Initial numerical setup. The pulsar, of a radius, r_⋆ and angular velocity, Ω, lies at the center of the spherical box of coordinates (r,ϕ) and radius r_max. The companion, of radius r_comp, is settled at a fixed distance d_comp along the ϕ = 0 direction. Initially, the box is empty of particles. Magnetic field lines (blue and red arrows) are radial, directed outwards on one hemisphere and inwards on the other hemisphere, according to the split-monopole configuration. The plane inclination in between both hemispheres is perpendicular to the magnetic moment μ shown in green. An absorbing layer is implemented at r_absorb = 0.9r_max. The light-cylinder radius R_LC is represented by the black dashed circle and the fast magnetosonic radius r_fms is given by the red dashed circle.