Presets
Playback
Plasma
Coronal values; the Lundquist number S = L vA / eta sets the regime.
Layers
Model checks
The science
The picture
In the solar corona, magnetic field lines of opposite direction press against each other in a thin current sheet. The sheet is modelled as a Harris sheet, B(y) = B0 tanh(y/λ), whose flux function is ψ = λ ln cosh(y/λ). A small tearing perturbation (the outer solution) grows into a magnetic island and field lines reconnect across the X-point.
Scales (CGS)
vA = B / √(4πρ) S = L vA / η η ≈ 109 T-3/2 cm2/s (Spitzer)Sweet-Parker reconnection has inflow vin = vA S-1/2; mass continuity vin L = vout δ with δ = L S-1/2 gives outflow vA. Coronal S is 1012 or more, so the Sweet-Parker rate is far too slow for a flare. Fast regimes: plasmoid-mediated reconnection (rate about 0.01 vA once S > 104) and Petschek, rate π/(8 ln S).
Energy
The magnetic energy density is B2/8π; a fraction of the field energy in a volume L3 is converted into heat, bulk flow and particle acceleration. The energy shown is an order-of-magnitude estimate, not a flare model.
Honest simplifications
- The field-line pattern is an analytic flux function with an island whose amplitude grows at a rate tied to the chosen reconnection rate; it is not a magnetohydrodynamic solution.
- Collisionless (Hall) reconnection and 3-D effects are not included.
- The Spitzer diffusivity uses a single constant, ignoring the Coulomb logarithm.
What to try
- Compare the three regimes at the default plasma: the Sweet-Parker rate is tiny, the others are fast.
- Large flare: higher field and sheet length raise the energy estimate by orders of magnitude.
- Cool dense chromosphere: high density and low temperature give a much smaller S.
- Raise the temperature: S grows as T^3/2 and the Sweet-Parker rate falls.