1 INTRODUCTION

One of the main phenomena discovered in experiments on the action of high-power, high-frequency (HF) radio waves on ionospheric plasma is the excitation of artificial, small-scale, ionospheric irregularities (hereinafter, for brevity, “irregularities”). The first experiments at the HF heating complex in Boulder (Thome and Blood, 1974) discovered that there is an intense, small-scale layering of ionospheric plasma in electron-concentration irregularities, which are significantly elongated along the magnetic field under the effect of high-power (O-mode), HF radio waves of ordinary polarization. The spatial scale of the irregularities is tens of meters across and several kilometers along the magnetic field. The maximal size of the irregularities across the magnetic field is determined by the expression l⊥ = c/fH, where c is the speed of light and fH is the heating frequency. Small-scale irregularities have been actively studied during past four decades at all HF heating complexes throughout the world, including Sura, Arecibo, EISCAT/Heating, HAARP, and SPEAR, which are located at the middle and high latitudes (e.g., Robinson, 1989; Gurevich, 2007; Yeoman et al., 2007; Frolov, 2017 and references therein). The excitation of irregularities upon O heating is explained in terms of the theory of thermal parametric (resonance) instability (Grach and Trakhtengerts, 1975; Vas’kov and Gurevich, 1975).

A high-power, HF radio wave of extraordinary (X mode) polarization is reflected at the altitude with the local plasma frequency \(f_{{\text{X}}}^{{\text{2}}}\) = fH(fH – fce) (fce is the electron gyrofrequency), which is lower than the reflection altitude of an O-polarized, HF radio wave and the altitude of upper hybrid resonance (\(f_{{{\text{UH}}}}^{{\text{2}}}\) = \(f_{{\text{H}}}^{{\text{2}}}\) = \(f_{{\text{P}}}^{{\text{2}}}\) + \(f_{{{\text{ce}}}}^{{\text{2}}},\) where fP is the plasma frequency). Hence, the irregularities cannot be excited due to thermal parametric (resonant) instability is impossible. Nevertheless, the results of numerous experiments performed by Arctic and Antarctic Research Institute (AARI) specialists at the EISCAT/Heating HF complex convincingly show that a high-power, HF radio wave of extraordinary polarization (X mode) emitted into the high-latitude ionospheric F region along the magnetic field (into the magnetic zenith) induces the generation of artificial, small-scale, ionospheric irregularities, artificial optical radiation in the red (630 nm) and green (557.7 nm) lines of atomic oxygen, the excitation of Langmuir and ion-acoustic plasma waves, and different spectral components in the artificial narrowband radio emission (Blagoveshchenskaya et al, 2011, 2014, 2015, 2017, 2018). It should be noted that the listed phenomena in the high latitude ionosphere F region upon X heating are induced at heating frequencies both lower and higher than the critical frequency of the ordinary component of the F2 layer (fH/foF2 ≤ 1 and fH/foF2 > 1) (Blagoveshchenskaya et al., 2010, 2014, 2015, 2018). Blagoveshchenskaya et al. (2015) showed that Langmuir and ion-acoustic plasma waves are excited at frequencies above foF2 in the range foF2 ≤ fH ≤ fxF2, where fxF2 is the critical frequency of the extraordinary component of the F2 layer, i.e., a high-power, HF radio wave of extraordinary polarization, is still reflected from the ionosphere. Let us recall that fxF2 = foF2 + fce/2 ≈ (foF2 + 0.7) MHz, where fce is the electron gyrofrequency. However, the artificial, small-scale, ionospheric irregularities that arise upon X heating continue to be excited even when the heating frequency fH exceeds fxF2 by up to ~2 MHz and the X-polarization pumping wave can no longer be reflected from the ionosphere (Blagoveshchenskaya et al., 2013, 2015).

An agreement was concluded between the AARI and the European Scientific Association EISCAT for the study of the phenomena induced by high-power, HF radio waves in the high-latitude ionosphere. Within this agreement, AARI specialists received the right to use for the experiments modern EISCAT equipment, which has no analogs in Russia in either the specifications or geographical location.

The goal of this work is an experimental study and analysis of the characteristics of artificial, small-scale, ionospheric irregularities generated in the high-latitude ionospheric F region by high-power, HF radio waves of extraordinary polarization (X mode) in a wide range of heating frequencies (4.0–8.0 MHz) (EISCAT/Heating complex). The work focuses on the results of experiments on the rise and relaxation times of the irregularities and the threshold powers of their excitation. Particular attention is paid to the consideration of the generation conditions of the irregularities upon X heating. The behavior and characteristics of the irregularities in the cases of O and X polarization of a high-power, HF radio wave are compared.

2 EXPERIMENTAL DESCRIPTION

The ionosphere was modified with the HF EISCAT/Heating complex (Tromsø, northern Norway (69.6° N, 19.2° E); L = 6.2, I = 78°). The specifications of the complex are described in (Rietveld et al., 2016). The control system for complex operation was upgraded in 2012. This allowed automatic setting of the radiation modes; almost instantaneous changes in the frequency and polarization of a high-power, HF radio wave; fast, stepwise changes in frequency within a specified range and in the radiation angle of the radio wave; switching of the type of antenna system; automatic radiation control; etc. (Rietveld et al., 2016). The penetration of O waves upon X heating and X waves upon O heating does not exceed 1%.

Many experiments on the effect of high-power, HF radio waves on the high-latitude ionospheric F region were carried out by AARI specialists in October–November and February–March from 2009 to 2016 in the afternoon and evening hours. The experiments were performed both at low (fH = 4.0–5.4 MHz) and high (fH = 5.4–8.0 MHz) heating frequencies. At fH = 4.0–5.4 MHz, the radiation was guided to the PAR 2 phased array with a pattern width of 12°–14° (at half power), which provided a maximal effective radiation power of Peff = 190–250 MW. In the heating frequency range of 5.4–8.0 MHz, the heating was performed at PAR 1 with a pattern width on the order of 5°–6° (at half power), which provided a maximal effective radiation power of Peff = 630–1200 MW depending on the heating frequency. In the experiments, high-power, HF radio waves of extraordinary (X mode) or ordinary (O mode) polarization were emitted in the magnetic field direction (the antenna pattern of the HF heating complex is 12° southward and inclined with respect to the vertical) in 10-min heating cycles with a 5-min pause.

To diagnose and study the characteristics of the irregularities excited by a high-power, HF radio wave of X or O polarization, we used the CUTLASS (SUPERDARN) coherent HF radar located in Hankasalmi, Finland (62.3° N, 26.6° E) (Lester et al., 2004). The measurements were performed in nonstandard mode simultaneously at three frequencies from 10 to 20 MHz, which allowed diagnostics of the irregularities of l⊥ = 7.5–15 m in size across the magnetic field (l⊥ = c/2 f, f is the radar frequency). The CUTLASS radar radiated to a narrow-band antenna with a beam ~3.3° wide oriented to the artificially disturbed region of the ionosphere above Tromsø (“beam” 5). The time resolution was 3 s and the range gate was 15 km.

To analyze and interpret the experimental results, we used the data of the radar of incoherent radio wave scattering (IS) at a frequency of 930 MHz (Rishbeth and van Eyken, 1993), spatially combined with the HF EISCAT/Heating complex. The measurements were carried out in the magnetic field direction in Tromsø (magnetic zenith, 12° to the south of the vertical). The time-altitude variations in the parameters of the ionospheric plasma (Ne, Te, Ti, and Vi) and of HF-enhanced plasma and ion lines (HFPL and HFIL) were calculated with the Grand Unified Incoherent Scatter Design and Analysis Package (GUISDAP) version 8.7 package (Lehtinen and Huuskonen, 1996).

An ionosonde was used during the experiments in Tromsø to monitor the state of the ionosphere and select the heating frequency. It recorded ionograms of ionosphere vertical sounding every 4 min.

3 OBSERVATION RESULTS

3.1 Behavior of Artificial, Small-Scale, Ionospheric Irregularities

Examination of the entire volume of experimental data showed significantly different characteristics of the irregularities upon X heating at low (fH = 4.0–5.4 MHz) and high (fH = 6.0–8.0 MHz) frequencies. At low heating frequencies, the CUTLASS radar operated at frequencies from 10 to 16 MHz, which provided diagnostics of irregularities with a size of l⊥ ≈ 9.3–15 m (l⊥ = c/2f, where c is the speed of light, and f is the operation frequency of the CUTLASS radar). During heating at high frequencies, CUTLASS operated at frequencies from 13 to 20 MHz, which made it possible to diagnose irregularities with a size of l⊥ ≈ 7.5–11.5 m.

Figure 1 shows CUTLASS (SuperDARN) radar data received from 1330 to 1520 UT on November 7, 2010, as a typical example of the behavior of irregularities upon X heating at low frequencies above the critical frequency of the F2 layer (fH/foF2 > 1). A high-power, HF radio wave was emitted in the magnetic zenith at a frequency of fH = 4.544 MHz in 10-min heating cycles with a 5-min pause. The effective radiation power was Peff = 85 MW.

Fig. 1.
figure 1

Power of irregularity-scattered signals at frequencies of 10, 11.5, and 13 MHz according to CUTLASS radar observations in Hankasalmi (Finland) from 1330 to 1520 UT on November 7, 2010. The top panel show the signals averaged over an artificially disturbed ionospheric region, and the three bottom panels show the power behavior in the coordinate distance (UT). A powerful, HF radio wave was radiated into the magnetic zenith at a frequency of fH = 4.544 MHz, Peff = 85 MW. The heating cycles and polarization used by the powerful, HF radio wave are marked on the time axis.

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The top panel of Fig. 1 shows the powers of signals scattered by the irregularities simultaneously at three frequencies of 10, 11.5, and 13 MHz, which correspond to backscattering by irregularities with sizes of l⊥ = 15, 13, and 11.5 m across the magnetic field, averaged over an artificially disturbed ionosphere region. The three lower panels characterize the behavior of the power of scattered signals in the range–universal time coordinates at the same frequencies. The range gate was 15 km; the “first gate” started at a range of 480 km. The signals scattered by the irregularities were recorded at distances from 780 to 1080 km, which corresponded to the “gate” numbers from 20 to 40. By the end of the O-heating cycle (1335–1345 UT), the generation of irregularities ceased, because foF2 decreased, and the heating frequency fH became higher foF2 (fH > foF2). Then, foF2 continued its gradual decrease from 4.1 MHz at 1345 UT to 3.1 MHz at 1515 UT. In that period, the heating was performed by a X-polarized pumping wave at a heating frequency of 4.544 MHz, which was significantly higher than foF2.

Figure 1 shows that the irregularities appeared within ~1 min after the start of the first X-heating cycle (1350–1400 UT) when heating from a cold start. The long irregularity relaxation time τrel after the EISCAT/Heating complex was switched off at 1400 UT was absolutely unexpected. Backscattering from irregularities at frequencies of 11.5 and 13 MHz took the entire 5-min pause between heating cycles. Hence, irregularities already existed by the beginning of the next heating cycle, as well as in the subsequent X-heating cycles, and only an increase in their intensity occurred during the cycle. Thus, the irregularity rise times τrise upon X heating strongly depends on the heating history. As for the decrease in foF2, first the signals at a higher frequency of 13 MHz (l⊥ = 11.5 m) were suppressed during the heating cycle from 1435 to 1445 UT, which was accompanied by amplification of scattered signals at a lower frequency of 11.5 MHz (l⊥ = 13 m). Then, with a further decrease in foF2 in the X-heating cycle (1505–1515 UT), the signals at a frequency of 11.5 MHz (l⊥ = 13 m) were suppressed, and the signals scattered from the irregularities at a frequency of 10 MHz (l⊥ = 15 m) were amplified. This behavior of the signals scattered by the irregularities indicates that energy transfers from small- to large-scale irregularities with a decrease in foF2.

Figure 2 shows the powers of signals scattered by the irregularities at three frequencies; they were recorded with the CUTLASS radar from 1530 to 1800 UT on November 3, 2013, and averaged over an artificially disturbed region of the ionosphere. The bottom part of Fig. 2 shows the behavior of the critical frequency of the F2 layer and the heating frequency during the experiment. A high-power HF radio wave at the frequency fH = 6.2 MHz was radiated in the magnetic zenith in 10-min heating cycles with a 5-min pause at an effective radiation power of Peff = 450 MW. CUTLASS operated at three frequencies (13, 16, and 18 MHz), which allowed diagnostics of irregularities with sizes of l⊥ = 11.5, 9.3 and 8.3 m across the magnetic field. During the experiment, the critical frequencies foF2 dropped from 6.7 MHz at 1530 UT to 5.2 MHz at 1800 UT, which allowed us to analyze the behavior of the irregularities upon X heating at frequencies both lower and higher than the critical frequency of the F2 layer (fH ≤ foF2 and fH > foF2). From 1530 to 1700 UT, when fH ≤ foF2, the irregularities could be excited both upon O and X heating. In that period, alternative O/X heating was performed. The irregularities sized l⊥ ≈ 8.3–11.5 m were excited upon both O and X heating, but their intensity during X heating was 4–6 dB lower as compared to O heating. From 1700 to 1800 UT, when the heating frequency exceeded foF2, it was possible to excite the irregularities only upon X heating. In that case, the irregularity intensity upon X heating at frequencies fH > foF2 was higher than at fH ≤ foF2. After 1700 UT, the smallest irregularities (l⊥ ≈ 8.3 m) were suppressed first and then 9.3-m irregularities across the magnetic field, but larger irregularities (l⊥ ≈ 11.5 m) intensified. Thus, we again can assume that energy is transferred from small- to large-scale irregularities upon heating at a high frequency of 6.2 MHz similar to the case of X-heating at a low frequency of 4.544 MHz.

Fig. 2.
figure 2

(a) Power of irregularity-scattered signals at frequencies of 13, 16, and 18 MHz averaged over an artificially disturbed ionospheric region according to CUTLASS radar observations in Hankasalmi (Finland) and (b) the behavior of the critical frequency of the F2 layer and heating frequency from 1530 to 1800 UT on November 3, 2013. A powerful, HF radio wave was radiated into the magnetic zenith at a frequency of fH = 6.2 MHz, Peff = 450 MW. The heating cycles and polarization used by the powerful, HF radio wave are marked on the time axis.

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3.2 Irregularity Rise and Relaxation Time

Let us consider in more detail the rise τrise and relaxation τrel times of the irregularities based on CUTLASS data upon alternative O/X heating at low (fH = 4.0–5.4 MHz) and high (fH = 6.0–8.0 MHz) frequencies, fH ≤ foF2. Under these conditions, irregularities can be generated both upon O and X heating of the ionospheric F region. Below, we consider the results of experiments performed with O/X heating at fH = 4.544 MHz (Peff = 130 MW) on October 20, 2016, and with heating at fH = 6.96 MHz (Peff = 550 MW) on October 26, 2013. A high-power, HF radio wave was emitted in the magnetic zenith in 10-min heating cycles and a 5-min pause starting from the first minute of an hour.

Figure 3 shows the behavior of the power of irregularity-scattered signals PISS according to the CUTLASS observations on October 20, 2016, and October 26, 2013, starting 1 min before and during the first 2 min after the EISCAT/Heating complex was turned on. Figures 3a–3c show the behavior of PISS on October 20, 2016, at frequencies of ~16 (O mode heating), ~16 (the second X-heating cycle), and ~13 MHz (X mode, in 1 h of heating). Let us recall that signals at frequencies of about 16 and 13 MHz are backscattered from 9.3-m and 11.5-m irregularities. Figures 3d–3f show the PISS behavior on October 26, 2013, at frequencies of ~18 (O mode), ~20 (the first X-heating cycle), and ~20 MHz (X mode, 45 min of X heating). The signals at these frequencies are backscattered from 8.3-m and 7.5-m irregularities. Figure 4 shows the PISS behavior on October 20, 2016, and October 26, 2013, during the last minute of heating and the first 2 min after the turning off of the EISCAT/Heating complex for the same heating cycles and CUTLASS frequencies as in Fig. 3.

Fig. 3.
figure 3

Power of irregularity-scattered signals averaged over an artificially disturbed ionospheric region and its behavior in the coordinate distance (UT) according to CUTLASS radar observations in Hankasalmi with a time resolution of 3 s starting 1 min before and during the first 2 min after the EISCAT/Heating complex was started on October 20, 2016, at a radiation a frequency of fH = 4.544 MHz and Peff = 130 MW (left panel) and on October 26, 2013, at fH = 6.96 MHz and Peff = 550 MW (right panel): (a) CUTLASS frequency ~16 MHz, O heating; (b) CUTLASS frequency ~16 MHz, the second X-heating cycle; (c) CUTLASS frequency ~13 MHz, the sixth X-heating cycle; (d) CUTLASS frequency ~18 MHz, O heating; (e) CUTLASS frequency ~20 MHz, the first X-heating cycle; (f) CUTLASS frequency ~20 MHz, the third X-heating cycle.

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Fig. 4.
figure 4

Power of irregularity-scattered signals averaged over an artificially disturbed ionospheric region and its behavior in the coordinate distance (UT) according to CUTLASS radar observations in Hankasalmi with a time resolution of 3 s during the last minute of a heating cycle and the first 2 min after the EISCAT/Heating complex was turned off on October 20, 2016, at a radiation frequency of fH = 4.544 MHz (left panel) and on October 26, 2013, at fH = 6.96 MHz (right panel). The heating cycles and CULTASS frequencies are the same as in Fig. 3.

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According to Figs. 3a, 3d, 4a, and 4d, the rise τrise and relaxation τrel times of the irregularities were almost the same upon O heating at frequencies fH = 4.544 and 6.96 MHz: τrise ≈ 6–9 s and τrel ≈ 40–60 s. Moreover, the ISS relaxation occurred in two stages. The fast relaxation stage (τrel1) lasted ~9–12 s, and the slow stage (τrel2) was ~30–50 s in length. A similar pattern of irregularity relaxation upon O heating of the ionospheric F region was observed in many other heating experiments at high and midlatitudes (e.g., Robinson, 1989; Frolov, 2017 and references therein).

Upon X heating of the high-latitude ionospheric F region, the behavior of the rise and relaxation times of the irregularities differs significantly when compared to O heating. First, τrise and τrel are much longer upon X heating than upon O heating both at low (fH = 4.544 MHz) and high (fH = 6.96 MHz) frequencies. The significant difference in the relaxation times of irregularities at low and high heating frequencies is also important (see Figs. 4b, 4c and 4e, 4f). Figure 4b clearly shows a relaxation time τrel higher than 120 s upon heating at fH = 4.544 MHz, while it is half as much (about 60 s) at fH = 6.96 MHz. After several X‑heating cycles at fH = 4.544 MHz, τrel already exceeded 300 s (pause duration). This follows from Fig. 3c, which clearly shows that irregularities already existed by the start of the cycle at 1546 UT. After the end of the X-heating cycle at 1556 UT, the irregularity intensity remains at the same level for ~60 s and only then begins to decrease gradually ( Fig. 4c). At a heating frequency of fH = 6.96 MHz under similar background geophysical conditions, τrel is significantly lower and does not exceed ~80 s (see Fig. 4f). The power of the signals scattered by the irregularities upon X heating at fH = 4.544 MHz exceeds the PISS at fH = 6.96 MHz by about 5 dB.

3.3 Threshold Excitation Powers of Artificial, Small-Scale, Ionospheric Irregularities

Two experiments with a stepwise increase in the effective radiation power of the EISCAT/Heating complex during the heating cycle were carried out to determine the threshold excitation powers of irregularities upon X heating of the high-latitude, ionospheric F region. The first experiment was performed under the most favorable conditions for the generation of irregularities: X heating to the magnetic zenith at the lowest frequency fH = 4.040 MHz in the early evening hours (1431–1441 UT) under quiet magnetic conditions (fH/foF2 > 1). The second experiment was carried out under the most unfavorable conditions for the generation of irregularities: X heating at the highest EISCAT/Heating frequency fH = 7.953 MHz, fH/foF2 < 1.

Figures 5 and 6 show the PISS behavior averaged over an artificially disturbed region of the ionosphere according to CUTLASS measurements with a stepwise change in the EISCAT/Heating effective radiation power. Figure 5 corresponds to the experiment on November 6, 2009, in which a high-power, HF radio wave was radiated into the magnetic zenith at a frequency of fH = 4.040 MHz (fH/foF2 > 1). During a heating cycle, the power stepwise changed by following the scheme: 20%, 50%, 70%, 85%, 100%, 100%, 85%, 70%, 50%, and 20% (1 min at each power level). The maximal effective radiation power was 130 MW. Figure 6 shows the PMIIN behavior on October 20, 2012, with heating at fH = 7.953 MHz (fH/foF2 < 1). The power stepwise changed by following the scheme: 10%, 30%, 50%, 70%, 100%, 100%, 70%, 50%, 30%, and 10% (1 min at each power level). The maximal effective radiation power in that experiment was 550 MW.

Fig. 5.
figure 5

Power of irregularity-scattered signals averaged over an artificially disturbed ionospheric region according to CUTLASS radar measurement data at a frequency of ~10 MHz on November 6, 2009, upon O and X heating at a frequency of fH = 4.040 MHz (fH/fоF2 > 1) (top). The power changes stepwise during heating cycles by the scheme 20, 50, 70, 85, 100, 100, 85, 70, 50, 20% (1 min at each power level) (bottom); maximal Peff = 130 MW.

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Fig. 6.
figure 6

Power of irregularity-scattered signals averaged over an artificially disturbed ionospheric region according to CUTLASS radar measurement data at frequencies of ~13 and 16.5 MHz on October 20, 20012, upon O and X heating at a frequency of fH = 7.953 MHz (fH/fоF2 < 1) (top). The power changes stepwise during heating cycles by the scheme 10, 30, 50, 70, 100, 100, 70, 50, 30, 10% (1 min at each power level) (bottom); maximal Peff = 550 MW.

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According to Fig. 5, no ISSs were recorded upon O heating at fH = 4.040 MHz (fH > foF2). Irregularities were diagnosed at a CUTLASS frequency of ~10 MHz, which corresponds to an irregularity size of l⊥ = 15 m. A change in the X polarization (1431–1441 UT cycle) resulted in ISS generation, not immediately after the starting of the heating complex but within 1.5–2 min, i.e., at the 50-% power level. This corresponds to an effective radiation power threshold of Рeff thr = 65 MW, at which the irregularities began to be excited upon X heating. A stepwise decrease in Peff during the second half of the heating cycle did not change the power of the scattered signals. After the end of the heating cycle at 1441 UT, the intensity of the irregularities gradually decreased; the relaxation time was τrel = 15 min.

Figure 6 shows the irregularities observed both upon O and X heating at a frequency of fH = 7.953 MHz, fH < foF2. CUTLASS measurements were carried out at frequencies of about 13 and 16.5 MHz, which corresponds to an irregularity size of l⊥ = 11.5 and 9.2 m. Upon O heating, the irregularities appeared immediately after the heating complex was turned on at the lowest (10%) level of Peff (55 MW), which exceeds the threshold of their excitation Рeff thr = 26 MW at a EISCAT/Heating frequency of fH = 7.953 MHz (Bryers et al., 2013). Upon X heating, the irregularities started to be recorded at much higher effective radiation powers Рeff thr = 165 MW (30% power level). With a stepwise decrease in Peff during the second half of the heating cycle, the irregularities disappeared at the 10% level of effective radiation power (55 MW).

Comparison of the threshold powers of irregularity excitation by high-power HF radio waves of extraordinary polarization at low and high heating frequencies (see Figs. 5 and 6) showed significant differences between them:

—PISS reached 40 dB at low heating frequencies (fH > foF2), while it was significantly lower (no higher than 10 dB) at high heating frequencies of (fH < foF2);

—the relaxation time of irregularities originating upon X heating at low heating frequencies (fH > foF2) was ~15 min after turning off of the heating complex radiating at the 20% power level (26 MW);

—at high heating frequencies (fH < foF2), the generation of irregularities ceased at the 10-% effective radiation power level (55 MW);

—the threshold power of irregularity excitation Рeff thr upon X heating at low frequencies (fH > foF2) is lower than at high heating frequencies (fH < foF2).

4 RESULTS AND DISCUSSION

Artificial, small-scale irregularities excited in the high-latitude ionosphere F region by high-power, HF radio waves of extraordinary polarization (X mode) were first detected with the HF EISCAT/Heating complex (Tromsø, Norway) (Blagoveshchenskaya et al., 2011). Analysis of the bulk of experimental data acquired at AARI in 2009–2016 confirms the excitation of irregularities with sizes of l⊥ ≈ 7.5–15 m across the magnetic field upon X heating in quiet background geophysical conditions. In this case, the irregularities are excited at heating frequencies that are both lower and significantly higher (up to 2 MHz) than the critical frequency of the ordinary component of F2 layer (fH/foF2 ≤ 1 and fH/foF2 > 1). This essentially differs from the conditions for the excitation of the irregularities upon O heating, which is possible only at heating frequencies fH ≤ foF2.

According to results of numerous experiments, the parameters of the irregularities with sizes of l⊥ ≈ 7.5–15 m upon X heating with an effective radiation power of Peff = 100–650 MW depend on the heating frequency fH (low fH = 4.0–5.4 or high fH = 6.0–8.0 MHz), the relationship between the heating frequency and the critical frequency of the F2 layer (fH ≤ foF2 or fH > foF2), and the history of heating (the cold start in the first X-heating cycle or subsequent X-heating cycles).

According to CUTLASS data (Hankasalmi), the rise τrise and relaxation τrel times of the irregularities upon X heating are always larger than those with O heating. The relaxation times of the irregularities with X heating at low and high heating frequencies also significantly differ. At high frequencies (fH = 6.0–8.0 MHz), τrise = 12–30 s and τrel = 60–90 s. At low frequencies (fH = 4.0–5.4 MHz), τrise ≈ 60–70 s (it can even reach 150 s at fH > foF2) and τrel = 100–130 s with X heating from a cold start (in the first X-heating cycle); τrel increases up to 200–250 s with X heating at frequencies fH > foF2.

In X-heating cycles with history, when the aftereffects of previous heating cycles act, τrise decreased and τrel increased. The irregularity relaxation time τrel exceeded 5 min at low heating frequencies (length of the pause between heating cycles), which led to the almost permanent existence of the irregularities during the experiment; τrel = 15 min upon X heating at low frequencies higher than foF2 during the last heating cycle (see Fig. 5).

Such unexpectedly large relaxation times of irregularities with a size of l⊥ ≈ 7.5–15 m across the magnetic field upon X heating of the high-latitude ionosphere F region suggest the existence of a mechanism for their maintenance. Analysis of the background geophysical situation based on data from the EISCAT incoherent scattering radar (at a frequency of 930 MHz), vertical sounding of the ionosphere in Tromsø, and the IMAGE magnetometer network in Scandinavia showed the origination of irregularities upon X heating in quiet magnetic conditions in the regular F2 layer without the precipitation of particles, longitudinal currents, or an electrojet. Taking into account all of the above, we propose that the excitation and maintenance of small-scale irregularities under the above quiet geophysical conditions are connected to the generation of large-scale irregularities, which is possible with heating by high-power, HF radio waves of ordinary and extraordinary polarizations at frequencies that are both lower and higher foF2 due to the self-focusing instability of the high-power, HF beam (Litvak, 1968; Gurevich and Karashtin, 1994; Guzdar et al., 1998).

As noted above, τrel = 60–90 s for irregularities upon X heating at high heating frequencies (fH = 6.0–8.0 MHz). Using the dependence of the characteristic relaxation times on the irregularity scale in the form τrel ∝ С\(l_{ \bot }^{{\alpha }}\) (Erukhimov et al., 1987; Myasnikov et al., 2001), we can approximately estimate the size L⊥ of large-scale irregularities responsible for maintaining irregularities 7.5–15 m in size. At a coefficient of α = 0.5, which is characteristic of the slow relaxation stage of small-scale irregularities (which can also be used to estimate the relaxation times of medium- and large-scale irregularities) and with allowance for a 1.5- to 2-fold increase in τrel (C = 1.5–2.0) when changing from daytime to evening observation hours (Erukhimov et al., 1987; Frolov et al., 1997), we find L⊥ ≈ 1000–3000 m. Let us emphasize once again that relaxation of small-scale irregularities proceeds during one stage upon X heating, in contrast to O heating, when the relaxation develops in two stages (fast and slow). It was also shown (Frolov, 2017 and references therein) that the irregularities that are excited upon O heating at frequencies above the critical frequency (fH > foF2) are larger those at fH < foF2. A similar situation was apparently observed with X heating. This follows from the increase in the irregularity relaxation time with heating at fH > foF2.

How are small-scale irregularities generated upon X heating of the ionosphere F region? Borisov et al. (2018) recently proposed a two-stage generation of irregularities upon X heating. Large-scale irregularities are generated in the first stage due to self-focusing instability. During the second stage, small-scale irregularities are excited due to the instability of the gradient-drift temperature. The means of irregularity generation upon O heating can be the same. Moreover, more intense, large-scale irregularities form upon O heating as compared to X heating due to self-focusing thermal instability (Frolov, 2017 and references therein). In this regard, it remains unclear why no irregularities form upon O heating at frequencies of fH > foF2, while X-polarization pumping wave excites very intense irregularities (Fig. 5).

Let us consider changes in the electron concentration upon O and X heating of the high-latitude ionosphere F region based on the data from the incoherent radio wave (930 MHz)–scattering radar in Tromsø. We used primary electron concentration measurements (raw data) Neraw in the altitude range 180–278 km with an altitude resolution of 1.5 km. Figures 7 and 8 show the time–altitude distribution of Neraw, as well as time variations in Neraw at fixed altitudes above the reflection altitude of high-power, HF radio waves upon O and X heating on November 7, 2010, and November 3, 2013, respectively.

Fig. 7.
figure 7

(a) Altitude-time distribution of raw data on the electron concentration Neraw in the altitude range 180–278 km with an altitude resolution of 1.5 km according to IS radar measurements in Tromsø (930 MHz) upon O and X heating at fH = 4.544 MHz and Peff = 85 MW from 1300 to 1500 UT on November 7, 2010; (b) time variations in Neraw values at fixed altitudes above the reflection altitude of a high-power, HF radio wave for the same experiment from 1300 to 1345 UT.

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Fig. 8.
figure 8

(a) Altitude-time distribution of raw data on the electron concentration Neraw in the altitude range 180–278 km with an altitude resolution of 1.5 km according to IS radar measurements in Tromsø (930 MHz) upon O and X heating at fH = 6.2 MHz and Peff = 450 MW and (b) time variations in Neraw values at fixed altitudes above the reflection altitude of a high-power, HF radio wave for the same experiment from 1530 to 1646 UT on November 3, 2013.

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The data above relate to IS radar measurements in the direction of the magnetic field. The increase in Neraw in heating cycles at the reflection altitudes of high-power, HF radio waves (Figs. 7a and 8a) are due to the excitation of HFILs in the IR spectrum. At these altitudes, the electron concentration cannot be correctly estimated.

Figures 7 and 8 clearly show a depletion of the electron concentration in O-heating cycles in comparison with the background values in the pauses, which is caused by the thermal heating of plasma. This is a typical manifestation of modification of the ionosphere in the field of a high-power, HF radio wave of ordinary polarization (Gurevich, 1978, 2007).

A different situation was observed upon X heating in the same background geophysical conditions. On November 7, 2010, the change to X heating at 1350 UT was accompanied by the excitation of very intense HFILs in a wide altitude range, which excluded the possibility of estimating real changes in Ne in X-heating cycles (see Fig. 7a). In the experiment on November 3, 2013, weak HFILs were excited in the X-heating cycles only at reflection altitudes of ~ 240 km (Fig. 8a). Under those conditions, Neraw were estimated at altitudes of 264, 267, and 270 km above the reflection altitude of a high-power X wave (see Fig. 8b). Figure 8b shows the increase in Neraw above the reflection altitude of a high-power, HF radio wave in X-heating cycles, in contrast to O heating, which results in decreased Neraw.

The results of experiments on elevation scanning (1° step) of an artificially disturbed ionospheric F region with IS radar showed an increase in the electron concentration in the magnetic field direction upon X heating in a narrow elevation angle range (~3° in width) up to the upper altitude of the IS radar measurements (Blagoveshchenskaya et al., 2015). There is reason to assume that such narrow channels of high electron density along the magnetic field are caused by the flow of accelerated electrons (Carlson et al., 1982) upon X heating, which can affect the generation of large-scale ionospheric irregularities. The acceleration of electrons upon X heating is experimentally confirmed by the excitation of extremely intense optical emissions in the red and green lines of atomic oxygen (Blagoveshchenskaya et al., 2014). The mechanism of filamentation instability suggested by Kuo (2014) can be considered as a cause of the small-scale stratification of large-scale irregularities.

Despite numerous experimental data on the behavior, parameters, and conditions for the excitation of artificial, high-power, small-scale (l⊥ ≈ 7.5–15 ) ionospheric irregularities by high-power, X-polarized, HF radio waves (EISCAT/Heating complex), it is still unclear how they are generated. This question requires further profound theoretical study, which is beyond the scope of this work.

CONCLUSIONS

Thus, we have shown the excitation of artificial, small-scale, ionospheric irregularities with a size of l⊥ ≈ 7.5–15 m across the magnetic field in the regular F2 ionospheric layer upon X heating of the high-latitude ionosphere F region under quiet conditions (no precipitation of particles, longitudinal currents, or electrojet). It was ascertained that the irregularities are generated when a high-power, HF radio wave of extraordinary polarization (X mode) is emitted into the magnetic zenith at frequencies that are both lower and much higher (up to 2 MHz) than the critical frequency of the F2 layer (fH ≤ foF2 and fH > foF2).

The irregularity rise and relaxation times and the threshold excitation powers upon X heating of the high-latitude ionosphere F region were determined. These parameters were found to significantly differ at low (fH = 4.0–5.4 MHz) and high (fH = 6.0–8.0 MHz) frequencies. The characteristics of the irregularities upon X heating substantially depend on the preheating conditions (the “cold” start in the first X-heating cycle or subsequent X-heating cycles).

The generation conditions and parameters of the irregularities are compared for the cases of exposure of the high-latitude ionosphere F region to high-power, HF radio waves of extraordinary (X mode) and ordinary (O mode) polarization. The rise and relaxation times and the threshold excitations powers significantly differ in these cases, which indicate different means of their generation.