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A set of reduced Hall magnetohydrodynamic (MHD) equations are used toevaluate the stability of large aspect ratio current sheets to the formation ofplasmoids (secondary islands). Reconnection is driven by resistivity in thisanalysis, which occurs at the resistive skin depth $d_\eta \equiv S_L^{-1/2}\sqrt{L v_A/\gamma}$, where $S_L$ is the Lundquist number, $L$ the length ofthe current sheet, $v_A$ the Alfv\'{e}n speed, and $\gamma$ the growth rate.Modifications to a recent resistive MHD analysis [N.\ F.\ Loureiro, A.\ A.\Schekochihin, and S.\ C. Cowley, Phys.\ Plasmas {\bf 14}, 100703 (2007)] arisewhen collisions are sufficiently weak that $d_\eta$ is shorter than the ionskin depth $d_i \equiv c/\omega_{pi}$. Secondary islands grow faster in thisHall MHD regime: the maximum growth rate scales as $(d_i/L)^{6/13} S_L^{7/13}v_A/L$ and the number of plasmoids as $(d_i/L)^{1/13} S_L^{11/26}$, compared to$S_L^{1/4} v_A/L$ and $S^{3/8}$, respectively, in resistive MHD.

Hall magnetohydrodynamic reconnection in the plasmoid unstable regime