Longitudinal wave-breaking limits in a unified geometric model of relativistic warm plasmas

The covariant Vlasov–Maxwell system is used to study the breaking of relativistic warm plasma waves. The well-known theory of relativistic warm plasmas due to Katsouleas and Mori (KM) is subsumed within a unified geometric formulation of the 'waterbag' paradigm over spacetime. We calculate the maximum amplitude E max of nonlinear longitudinal electric waves for a particular class of waterbags whose geometry is a simple three-dimensional generalization (in velocity) of the one-dimensional KM waterbag (in velocity). It has been shown previously that the value of lim v → c E max (with the effective temperature of the plasma electrons held fixed) diverges for the KM model; however, we show that a certain class of simple three-dimensional waterbags exhibit a finite value for lim v → c E max , where v is the phase velocity of the wave and c is the speed of light.