Powerful electromagnetic pulses are transmitted by incoherent scatter radars (ISRs) into the ionosphere, causing electrons to oscillate and re-radiate along the radar scattering wave vector. The scattering wave vector depends on the radar operating frequency and geometry. The scattered signal is collected by the radar and analyzed as a power spectrum . ISRs probe the ionospheric plasma at a wavelength much greater than the Debye length, λD i.e. 1α=1ksλD≫1, where ks=2π/λs, ks and λs are the scattering wavenumber and wavelength, respectively. The electron Debye length is defined as λD=ϵ0kBTe/nee2 where ϵ0 is the permittivity of free space, kB is the Boltzmann constant, Te is the electron temperature, ne is the electron density and e is the electron charge. ISRs provide valuable information about the collective interactions in the plasma. Most of the scattered power is present at pairs of frequencies corresponding to the natural electrostatic modes of the plasma, where the resonance condition of the magnetized plasmas is satisfied . The Doppler shift of each frequency can be either positive, indicating a wave travelling towards the radar, or negative, signifying a wave travelling away along the scattering direction. These resonant frequency pairs are classified as ion lines and plasma lines, corresponding to ion acoustic waves and Langmuir waves, respectively .

Most of the scattered power is contained within the ion lines. The integrated power of the ion line in thermal equilibrium is given by and 2Ii=α41+α21+α2+α2Te/Ti, where Ti is the ion temperature. The ion line spectrum is fitted to a model power spectrum, under the assumption of scatter from a uniform plasma in thermal equilibrium i.e. the electron and ion velocity distributions are Maxwellian. The three-dimensional isotropic Maxwellian velocity distribution for species s is given by 3fs(v)=ms2πkBTs32exp⁡-ms(v-us)22kBTs, where ms is the mass, Ts the temperature, and us the bulk drift velocity of species s (either electron e or ion i). The ionospheric plasma parameters ne,Te,Ti and ui are estimated from the ion line for each range gate. In this case, the range gate is equal to the spatial resolution of the analysis. These parameters characterize the uniform background ionospheric plasma along the direction of the scattering wavevector . For a thermal plasma, the integrated power in one plasma line is written as: 4Ip=12α2. when the condition Eq. () is satisfied, then the ratio of the integrated power in the plasma line (Ip) and the ion line (Ii) is given by 5IpIi≈12α21+TeTi.

This implies that plasma lines generally contain less power than the ion lines, as seen in Eq. (), and are difficult to observe in uniform plasmas in thermal equilibrium. However, photoionization or auroral precipitation can generate a suprathermal population and the power in the plasma line spectra can be enhanced . Plasma lines may also be strongly enhanced by plasma instabilities and Langmuir turbulence. Such processes can lead to intensities several orders of magnitude above the thermal level, and have been studied both theoretically and observationally. For example, presented a numerical study of Langmuir turbulence driven by low-energy electron beams, while reported the first direct evidence of naturally occurring cavitating Langmuir turbulence in the ionosphere. A comprehensive review of these processes is given by .

Plasma line measurement enables the study of several properties that are not directly available with only the measurement of the ion lines. For example, plasma lines allow for the analysis of fine structures in suprathermal electron velocity distribution at velocities imposed by the plasma line frequency and the radar frequency . Electron density and temperature estimates are also improved by plasma lines . Plasma line asymmetry can be used to measure electron drift velocity and electron density, which, together with ion drift velocity, provide an estimate of the ionospheric current . Plasma line measurements facilitate the determination of additional parameters, like ion composition and ion-neutral collision frequency by providing extra constraints, reducing ambiguity between parameters.

Plasma lines have been the subject of numerous studies. Investigations of plasma lines along the magnetic field at high latitudes have encompassed experimental studies , theoretical modelling as well as comparing experimental data with theoretical modelling . Plasma line parameters at oblique angles to the magnetic field have also been explored through experimental measurements at low latitudes and comparative studies combining theoretical models with experimental data at both low latitudes and high latitudes . focused exclusively on plasma lines in the E-region, while considered plasma lines in the F-region as well. However, these studies do not address high-latitude F-region plasma line intensity measurements as a function of phase energy at low aspect angles, a gap we aim to fill.

In Sect.  we present a description of the EISCAT UHF radar experimental setup and IP2 scanning technique used to collect the data presented here. Section  covers the general methodologies for supervised and unsupervised detection of plasma lines, parameter extraction using Gaussian model fitting and intensity derivation. In Sect. , we summarize the main findings from applying these methodologies to ISR data collected with the EISCAT UHF radar in Tromsø between 07:00–15:00 UT from 26 to 31 January 2022. Finally, Sect.  discusses the advantages and disadvantages of the supervised and unsupervised detection methodologies, examines plasma line intensity variations as a function of time, altitude, phase energy, and the aspect angle between the magnetic field and the scattering wavevector, and suggests areas for future research.

The data analyzed in this study were collected with the EISCAT UHF radar in a scanning sequence as part of a common programme experiment known as the IP2 or CP2 experiment. The IP2 scan consists of a beam-swing sequence where the antenna points in three directions in a short cycle. The details of the radar scan sequence are described in Table . It takes 15 s for the radar to manoeuvre between pointing directions, and therefore, the radar scan cycle duration is 4 min. The scattering wavevector is the difference between the received and transmitted wavevector ks=kr-kt. For a monostatic radar, i.e. a radar with same antenna to transmit and receive and transmitting and receiving at the same operating frequency fradar, kt and kr have the same magnitude kt=kr=2πfradar/c with c the speed of light in vacuum and the scattering wavevector is ks=-2kt with wavenumber ks=4πfradar/c. For the EISCAT UHF radar, ks=39m-1.

The radar has a transmitter frequency of 927 MHz (wavelength λ=32.2cm), a peak power of 1 MW and a 11 % duty cycle. The experiment uses a 32 bit alternating code transmitter scheme with a baud length of 20 µs. Each code consists of 64 subcycles of duration 5.58 ms, resulting in a total cycle duration of 0.357 s. Measurements have a pre-integration time of 5 s, with a total of 14 cycles included in each data dump. It is assumed that the ionosphere remains stationary throughout this time resolution.

The raw data collected by the radar consists of the autocorrelation function (ACF) evaluated at discrete time lags . Plasma line ACFs are sampled with a lag increment of 0.4 µs, and the maximum lag is 320 µs, resulting in a total of 800 lags. The power spectrum is derived by taking the Fourier transform of the ACF. The resulting frequency resolution of the power spectrum is 1.56 kHz and a bandwidth of 2.5 MHz. The spectra consist mostly of white noise, with the possibility of a narrow-banded plasma line signal being present. Plasma line data from two downshifted receiver bands (between -5.25 and -2.75 MHz, and between -7.65 and -5.15 MHz) were analyzed. Data were examined from 07:00 to 15:00 UT every day between 26–31 January 2022. The spectral and range characteristics of the ion line and plasma line channels are given in Table .

The analysis of plasma line data using the supervised methodology revealed detectable enhancements for about 10 % of the total observational time. Plasma lines were observed 26 %, 5 % and 5 % of the total pointing time in the field-aligned, east and vertical directions, respectively. Over the entire analysis period (26–31 January 2022 with 8 h per day between 07:00–15:00 UT, except on 26 January between 08:00–15:00 UT), the unsupervised methodology detected 110 plasma lines, while the supervised methodology detected 275. Both methodologies are robust against noise factors such as (a) localized noise at specific altitudes, as shown in Fig. , and (b) higher noise around the centre frequency of the filters where the plasma line profile is superimposed, as shown in Fig. . The filtering and noise removal technique from enhances plasma lines despite these challenges, facilitating plasma line profile detection. Here, we present the results of the analysis for 29 January 2022 07:00–15:00 UT only.

The plasma line data fit well to the Gaussian model (see Fig. ), as was also shown in . Figure  shows the altitude profile of the plasma line parameters derived from the fit in Fig. . It can be seen that the derived plasma line frequency exhibits a smooth variation in altitude, with the maximum in the magnitude of plasma line frequency at the F2 peak altitude of 251.5 km. This behaviour is due to the plasma frequency's quasi-parabolic variation with altitude around the peak at hmF2, as pointed out in . Near the F-layer peak, the reduced frequency spreading leads to a stronger and narrower plasma line at the altitude with the highest electron density. In contrast, the steeper gradient of the plasma frequency away from the peak causes more frequency spreading of the plasma line signals above or below the F-layer peak. This trend is evident in Figs.  and , where the plasma line width is narrowest at the F2 peak and gradually broadens above and below this altitude.

Figure  shows the electron density and temperature estimates as a function of time and altitude obtained from GUISDAP using the ion line data from 29 January 2022. A scaling parameter known as the Magic constant must be specified in GUISDAP for the ion line analysis. The Magic constant is calibrated to ensure that the electron density derived from the plasma line matches that obtained from the ion line. A different Magic constant was calculated for each day of the experiment. GUISDAP assumes Maxwellian electron and ion velocity distributions to estimate these parameters. The parameters are plotted over the same time period, from 07:00 to 15:00 UT, and the same altitude range, 107–374 km (see Table ), where the plasma lines were analyzed. The black vertical lines indicate the time interval during which plasma lines were detected using the supervised methodology as demonstrated in Fig. . During this interval, electron density increases to ≈5×1011m-3, corresponding to a plasma frequency of ≈6MHz, between 230 and 280 km, i.e. around the F-layer peak where scale height is largest. As a result, most of the plasma lines observed are in the same altitude range. Figure  shows the estimated plasma line parameters as function of time and altitude derived using the plasma line parameter extraction technique (see example provided in Figs.  and ) from all positive plasma line detections at different times and altitudes on 29 January 2022, following the supervised methodology illustrated in Fig. , with analysis similar to .

The plasma line is observed only in the downshifted channel, with frequency magnitudes between 5.5 to 6.7 MHz. The plasma line frequency increases gradually from 10:00–11:20 UT (Fig. ), driven by an increase in the photoelectron population from solar EUV radiation. An additional feature visible in Fig.  is the quasiperiodic undulation of the detected plasma line location, corresponding to vertical shifts of the F-region lower boundary. Similar variations can be seen in the electron density derived from the ion line data (Fig. ) and were also observed on other days of the experiment. The exact cause of these undulations is uncertain. However, possible drivers such as atmospheric gravity waves or magnetospheric Pc5 ULF waves could be worth investigating in future studies. The plasma line enhancement mechanism itself depends primarily on the presence of suprathermal electrons, and is not directly altered by altitude variations of the F-region boundary.

We have similar plots to those shown in Figs.  and  for the other days, which are provided in the Supplementary Material (Figs. S1–12). The background electron density and temperatures, as shown in Fig. , do not vary significantly from day to day. The variation in background electron density over different days is between ≈2×1011 to 9×1011m-3. As can be seen from Eq. (), the phase energy depends on the plasma line frequency and therefore the background electron density. Since the electron density naturally fluctuates from one day to another, the range of the phase energy explored will consequently vary.

We discussed two methodologies for detecting plasma lines. The first, a supervised approach based on image morphological processing, requires manual tuning of binary threshold and erosion/dilation parameters. This approach requires an initial guess of the parameters followed by iterative adjustments. In our case, we began with the parameters used by for ESR IPY experiments and refined them until no false positives were detected for a given day and channel. However, selecting parameters in this supervised approach relies heavily on trial and error, requiring many adjustments based on the observation day, radar channel, and radar type. In contrast, the methodology based on connected component analysis is an unsupervised approach, as the detection thresholds are not manually defined but are automatically derived from statistical estimators and the distribution of the connected component sizes. This data-driven approach establishes thresholds for converting spectral images to binary format and for detecting plasma lines in entire datasets for a given day, channel, and radar, eliminating the need for initial assumptions or manual adjustments. As a result, the unsupervised approach is more adaptable to different radars.

The supervised methodology detected more plasma lines than the unsupervised. Both supervised and unsupervised methodologies were tuned to avoid false positives. The supervised methodology may have a higher sensitivity to weaker plasma lines, while the unsupervised with statistically derived thresholds, is more conservative and may miss some weaker signals. Each methodology has its strengths depending on the goals of the analysis. The supervised methodology may be preferable when the goal is to maximize detection sensitivity, while the unsupervised methodology is more suitable for working with large datasets spanning multiple days or different radars.

88 % of the plasma lines detected in the downshifted channels occurred at the magnitude of frequencies above 5.25 MHz, with the lowest detected plasma line frequency across all six days being 4.7 MHz. This means that the plasma lines detected in the downshifted channel between 2.75 to 5.25 MHz occurred near the edge of the filter. In the experiment, no data were recorded in the upshifted channel at frequencies above 5.25 MHz. Although data were recorded at upshifted frequencies between 2.75 to 5.25 MHz, no plasma lines were detected in this range, possibly because plasma lines in downshifted channels likely occur above 5.25 MHz. One of the initial objectives of this study was to estimate ionospheric currents using plasma lines observed at both upshifted and downshifted frequencies. However, the absence of corresponding upshifted plasma lines prevents us from calculating ionospheric currents in the present analysis.

We can nevertheless analyze plasma line intensity as a function of phase energy. This provides fine-grained details about the suprathermal electron velocity distribution at the corresponding velocity range. The phase energy of the plasma line corresponds to the kinetic energy of the electrons that are in resonance with the electrostatic wave. Since the F10.7 index, the electron density and temperature do not exhibit substantial variations across the entire analysis period, we combine data from each day (26 to 31 January 2022 07:00–15:00 UT) to plot the plasma line intensity, kBTp, as a function of phase energy, Eϕ, calculated from the derived plasma line frequency using Eq. ()

Figure  shows plasma line intensity versus phase energy at different altitudes, using plasma line measurements from 26 to 31 January 2022. Plasma line intensity is a function of time, altitude, phase energy and aspect angle; here, we integrate it over time and aspect angles to display it as a function of phase energy and altitude. The figure uses box plots to represent plasma line intensity across uniform phase energy intervals: each box's central line shows the median plasma line intensity, with top and bottom edges indicating the upper and lower quartiles (the 75th and 25th percentiles, respectively). The interquartile range (IQR) is the distance between these quartiles. Outliers, defined as samples exceeding 1.5⋅IQR from the top or bottom of the box, are represented by the symbol “o”. Additionally, the whiskers extend from each box: one connects the upper quartile to the non-outlier maximum (the highest value that is not an outlier), and the other connects the lower quartile to the non-outlier minimum (the lowest value that is not an outlier).

As seen in Fig. , plasma line intensities are grouped into three altitude ranges. 66 % of the plasma lines are detected between 233.1–257.8 km (corresponding to the range around the F2 peak), 22 % detected between 208.5–233.2 km (below the F2 peak) and 12 % detected between 257.8–282.5 km (above the F2 peak). The highest-frequency plasma line observed occurred at 6.76 MHz, corresponding to an altitude of about 246 km, which lies near the middle of the altitude range where plasma lines were detected. As can be seen in Fig. , the intensity of the plasma line is largest around the F2 density peak, which explains why most of the plasma lines are observed in the range 233.1–257.8 km.

The plasma line frequency bands extend from -7.65 to -2.75 MHz, as described in Sect. . Using Eq. (), it can be determined that the EISCAT UHF system can probe an energy interval of 0.6–4.4 eV. However, as shown in Fig. , the observed plasma lines are confined to the energy range of 1.7–3.4 eV. This indicates that, despite detecting hundreds of plasma lines, only 45 % of the total phase energy range accessible is effectively explored. This suggests that, even with multiple days of observations, the daytime ionospheric conditions between consecutive days were relatively similar. While plasma lines with phase energies below 1.7 eV may exist, they are likely obscured by noise due to the lower plasma densities, and therefore, lower SNR.

As the resonance phase energy increases, the plasma line intensity increases for all the altitude groups, peaking around a phase energy of 3 eV, after which it starts decreasing again. This result is consistent with the model predictions by where F-region photoelectron-enhanced plasma lines observed by EISCAT UHF radar peaks at approximately 2.7 eV. The variation in plasma line intensity can be understood in terms of the balance of several damping and excitation mechanisms, including collisional damping, thermal Landau damping, and photoelectron Landau damping . For phase energies below 4 eV, the dominant processes are thermal Landau damping and Cerenkov excitation of thermal electrons . The magnitude of Landau damping depends on the slope of the reduced one-dimensional velocity distribution function of the electrons along the direction of the scattering wave vector. Smaller Landau damping corresponds to larger plasma line intensity. The presence of a suprathermal electron population introduces a high-energy tail to the distribution function, decreasing the slope at higher energies and thereby, reducing Landau damping. Consequently, as phase energy increases, the plasma line intensity increases. This differs from higher phase energies, where inverse Landau damping of photoelectron peaks can provide an additional source of wave growth . It is also worth noting there do not seem to be any significant or systematic differences in plasma line intensity between the altitude groups for any given energy, indicating that the suprathermal populations are very similar at these altitudes.

Figure  presents plasma line intensity as a function of phase energy for the available aspect angles and integrated over altitude and the six days from 26–31 January 2022 07:00–15:00 UT. The data are visualized as box plots similarly to Fig. . It can be seen that the plasma line intensity generally decreases as the aspect angle increases. This result is consistent with the findings of that accounted for the magnetisation of suprathermal electrons in their derivation. suggested that the Landau damping increases with the aspect angle. This implies that the reduced one-dimensional electron velocity distribution function becomes steeper at higher aspect angles, meaning that more electrons absorb energy from the wave. This can be a possible reason for the reduction in plasma line intensity at higher aspect angles. More recent work by shows that plasma line intensity is roughly constant up to ∼ 10° and increases between 10–20°. In their study, the intensity variation in the phase energy regime is dominated by the inverse Landau damping of the photoelectron peaks. For the relatively low phase energies considered here (< 4 eV), however, the dominant mechanisms governing the observed variations remain Landau damping and Cerenkov excitation , and a detailed modelling with suprathermal electron distribution is left for future work.

Even though the data are taken from multiple days covering different phase energy intervals, there is an overall smooth variation of plasma line intensity with phase energy as seen in Figs.  and . This suggests that the suprathermal electron velocity distribution at the corresponding velocities does not vary significantly over the observation campaign.

Plasma line enhancements above the thermal level depend directly on the suprathermal electron flux. During daytime, the prolonged input of solar EUV energy produces suprathermal electron fluxes over an extended period, resulting in more frequent plasma line detections, particularly around the F-layer peak where electron density is highest. At night, suprathermal electron flux is generated through transient auroral activity, resulting in observable plasma line enhancements. For nighttime observations, careful selection of the integration time is necessary, as too long an interval could average out short-lived enhancements and make plasma lines harder to detect.

Regarding seasonal variations, we expect statistical plasma line occurrence to vary in line with the study from . In particular, May–July will offer the highest number of plasma line observations due to prolonged solar illumination and high suprathermal electron fluxes. Both solar EUV radiation and auroral precipitation can contribute during March–April and August–October, allowing plasma line detection under a wider range of conditions. Therefore, there can be more observations over wider phase energy intervals to build figures similar to Figs.  and  for plasma lines observed due to both solar EUV radiation and auroral precipitation.

The primary objective of the present paper is to develop a processing pipeline and demonstrate that methodology for plasma line detection and analysis. The methodology presented can be applied in future long-term studies to investigate how plasma line occurrence and phase energy distributions vary with season, time of day, and aspect angle. A proper exploration of the seasonal and diurnal variations would require multiple observations spanning the year under varying conditions, which is beyond the scope of the current work but could be pursued in future studies.

Previous studies have modelled plasma line intensity using suprathermal electron population angular differential energy fluxes computed by an ionospheric electron transport code . Building on the plasma line model described in , we aim to further develop an aspect angle dependent plasma line intensity model and apply it to the current dataset. This approach, which will be detailed in a future paper, will use the general-purpose plasma line analysis pipeline we developed here. Unlike previous models , which assumed isotropic electron distributions and did not include pitch-angle dependence, our approach will build on the framework of and incorporates numerical electron transport modelling to obtain anisotropic electron velocity distribution functions. This will allow for a more realistic treatment of photoelectron populations under local geomagnetic conditions in incoherent scatter spectral modelling.

The methodologies presented here have facilitated the detection of hundreds of plasma line events, significantly increasing the volume of data available for theoretical validation compared to previous studies. The only limitation of the dataset is the number of pointing directions to the magnetic field which is imposed by the experiment design. This is where advanced radar systems like EISCAT 3D will be useful. Unlike the current EISCAT systems with mechanically steered antennas, EISCAT 3D with phased array antenna technology will enable the beam to be steered at different aspect angles with higher time resolution. This capability will greatly expand the dataset for studying the aspect angle dependence of plasma line parameters.