Circular polarization of synchrotron radiation in high magnetic fields

The general model for incoherent synchrotron radiation has long been known, with the first theory being published by Westfold in 1959 and continued by Westfold and Legg in 1968. When this model was first developed, it was applied to radiation from Jupiter, with a magnetic field of approximate to 1G. Pulsars have a magnetic field of approximate to 10(12) G. The Westfold and Legg model predict a circular polarization which is proportional to the square root of the magnetic field, and consequently predicts greater than 100 per cent circular polarization at high magnetic fields. Here a new model is derived based upon a more detailed analysis of the pitch angle distribution. This model is concerned with the frequency range f(B0)/gamma << f less than or similar to f(B0), noting that f(B0) = 2.7 x 10(7) B, which for a relatively high magnetic field (similar to 10(6)-10(8) G) leaves emission in the optical range. This is much lower than the expected frequency peak for a mono-energetic particle of 0.293eB/4 pi m(e)c gamma(2). We predict the circular polarization peaks around 10(7) G in the optical regime with the radiation almost 15 per cent circularly polarized. The linear polarization changes from about 60 to 80 per cent in the same regime. We examine implications of this for pulsar studies.