[en] High current (I approximately 10 kA) hollow beams of relativistic electrons may be created and transported only if an axial magnetic field of the order of 1 tesla is present at the emitting surface. This magnetic field imparts canonical angular momentum to the particles. The canonical angular momentum is a constant of the motion in azimuthally symmetric systems, and if the beam is extracted from the magnetic field, it acts as an effective emittance. It is shown that this emittance can be so large as to render impossible the transport of the beam in ''self-pinched'' equilibrium with a radius of the order of a few cm