Magnetic Reconnection — Sweet-Parker vs Petschek
Current sheet · Plasmoid instability · Alfvén speed · Reconnection rate
Plasma Parameters
Sweet-Parker
Petschek
Plasmoid
Lundquist number S = Lv_A/η:
1000
Alfvén speed v_A:
1.0
Upstream B₀:
1.0
Animation speed:
1
SP rate M_SP:
—
Petschek rate M_P:
—
Sheet thickness δ:
—
Sheet length L_cs:
—
Reconnection rates:
Sweet-Parker: M_SP = S^{-1/2}
Petschek: M_P ~ π/(8 ln S)
At S=10⁶: SP rate ~ 10⁻³ (too slow), Petschek ~ 0.1 (fast).
Plasmoid instability:
long Sweet-Parker sheets are tearing-mode unstable → plasmoids form → fast reconnection at S > S_c ~ 10⁴.
Key: energy stored in antiparallel B fields is released as heat + particle acceleration. Drives solar flares, CMEs, magnetospheric substorms.