a) The local-dipole loop geometry for a specific case (red line; radius a is chosen as the distance from the center to one footpoint of co-latitude θ_F): La = A + c = 4.91a; b) an example of a stretched global dipole field line (red): the loop apex height A = 0.1   R_s (solar radius), and θ_F = π/2 − π/64. The blue line represents a standard dipole field line passing through the same footpoints of the red loop on solar surface, while the green one represents a dipole field line of the same apex height of the red loop. See Sect. 4 for details.