Fast Reconnection in Extended High-Lundquist-Number Current Sheets Due to the Plasmoid Instability

Extended thin current sheets often form in the Earth's magnetotail in the growth phase of a substorm. Thin current sheets in such large systems that exceed a critical value of the Lundquist number are unstable to a super-Alfvénic tearing instability, referred to hereafter as the plasmoid instability. While the existence of the plasmoid instability has been known for some time, it is only recently that the precise properties of the instability have been determined. The scaling of the growth rate of the fastest growing plasmoid instability with respect to the Lundquist number is shown to follow from the classical dispersion relation for tearing modes. This super-Alfvenic instability produces a large number of small plasmoids in the linear regime that coalesce to form plasmoids of significant size in the nonlinear regime. As a result of the instability, the system realizes a nonlinear reconnection rate that appears to be weakly dependent on the Lundquist number, and larger than the Sweet-Parker rate by an order of magnitude (for the range of Lundquist numbers considered). This regime of fast reconnection appears to be realizable in a dynamic and highly unstable thin current sheet, without requiring the current sheet to be turbulent.