Transition from collisional to kinetic regimes in large-scale reconnection layers

Abstract

Using first-principles fully kinetic simulations with a Fokker-Planck collision operator, it is demon strated that Sweet-Parker reco=ection layers are unstable to a chain of plasmoids (secondary is lands) for Lundquist numbers beyond S ;C; 1000. The instability is increasingly violent at higher Lundquist number, both in terms of the number of plasmoids produced and the super-Alfvenic growth rate. A dramatic enhancement in the reconnect ion rate is observed when the half-thickness of the current sheet between two plasmoids approaches the ion inertial length. During this transi tion, the reconnection electric field rapidly exceeds the runaway limit, resulting in the formation of electron-scale current layers that are unstable to the continual formation of new plasmoids.PACS numbers: 52.35. Vd, 52.35.Py, The conversion of magnetic energy into kinetic energy through the process of magnetic reconnect ion remains one of the most challenging and far reaching problems in plasma physics. One key issue is the scaling of the recon nection dynamics for applications where the system size is vastly larger than the kinetic scales. The magnetohy drodynamics (MHD) model should provide an accurate description of collisional reconnect ion where the resis tive layers are larger than the ion kinetic scale. tween islands approach the ion kinetic scale. This regime is typically referred to as kinetic or fast reconnection since a variety of two-fluid and kinetic models predict rates that are weakly dependent on the system size and dis sipation mechanism [6,7] (the precise scalings are still a subject of controversy [8,9]). In neutral sheet geom etry, both two-fluid simulations [10,11] and theory [12J predict an abrupt transition from the collisional to the kinetic regime when 8 sp ::; d i where d i is the ion inertial length. In this geometry, d i is comparable to the ion gy roradius, and in the kinetic regime d i is also compa.rable to the ion crossing orbit scale.Recently, this transition between collisional and kinetic reconnection was proposed as the central mechanism in regulating coronal heating [13-15J. However, these es timates were based on the assumption of a stable SP layer within the collisional regime. To properly describe the dynamics at high Lundquist number, it is crucial to consider how plasmoid formation ma.y influence the tran sition. To address this problem, this work employs fully kinetic particle-in-cell (PIC) simulations with a Monte Carlo treatment [16] of the Fokker-Planck collision op erator. For Lundquist numbers where the SP layers are stable 5 ;s 1000, this powerful first-principles approach has demonstrated a clear transition between the colli sional and kinetic regimes near the expected thresholdHere we demonstrate that SP layers are in creasingly unstable to plasmoid formation in large-scale systems. The observed growth rate is super-Alfvenic, al lowing the islands to grow to large amplitude before they are convected downstream. A dramatic enhancement in the reconnection rate is observed when the current...

The Impact of Microscopic Magnetic Reconnection on Pre-Flare Energy Storage

“…This generalizes the result by Daughton et al (2009a) result in Equation (5). Solving for B up,c gives…”

“…No quantitative model of their impact on Sweet-Parker reconnection exists, but evidence suggests it gets faster (Matthaeus & Lamkin 1986;Lazarian & Vishniac 1999;Lapenta 2008;Loureiro et al 2009;Bhattacharjee et al 2009). Secondary islands make sheets thinner (Shibata & Tanuma 2001), as confirmed by simulations (Daughton et al 2009a(Daughton et al , 2009bCassak et al 2009). These effects are critical; if secondary islands make reconnection fast or hasten the transition to collisionless reconnection, it is unclear how pre-flare energy accumulates.…”

“…The model employed here, for example, does not take into account possible hierarchical secondary island scenarios (Shibata & Tanuma 2001;Daughton et al 2009a;Bhattacharjee et al 2009). Regardless, the present results conclusively show that embedded effects can be considerable, and need to be taken into account when modeling coronal reconnection.…”

“…Daughton et al (2009a) provide a possible starting point by assuming that fragments of the diffusion region obey the Sweet-Parker model, allowing one to predict the scaling with the number of islands N. With N islands, the length L of each segment scales like L ∼ L SP /N. From Equation (1), the thickness of the fragmented layer scales like…”

“…No accepted theory exists, but recent work by Daughton et al (2009a) and Loureiro et al (2007) provides a starting point. We argue that secondary islands are ubiquitous in coronal reconnection.…”