The propagation of dense energetic neutralized ion beams or plasmoids injected into a plasma across the ambient magnetic field under ionospheric conditions is considered. Using a simple physical model supported by two-dimensional hybrid simulations, it is shown that thin dense beams can propagate ballistically over lengths many times their gyroradius. This occurs when the following conditions are satisfied: Δ/R_o ⪡ 1, where Δ is the cross field beam width and Ro the gyroradius of an ambient ion having a velocity equal to the beam velocity u_b, and n_bM_b/n_oM_o ⪢ 1, where n_b(M_b), n_o (M_o) are the density (mass) of beam and ambient ions. The scaling of the ballistic propagation lengths and times with beam and ambient parameters is presented along with comments on the applicability of the model to space and astrophysics.