Polarization of a transverse wave travelling in ionosphere with polarization direction perpendicular to earths magnetic field

Assume a transverse electromagnetic wave entering ionosphere such that its electric field is perpendicular to Earth's magnetic field. Now, I read that as it will enter plasma, the wave will tend to be elliptically polarized. In other words: if Earth's magnetic field $B$ is in $z$-direction, electric field $E$ of the wave is in $y$-direction and propagation vector $k$ lies in $x$-direction, then it says that $E$ will develop a component along $x$ too. How does that happen?