AC28 · Magnetic stresses release energy

Magnetic Reconnection

Where does the energy go when a magnetic field rearranges? Magnetic stresses accelerate the plasma. Electric resistance and viscosity convert part of the magnetic and fluid energy into heat. A thin nonideal region lets magnetic flux change its connection to the moving fluid.

Drag a probe through a current layer. Follow the field, the outflow and the magnetic energy converted into motion and heat.

Field at the probe $0.873$

Flow at the probe $0.181$

Electric current at the probe $-0.971$

Local Ohmic power $0.0188$

AC28

Follow the field through a current layer

Probe horizontal coordinate

0.800

x/L_0

Probe vertical coordinate

2.40

y/L_0

Colour the plasma by

Drag the gold probe through the plane. Its highlighted magnetic contour and four measurements follow the same saved state.

Independent Python solution at the selected time

Saved times, units and numerical limits

These are three actual native states. Evolution advances the same MHD equations within the selected tested interval. Transport coefficients change only with the four discrete cases.

t_A=L_0/v_A,\quad q_0=B_0^2/(\mu_0t_A)

Readouts use the field, Alfvén speed, current and power-density scales defined in the course. The periodic plane has equal horizontal and vertical coordinate scales. No solar length, density or magnetic-field calibration is assigned.

-8\leq j/j_0\leq8

Current colour has this fixed range. Power colour uses zero to two in the normalized power density. Moving glyphs show instantaneous velocity, with schematic playback; they are not tracked electrons.

Reload with cooperative calculation Reproduce the local-induction failure and grid check

Model assumptions

This periodic two-dimensional incompressible viscoresistive-MHD initial-value model releases a specified initial magnetic stress. Four discrete cases have independent 128/256-grid and time-step checks. Current colour, magnetic contours, velocity and energy records share the selected numerical state. Flow glyph motion depicts instantaneous velocity; playback speed and colours are schematic. Dissipation is stored as global heat, without a temperature equation. There is no photospheric footpoint driver, flare trigger, particle acceleration, three-dimensional evolution or radiative prediction. The separate GOES tutorial measures actual band irradiance; partial-minute fluence estimates assume the available seconds represent the full minute.

One numerical state

Magnetic stresses launch outflows

Selected physical time $1\,t_A$

Field energy becomes motion and heat

t/t_A,\quad E/(B_0^2/\mu_0)

Domain-mean energy densities. Blue: magnetic. Green: kinetic. Orange and purple: Ohmic and viscous heat.

$(E_B+E_K+Q_\Omega+Q_\nu)/E_0=1.000$

Magnetic flux between the two nulls

t/t_A,\quad[\psi(O)-\psi(X)]/(B_0L_0)

Gold: the selected island’s signed flux contrast. Both nulls can undergo diffusion.

\dot\psi(O)-\dot\psi(X)=E_z(X)-E_z(O)

What this calculation resolves

The four fixed cases release an initially stressed periodic field. Local induction, finer-grid fields and time-step errors are checked separately from the global energy sum. A retained coarse ideal case demonstrates why conservation alone is insufficient. Solar footpoint driving, flare onset, particles and emitted light need additional models.

The canvas preview samples a verified 128-grid Python state; the full saved input is checked before JavaScript evolution.

Start with the essentials

Focus question: Where does magnetic energy go in this model?
One-sentence intuition: The magnetic field accelerates the fluid; electric resistance and viscosity feed separate dissipative reservoirs.

Core mathematical model

Flux carried by the moving fluid

\partial_t\psi+\mathbf v\cdot\nabla\psi=\eta\nabla^2\psi

Magnetic contours follow constant $\psi$ . Here $\eta$ is dimensionless magnetic diffusivity. The ideal case sets it to zero.

Two coupled divergence-free fields

\mathbf B=(\psi_y,-\psi_x),\qquad\mathbf v=(\phi_y,-\phi_x)

The magnetic potential and the streamfunction supply the field and velocity in the same periodic plane.

The closed unforced energy sum

E_B+E_K+Q_\Omega+Q_\nu=E_0

The initial energy moves between magnetic and kinetic forms and accumulates in the two heat reservoirs. These normalized reservoirs do not determine a temperature.

Both magnetic nulls can diffuse

\frac{d}{dt}[\psi(O)-\psi(X)]=E_z(X)-E_z(O)

A closed periodic island also diffuses at its O point. The difference needs both local electric fields.

Common difficulties

Field lines as objects

Typical misconceptionA drawn magnetic line is a thread made of particles.

Better mental modelThe line is a contour describing the instantaneous field. A fluid element follows the velocity, which is a different vector field.

Energy as the only numerical test

Typical misconceptionAn almost perfect energy sum proves that reconnection is resolved.

Better mental modelA retained low-grid ideal example conserves global quantities while changing flux at magnetic nulls incorrectly. Local induction and a finer grid must also agree.

Heat as brightness

Typical misconceptionThe dissipated-energy curve is the light curve of a solar flare.

Better mental modelCalculating emitted X-rays also needs density, thermodynamics, conduction, radiation and instrument response. The GOES tutorial analyzes measured band irradiance separately.

Run the experiment

01
Find the outflow
Watch the default state, then drag the gold probe across the bright current layer.
What to observe: The green arrows and probe values trace the calculated fluid velocity. The gold curve is the magnetic contour through the probe.
02
Remove irreversible heating
Choose Ideal flow and inspect the two energy curves.
What to observe: Magnetic and fluid energy exchange while the dissipative reservoirs remain zero over the tested short interval.
03
Change the actual transport process
Compare Diffusion and Viscosity, returning to the same saved time in the advanced group.
What to observe: Diffusion acts on the magnetic field. Viscosity damps the fluid. Their different energy curves follow different solutions.
04
Check a saved state
Save JSON and the history CSV. Compare the selected time, field map, probe and energy values.
What to observe: They retain the same case and numerical state; normalized values need a specified physical length, field and density before solar units can be assigned.

Magnetic Reconnection

Magnetic stresses launch outflows

Field energy becomes motion and heat

Magnetic flux between the two nulls

Follow magnetic energy into motion and heat

Core mathematical model

Flux carried by the moving fluid

Two coupled divergence-free fields

The closed unforced energy sum

Both magnetic nulls can diffuse

Common difficulties

Field lines as objects

Energy as the only numerical test

Heat as brightness

Run the experiment

Find the outflow

Remove irreversible heating

Change the actual transport process

Check a saved state

Related experiments and articles

From magnetic stress to reconnection