The penetration of plasma clouds, or plasmoids, across abrupt magnetic barriers (of the scale less than a few ion gyro radii, using the plasmoid directed velocity) is studied. The insight gained earlier, from experimental and computer simulation investigations of a case study, is generalised into other parameter regimes. It is concluded for what parameters a plasmoid should be expected to penetrate the magnetic barrier through self-polarization, penetrate through magnetic expulsion, or be rejected from the barrier. The scaling parameters are n e , v 0 , B perp , m i , T i , and the width w of the plasmoid. The scaling is based on a model for strongly driven, nonlinear magnetic field diffusion into a plasma, which is a generalization of the laboratory findings. The results are applied to experiments earlier reported in the literature, and also to the proposed application of impulsive penetration of plasmoids from the solar wind into the Earth's magnetosphere.