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Magnetic insulation obtained by employing the magnetic field of the line current in coaxial vacuum‐transmission lines is studied in experiments on two different relativistic electron‐beam accelerators, spanning the voltage range 0.4–10 MV. Effective magnetic insulation at fields up to 1.3 MV/cm is demonstrated. The self‐limiting impedance is measured and compared to a number of theories for magnetic insulation and it is found that none of the ’’standard’’ theories successfully describes the data. However, computer simulations using a self‐consistent two‐dimensional particle code give good agreement with the experimental data, as does a proposed modification of the parapotential flow model.