Intense beams of relativistic electrons have been extracted from the electrode space of flash X-ray machines and projected into plasma columns and drift spaces. In the plasma columns the beam pinches itself and propagates to a target at the end of the discharge. The plasma column is produced by a conventional pinch discharge in argon and the magnetic field of the plasma column is sufficient to guide the high energy beam around rather sharp curves with little loss of energy. In addition to the very interesting properties of the beam itself, and its applications in thermonuclear work, the possibility of using these beams for a relatively inexpensive, ion accelerator which may produce intense pulses of heavy ions with energies as high as 10 to the 12th power eV per nucleon has recently stimulated research. It is the purpose of the paper to describe the principal experimental results so far obtained, and to derive an expression for the maximum current which a beam may possess by use of the Bennett theory and the equilibrium current distribution which the beam must assume. It will also be shown that this expression reduces to the Alfven limit in a frame in which the beam's space charge is fully neutralized, and indicates that beams which exceed the Alfven limit may be expected to propagate in the laboratory frame. (Author).