Relative helicity H_{R (LFF)} (solid line) and energy E_LFF (dashed line) of the linear force-free field within the magnetic boundary surface r_L = 7.0 R vs. the force-free parameter α. The radial field at the photosphere r = R is the same as for the non-linear field of Wolfson (1995) with n = 0.5 discussed in Sect. 2.2.1. The absolute minimum energy of the potential field with the same boundary conditions at the photosphere E_P is indicated by the horizontal dotted line. The relative helicity H_R(NLFF) of the non-linear field is indicated by the horizontal dash-dotted line, while the vertical dash-dotted line gives the corresponding value α₀ of the parameter α and energy E_LFF of the linear field with the same relative helicity as the non-linear field (see the text).