Fast Magnetic Reconnection: “Ideal” Tearing and the Hall Effect

Abstract

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 ∼ S −1/3 the time scale for the instability to develop becomes of the order of the Alfvén 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 threedimensional 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 (di/L) 0.29 (1/S) 0.19 , at which point the instability growth rate becomes Alfvénic 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.

Fast Recursive Reconnection and the Hall Effect: Hall-MHD Simulations

“…The evolution is similar with Run 0 at t ≤ 5: a secondary current sheet is formed and stretched along x direction with thickness a 1 ≈ 0.0016. Then the secondary current sheet breaks into small plasmoids at t ≈ 5, earlier than Run 0 as expected: tearing instability has larger growth rate with Hall term [20]. Very soon after the break up of the secondary current sheet, a single X-point configuration, which is a typical structure of Hall-reconnection, is formed (between t = 5.2 and t = 5.6).…”

Marginal Stability of Sweet–Parker Type Current Sheets at Low Lundquist Numbers

“…At each step, the Lundquist number decreases, and finally they will cross the critical S at which further disruption is quenched. However, at those scales where S becomes small enough, kinetic effects, explored in (Pucci et al 2017), become fundamental. We plan to address this question in subsequent works.…”

Fast magnetic reconnection: The ideal tearing instability in classic, Hall, and relativistic plasmas.

“…with d i0 being the asymptotic value of the ion inertial length. The Hall term is not negligible when the ion inertial length becomes comparable to the width δ of the inner resistive layer of the tearing instability [14]. For the fastest growing mode, the inner width δ is described by the equation δ/a S −3/10 a ∆ 1/5 [15], where S a is given in Eq.…”

“…We can identify three regimes: a MHD regime (η H S −1/2 ) where the Hall term does not play a relevant role, a mild Hall regime (η H S −1/2 ), where the ion inertial scale is comparable to the thickness of the inner layer, and a strong Hall regime (η H S −1/2 ), where reconnection is dominated by the Hall effect and the classic theory of the tearing instability is no longer valid. The linear phase of the tearing instability in these three regimes has already been investigated by [14] in the case of a Harris current sheet in pressure equilibrium. They verified the existence of these regimes, and showed that the linear growth rate start increasing for, e.g., values d i /δ ∼ 3 at S = 10 6 .…”