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.
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