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

Abstract

The covariant Vlasov-Maxwell system is used to study 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 $E_{\text{max}}$ of non-linear longitudinal electric waves for a particular class of waterbags whose geometry is a simple 3-dimensional generalization (in velocity) of the 1-dimensional KM waterbag (in velocity). It is well known that the value of ${\lim }_{v\to c}{E}_{\text{max}}$ (with the effective temperature of the plasma electrons held fixed) diverges for the KM model; however, we show that a certain class of simple 3-dimensional waterbags yields a finite value for ${\lim }_{v\to c}{E}_{\text{max}}$, where $v$ is the phase velocity of the wave and $c$ is the speed of light.

17 pages, 4 figures (5 graphics files)

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