Editing Ionosphere (section)

===Radio communication{{anchor|Radio application}}===
<!-- This section is linked from [[Triple J]] -->
Due to the ability of ionized atmospheric gases to [[refract]] high frequency (HF, or [[shortwave]]) radio waves, the ionosphere can reflect radio waves directed into the sky back toward the Earth. Radio waves directed at an angle into the sky can return to Earth beyond the horizon. This technique, called "skip" or "[[skywave]]" propagation, has been used since the 1920s to communicate at international or intercontinental distances. The returning radio waves can reflect off the Earth's surface into the sky again, allowing greater ranges to be achieved with multiple [[Hop (telecommunications)|hop]]s. This communication method is variable and unreliable, with reception over a given path depending on time of day or night, the seasons, weather, and the 11-year [[sunspot cycle]]. During the first half of the 20th century it was widely used for transoceanic telephone and telegraph service, and business and diplomatic communication. Due to its relative unreliability, shortwave radio communication has been mostly abandoned by the telecommunications industry, though it remains important for high-latitude communication where satellite-based radio communication is not possible. Shortwave broadcasting is useful in crossing international boundaries and covering large areas at low cost. Automated services still use [[shortwave radio]] frequencies, as do [[radio amateur]] hobbyists for private recreational contacts and to assist with emergency communications during natural disasters. Armed forces use shortwave so as to be independent of vulnerable infrastructure, including satellites, and the low latency of shortwave communications make it attractive to stock traders, where milliseconds count.<ref>{{cite journal | url=https://ieeexplore.ieee.org/document/9311865 | doi=10.1109/TWC.2020.3046475 | title=Receiver Designs for Low-Latency HF Communications | year=2021 | last1=Arikan | first1=Toros | last2=Singer | first2=Andrew C. | journal=IEEE Transactions on Wireless Communications | volume=20 | issue=5 | pages=3005–3015 | s2cid=233990323 }}</ref>

====Mechanism of refraction====
When a radio wave reaches the ionosphere, the [[electric field]] in the wave forces the electrons in the ionosphere into [[oscillation]] at the same frequency as the radio wave. Some of the radio-frequency energy is given up to this resonant oscillation. The oscillating electrons will then either be lost to recombination or will re-radiate the original wave energy. Total refraction can occur when the collision frequency of the ionosphere is less than the radio frequency, and if the electron density in the ionosphere is great enough.

A qualitative understanding of how an electromagnetic wave propagates through the ionosphere can be obtained by recalling [[geometric optics]]. Since the ionosphere is a plasma, it can be shown that the [[refractive index]] is less than unity. Hence, the electromagnetic "ray" is bent away from the normal rather than toward the normal as would be indicated when the refractive index is greater than unity. It can also be shown that the refractive index of a plasma, and hence the ionosphere, is frequency-dependent, see [[Dispersion (optics)]].<ref>{{cite book|last1=Lied|first1=Finn|title=High Frequency Radio Communications with Emphasis on Polar Problems|date=1967|publisher=Advisory Group for Aerospace Research and Development|pages=1–6}}</ref>

The [[critical frequency]] is the limiting frequency at or below which a radio wave is reflected by an ionospheric layer at vertical [[angle of incidence (optics)|incidence]]. If the transmitted frequency is higher than the [[plasma frequency]] of the ionosphere, then the electrons cannot respond fast enough, and they are not able to re-radiate the signal. It is calculated as shown below:

: <math>f_{\text{critical}} = 9 \times\sqrt{N}</math>

where N = electron density per m<sup>3</sup> and f<sub>critical</sub> is in Hz.

The Maximum Usable Frequency (MUF) is defined as the upper frequency limit that can be used for transmission between two points at a specified time.

: <math>f_\text{muf} = \frac{f_\text{critical}}{ \sin \alpha} </math>

where <math>\alpha</math> = [[angle of arrival]], the angle of the wave relative to the [[horizon]], and sin is the [[sine]] function.

The [[cutoff frequency]] is the frequency below which a radio wave fails to penetrate a layer of the ionosphere at the incidence angle required for transmission between two specified points by refraction from the layer.