Avalanche Photon Cooling by Induced Compton Scattering: Higher-Order Kompaneets Equation

Induced Compton scattering (ICS) is an interaction between intense electro-magnetic radiations and plasmas, where ICS transfers the energy from photons to plasmas. Although ICS is important for laser plasma interactions in laboratory experiments and for radio emission from pulsars propagating in pulsar wind plasmas, the detail of photon cooling process has not been understood. The problem is that, when ICS dominates, evolution of photon spectra is described as a nonlinear convection equation, which makes photon spectra to be multi-valued. Here, we propose a new approach to treat evolution of photon spectra affected by ICS. Starting from the higher-order Kompaneets equation, we find a new equation that resolves the unphysical behavior of photon spectra. In addition, we find the steady-state analytic solution, which is linearly stable. We also successfully simulate the evolution of photon spectra without artificial viscosity. We find that photons rapidly lose their energy by ICS with continuously forming solitary structures in frequency-space. The solitary structures have the logarithmically same width characterized by an electron temperature. The energy transfer from photons to plasma is more effective for broader spectrum of photons such as expected in astrophysical situations.