In the solar corona, the magnetic pressure is dominant and thus the plasma β (=8πp/B^2), which is the ratio between the gas pressure p and the magnetic pressure B^2/8π, is sufficiently smal. In such circumstance, the gas pressure can be neglected and the equilibrium is achieved when the Lorentz force vanishes, i.e., the magnetic tension and the magnetic pressure are balanced.

JxB=0       (1)

In order to reproduce the magnetic fields in active regions, we have to numerically solve the nonlinear equation (1) based on the magnetic field at the photosphere.