On the maximum current for a self-focusing relativistic electron beam

The maximum possible current has been calculated in a relativistic electron beam-plasma equilibrium. The self-consistent analysis reads Imax<(m0 c3/e)βbγb, where γb=(1−βb2)−1/2 for the charge-neutralized relativistic beam having a large radius compared with the beam thermal Debye length. The special case found in the literature is reproduced [H. Alfvén, Phys. Rev 55, 425 (1939)]. The present work is essential for relativistic electron transport in fast ignition of targets for laser fusion.