Trajectories of 1000 primary protons in a double-dipole magnetic field obtained in simulations with the GC approach. The primary protons are released from two different extended sources of ellipsoidal form: one centred at x = 0, y = 0 and z = 2000 km (a) and the other centred at x = 0, y = 0 and z = 5000 km (b). In both cases the primary protons are assumed to have an isotropic angular distribution and a power-law energy distribution of spectral index δ = 2 in the range 0.2–1.0 GeV. Panels c and d show the maps of secondary photons crossing the xy-plane at z = 0 that are produced in the chromosferic–photospheric region by 3 × 10⁶ primary protons released from the sources depicted in panels a and b, respectively.