Volume 124, Issue 1 p. 603-615
Research Article
Free Access

The Intensities of High Frequency-Enhanced Plasma and Ion Lines During Ionospheric Heating

Jun Wu,

Corresponding Author

Jun Wu

National Key Laboratory of Electromagnetic Environment, China Research Institute of Radio Wave Propagation, Beijing, China

Correspondence to: J. Wu,

wujun1969@163.com

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Jian Wu,

Jian Wu

National Key Laboratory of Electromagnetic Environment, China Research Institute of Radio Wave Propagation, Beijing, China

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M. T. Rietveld,

M. T. Rietveld

EISCAT, Ramfjordbotn, Norway

Now at UiT, The Arctic University of Norway, Tromsø, Norway

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I. Haggstrom,

I. Haggstrom

EISCAT Scientific Association, Kiruna, Sweden

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Zhengwen Xu,

Zhengwen Xu

National Key Laboratory of Electromagnetic Environment, China Research Institute of Radio Wave Propagation, Beijing, China

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Yabin Zhang,

Yabin Zhang

National Key Laboratory of Electromagnetic Environment, China Research Institute of Radio Wave Propagation, Beijing, China

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Tong Xu,

Tong Xu

National Key Laboratory of Electromagnetic Environment, China Research Institute of Radio Wave Propagation, Beijing, China

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Haisheng Zhao,

Haisheng Zhao

National Key Laboratory of Electromagnetic Environment, China Research Institute of Radio Wave Propagation, Beijing, China

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First published: 13 December 2018
Citations: 1

Abstract

An ultrahigh frequency (UHF) observation during an ionospheric heating campaign at European Incoherent SCATter scientific association (EISCAT) demonstrates that the electron temperature and the intensities of the enhanced plasma and ion lines systematically vary as a function of the pump frequency near the fifth electron gyroharmonic. Specifically, with the change in the pump frequency, the weaker the enhancement in the electron temperature is, the more intense the intensities of the enhanced ion line is. The analysis shows that the enhanced electron temperature plays a significant role in determining the intensities of the enhanced Langmuir and ion acoustic waves by the parametric decay instability and the oscillation two-stream instability, and the intensities of the enhanced plasma and ion lines depend on whether the enhanced Langmuir and ion acoustic waves satisfy the Bragg condition exactly or approximately. Moreover, an alternative explanation for the overshoots in the enhanced plasma and ion lines is presented, namely, the overshoots may be attributed not only to the anomalous absorption of the pump but also to the modifications of the plasma on the traveling path of the enhanced Langmuir and ion acoustic waves.

Key Points

  • The enhanced electron temperature plays a significant role in determining the wave numbers of the enhanced Langmuir and ion acoustic waves
  • The intensities of HFPL and HFIL depend on whether the enhanced Langmuir and ion acoustic waves satisfy the Bragg condition exactly or approximately
  • The overshoots in the HFPL and HFIL may be attributed not only to the anomalous absorption but also to the enhanced electron temperature

1 Introduction

During the ionospheric heating experiments, two of the most interesting physical phenomena are the high frequency-enhanced plasma line (HFPL) and the high frequency-enhanced ion line (HFIL) observed by incoherent scatter radar (ISR), which are attributed to the parametric decay instability (PDI) and the oscillation two-stream instability (OTSI, Carlson et al., 1972; Gordon & Carlson, 1974; Kantor, 1974; Stubbe et al., 1992). PDI and OTSI have been extensively studied (Chen & Fejer, 1975; Drake et al., 1974; DuBois & Goldman, 1965, 1967; Fejer, 1979; Kohl et al., 1993; Kuo & Chen, 1978; Kuo & Fejer, 1972; Perkins & Flick, 1971; Perkins et al., 1974; Rosenbluth, 1972; Silin, 1965; Stubbe et al., 1992; Wu et al., 2006, 2007). Based on some measurements obtained by ISR, the spectrum structure of the HFPL and HFIL (Carlson et al., 1972; Fejer & Kuo, 1973; Gordon & Carlson, 1974; Hagfors et al., 1983; Kantor, 1974; Kohl et al., 1993; Nordling et al., 1988; Stubbe et al., 1992), the threshold to excite the PDI and OTSI (Bryers et al., 2013; Fejer, 1979; Perkins & Flick, 1971; Perkins et al., 1974; Weinstock & Bezzerides, 1972), the time characteristics of the PDI and OTSI (Carlson et al., 1972; Gordon & Carlson, 1974; Jones et al., 1986; Kantor, 1974; Kohl et al., 1993; Stubbe et al., 1985), and the altitude characteristics of the PDI and OTSI (Ashrafi et al., 2006; Djuth et al., 1994; Kohl et al., 1993; Stubbe et al., 1992; Wu et al., 2017b, 2018) have been studied. Moreover, DuBois et al. (1988, 1990, 1993) originally presented a theoretical approach referred to as strong Langmuir turbulence, which resulted in new insight into the HFPL and HFIL. Furthermore, a numerical model for the resonant interaction and acceleration of electrons by SLT was developed by Eliasson et al. (2012). For a typical ionosphere, the PDI, OTSI, and strong Langmuir turbulence may coexist (Djuth & DuBois, 2015; DuBois et al., 1991).

During the daytime, photoelectrons naturally enhance the intensity of the plasma line by 1–2 orders of magnitude over the thermal level (Carlson et al., 1972; Kantor, 1974), whereas the HFPL and HFIL can be 3–5 orders of magnitude more intense than the thermal level (Carlson et al., 1972; Kantor, 1974; Showen & Kim, 1978). Carlson et al. (1972) determined the dependence of the intensity of the HFPL on the pump power, which clearly exhibits a hysteretic effect. The HFPL and HFIL become more intense as the pump power goes up, as is expected (Kohl et al., 1993; Stubbe et al., 1992). However, as a result of experiments carried out at European Incoherent Scatter Scientific Association (EISCAT), Bryers et al. (2013) presented some observations that the maximum intensities of the HFPL and HFIL were found for a pump effective radiated power (ERP) of 52.3 MW, whereas for a pump ERP of 104.5 MW, the intensities of the HFPL and HFIL were reduced, for which an explanation was that the pump power was anomalously absorbed by the striations. Moreover, for a pump ERP of 26.3 MW, the HFIL was generally more persistent than that for the pump ERPs of 52.3 MW and 104.5 MW. Due to ionospheric preconditioning, the HFPL and HFIL cannot be fully enhanced at the subsequent turn on unless the pump has been off for at least 10 s (Djuth et al., 1986; Jones et al., 1986). In addition, Duncan (1985) claimed that the changes in the intensity of the HFPL by a factor of 20 might be brought about by a relatively small change in the profile of the background electron density, which could shift the exciting altitude of the HFPL between the maxima and minima of the pump Airy pattern. A temporal modulation of the intensity of the HFPL observed at Arecibo was attributed to intermediate scale plasma irregularities drifting through the radar beam (Robinson, 1985). Particularly, a remarkable feature of the intensities of the HFPL and HFIL on time scales of seconds, termed overshoot, is observed frequently but not universally when the pump is initially switched on (Djuth et al., 1994; Kohl et al., 1993; Showen & Kim, 1978). Some observations presented by Djuth et al. (1994, see plates 1 and 2) demonstrate that the overshoot in the HFPL occurs ~ 2 s after the pump is initially switched on, and thereafter, the HFPL becomes weaker in intensity with increasing time. Some explanations claim that the overshoot may be caused either by the pump inducing field-aligned irregularities, which scatter the pump before the pump can arrive at the parametric resonance altitude (Das & Fejer, 1979; Fejer, 1979; Fejer et al., 1983; Showen & Kim, 1978), or by the anomalous absorption of the pump attributed to the excitation of small-scale field-aligned irregularities beneath the parametric resonance altitude (Fejer, 1979; Fejer & Kopka, 1981; Gurevich, 2007). Additionally, Muldrew (1978) suggested that the overshoot may be due to the effects of ionospheric heating on the ducts and on the ambient plasma. However, the above studies of the overshoots in the HFPL and HFIL neglected the modifications of the ionospheric plasma induced by ionospheric heating, which may further significantly impact the traveling characteristics of the enhanced Langmuir and ion acoustic waves.

In this paper, a systematic variation in the intensities of the HFPL and HFIL induced by an O mode pump near the fifth gyroharmonic is examined, and furthermore, an explanation for the systematic intensity variation is given. In addition, an alternative explanation for the overshoots in the HFPL and HFIL is presented.

2 Experiments and Data

An ionospheric heating campaign was conducted at EISCAT near Tromsø (69.58°N, 19.21°E, magnetic dip angle I = 78°) at 12:32:30–14:30 UT (Universal Time) on 11 March 2014, during which the ionospheric and geomagnetic conditions were relatively inactive. A detailed description of the experimental arrangement has been given by Wu et al. (2016, 2017a). Briefly, the experiment involved an EISCAT heater (Rietveld et al., 1993, 2016) used to modify the F region of the ionosphere, and EISCAT ultrahigh frequency (UHF) ISR (Rishbeth & Van Eyken, 1993) utilized as the principal diagnostic means. The O mode pump frequency fHF was operated from 6.7 to 7 MHz and changed in a step of 2.804 kHz with a period of 10 s, as exhibited in the bottom panel of Figures 1-3. The ERP of the pump was calculated to be in the range 56–78 MW. The beams of the EISCAT heater and UHF ISR were pointed parallel to the magnetic field line direction (actually 12° south of the zenith). Moreover, the radar data were analyzed using version 8.7 of the Grand United Incoherent Scatter Design and Analysis Package (Lehtinen & Huuskonen, 1996) to obtain the electron temperature, Te, and the electron density, Ne, and version 2.67 of real-time graphic software to obtain the plasma and ion lines. Additionally, to measure the effect induced by the pump at each frequency step, the analysis used an integration time of 10 s.

Details are in the caption following the image
(top to bottom) The normalized ion line at some altitudes of 215.43 (first panel), 212.5 (second panel), 209.57 (third panel), 206.63 (fourth panel), 203.7 (fifth panel), and 200.77 km (sixth panel) versus heating cycles (seventh panel).
Details are in the caption following the image
(top to bottom) The normalized plasma line at some altitudes of 210.25 (first panel), 207.32 (second panel), 204.39 (third panel), 201.45 (fourth panel), 198.52 (fifth panel), and 195.58 km (sixth panel) versus heating cycles (seventh panel), where t1 and t2 are the same as Figure 1.
Details are in the caption following the image
The electron temperature Te versus heating cycles, where t1 and t2 are the same as Figure 1.

To facilitate the following description and discussion, a convention is adopted according to the dependence of the ion line intensity on fHF, as illustrated in Figure 1. Specifically, the pump frequency band of [6.7 MHz, 7 MHz] will be divided into three bands, namely, the higher band (HB), the gyrofrequency band (GB, close to the fifth electron gyroharmonic 5fce, where fce is the local electron gyrofrequency with a value of ~ 1.366 MHz at an altitude of ~ 200 km in Tromsø), and the lower band (LB). In the first cycle, for instance, we choose the HB to be the range of [7 MHz, 6.871028 MHz), the GB to be the range of [6.871028 MHz, 6.837383 MHz], and the LB to be the range of (6.837383 MHz, 6.7 MHz], which temporally correspond to [12:30:00 UT, t1), [t1, t2], and (t2, 12:48:00 UT], respectively, as marked on the abscissa in Figure 1. The parameters t1 and t2 denote 12:37:40 and 12:39:40 UT, respectively, () is the open interval, and [] is the closed interval. Indeed, the above division in each cycle should be slightly different from each other owing to the perturbation of the geomagnetic field.

The first to sixth panels of Figure 1 illustrate the normalized ion lines at several altitudes of 215.43, 212.5, 209.57, 206.63, 203.7, and 200.77 km respectively, demonstrating that the intensity of the HFIL varies systematically as a function of fHF. When fHF is in the GB, some enhanced spikes in the center of the HFIL attain ~ 1 in intensity, which is a manifestation of the OTSI (Kohl et al., 1993; Stubbe et al., 1992), whereas those enhanced shoulders lying at a frequency of ~ 9.45 kHz reach ~ 0.6 to ~ 0.9 in intensity, which is a confirmation of the PDI (Kohl et al., 1993; Stubbe et al., 1992). Those enhanced spikes and shoulders occur only at an altitude of 206.63 km in the first cycle, 215.43 km in the second cycle, 209.57 km in the third cycle, and 212.5 km in the fourth cycle. At other altitudes, some gaps or weak ion line spectra appear, which are caused by a normalization to the strongest value of the ion line at any particular time and altitude, and do not imply a real decrease in the ion line or any unusual response.

When fHF lies in the HB, the intensity of the HFIL becomes weaker than that in the GB. Those enhanced spikes exhibit some values of ~ 0.6 to ~ 0.85 in intensity, and the intensities of those enhanced shoulders are up to ~ 0.4 to ~ 0.7. Moreover, the HFILs are distributed within a wide altitude range due to the thermal effect induced by ionospheric heating on the traveling path of an ion acoustic wave (Wu et al., 2018). In the LB, however, no HFIL is found.

The altitude of the HFPL is usually approximately 3–5 km lower than that of the HFIL at EISCAT UHF (Kohl et al., 1993; Stubbe et al., 1992). Accordingly, the downshifted plasma lines within the frequency range of [−6.7 MHz, −7.25 MHz] at several altitudes of 210.25, 207.32, 204.39, 201.45, 198.52, and 195.58 km are provided in the first panel to the sixth panel of Figure 2, respectively, which demonstrates the systematic variation in the intensity of the HFPL as a function of fHF. At those altitudes, two bands of the HFPL are evident. The upper band is the spread of the HFPL and occurs in the GB and in a pump frequency range of (~6.91 to ~ 7.0 MHz], and the LB lies at the frequency fHF − fia, as is expected as the decay line from PDI, where fia is the frequency of the ion acoustic wave and has a value of ~ 9.45 kHz. Some alternative explanations for the upper band of the HFPL were given, but its nature still remains open (Borisova et al., 2016; Wu et al., 2017a). Here we are concerned about the LB of the HFPL, namely, the decay lines.

In the GB and HB, the HFPLs are up to ~ 0.6 to ~ 1 in intensity and occur within a wide altitude range. This altitude extension of the HFPL in the GB and HB should be due to the altitude ambiguity brought about by the radar height resolution of ~ 3 km (Wu et al., 2018). In addition, some weakening intervals of the plasma line are caused by the normalization, but they occur in the GB and HB. Similar to the HFIL, no HFPLs were found in the LB.

Figure 3 gives the altitude profile of Te with a height resolution of 13–19 km, demonstrating that the enhanced Te is a function of fHF near an altitude of ~ 200 km. That is, TeLB200 > TeHB200 > TeGB200, where TeLB200, TeHB200, and TeGB200 are the electron temperatures in the LB, HB, and GB, respectively, near an altitude of ~ 200 km. This systematic variation in Te is dependent on the dispersion behavior of the electrostatic upper hybrid waves excited by an O mode pump lying in the GB, HB, and LB (Wu et al., 2017a). Indeed, the test particle simulations given by Najmi et al. (2017) also show that the pump at 3.8fce produces the bulk electron heating, whereas the pump at 4.01fce develops a high-energy tail of the electron distribution.

The HFIL and the HFPL in Figures 1 and 2, respectively, are considered as the confirmation of the PDI and the OTSI. Alternatively, Carlson et al. (2017) suggested that the high-energy tail of the electron distribution can excite Langmuir waves through the electron Landau damping, implying the enhanced Te in the HB may give rise to the enhanced thermal plasma line. However, it is obvious that the HFIL and the HFPL occur in the GB, although Te in the GB is not remarkably enhanced, as shown in Figures 1-3. Moreover, the HFPL lies at the frequency fHF − fia, as is expected as the decay line from PDI, where fia ≈ 9.45 kHz. This implies that the HFIL and the HFPL in Figures 1 and 2 are not induced by the high-energy tail but most likely by the PDI and the OTSI.

For the following discusses, Figure 4 presents the ratio of the oxygen ion density urn:x-wiley:21699380:media:jgra54698:jgra54698-math-0001 to the electron density Ne as a function of the altitude within an altitude range of [125 km, 375 km], which is given by the International Reference Ionosphere 2007 (Bilitza & Reinisch, 2008). For the sake of simplicity, only O+, urn:x-wiley:21699380:media:jgra54698:jgra54698-math-0002, and NO+ are considered in the present study, whereas hydrogen ions H+, atomic nitrogen ions N+, and helium ions He+ are ignored due to their small mass or small percentage. Indeed, the frequency of the ion acoustic wave mode corresponding to H+ should be urn:x-wiley:00948276:media:jgra54698:jgra54698-math-0103, which is excluded in the ion line channel of [- 40kHz, 40kHz] of UHF radar, where kr is the wave number of UHF radar, γ is the adiabatic index, KB is the Boltzmann constant, urn:x-wiley:00948276:media:jgra54698:jgra54698-math-0104 is the mass of H+, Te is set as the 2000 K. In other words, the ion acoustic wave mode corresponding to H+ can not be observed by the UHF radar. Similarly, the frequencies of the ion acoustic wave modes corresponding to N+ and urn:x-wiley:00948276:media:jgra54698:jgra54698-math-0105 are ~ 12.2 kHz and ~ 22.8 kHz respectively, which greatly deviate from the examined frequency of the enhanced ion line ~ 9.45 kHz. In Figure 4, urn:x-wiley:21699380:media:jgra54698:jgra54698-math-0004 decreases monotonically with a decrease in the altitude and has a value of 0.5 at an altitude of ~ 208 km, implying that urn:x-wiley:21699380:media:jgra54698:jgra54698-math-0005 increases monotonically with a descent in altitude and O+ dominates above altitude ~ 208 km, where urn:x-wiley:21699380:media:jgra54698:jgra54698-math-0006 represents the nitric oxide ion density plus the molecular oxygen ion density. Here it should be noted that IRI-2007 is invoked by the Grand Unified Incoherent Scatter Design and Analysis Package (Lehtinen & Huuskonen, 1996), although the profile of urn:x-wiley:00948276:media:jgra54698:jgra54698-math-0102 given by IRI-2007 may not be a reliable representation of the ionospheric composition.

Details are in the caption following the image
The ratio of urn:x-wiley:21699380:media:jgra54698:jgra54698-math-0007 to Ne as an altitude function.

The systematic variation in the intensities of the HFPL and HFIL induced by the pump near the fifth gyroharmonic can be summarized as follows: (1) in the GB, both HFPL and HFIL are intense, (2) in the HB, only the HFPL is intense, whereas the HFIL becomes weaker than in the GB, and (3) in the LB, the HFPL and HFIL are not observed.

3 Discussion

With regard to the field-aligned observation of ISR during monostatic operation, Langmuir and ion acoustic waves traveling in a nonuniform but stationary ionosphere should obey the respective dispersion relations (Baumjohann & Treumann, 1997)
urn:x-wiley:21699380:media:jgra54698:jgra54698-math-0008(1)
urn:x-wiley:21699380:media:jgra54698:jgra54698-math-0009(2)
where ωL is the angular frequency of the Langmuir wave, ωpe is the Langmuir angular frequency of the plasma, γ is the adiabatic index, KB is the Boltzmann constant, me is the electron mass, kL is the wave number of the Langmuir wave, ωia is the angular frequency of the ion acoustic wave, mi is the ion mass, and kia is the wave number of the ion acoustic wave. When the Langmuir wave is traveling, ωL will not change, whereas kL may change and should be determined by the ωpe and Te on the traveling path of the Langmuir wave. In the same manner, the change in kia should depend on the mi and Te on the traveling path of the ion acoustic wave.

The density fluctuations in the plasma can be expressed in the terms of a temporal and three-dimensional spatial Fourier transformation. Each Fourier component represents a plane wave traveling in the direction of k in the spatial transformation, where k is the wave vector. The ISR chooses the Fourier component causing the constructive interference in the observing direction. In other words, the ISR can only observe those plasma waves satisfying the Bragg condition k = 2kr in the case of backscattering, where kr is the wavenumber of the ISR (Stubbe et al., 1984; Rietveld et al., 1993; Kohl et al., 1993; Hagfors, 2003). Actually, those plasma waves within a small range of k may also contribute (Hagfors, 2003).

When kL = 2kr, that is, the Bragg condition of the ISR is exactly satisfied by the Langmuir wave, so that constructive interference with the Langmuir wave should be strong, and the intense plasma line is observed by ISR, where kr is the wave number of the ISR. If kL is approximately equal to 2kr, that is, the Langmuir wave approximately satisfies the Bragg condition of the ISR, then the weak constructive interference with the Langmuir wave will take place, and the intensity of the plasma line observed by ISR will become weak. When kL does not remarkably satisfy the Bragg condition of ISR, the constructive interference with the Langmuir wave will not occur, and the plasma line will not be observed by ISR. This behavior also holds for the ion acoustic wave.

Having stated several theoretical relations, we will take the observation in the fourth cycle as an example and further examine the intensity characteristics of the HFPL and HFIL in the GB, HB, and LB. Moreover, the overshoots in the HFPL and HFIL is discussed further.

3.1 In the GB

In the GB, TeGB at an altitude of ~ 200 km is slightly enhanced by ~ 10% over the background ionosphere level due to the absence of the trapping of the upper hybrid wave in small-scale irregularities (Dysthe et al., 1982; Gurevich et al., 1995, 1996; Mjølhus, 1993; Robinson et al., 1996; Wu et al., 2017a). Then, TeGB can be approximately considered a constant within the altitude range examined, where TeGB is the mean electron temperature in the GB. Thus, the change in kiaGB should be determined only by mi, where kiaGB is the wave number of the enhanced ion acoustic wave in the GB. Due to the monotonicity of the profile of mi, kiaGB should exactly satisfy the Bragg condition of radar at a particular altitude, where an intense HFIL is available. Figure 5a gives the profiles of mi and TeGB, which can be described as follows: mi becomes larger with a decrease in the altitude, and TeGB demonstrates the gradient of ~ − 8.85 K km−1 above the altitude of ~ 199.6 km, implying that TeGB slightly decreases with an increase in altitude and can be reasonably considered a constant at altitudes above 199.6 km. In Figure 5b, kiaGB = 2kr at an altitude of ~ 220 km, that is, the intense HFPL should be observed at an altitude of ~ 220 km.

Details are in the caption following the image
The profiles of (a) mi and TeGB, (b) kiaGB and 2kr, (c) urn:x-wiley:21699380:media:jgra54698:jgra54698-math-0016 and TeGB, and (d) kLGB and 2kr within the altitude range of [162.1 km, 245.8 km]. The effective ion mass urn:x-wiley:21699380:media:jgra54698:jgra54698-math-0017, where urn:x-wiley:21699380:media:jgra54698:jgra54698-math-0018 is given in Figure 4, urn:x-wiley:21699380:media:jgra54698:jgra54698-math-0019, and urn:x-wiley:21699380:media:jgra54698:jgra54698-math-0020. Since urn:x-wiley:21699380:media:jgra54698:jgra54698-math-0021, urn:x-wiley:21699380:media:jgra54698:jgra54698-math-0022, and NO+ are considered in the combining way. TeGB is the mean of the electron temperature within the time internal of [14:07:20 UT, 14:09:10 UT]. The parameter ωia has a value of 2π × 9.45 kHz; ωL is computed by ωL = 2π × (6.8 MHz − 9.45 kHz); and urn:x-wiley:21699380:media:jgra54698:jgra54698-math-0023, where Ne is the mean of the electron density within the time internal of [14:07:20 UT, 14:09:10 UT].

With the comparison between the second panel of Figure 1 and Figure 5b, however, the HFIL in the GB in the fourth cycle is observed at an altitude of 212.5 km, whereas Figure 5b indicates that it should be at an altitude of ~ 220 km. The altitude error may be caused by the uncertainty in the profile of mi. Indeed, the profile of mi is obtained by urn:x-wiley:21699380:media:jgra54698:jgra54698-math-0024, where urn:x-wiley:21699380:media:jgra54698:jgra54698-math-0025 is given by International Reference Ionosphere 2007 (Bilitza & Reinisch, 2008). Considering a larger gradient of mi and a constant TeGB above the altitude of 186.2 km, a larger gradient of kiaGB above the altitude of 186.2 km will be available according to the derivation of the dispersion relation (2) urn:x-wiley:00948276:media:jgra54698:jgra54698-math-0106, that is, the altitude of kiaGB = 39 m−1 may be shifted downwards.

In the similar manner, considering a constant TeGB and the monotonicity of the profile of ωpe within the altitude range examined, kLGB will be dependent only on ωpe and should exactly satisfy the Bragg condition of radar at a particular altitude, where kLGB is the wave number of the enhanced Langmuir wave in the GB. In Figure 5c, urn:x-wiley:21699380:media:jgra54698:jgra54698-math-0028 increases monotonically with a decrease in altitude. Moreover, urn:x-wiley:21699380:media:jgra54698:jgra54698-math-0030 becomes negative above an altitude of ~ 208.5 km, where the enhanced Langmuir wave should be reflected. Correspondingly, kLGB above an altitude of ~ 208.5 km becomes zero, as indicated in Figure 5d. Figure 5d also illustrates that the profile of kLGB is exactly equal to 39 m−1 at an altitude of ~ 206.8 km, namely, the intense HFPL can be observed at an altitude of ~ 206.8 km.

3.2 In the HB

Eliasson and Papadopoulos (2015) presented a numerical result that after the anomalous absorption at the upper hybrid resonance altitude, the fraction of the pump energy can reach the reflection altitude of the pump where Langmuir turbulence can be excited. Indeed, the anomalous absorption at the upper hybrid resonance altitude can lead to a decrease in the intensity of the pump when arriving at the parametric resonance altitude, then the intensity of the HFIL becomes weak in the HB (Das & Fejer, 1979; Fejer, 1979; Fejer et al., 1983; Fejer & Kopka, 1981; Gurevich, 2007; Showen & Kim, 1978). In addition, the enhancement in TeHB of up to ~ 35% should play an important role in the decrease in the intensity of the HFIL, where TeHB is the mean electron temperature in the HB. Unlike TeGB, TeHB cannot be considered a constant on the traveling path of the enhanced ion acoustic wave. Thus, the change in kiaHB should be determined by mi and TeHB, where kiaHB is the wave number of the enhanced ion acoustic wave in the HB. In Figure 6a, the profile of TeHB has the gradient of ~ − 17.77 K km−1 above the altitude of 199.6 km. Figure 6b shows that kiaHB is equal to ~37 m−1 and approximately satisfies the Bragg condition of ISR within the altitude range of [199.6, 245.8 km], in which the weak HFIL should be available. In fact, some observations presented by Bryers et al. (2013), namely, the intense HFIL for a pump ERP of 52.3 MW and the weak HFIL for a pump ERP of 104.5 MW, may support the above argumentation. For a pump ERP of 104.5 MW, the strongly enhanced Te facilitates a deviation in the wave number of the enhanced ion acoustic wave from the Bragg condition within the altitude range examined, and the HFIL becomes weaker. In addition, the HFPL and HFIL cannot be fully enhanced at the subsequent turn on unless the pump has been off for at least 10 s (Djuth et al., 1986; Jones et al., 1986). Indeed, in the F region, the decay time of the enhanced Te varies between 17 and 35 s (Mantas et al., 1981), during which the wave number of the enhanced ion acoustic wave can still deviate from the Bragg condition.

Details are in the caption following the image
The same as Figure 5 but for that in the HB. TeHB is the mean of the electron temperature within the time internal of [14:11:20 UT, 14:18:00 UT], ωL is computed with ωL = 2π × (7 MHz − 9.45 kHz), and Ne is the mean of the electron density within the time internal of [14:11:20 UT, 14:18:00 UT]. The profile of mi is as in Figure 5. HB = higher band.

In comparing the second and third panels of Figure 1 with Figure 6b, the error in the extending altitude range, namely, ~ 8.8 km in Figure 1 and ~ 45 km in Figure 6b, may be due to the uncertainty in the profile of mi (Wu et al., 2018). In addition, Figure 6b suggests that kiaHB = 39 m−1 at an altitude of ~ 196 km, where an intense HFIL should be observed. In Figure 1, however, no intense HFIL is found at an altitude of ~ 196 km in the HB. Indeed, the sharp change in TeHB near an altitude of 199.6 km may lead to a very narrow layer of kiaHB = 39 m−1, the scale of which may be far smaller than the radar height resolution of ~ 3 km, so that the intense HFIL may be diluted in one range gate of radar.

Figure 6c indicates urn:x-wiley:21699380:media:jgra54698:jgra54698-math-0036 in the HB and TeHB, where the profile of urn:x-wiley:21699380:media:jgra54698:jgra54698-math-0037 is very similar to that in the GB, implying that the profile of ωpe has not been remarkably modified by ionospheric heating. Figure 6d shows that kLHB = 2kr = 39 m−1 at an altitude of ~ 204.5 km, where kLHB is the wave number of the enhanced Langmuir wave in the HB. This implies that the intense HFPL can be observed at an altitude of ~ 204.5 km.

With regard to the intensity and altitude of the HFPL in the GB and HB, both Figures 5d and 6d are in perfect agreement with the observations presented in Figure 2. For a typical ionosphere, ωpe is on the order of megahertz, whereas urn:x-wiley:21699380:media:jgra54698:jgra54698-math-0039 is on the order of kilohertz. This implies that the profile of Ne dominates over the profile of Te in kL. Even Te is greatly enhanced by ionospheric heating, and kL will still exactly satisfy the Bragg condition at a particular altitude, where the intense HFPL can be observed. This behavior may be the reason for why the intense HFPL is observed both in the GB and HB.

3.3 In the LB

Similar to that in the HB, TeLB is greatly enhanced by ~ 55% and cannot be considered a constant within the altitude range examined, where TeLB is the mean electron temperature in the LB. Thus, kiaLB should be determined by mi and TeLB, where kiaLB is the wave number of the enhanced ion acoustic wave in the LB. Figure 7a indicates the profile of TeLB, which exhibits gradients of ~0.74 K km−1 within the altitude range of [199.6, 214.4 km] and ~ − 26.59 K km−1 above the altitude of 214.4 km. In Figure 7b, kiaLB shows kiaLB ≈ 34 m−1 within the altitude range of [199.6, 245.8 km]. In other words, the enhanced ion acoustic wave should not be observed by ISR due to the remarkable deviation of kiaLB from 2kr within the altitude range examined.

Details are in the caption following the image
The same as Figures 5 and 6 but for that in the LB. TeLB is the mean of the electron temperature within the time internal of [14:00:00 UT, 14:06:00 UT], ωL is computed with ωL = 2π × (6.7 MHz – 9.45 kHz), and Ne is the mean of the electron density within the time internal of [14:00:00 UT, 14:06:00 UT]. The profile of mi is as in Figures 5 and 6. LB = lower band.

In Figure 7d, kLLB = 39 m−1 at an altitude of ~ 206 km, where kLLB is the wave number of the enhanced Langmuir wave in the LB. This result implies that the HFPL should be observed by ISR at an altitude of ~ 206 km.

Figures 7b and 7d reveal that in the LB, HFIL should not be observed, but the HFPL should be observed. Evidently, however, both the HFIL and HFPL are not observed in the LB, as demonstrated in Figures 1 and 2, respectively. A possible reason for the absence of the HFPL may be the great damping of the enhanced Langmuir wave in the LB. Comparing Figure 7d with Figures 5d and 6d, wave numbers of the enhanced Langmuir wave in the LB, GB, and HB are principally dependent on the profile of Ne, although Te plays a role in wave number of the enhanced Langmuir wave. However, the profile of Ne is not significantly modified in the LB, GB, and HB as shown in Figures 5c, 6c, and 7c. Therefore, since the enhanced Langmuir waves in the GB and HB are not obviously damped, the enhanced Langmuir wave in the LB may also not be damped. In other words, the damping of the enhanced Langmuir wave appears to not be the reason for the absence of the HFPL in the LB.

The other explanation for the simultaneous absence of the HFPL and HFIL may be that the PDI and OTSI are not excited in the LB, which may be due to the strong anomalous absorption of the pump, the pump of a lower ERP, or both. When fHF gradually approaches mfce from below, the anomalous absorption of the pump falls considerably and is totally absent at mfce but grows sharply above mfce, where m = 2, 3, 4, 5, 6 for a typical ionosphere (Gurevich, 2007; Gurevich et al., 1996; Stocker et al., 1993; Stubbe et al., 1994). Therefore, the anomalous absorption of the pump in the LB will be relatively larger than that in the GB, ~ 6 dB (Gurevich, 2007; Gurevich et al., 1996; Stocker et al., 1993; Stubbe et al., 1994). Moreover, the gain of antenna depends on the pump frequency and consequently the ERP of the pump in the LB may be somewhat lower than that in the GB and HB. In our case, the ERP of the pump is calculated to be in the range 56–78 MW, where the thresholds of the TPI and OTSI can be exactly satisfied (Bryers et al., 2013).

For a pump in free space, the electric field E (V/m) at a range R (km) from a transmitter with ERP (kW) is given by urn:x-wiley:21699380:media:jgra54698:jgra54698-math-0047 (Rietveld et al., 1993; Robinson, 1989). Considering the anomalous absorption of 6 dB and a pump ERP of 56 MW in the LB, E should be ~0.15 V/m at the parametric resonance altitude. Furthermore, the thresholds of PDI and OTSI are, respectively, given by (Bryers et al., 2013; Fejer, 1979)
urn:x-wiley:21699380:media:jgra54698:jgra54698-math-0048(3)
urn:x-wiley:21699380:media:jgra54698:jgra54698-math-0049(4)
where Ti is the ion temperature, ν is the electron collision frequency and is taken to be urn:x-wiley:21699380:media:jgra54698:jgra54698-math-0050 (Showen & Behnke, 1978), and Bmax is a function of Te/Ti and has a value of ~0.56 for Te/Ti = 1.6~2 (Stubbe et al., 1984). Here Ti, Te/Ti, and Ne are ~1200K, ~1.6, and ~3.67 × 1011m−3, respectively, which are the mean measurements of the UHF radar within the time interval of [14:18:20 UT, 14:30:00 UT]. Thus, the thresholds of the PDI and OTSI are obtainable, namely, EPDI ≈ 0.154 V/m and EOTSI ≈ 0.186 V/m. Obviously, the pump reaching the parametric resonance altitude cannot excite the PDI and OTSI in the LB. Thus, it is most likely that the disappearances of the HFIL and HFPL in the LB are due to the absence of the PDI and OTSI.

3.4 Overshoot in the HFIL and HFPL

Although no overshoots in the HFPL and HFIL are found in the present observation due to the integration time of 10 s, we would like to discuss it further. When the pump is abruptly turned on, the remarkable enhancements in the HFPL and HFIL are termed overshoot, which rises for 2–4 ms or possibly up to 8 ms, lasts on the order of 5 s, and thereafter falls to the steady state enhancement for 4–6 s (Showen & Behnke, 1978; Showen & Kim, 1978). The explanation for the overshoots in the HFPL and HFIL may be that the pump becomes strongly reduced before it arrives at the parametric resonance altitude, either by anomalous absorption (Fejer, 1979; Fejer & Kopka, 1981; Gurevich, 2007) or by an electron density irregularity that scatters the pump (Das & Fejer, 1979; Fejer et al., 1983; Showen & Kim, 1978).

However, previous studies of the overshoots in the HFPL and HFIL have neglected the modifications of the ionospheric plasma, such as the modifications of the profiles of Te and Ne by ionospheric heating, which may have a significant impact on the wave numbers of the enhanced Langmuir and ion acoustic waves. During a period of a few seconds after turning on the pump, the modification of Ne is expected to be small and can be ignored in the F region since it occurs mainly because of the expansion of the plasma along the magnetic field as the plasma is heated, and consequently, the thermal pressure rises. For the sake of simplicity, the anomalous absorption of the pump and the modification of Ne will be ignored in the following discussion, whereas the impact of the enhanced Te on the wave numbers of the enhanced Langmuir and ion acoustic waves is emphasized.

The results given by Vas'kov and Gurevich (1975), Dysthe et al. (1982), and Mjolhus (1983) show that the pump can excite an upper hybrid wave at the upper hybrid resonance altitude, and the excitation efficiency of the upper hybrid wave is proportional to the gradient of the small-scale irregularity. The upper hybrid wave dissipates energy by being trapped in those small-scale irregularities, and consequently, Te is greatly enhanced. During the initial evolution on a timescale of a few seconds, however, Te will not be greatly enhanced due to the undeveloped small-scale irregularity and less anomalous absorption. Afterward, the small-scale irregularities govern the anomalous absorption of the pump, and Te is greatly enhanced. Moreover, it is well known that the growth times of the PDI and OTSI are on the order of milliseconds (Robinson, 1989), which are very short compared to the growth time of Te at the upper hybrid resonance altitude.

At the initial stage of evolution after the pump turns on, Te on the traveling path of the enhanced Langmuir and ion acoustic waves will not be greatly enhanced and can be considered a constant. Thus, kL and kia should be dependent only on ωpe and mi, as indicated in the dispersion relations (1) and (2), respectively. Furthermore, due to the monotonicity of the altitude profiles of ωpe and mi on the traveling path of the enhanced Langmuir and ion acoustic waves, kL and kia should exactly satisfy the Bragg condition at a particular altitude, where the strong HFPL and HFIL are observed by ISR, as illustrated in Figures 5b and 5d.

After the initial evolution, Te is greatly enhanced at the upper hybrid resonance altitude, and the thermal energy is conducted on the traveling path of the enhanced Langmuir and ion acoustic waves. Then, kL and kia will depend not only on the profiles of ωpe and mi, respectively, but also on the profile of Te. For the enhanced ion acoustic wave, the enhanced Te on the traveling path of the enhanced ion acoustic wave may lead to a slight deviation in kia from 2kr, that is, kia will approximately satisfy the Bragg condition on the traveling path of the enhanced ion acoustic wave, as illustrated in Figure 6b. As a result, the intensity of the HFIL becomes weak and falls to the steady state enhancement. Furthermore, if an extreme enhancement in Te is available, kia will remarkably deviate from the Bragg condition on the traveling path of the enhanced ion acoustic wave, as illustrated in Figure 7b. Thus, the HFIL will fall to the thermal level and will not be observed.

Unlike the enhanced ion acoustic wave, kL is principally dependent on the profile of urn:x-wiley:00948276:media:grl58481:jgra54698-math-1001, although it is not independent of the profile of Te. Considering a density profile of small gradient within the altitude range examined, however, the profile of Te may dominate kL, that is, ωpe can be approximately considered a constant and consequently kL will be dependent on the profile of Te within the altitude range examined. Thus, the enhanced Te on the traveling path of the enhanced Langmuir wave may lead to a slight deviation of kL from 2kr. As a result, the HFPL falls to the steady state enhancement.

Thus, the overshoots in the HFPL and HFIL may be attributed not only to the anomalous absorption of the pump but also to the modification of the plasma induced by ionospheric heating. Particularly, the enhanced Te may facilitate a significant deviation in the wave numbers of the enhanced Langmuir and ion acoustic waves from the Bragg condition and may weaken the HFPL and HFIL after the initial evolution of a few seconds. Obviously, this behavior may complicate the explanation of the overshoots in the HFPL and HFIL.

Indeed, the overshoots in the HFPL and HFIL occur frequently but not universally (Kohl et al., 1993; Showen & Kim, 1978). In general, if fHF is fixed at a frequency very close to mfce, the anomalous absorption of the pump falls considerably (Gurevich, 2007; Gurevich et al., 1996; Stocker et al., 1993; Stubbe et al., 1994), and Te on the traveling path of the enhanced Langmuir and ion acoustic waves will be somewhat enhanced. Thus, the strong HFPL and HFIL should be persistent just as the HFIL and HFPL in the GB in Figures 1 and 2. In other words, the overshoots in the HFPL and HFIL should not occur.

In addition, if a pump of a low ERP is employed, no overshoots in the HFIL and HFPL should be observed as a result of the somewhat enhanced Te on the traveling path of the enhanced Langmuir and ion acoustic waves. This finding may be supported by the persistent HFIL and HFPL for a pump ERP of 26.3 MW presented by Bryers et al. (2013).

Additionally, considering a pump at a high ERP for an ionosphere with a large gradient, Te will be greatly enhanced after the initial evolution of a few seconds. The parameter kia may slightly deviate from the Bragg condition on the traveling path of the enhanced ion acoustic wave, and the intensity of the HFIL may fall considerably just as the HFIL in the HB in Figure 1. Thus, the overshoot in the HFIL should be observed. However, the overshoot in the HFPL should not necessarily occur owing to the domination of ωpe over Te in kL, just as the HFPL in the HB in Figure 2. This finding is also supported by the result presented by Bryers et al. (2013), which shows that for high pump power, only the overshoot in the HFIL is observed. Moreover, if a pump with a high ERP and an ionosphere with a small gradient are considered, both kia and kL will deviate from the Bragg condition on the traveling path of the enhanced ion acoustic and Langmuir waves; thus, the overshoots in the HFIL and HFPL may simultaneously occur. It should not be necessary that the overshoot in the HFIL simultaneously accompanies the overshoot in the HFPL. Indeed, the traveling characteristics of a Langmuir wave is very different from those of an ion acoustic wave.

In addition, with regard to an ionosphere with a large background Te, even a pump with a large ERP is employed, and it may be difficult to greatly enhance Te compared to the background Te. Therefore, the impact of the enhancement in Te on the traveling Langmuir and ion acoustic waves will be slight. In this case, the HFPL and HFIL may be persistent.

4 Conclusions

An observation during an ionospheric heating campaign with the pump frequency near the fifth electron gyroharmonic demonstrates that the intensities of the HFIL and HFPL vary systematically as a function of the pump frequency, namely, (1) in the GB, the HFPL and HFIL are intense, (2) in the HB, the HFPL is still intense, whereas the HFIL becomes weak, and (3) in the LB, the HFPL and HFIL are not observed.

The analysis shows that the enhanced electron temperature as well as thermal conduction plays a significant role in the systematic variation in the intensities of the HFPL and HFIL induced by the PDI and OTSI. (1) In the GB, due to no significant enhancement in the electron temperature on the traveling path of the enhanced Langmuir and ion acoustic waves, the wave numbers of the enhanced Langmuir and ion acoustic waves exactly satisfy the Bragg condition within the altitude range examined. Thus, the strong constructive interferences with the enhanced Langmuir and ion acoustic waves occur. (2) In the HB, however, due to the significantly enhanced electron temperature on the traveling path of the enhanced Langmuir and ion acoustic waves, the wave numbers of the enhanced Langmuir and ion acoustic waves approximately satisfy the Bragg condition, and consequently, the weak constructive interferences with the enhanced Langmuir and ion acoustic waves take place. (3) In the LB, the PDI and OTSI are not excited owing to a low ERP pump and the strong anomalous absorption taking place at the upper hybrid resonance altitude.

Moreover, the overshoots in the HFPL and HFIL are discussed further, and an alternative explanation for the overshoots in the HFPL and HFIL is presented. In addition to the anomalous absorption of the pump, the modifications of plasma induced by ionospheric heating, especially the enhanced electron temperature as well as the thermal conduction, should contribute to the overshoots in the HFPL and HFIL. These modifications may be the reason for why the overshoots in the HFPL and HFIL occur frequently but not universally.

Acknowledgments

We would like to thank the engineers of EISCAT in Tromsø for keeping the facility in excellent working condition and Tromsø Geophysical Observatory, UiT The Arctic University of Norway, for providing the magnetic data of Tromsø recorded on 11 March 2014. The data of UHF radar can be freely obtained from EISCAT (http://www.eiscat.se/schedule/schedule.cgi). The EISCAT scientific association is supported by China (China Research Institute of Radiowave Propagation), Finland (Suomen Akatemia of Finland), Japan (the National Institute of Polar Research of Japan and Institute for Space-Earth Environmental Research at Nagoya University), Norway (Norges Forkningsrad of Norway), Sweden (the Swedish Research Council), and the UK (the Natural Environment Research Council).