Figure 1: Scatter of 430 MHz from an object or from electrons in the ionosphere.
The ionosphere is the ionized section of the Earth's upper atmosphere between 80 and 600 Km altitude, where solar radiation ionizes atoms and molecules or in other terms, extracts electrons from those, thereby creating the corresponding positively charged molecules or atoms i.e. ions and a large content of electrons. Solar radiation consists of extreme UV and x-ray photons which are highly energetic and can therefore dislodge electrons upon collision with molecules and atoms found at this area, such as molecular and atomic oxygen, molecular nitrogen, hydrogen and helium. The generated ions and electrons of the ionosphere constitute the ionospheric plasma. The total electron content (TEC) is one of the most significant ionospheric parameters, as electromagnetic signals transmitted in the ionosphere, e.g. from GPS satellites, may be scattered by the electrons and be deflected causing signal distortion and delay. It is therefore important to measure the total electron content in order to perform corrections on the signal for different applications such as improving geolocation.
When an electromagnetic wave propagating into the ionosphere is incident on an electron, it can be accepted that only its electric component, the oscillating electric field will act upon the electron. The electron will move in the direction of the oscillating electric field, will be accelerated similarly to an electromagnetic dipole (antenna) and by oscillating, it will emit electromagnetic dipole radiation (ref.). The procedure of excitation by electromagnetic radiation followed by re-emission of EM radiation is equivalent to elastic scattering of EM radiation and is termed Thomson scattering. The photons that are scattered elastically by an electron are those whose wavelength is larger than the Compton wavelength* of the electron which is in the order of the picometer (10-12 m) (NIST reference https://physics.nist.gov/cgi-bin/cuu/Value?ecomwl). Practically, photons with wavelengths larger than that of hard x-rays or alternatively frequencies lower than the pentahertz order of magnitude will be elastically scattered by the electron.
(cf. EM chart https://en.wikipedia.org/wiki/Electromagnetic_spectrum).
It can be concluded that all man-made electromagnetic signals in the ionosphere are scattered by electrons. Given that the electrons are moving at varying velocities due to ionospheric dynamics and random thermal motion, the scattered or reflected signal from each electron will have a Doppler-shifted frequency which may be different for each electron. The higher the temperature, the more variable the thermal motion of the electrons and the velocities. Ground receiver stations receive a signal composed of the superposition of the re-radiated/scattered waves from all the electrons in the path of the incoming wave. As a result, the scatter signal is not coherent but is termed incoherent. The scattered signal does not consist of one frequency but of a distribution of frequencies which becomes larger with higher temperatures. This is illustrated in Figure 2 (modified figure from presentation by A. Coster of the MIT Haystack Observatory).
Figure 2: The frequency from a RADAR gun is f0. The return signal from one runner demonstrates a Doppler-shift. The return signal from a group of runners is a superposition of all Doppler-shifted signals from individual runners and is thus termed "incoherent".
The positively charged ions having a much larger mass are not excited by the incoming electromagnetic wave in the way electrons are, and therefore they do not re-radiate the signal. However, the electrons tend to remain close to the positively charged ions, which by their large mass and small velocity influence restrictively the motion of the electrons. As a result, the distribution function of the electrons is modified by the positive ions. By analyzing the incoherent scatter signal received, we can determine both electron and ion properties, such as electron content/density, electron temperature, ion temperature, ion composition and electron/ion velocities.
In Figure 3, the transmission frequency of the RADAR of 430 MHz is represented with the vertical line and the frequencies scattered by the electrons are represented with the red line of the curve. We have different frequencies or a spectrum of frequencies, each of which is associated with a certain power. We can understand that some electrons have a (scattered) frequency that is higher than 430 MHz and some electrons have one that is lower than 430 MHz. The electrons that are moving in the direction of the RADAR wave appear to provide a frequency that is higher and those that are moving in the opposite direction appear to provide a frequency that is lower.
Figure 3: Spectrum of Arecibo incoherent scatter radar transmitted signal (430 MHz) and reflections from electrons (modified figure from Arecibo site).
The more electrons there are, the more power we receive. Therefore, the sum of all the power underneath the red line, which is represented by the grey area, is a measure of the number of electrons in the ionosphere.
The higher the temperature, the more intense the random thermal motion will be, the more increased the randomness will be and therefore the more variable the frequencies that are scattered will be. The larger the variability, the greater the spectral width represented by the horizontal black line with arrows shown in the picture. A larger variability is linked to an increased temperature. Thus, the spectral width reflects the electron temperature.
In the presence of ions, which do not themselves scatter the signal, the scattering behavior of the electron changes. The positively charged ions tend to attract the electrons, hold them nearby and therefore restrict their motion. This means that the speed of the ions shows up in the overall motion of the electrons. Consider for instance Figure 4 below (from this page from the Arecibo observatory). It represents the scattering from an electron population coexisting with O+ ions and H+ ions. We expect that the O+ ions will restrict more the electron motion and by extension electron temperature than the H+ ions and therefore two different line widths corresponding to electron temperature will appear. For this example, it is given that the temperature of the O+ and the H+ ions are identical. In general, if two or more ions are present, we have a complicated spectrum with more than one widths. Using modelling approaches for spectrum analysis, it is possible to determine the temperature of the ions and also determine ion identity/composition in general.
Please refer also to the page "Measuring temperatures and composition in the ionosphere".
Figure 4: Spectrum of Arecibo incoherent scatter radar transmitted signal (430 MHz) and reflections from electrons in the presence of two ions, O+ and H+ (from Arecibo site).
The incoherent scatter RADAR is a powerful instrument for ionospheric measurements. As mentioned in this article by EISCAT, a complete theory describes the spectrum of the scattered signal and inexpensive signal processing is possible.
The signal from the electrons shown in Figure 3 and Figure 5 presents two peaks. It was originally hypothesized that these would correspond to the thermal velocity of the electrons. Quite surprisingly, it was found that these represented the thermal velocity of the ions and as a result the term "ion line" was introduced. This is explained by the fact that the electrons are linked to the ions by attractive forces and actually constitute clouds around the ions. As the scattering is due to the clouds surrounding the ions, it features ion properties.
In Figure 5, the frequency fT gives the line-of-sight component of the mean ion velocity Vi (reference: https://bit.ly/33kT48Y slide 4). According to this reference, if several positions are used, the complete vector flow velocity can be found. In the F region the ion flow velocity yields the perpendicular electric field components via the relationship:
According to the above reference, the ion flow velocity parallel to B is much more complicated, since many factors contribute, such as the component of the neutral wind along B, the ion pressure gradient, and gravitational forces.
According to this reference, "the incoherent scatter radar measures a line-of-sight (LOS) component of the plasma convection velocity (VLOS) in the ionospheric F-region. Supposing that the plasma flow has no a component along the geomagnetic field B (or at least this component is significantly less than the plasma velocities perpendicular to B) and the flow is following only the E × B drift, one can calculate an electric field tangential component, perpendicular to the radar beam direction Eθ = −VLOS × B. The electric field component along the radar beam is referred as a radial component (Er), but it is not directly measured. (...).
According to this reference, "at the F-region heights, the ion drift velocity perpendicular to the geomagneticfield (B) is directly related to the E-field when the ion-neutral collision frequency is much smaller than the ion gyro-frequency. As a result, the F-region vector E-field is routinely obtained by incoherent scatter radars (ISR). In the E-region, Tsunoda et al.  reported E-field measurements from the rotation of the ion vector velocity. In addition to the ISR methods, spectral characteristics extracted from VHF coherent echoes have also been used to estimate vector E-field." This study measures the vertical E-field in the E-region.
Figure 5: ISR spectrum showing the ion line (double humped). Frequency fT differs from the frequency of the ISR RADAR by f0 (from ppt by M.C. Kelley slide 4)
A typical incoherent scatter spectrum shown in Figure 6 (from Bhatt A. 2010) consists of a double humped ion line (I) in the middle, the gyroline (GL) and the plasma line (PL). The gyroline and the plasma line are much weaker (by approximately three orders of magnitude). The gyroline depends on the magnetic field and can be used to probe it. However, as the line is weak, it generally requires relatively long incoherent integration times to measure. Measurements were performed ﬁrst at Arecibo by Behnke and Hagen (1978) and later at the European Incoherent Scatter (EISCAT) VHF radar by Bjørna et al. (1990). A recent study by Hysell et al (2017) updates the theory of the gyrolines by providing a new mathematical derivation. It is cited in the popular science article "Mystery of the Ionosphere’s “Gyro Line” Solved" and also at this blog post from the Arecibo Observatory entitled "the sensitivity of the Arecibo Observatory made possible to observe Gyrolines".
Figure 6: ISR spectrum showing the double humped ion line (I), the plasma line (PL) and the gyroline (GL). (From Bhatt A. 2010).
A most important ionospheric parameter is the total electron content which increases among other during storms. Increased electron numbers may generate interference for GNSS and communication systems by distorting signals (Figure 7).
Figure 7: Distortion of GPS signals due to the ionospheric electrons (reference).
The total electron content is measured by the Global Navigation Satellite Systems by using two frequencies transmitted by the satellites. The measurement is based on the delay in the reception of the frequencies due to electron scattering. All GNSS operate on two or more frequencies. For instance, GPS satellites transmit electromagnetic waves for positioning on frequencies L1 (1575.42 MHz) and L2 (1227.60 MHz). Most of our devices have single-frequency receivers which capture only L1. There are also dual-frequency receivers which capture both L1 and L2.
By using a dual-frequency receiver, it is possible to measure the delays of arrival of the L1 and the L2 signals which are considered to travel along the same path in the ionosphere. The electrons on this path are scattering and thereby delaying the signal. By analyzing the delay, we can determine the electron content encountered on the path.
An important reference is represented by the following article by the MIT Haystack Observatory, home to one of the largest Incoherent Scatter Radar (ISR), Millstone Hill, supported by the NSF: https://www.haystack.mit.edu/geospace/geospace-projects/using-gnss-to-measure-ionospheric-tec.
Another reference: "Monitoring the Ionosphere with Integer-Leveled GPS Measurements" https://www.gpsworld.com/innovation-a-better-way-monitoring-the-ionosphere-with-integer-leveled-gps-measurements/ "It's not just for positioning, navigation and timing."
The International GNSS Service: https://www.igs.org/wg/ionosphere (IGS Central Bureau is at the NASA Jet Propulsion Laboratory)
NASA Service for TEC: https://cddis.nasa.gov/Data_and_Derived_Products/GNSS/gnss_ionovtec.html
(Also termed "vertical incidence sounders")
Sounders are HF transmitters which scan the ionosphere in a typical range of 1 MHz to 10 MHz. They transmit pulses of increasing frequency which reach increasing altitude layers in the ionosphere and are returned by those. The resulting profile profile which is termed an ionogram can be used to calculate different ionospheric parameters including electron content (an ionogram is converted to an electron density profile). A typical ionogram is shown in Figure 8.
The sensitivity of sounders is lower than that of the incoherent scatter RADAR which are very expensive instruments. Geospace facilities use sounders to obtain quick profiles which can also be used to calibrate the incoherent scatter RADAR.
IARPA had launched in 2019 a "passive characterization of the ionosphere" challenge for processing of sounder receiver data (ref.). Participants had to develop "an algorithm that characterizes, monitors, and models ionospheric variation effects on high frequency emissions" (ref.).
"A Stark broadening method to determine simultaneously the electron temperature and density in high-pressure microwave plasmas" https://iopscience.iop.org/article/10.1088/0022-3727/40/19/023:
"Usually, when the electron temperature is previously known, the Stark broadening of certain spectral lines spontaneously emitted by the plasma is used to determine the electron density in a rapid and inexpensive way. However, comparing two or more broadening of lines can allow us to diagnose the electron density and temperature simultaneously. To carry out this cross-point method, we must know the Stark broadening dependence on the electron temperature and density for different lines. In this work we have used the first three Balmer series hydrogen lines, whose Stark broadenings were calculated by means of a recent micro-field model existing in the bibliography."