Energy transfer by a relativistic electron beam is restricted by the interaction of the electrons with the magnetic fields produced by the total beam and plasma current. In the absence of plasma current, various proposed configurations of current have an effective limit for energy carried by the electrons approximately equal to the conventional Alfven limit. This restriction appears to prevent establishment of energy transport sufficient for fusion application. If plasma currents are included, the total current may lie within the Alfven limit. This paper reviews and summarizes the work of four previous authors.