Quantum-electrodynamical parametric instability in the incoherent photon gas

We present a theory for the quantum-electrodynamical (QED) parametric scattering instability of an intense photon pulse in an incoherent radiation background. The pump electromagnetic (EM) wave can decay into a scattered daughter EM wave and an acousticlike wave due to the QED vacuum polarization nonlinearity. By a linear instability analysis we obtain a nonlinear dispersion relation for the growth rate of the scattering instability. The nonlinear QED scattering instability can give rise to the exchange of orbital angular momentum between intense Laguerre-Gaussian mode photon pulses and the two daughter waves, which may be a useful method to detect the highly energetic photon gases existing in the vicinity of rotating dense bodies in the Universe, such as pulsars and magnetars. The observation of the scattered waves may reveal information about the twisted acoustic waves in the incoherent photon gas.