Current sheets formed in magnetic reconnection events are found to be unstable to high-wavenumber perturbations. The instability is very fast: its maximum growth rate scales as S14vALCS, where LCS is the length of the sheet, vA the Alfvén speed, and S the Lundquist number. As a result, a chain of plasmoids (secondary islands) is formed, whose number scales as S38.

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Going to the next order in our outer solution results in an additional subdominant contribution to Δ comparable to the second term in Eq. (15). Note that while the contribution of the second term in Eq. (13) to Δ is negligible, the term itself cannot be dropped because it ensures that the solution has a finite value at ξ=0. Note also that there exists an unstable solution that is entirely confined inside the current sheet, so that Ψ(±ξ0)=0. For this solution, C1±=0 in Eq. (11) and to the lowest order in κ2ϵ2, Δ is given just by the second term in Eq. (15). Solving Eq. (10) to the next order in κ2ϵ2, we find Δ(κ)0.571.47κ2ϵ2. The growth rate then is obtained from Eq. (18) in the limit Λ1. The result is γΓ00.61κ25Δ(κ)45, whence κmax0.28ϵ1 and γmaxϵ25. We will not consider this solution because it grows slower than the unconfined mode and its validity hinges on the numerical smallness of κmax2ϵ20.08.

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