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By superimposing a coaxial conduction current on the beam current of relativistic electrons passing through high‐permeability magnetic materials, the Lorentz field, β × B, can be made an appreciable fraction of the stopping electric field, G = e-1 dU/dz, of the electron in the material, implying that a state of compression is quite possible. A model of the repulsive field Eσ for the electron beam, arising from momentum being scattered radially from the axial momentum of the beam, is given. The equation of the resultant field acting on an electron provides the information to determine the condition for a pinch to occur. Experimental means of interpreting the results are indicated.