Two sheared, opposite-polarity magnetic arcades store free (non-potential) energy in the component of the field that is not force-free-relaxed. The stored free-energy density follows the standard magnetic-energy-density formula, and the arcade's volume scales with the active-region size:
B_free = B·sin(δ) [sheared component, δ = shear angle]
u_free = B_free² / (2μ0) [J/m³, magnetic energy density]
V = L³ [m³, active-region volume]
E = η · u_free · V [J, energy released this event, η = reconnection efficiency]
Reconnection proceeds at a fraction of the Alfvén speed (Petschek-type outflow, v_out ≈ 0.1·v_A, v_A = B/√(μ0·ρ)), which sets the impulsive-phase timescale τ = L / v_out. A fixed fraction of E becomes the kinetic energy of an ejected plasma blob (CME proxy) of mass m = ρ·f_eject·V, so its ejection speed follows directly from energy conservation:
KE = 0.3 · E
v_CME = √(2·KE / m)
The rest of the energy radiates; a small fraction of that lands in the GOES soft X-ray band. The corresponding flux at Earth (Power / 4πd²) is compared against the real GOES thresholds (A ≥ 10⁻⁸, B ≥ 10⁻⁷, C ≥ 10⁻⁶, M ≥ 10⁻⁵, X ≥ 10⁻⁴ W/m²) to classify the flare — the same A/B/C/M/X scheme used for real solar flares.
- Field strength, shear angle and region size all raise or lower the stored free energy and therefore the flare class.
- Reconnection efficiency sets what fraction of the stored energy this particular event actually releases.
- Coronal density (10⁻¹² kg/m³) and the kinetic/radiative energy split are fixed, textbook-typical constants — everything else responds to the sliders.