Maps of cumulative 1 AU crossings in a heliocentric coordinate system corotating with the Sun, for monoenergetic SEP proton populations, with energy as indicated in each panel. Left column: A⁺ configuration of the IMF; right column: A⁻ configuration. The 8 × 8° injection region at the Sun is located at longitude 76° and latitude 11°, above the HCS, and the zero of the coordinate system on the 1 AU map has been shifted so that the flux tube through the injection region appears at N11W76 on this map. The tilt of the HCS is α_nl = 37°. All simulations used N = 10 000 protons, solar wind speed v_sw = 400 km s⁻¹, and mean free path λ = 0.1 AU. Contour lines are plotted for the following values of the number of crossings: 1000 (green), 316 (blue), 100 (lilac), 31 (red), and 10 (black).