The shape of a magnetic arcade embedded in the solar corona

We have generated two-dimensional magnetic arcades, with invariance along the longitudinal axis, by solving, with invariance along the longitudinal axis, by solving, together, the Grad-Sharanov equation between the arcade and the corona. We have used a particular class of magnetic fields in which the slope of the magnetic field lines only depends on coordinate and, with this approach, we have been able to obtain general expressions for the magnetic field components, which only depend on the gas pressure profile, without the need to know the analytical expression for the flux function. These expressions for the magnetic field components have allowed us to generate potential and non-potential fields and to obtain some conclusions about the half-width, height and magnetic field flux of the different arcades.