Photon kinetics and collective plasma dynamics in the presence of two populations of photons*

We use a photon fluid description and a generalized photon kinetic theory, based on the Wigner-Moyal description, to capture capture collective plasma dynamics in the relativistic regime driven by broadband incoherent or partially coherent sources. We consider a population of soft photons, coupled with the plasma via the ponderomotive force, and a population of hard photons, whose interaction with the plasma can include single scattering mechanisms. We explore several plasma instabilities/modifications to the collective plasma dynamics present in this scenario due to the presence of hard photons. Comparisons with numerical simulations are also presented.