Conversion Measure of Faraday Rotation-Conversion with Application to Fast Radio Bursts

Faraday rotation-conversion is the simultaneous rotation of all three Stokes polarization parameters, Q, U, and V, as an electromagnetic wave propagates through a magnetized plasma. In this regime, the Faraday plasma screen is characterized by more than just a rotation measure. We define the conversion measure that characterizes the wavelength-dependent conversion between the linear and circular polarization. In a cold plasma, the conversion occurs at the localized regions along the wave's path, where the large-scale magnetic field is perpendicular to the propagation direction. We show that the number of these regions along the line of sight through the screen, and their individual contributions to the conversion measure, can be inferred from the polarization measurements. We argue that the simultaneous measurement of wavelength-dependent linear and circular polarization might give an important insight into the magnetic-field geometry of the Faraday screen in FRB 121102 and other repeating fast radio bursts.