Wave-Breaking Amplitude of Relativistic Oscillations in a Thermal Plasma

The maximum amplitude of relativistic plasma oscillations (${\upsilon }_{\mathrm{ph}}$ near $c$) is obtained with a combined one-dimensional waterbag and warm-fluid model. The waterbag description is used to obtain expressions for the pressure and internal energy as functions of the proper density. A relativistic Euler's equation that is valid for arbitrarily large amplitudes and an analytic expression for the wave-breaking amplitude in the limit ${\upsilon }_{\mathrm{ph}}\cong c$ are obtained. Even a small amount of thermal energy can significantly reduce the maximum plasma-wave amplitude relative to the cold wave-breaking value. The significance of the results for recent accelerator schemes is discussed.