Forward modelling of the Cotton-Mouton effect polarimetry on EAST tokamak

Measurement of plasma electron density by far-infrared laser polarimetry has become a routine and indispensable tool in magnetic confinement fusion research. This article presents the design of a Cotton-Mouton polarimeter interferometer, which provides a reliable density measurement without fringe jumps. Cotton-Mouton effect on Experimental Advanced Superconducting Tokamak (EAST) is studied by Stokes equation with three parameters $(s_1, s_2, s_3)$. It demonstrates that under the condition of a small Cotton-Mouton effect, parameter $s_2$ contains information about Cotton-Mouton effect which is proportional to the line-integrated density. For a typical EAST plasma, the magnitude of Cotton-Mouton effects is less than 2${\text{π}}$ for laser wavelength of 432 $\mu {\rm{m}}$. Refractive effect due to density gradient is calculated to be negligible. Time modulation of Stokes parameters ($s_2$, $s_3$) provides heterodyne measurement. Due to the instabilities arising from laser oscillation and beam refraction in plasmas, it is necessary for the system to be insensitive to variations in the amplitude of the detection signal. Furthermore, it is shown that non-equal amplitude of X-mode and O-mode within a certain range only affects the DC offset of Stokes parameters ($s_2$,$s_3$) but does not greatly influence the phase measurements of Cotton-Mouton effects.