  Spinning black holes can transfer a significant fraction of their energy to
ultralight bosonic fields via superradiance, condensing them in a co-rotating
structure or "cloud". This mechanism turns black holes into powerful particle
detectors for bosons with extremely feeble interactions. To explore its full
potential, the couplings between such particles and the Maxwell field in the
presence of plasma need to be understood. In this work, we study these
couplings using numerical relativity. We first focus on the coupled
axion-Maxwell system evolving on a black hole background. By taking into
account the axionic coupling concurrently with the growth of the cloud, we
observe for the first time that a new stage emerges: that of a stationary state
where a constant flux of electromagnetic waves is fed by superradiance, for
which we find accurate analytical estimates. Moreover, we show that the
existence of electromagnetic instabilities in the presence of plasma is
entirely controlled by the axionic coupling; even for dense plasmas, an
instability is triggered for high enough couplings.
