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A relativistic electron beam propagating through plasma induces a returncurrent in the system. Such a system of counterstreaming forward and returncurrent is susceptible to host of instabilities out of which Weibel remains adominant mode for destabilizing the system. Weibel instability has been widelyinvestigated in simulations, experiments, as well as, analytically using fluidand kinetic treatments. A purely growing mode like Weibel instability can alsobe understood by using conservation theorems and energy principle analysis. Anelectrostatic analog to the Weibel instability, two stream instability in abeam plasma system has already been investigated using energy principleanalysis [Lashmore-Davies 2007]. A detailed analytical description ofconservation theorem for 2D Weibel instability in a beam plasma system has beencarried out in this manuscript.

Energy principle for 2D electromagnetic, relativistic, interpenetrating, counter streaming plasma flows