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enter image description here

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?

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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.

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

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