Experiments are reported where a collisionfree plasma cloud penetrates a magnetic barrier by self-polarization. We here focus on the resulting anomalous magnetic field diffusion into the plasma cloud, two orders of magnitude faster than classical, which is one important aspect of the plasma cloud penetration mechanism. Without such fast magnetic diffusion, clouds with kinetic β k below unity would not be able to penetrate magnetic barriers at all. Tailor-made diagnostics has been used for measurements in the parameter range with the kinetic β k ≈ 0.5 to 10, and with normalized width w/r gi of the order of unity. Experimental data on hf fluctuations in density and in electric field has been combined to yield the effective anomalous transverse resistivity η EFF . It is concluded that they are both dominated by highly nonlinear oscillations in the lower hybrid range, driven by a strong diamagnetic current loop that is set up in the plasma in the penetration process. The anomalous magnetic diffusion rate, calculated from the resistivity η EFF , is consistent with single-shot multi-probe array measurements of the diamagnetic cavity and the associated quasi-dc electric structure. An interpretation of the instability measurements in terms of the resistive term in the generalized (low frequency) Ohm's law is given.