Nonlinear Inverse Comption Radiation and the Circular Polarization of Diffuse Radiation from the Crab Nebula

A detailed calculation is given of the high-frequency radiation from very relativistic particles moving in a strong, circularly polarized electromagnetic wave. Tbe wave has amplitude E0 such that v0 = eE0/mc 1, where Q is the circular frequency of the wave and m and e are respectively the mass and the absolute value of the charge, and the particle density is assumed to be low enough for vacuum propagation conditions to apply. The particles are assumed to have energies yfllc2 such that y v02. The resulting radiation is shown to have a degree of circular polarization oCv0 -` independent of the radiated frequency, but the total intensity emitted by a stationary system of electrons, all of which drift at angles greater than voly to the propagation direction of the wave, is shown to be identical to synchrotron radiation from relativistic electrons gyrating at large pitch angles in a magnetic field of strength E0/ 2. The results are used to show that the circular polarization of this "nonlinear inverse Compton" mechanism, when combined with the vacuum oblique-rotator approximation for pulsar environments, may be in disagreement with observational upper limits on the fractional circular polarization of the diffuse emission from the Crab nebula.