Approximate Expression of Ellipse Polarization Degree for Gyrosynchrotron Radiation

We study the elliptical polarization degree (EPD) of gyrosynchrotron radiation for the case of transverse propagation. The EPD decreases with increasing ellipticity R (i.e., ratio of the major and miner axial lenths) and with decreasing electron energy spectral index δ. The EPD value varies from 0.55 to 0.15 in the whole range of 3 ≤ R ≤ 10 and 2 ≤ δ ≤ 7. An approximate expression for the EPD is proposed, in which we assume that the emitting electrons have an isotropic pitch angle distribution and a power law distribution in energy. The expression is designed for the electron energy spectral index δ from 2 to 7, as well as the harmonic numbers s from 2 to 70 with a statistical error of ±6%. The expression can be applied to the polarization analysis and magnetic field strength diagnostic for solar limb events.