What is the Lundquist number S?

S = v_A L/η_m measures how strongly advection dominates magnetic diffusion. Here η_m is magnetic diffusivity in m²/s. Large S means a thin sheet and slow Sweet–Parker inflow v_in ~ v_A/√S.

Why is reconnection “slow” in Sweet–Parker?

As S grows, δ/L ~ 1/√S shrinks but the inflow needed to carry flux into the sheet also scales as 1/√S, giving a rate that decreases with S in this model — unlike many observed fast events.

Outflow along the sheet is set by magnetic tension and is of order the Alfvén speed v_A in the Sweet–Parker picture.

Hall effect, ion inertia, tearing modes, 3D turbulence, guide fields, and non-steady Petschek or plasmoid physics are not included.

Magnetic Reconnection (Sweet–Parker)

Toy Sweet–Parker X-point: opposite B-regions, current sheet, inflow v_in ≈ v_A/√S and outflow, Lundquist number S and sheet thickness δ/L.

About this model

Magnetic reconnection converts stored magnetic energy into plasma heating and bulk flows when oppositely directed magnetic flux is brought together in a thin current sheet. The Sweet–Parker steady-state model balances magnetic flux transport into a resistive diffusion region of half-thickness δ and length L with Alfvénic outflow along the sheet. In dimensionless form the Lundquist number S = v_A L/η_m (with Alfvén speed v_A = B/√(μ₀ρ) and magnetic diffusivity η_m) controls the sheet aspect ratio δ/L ≈ 1/√S and the inflow (reconnection) speed v_in ≈ v_A/√S, while outflow is of order v_A. Large S implies thin sheets and slow reconnection in this classical picture — motivating fast-reconnection models in space and laboratory plasmas. This simulator shows a stylized X-point geometry with oppositely directed field regions, a highlighted current sheet, inflow and outflow arrows, and plots of v_in/v_A and δ/L versus S, with η_m inferred from S = v_A L/η_m. It is a 2D steady Sweet–Parker cartoon without Hall physics, tearing instability, or time-dependent Petschek jets.

Who it's for: Undergraduate plasma or space-physics students after Alfvén waves; before substorms, solar flares, or kinetic reconnection theory.

Key terms

Magnetic reconnection
Sweet–Parker model
Current sheet
Lundquist number
X-point
Inflow and outflow
Alfvén speed

How it works

Sweet–Parker magnetic reconnection toy: X-point field lines, current sheet, inflow/outflow, Lundquist number S, and reconnection rate v_in ≈ v_A/√S.

Frequently asked questions

What is the Lundquist number S?: S = v_A L/η_m measures how strongly advection dominates magnetic diffusion. Here η_m is magnetic diffusivity in m²/s. Large S means a thin sheet and slow Sweet–Parker inflow v_in ~ v_A/√S.
Why is reconnection “slow” in Sweet–Parker?: As S grows, δ/L ~ 1/√S shrinks but the inflow needed to carry flux into the sheet also scales as 1/√S, giving a rate that decreases with S in this model — unlike many observed fast events.
What is v_out?: Outflow along the sheet is set by magnetic tension and is of order the Alfvén speed v_A in the Sweet–Parker picture.
What is omitted?: Hall effect, ion inertia, tearing modes, 3D turbulence, guide fields, and non-steady Petschek or plasmoid physics are not included.

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Magnetic Reconnection (Sweet–Parker)

About this model

How it works

Frequently asked questions

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