Measurement of electron parameters, H+(proton) and other ion parameters based on spectroscopy of the RADAR signals scattered off electrons
The ionosphere is the ionized section of the Earth's upper atmosphere consisting of molecules and atoms being ionized or having electrons extracted due to solar radiation (UV photoionization). For instance, molecular oxygen and molecular nitrogen, atomic oxygen, hydrogen and helium may be ionized, thereby producing the corresponding positively charged molecules or atoms i.e. ions and a large content of electrons. It is noted that ions and electrons constitute the 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 bounce off 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 (e.g. improve geolocation). When an electromagnetic wave propagates into the ionosphere, the electrons acting as an antenna are excited by the incoming wave and re-radiate it. In other terms, they do not absorb the wave but they reflect it or scatter it. Given that the electrons are moving at varying velocities due to ionospheric dynamics and random thermal motion, the reflection or re-radiated signal from each electron will have a Doppler-shifted frequency. The higher the temperature, the more variable the thermal motion of the electrons becomes. The re-radiated or scattered wave/signal does not consist of one frequency but of a distribution of frequencies which becomes larger with higher temperatures. The 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 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 establish relationships between electron content/density, electron temperature, ion temperature, ion composition and electron/ion velocities.
In Figure 1, the transmission frequency of the RADAR of 430 MHz is represented with the vertical line and the frequencies scattered off the electrons are represented with the 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 1: 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 spectrum, 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 and therefore the more variable will be the frequencies that are scattered. The larger the variability, the greater the spectral width represented by the line 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 reflect/scatter the signal, the scattering behavior of the electron changes. The positively charged ions tend to attract the electrons and hold them nearby (and also restrict their motion). This means that the speed of the ions shows up in the overall motion of the electrons. Consider for instance Figure 2 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.
Figure 2: 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).
Please refer also to the page "Measuring temperatures and composition in the ionosphere".
From ion velocity to electric field
As mentioned at this reference (https://bit.ly/33kT48Y) on slide 4, the frequency fT "gives the line-of-sight component of the mean ion velocity Vi . 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:
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
Figure 3: (Top) From ion velocity to electric field. (Bottom) Rayleigh scattering and Mie scattering (https://bit.ly/33kT48Y).
The first Arecibo observations
On slide 6, we can appreciate "the first simultaneous observations of both ion and electron scattering lines (called plasma lines). The data were taken in the altitude range 1460–2486km over Arecibo, where H+ is the dominant ion."
The first incoherent scatter radar (ISR) site was Arecibo, Puerto Rico, in 1959. "At the time of writing, there are 15 such sites" (slide 3).
Rayleigh scattering and Mie scattering
Except for RADAR, also LIDAR can be used. We refer to Rayleigh scattering from air molecules and Mie scattering from aerosols and clouds. Please refer to attached figure which also shows meteor trails for which we distinguish head and tail scattering referred to as head and trail echos.
Total Electron Content (TEC) prediction using GPS signals
"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."
"Solvers are challenged to characterize the ionosphere with selected digitized radio-frequency (RF) spectrum recordings from sounder receiver data, but not any transmitter data."
"to develop an algorithm that characterizes, monitors, and models ionospheric variation effects on high frequency emissions."
Ionospheric sounders or ionosondes are RADARs/transmitters for the examination of the ionosphere.
"An ionogram is a display of the data produced by an ionosonde. It is a graph of the virtual height of the ionosphere plotted against frequency. Ionograms are often converted into electron density profiles."
(Link included above in ionospheric parameters).