Reconnection Rate Lab

System log₁₀ S (Lundquist number)

Sheet aspect ratio δ/L = S^−1/2
Sweet–Parker rate M_A = v_in/v_A = S^−1/2
Petschek rate M_A ≈ π/(8 ln S)
Alfvén time τ_A = L/v_A
Sweet–Parker time τ = τ_A√S
Observed timescale
Verdict

The Sweet–Parker sheet is long and thin: plasma must squeeze out the ends, and the rate collapses as S^−1/2. Petschek opens the outflow into a short diffusion region with standing slow shocks, giving a rate that falls only logarithmically. The green band is what is actually observed. This gap — many orders of magnitude at astrophysical S — is the reconnection problem, and it is why the field moved on to plasmoid instability and collisionless (Hall) reconnection.