to reach larger aspect ratios before becoming rapidly unstable in pile-up type regimes. Scalings with Lundquist and Prandtl numbers are discussed as well as the transition to kinetic reconnection.
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 Alfvén time calculated on the macroscopic scale. 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 de2/L2, 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.
In many space, astrophysical, and laboratory plasmas the energy contained in the magnetic field or plasma flow exceeds the thermal energy. Magnetic field ( ) annihilation, often enabled by magnetic reconnection, transfers magnetic energy to particles. Shocks transfer bulk flow energy to particles. If there is a sufficiently large energy transfer, strong turbulence (∣ ∣/∣ B ∣ ∼ 1) develops, which, in turn, can result in nonthermal acceleration. In this article, we investigate acceleration in a finite-sized region of strong turbulence driven by magnetic reconnection with analytical modeling and test-particle simulations. This research is based on detailed observations in the Earth’s magnetotail. We find that the primary transfer of magnetic energy to particle energy is advanced by large-amplitude electric field structures ( ) generated by the strong turbulence. To no surprise, ion energization is dominated by intense DC , near the ion cyclotron frequency (f ci ), and/or variations at scales near the ion gyroradius. Electron energization comes from higher-frequency . The turbulent cascade continuously regenerates near f ci and higher frequencies. Importantly, the turbulence also creates magnetic depletions that can trap particles and considerably increase their dwell time in regions of strong energization, which substantially enhances nonthermal acceleration. Moreover, energization is primarily perpendicular to , so particles have difficulty escaping regions of depleted , which can lead to near runaway acceleration. We discuss how this process may be active in large-scale settings such as supernova shells and may contribute, at least in in part, to the development of the cosmic ray spectrum.
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 plasmas 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/a ∼ 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.
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