# 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?

• Usually E-M-Modes in strongly magnetized plasmas do not propagate perpendicular to k. They propagate along the B-Field and are clockwise (interacting with protons) and counter-clockwise (interacting with electrons) oriented. The mixed amplitudes give you elliptical polarization. Is that what you are asking? Nov 10, 2014 at 23:08
• @AtmosphericPrisonEscape - This is not true and I think you are confusing k with B. Electromagnetic waves can propagate at all angles relative to B. By propagate, one needs to distinguish between phase or group, but both can be at any arbitrary angle relative to B. It is true that different modes cannot propagate at all angles, but if one includes all modes then this issue is removed. Nov 27, 2014 at 15:57

In your case it sounds like a combination of refraction and interaction (with the charged particles) occurs. If $\hat{k}$ $\parallel$ $\hat{x}$ initially, then the phase fronts are moving in the $\hat{x}$ direction. This is the direction that defines how the waves interact with the particles. If the wave starts to couple to the plasma (e.g., it causes electrons to slosh around rather than passing through without interacting), then the motion of the particles can cause local time-varying charge separations, which are electric fields.