Elliptic Polarization of Synchrotron Radiation

Abstract

Although the synchrotron emission from a single electron moving with an ultrarelativistic velocity β c in a magnetic field B 0 is elliptically polarized, the characteristics of the polarization ellipse being determined by the position of the direction of observation n relative to the cone swept out by the direction u of the velocity vector about the direction of B 0 , the resultant emission from a distribution of such gyrating electrons is, to a first approximation, linearly polarized in the direction perpendicular to the projection of B 0 on to the plane transverse to n . The reasons for this are that for a single electron the emission is effectively confined to within a small angular distance O(ξ) of u , where ξ = √ (1 − β 2 ) ≪ 1 and that (i) the fourth Stokes parameter is to this approximation an odd function of the angle ip between n and u at its closest approach, and (ii) the number of electrons passing within equal angular distances ψ = ±O(ξ) are equal. It follows that if ξ is large enough it is possible for the next approximation to the fourth Stokes parameter for a distribution of electrons to be significant, so that the resultant emission is elliptically polarized.