Bose-Einstein condensation of a finite number of photons propagating inside a plasma-filled microcavity is investigated. The nonzero chemical potential is provided by the electrons, which induces a finite photon mass and allows condensation to occur. We derive an equation that models the evolution of the photon-mode occupancies, with Compton scattering taken into account as the mechanism of thermalization. The kinetic evolution of the photon spectrum is solved numerically, and we find evidence of condensation down to nanosecond timescales for typical microplasma conditions, $n_e\sim {10}^{14}–{10}^{15}{\text{cm}}^{-3}$. The critical temperature scales almost linearly with the number of photons, and we find high condensate fractions at microcavity-plasma temperatures, for experimentally achievable cavity lengths ($100–500\mu \mathrm{m}$) and photon numbers (${10}^{10}–{10}^{12}$).

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• Kinetic theory
• Photon statistics
• Plasma thermodynamics
• Bose-Einstein condensates