# What causes the sudden change in atmospheric reflection of long-band radio waves? This picture shows up a lot. The explanations that tend to accompany it say that the long-band radio waves above ~10m are reflected, whereas other wavelengths are scattered or absorbed or transmitted.

Question: Why the sudden qualitative change around 10m? What process causes 5m waves to pass through and 20m waves to reflect?

## 1 Answer

The refractive index of a plasma is $$\sqrt{\epsilon_r}$$, where the relative permittivity is given by $$\begin{equation} \epsilon_r = 1 - \frac{n_e e^2}{\epsilon_0 m_e \omega^2}=1 - \frac{\omega_p^2}{\omega^2}\,, \end{equation}$$ where $$\omega_p$$ is known as the plasma frequency.

The refractive index will become imaginary when $$\omega<\omega_p$$ and an EM wave will not propagate.

In the Earth's ionosphere, the electron number density $$n_e\simeq 10^{12}$$ m$$^{-3}$$ and $$\omega_p \simeq 6\times 10^7$$ rad/s, corresponding to a wavelength of $$\simeq 30$$ m.

So I think that is the origin of the rather sharp cut-off in transmission on your plot.

• Note also that the horizontal axis in this plot is logarithmic, which makes the transition look much more sudden than it really is. – niels nielsen Apr 21 at 20:47