Wave-breaking limits for relativistic electrostatic waves in a one-dimensional warm plasma

The propagation of electrostatic plasma waves having relativistic phase speed and amplitude has been studied. The plasma is described as a warm, relativistic, collisionless, nonequilibrium, one-dimensional electron fluid. Wave-breaking limits for the electrostatic field are calculated for nonrelativistic initial plasma temperatures and arbitrary phase velocities, and a correspondence between wave breaking and background particle trapping has been uncovered. Particular care is given to the ultrarelativistic regime (γφ2kBT0/(mec2)>>1), since conflicting results for this regime have been published in the literature. It is shown here that the ultrarelativistic wave-breaking limit will reach arbitrarily large values for γφ→∞ and fixed initial temperature. Previous results claiming that this limit is bounded even in the limit γφ→∞ are shown to suffer from incorrect application of the relativistic fluid equations and higher, more realistic wave-breaking limits are appropriate