This is a simplified 2D resistive-magnetohydrodynamic (MHD) model of magnetic reconnection. Two regions of oppositely directed magnetic field are pressed together. A thin current sheet forms at the central X-point, where finite resistivity lets field lines break and reconnect. The reconnected field snaps outward, launching plasma jets and converting stored magnetic energy into plasma kinetic energy — the same process that powers solar flares and geomagnetic substorms.
Induction (resistive MHD):
∂B/∂t = ∇×(v×B) + η ∇²B
Sweet-Parker rate:
v_in / v_A = δ / L = 1 / √S
Lundquist number:
S = L v_A / η
Alfvén speed:
v_A = B₀ / √(μ₀ ρ)
Current density:
J = (1/μ₀) ∇×BA single large solar flare can release about 10²⁵ joules in minutes — comparable to a billion megatons of TNT, or the entire Sun's output for a fraction of a second concentrated in one active region. Magnetic reconnection is what unlocks that energy so explosively.
Magnetic reconnection is a process in which oppositely directed magnetic field lines in a plasma break and rejoin into a new topology. The change releases stored magnetic energy explosively, converting it into plasma kinetic energy, heat, and accelerated particles. It is the fundamental engine behind solar flares, coronal mass ejections, and geomagnetic substorms.
The X-point is the location where the magnetic field strength drops to zero and field lines from opposite directions cross in an X-shaped pattern. A thin current sheet forms there. Magnetic field lines are carried into the X-point by inflow, break their connections, and reconnect, then snap outward as high-speed plasma jets along the outflow direction.
The Sweet-Parker model is the classic steady-state picture of resistive reconnection. Plasma flows into a long, thin diffusion region of length L and width δ, reconnects, and flows out at the Alfvén speed. Mass conservation gives the inflow speed vin = vA·δ/L, and the dimensionless reconnection rate scales as 1/√S, where S is the Lundquist number.
The Lundquist number S = L·vA/η measures the ratio of resistive diffusion time to Alfvén crossing time, where η is the magnetic diffusivity (resistivity). In the corona S can reach 10¹² or more. Sweet-Parker predicts a reconnection rate proportional to 1/√S, which is far too slow to explain observed flares, motivating fast-reconnection mechanisms.
With coronal Lundquist numbers near 10¹², the Sweet-Parker rate 1/√S implies energy release over months, yet flares erupt in minutes. The resolution is fast reconnection: the Petschek mechanism with standing slow-mode shocks, or tearing-mode instabilities that fragment the long current sheet into plasmoids, both of which raise the rate to a weak (near-logarithmic) dependence on S.
Sheared and twisted coronal magnetic fields store enormous free energy. When a current sheet thins to kinetic scales, reconnection switches on, releasing up to 10²⁵ joules in a large flare. Reconnected field lines retract, heating plasma to tens of millions of kelvin and accelerating particles that stream down to the chromosphere, producing the characteristic flare ribbons and hard X-rays.
A substorm is a transient disturbance of Earth's magnetosphere. The solar wind stretches the nightside magnetotail, storing magnetic energy until reconnection at a near-Earth X-line releases it. Plasma is hurled earthward, injecting energetic particles into the inner magnetosphere and igniting bright auroral displays. Substorms typically last one to three hours.
When a current sheet becomes long and thin enough, the tearing instability breaks it into a chain of magnetic islands called plasmoids, each wrapped by closed field lines. Plasmoids form, merge, and are ejected along the outflow, opening many small reconnection sites at once. This plasmoid-mediated reconnection makes the rate nearly independent of the Lundquist number.
The resistivity (magnetic diffusivity η) sets how readily field lines slip through the plasma at the current sheet. Higher resistivity widens the diffusion region, lowers the effective Lundquist number, and speeds up reconnection and outflow jets. Lower resistivity makes the field more frozen-in, narrowing the sheet and slowing the topology change, mirroring the 1/√S Sweet-Parker scaling.
In ideal magnetohydrodynamics with zero resistivity, magnetic field lines are frozen into the plasma: fluid elements that share a field line stay connected forever, so topology cannot change. Reconnection requires this condition to break, which happens only in the thin diffusion region where finite resistivity (or kinetic effects) allows field lines to slip, cut, and rejoin into a new configuration.
This simulation animates a simplified 2D resistive magnetohydrodynamic (MHD) model of magnetic reconnection: an analytic Harris-like current sheet with Bx = B0·tanh(y/δ), where the sheet half-width δ is derived every frame from the Sweet-Parker balance δ/L = 1/√S. The Lundquist number S = L·v_A/η compares the Alfvén crossing time to resistive diffusion, so raising resistivity η instantly narrows S, widens the diffusion region, and speeds up the reconnection rate that opens a small reconnecting field component at the X-point. Plasma particles are spawned in the inflow, cross the diffusion region, then get kicked outward near the local Alfvén speed v_A = B0/√ρ, visualising energy converting from magnetic to kinetic in real time.
An X-point current sheet where oppositely directed field lines (traced live with RK2 streamline integration) reconnect and snap outward into two plasma jets, while the energy bars track the live conversion from stored magnetic energy to plasma kinetic energy as the reconnection rate rises and falls with the Sweet-Parker target.
Drag the four sliders — Resistivity η, Field strength B₀, Inflow drive, and Plasma density ρ — to reshape the sheet and jets live. Toggle Field lines vs. Current |J| to switch views, click or tap near the X-point to give the sheet a manual "poke" that briefly boosts the reconnection rate, and use Pause/Reset or the Info button for the full equation reference.
In the solar corona the Lundquist number can reach 10¹² or higher, so the classic Sweet-Parker rate of 1/√S predicts reconnection so slow it would take months — yet real flares release up to 10²⁵ joules and finish in minutes, which is why solar physicists had to find faster mechanisms like plasmoid-mediated reconnection.
Bx = B0·tanh(y/δ) is the classic Harris sheet: it smoothly reverses sign across the mid-plane (positive above, negative below) while staying nearly uniform far from y = 0, which is exactly the reversed-field geometry that sets up a current sheet and X-point. It is a standard analytic stand-in for the field configuration that MHD simulations of reconnection produce numerically.
Resistivity η enters the Lundquist number S = L·v_A/η on the bottom, so turning η up lowers S. The code's Sweet-Parker rate function returns drive/√S, so a lower S directly raises the target reconnection rate, which also widens the diffusion-region half-width δ ∝ 1/√S used to draw the current sheet and set the field profile.
The magnetic energy bar decreases at a rate proportional to the current reconnection rate (energy converted ≈ recRate × 0.9 × dt each frame), while the kinetic energy bar is computed directly from the live velocity of every plasma particle on screen. Together they show magnetic energy being converted into the kinetic energy of the outflow jets as the simulation runs.
Clicking or tapping near the mid-plane (within 0.35 simulation units of y = 0) manually nudges the reconnection rate upward by a small amount that fades with distance from the click's x-position. It is a quick way to simulate a local disturbance triggering faster reconnection, similar to how a perturbation can seed the onset of a real reconnection event.
Field lines mode traces magnetic streamlines with RK2 integration from the left and right edges, colouring the upper (blue) and lower (orange) reversed regions separately so you can see them bend into the X-point. Current |J| mode instead renders a heat map of |∇×B|, computed from the sech²(y/δ) derivative of the tanh profile, which peaks exactly on the thin current sheet at y = 0.