Solar-wind protons compress Earth's dipole field into a magnetopause (Shue 1997 empirical model), leak in through dayside reconnection when the IMF turns southward, and precipitate along dipole field lines to draw the auroral oval.
R₀, Eₘ and the oval latitude are computed live from the sliders via the Shue (1997) magnetopause model and dipole L-shell geometry — not animation presets.