# Ionospheric Distortion

## 1 Ionospheric Distortion

Ionospheric refraction is a problem that gets worse the lower in frequency that you go. The issue is that the ionosphere around the earth has an index of refraction that is significantly different from the space above and below it, as seen by radio waves. If you’ve ever seen a fish in a pond and tried to stab it with a spear, only to find that you’ve missed ridiculously high, you know what I’m talking about.

An example of refraction at an interface between media with low and high indices of refraction

For a plasma, the index of refraction is given by

${\displaystyle n={\sqrt {1-{\frac {\omega _{p}^{2}}{\omega ^{2}}}}},\,\!}$

where ${\displaystyle \omega _{p}\equiv {\sqrt {\frac {n_{e}e^{2}}{\epsilon _{0}m_{e}}}}}$ is the plasma frequency, which is determined by the number density of electrons ${\displaystyle n_{e}}$, the electric charge ${\displaystyle e}$, the emissivity of free space ${\displaystyle \epsilon _{0}}$, and the electron mass ${\displaystyle m_{e}}$. For our atmosphere, a typical ${\displaystyle \omega _{p}}$ is of order 5 MHz.

As you might guess from the frequency-dependence of the index of refraction, the refraction angle through the ionosphere is generally frequency dependent, with ${\displaystyle \Delta \theta \propto \nu ^{-2}}$.

Now all of this wouldn’t be so bad, except that the ionosphere is not static. It varies dramatically depending on time of day and solar weather, as charged particles from the solar wind interact with the Earth’s magnetic field. The timescale for variation is of order 10 seconds, the length scale for turbulence in the ionosphere is of order 1 km, and the direction and magnitude of the refraction angle vary considerably across the sky. At low frequencies, seeing through the ionosphere is something like trying to see out of a windshield with rain pouring down. Effective (and computationally feasible) methods for correcting for time-dependent ionospheric distortion is an active field of research.