Stimulated electromagnetic emissions during pump frequency sweep through fourth electron cyclotron harmonic



[1] The frequency of a high-power HF radio wave incident on the ionosphere was swept, using a computer-controlled transmitter signal, in <10 s within a 60-kHz-wide frequency band approximately centered on the fourth harmonic of the electron cyclotron frequency. Measurements of the spectral behavior of stimulated electromagnetic emissions (SEE) across this harmonic after preconditioning could thereby be made with unprecedented resolution, speed, and ionospheric stability. Comparison of local electron cyclotron frequency estimations based on the experimental data reveals discrepancies between certain downshifted maximum models and the empirical broad upshifted maximum (BUM) feature formula ΔfBUM = f0nfce. Weak emissions related to the BUM were discovered below the nominal BUM cutoff frequency. Finally, we observed that the intensity of certain SEE components differed depending on the whether the pump frequency sweep was ascending or descending.

1. Introduction

[2] Stimulated electromagnetic emission (SEE) is secondary HF radiation induced by an HF electromagnetic wave, acting as a pump wave, transmitted into the ionosphere from ground-based radio facilities [Thidé et al., 1982]. The SEE are influenced by a number of factors such as ionospheric conditions and pump parameters such as power, polarization, duty cycle, and frequency [Thidé et al., 1982; Stubbe et al., 1984; Leyser et al., 1993]. However, in terms of the overall spectral character of the steady state SEE, the most important factor is the pump frequency's proximity to a harmonic of the local electron cyclotron frequency. For instance, a spectral feature of SEE known as the broad upshifted maximum (BUM) is only observed when the pump frequency is near or slightly above a cyclotron frequency harmonic, while another common spectral SEE feature called the downshifted maximum (DM) exhibits a minimum in intensity when the pump frequency is in a region around a cyclotron frequency harmonic.

[3] Several workers in the past have measured the dependence of the SEE spectra on the offset of the pump frequency from the gyroharmonic [Leyser et al., 1989, 1992, 1994; Stubbe et al., 1994; Frolov et al., 1998]. Such experiments have been important in understanding how the fundamental dependence of the SEE on the pump frequency and the role of the gyroharmonic, but the manual technique used to date had limitations which in turn left certain fundamental questions unresolved. The limitations were that either the time required to complete one frequency step was long, tens of seconds to minutes (a length of time during which ionospheric conditions could easily change) or the number steps and hence frequency resolution, were limited, typically 10–20 steps.

[4] In this paper we present the results of an experiment to measure SEE close to the fourth gyroharmonic using a frequency stepping technique which achieved frequency step speeds of τstep = 0.07 s and could span a bandwidth of 60 kHz. This was possible by using a computer controlled signal generator and a broadband signal analysis receiver system. Using this technique, we were able to measure the fine structure of the SEE dependence on the pump frequency offset from a gyroharmonic which provides evidence for discerning between certain theoretical models for SEE generation.

2. Experiment

[5] The experiment was conducted during 1414–1511 LT (= UT + 4 hours) on 27 September 1998 at the Sura ionospheric pumping facility, near Nizhny Novgorod, Russia. The Sura facility consists of three 200-kW transmitters each with a Gaussian output filter with an 80 kHz band pass. The center frequency of each filter is tunable, but it requires several minutes to retune. The basic idea of the experiment was to utilize the available output bandwidth and sweep the pump frequency through the fourth gyroharmonic. The frequency sweep was semicontinuous, consisting of a series of pulses each with a constant carrier frequency which was stepped between the pulses.

[6] The experiment was conducted as follows: First, a rough estimate of the fourth gyroharmonic was made by measuring the BUM and using the empirical formula as given by Leyser et al. [1989]

equation image

where n is the harmonic number, fce is the electron cyclotron frequency, fBUM is the BUM peak frequency, and ΔfBUM = fBUMf0. All three of the Sura transmitters were then tuned so that the center frequency of their output filters were set to the estimated fourth gyroharmonic. Then the ionosphere was preconditioned by transmitting O-mode CW for 2 min at the frequency 30 kHz below the estimated fourth gyrofrequency. Directly after the preconditioning, a customized signal sequence generated by a computer controlled HP3325 function generator was converted into a O-mode pump by the Sura transmitters. The signal sequence employed, illustrated in Figure 1, amounts to a discrete frequency stepping of the pump. The scheme consisted of a sequence of pulses of duration τstep, with a frequency which was either increased or decreased relative to the previous pulse, in constant absolute steps of Δfsteps. The sequence was such that the pulse carrier frequency was increased monotonically an integer number of pulse steps, and then decreased monotonically an equal number of integer steps. In what follows, we will call this monotonically increasing sequence an up sweep, and analogously the decreasing sequence will be called a down sweep and an up sweep followed by a down sweep, or vice versa, will be called a full sweep.

Figure 1.

A portion of the pump time–frequency control scheme, showing slightly more than one full sweep. The pump is programmed to transmit a sequence of discrete pulses which ascend or descend linearly in frequency centered on the assumed fourth gyroharmonic which was 5410 kHz in this experiment. This sequence continued indefinitely and is preceded by a CW pulse of 2 min duration.

[7] In practice, the preestimated fourth gyroharmonic was 5410 kHz, the sweep covered the frequency range 5380–5441 kHz using 62 steps with Δfstep = 1 kHz, and the shortest time between steps that could be achieved with our hardware configuration was τstep = 0.07 s which is equivalent to a maximum pulse repetition rate of about 15 Hz. The duty cycle of the pulses was about 96% in practice.

[8] At the receiving end, the output of the Sura receiving antenna, configured for O mode reception, was connected to an HP3587S real-time 23 bit sampling signal analysis system with a maximum sampling rate of 20 × 106 samples/s. The center frequency of the HP3587S was set to the same estimated gyrofrequency as was used in the transmitter scheme and its frequency span was set to 500 kHz. These settings were not altered during the sweep sequence. The large frequency span is necessary so that the full frequency sweep could be recorded, including the upshifted SEE components on the high-frequency end of the sweep and the downshifted SEE components on the low-frequency end of the sweep. For the analysis of the SEE spectra we used roughly the last 50 ms of each 0.07 s pump frequency step, when a stationary state was definitely achieved (see also section 4).

3. Results

[9] We now look at the results of the sweep experiment and in particular the sweep sequence which commenced 1503:50 LT and continued until 1511:00 LT. Two portions of this sequence were recorded, one with data from the interval 1504:40–1505:20 LT and the other containing the interval 1505:30–1506:10 LT. The pump sweeps in these data records had the shortest sweep time obtained during the whole experiment and are therefore of special interest.

3.1. Overall Detailed Gyroharmonic Dependence of SEE

[10] The overall HF response of the ionosphere to the frequency swept pump in the vicinity of the fourth cyclotron harmonic can be seen in the spectrogram of Figure 2 and in the stack of spectra in Figure 3a. Figure 2 shows one full sweep essentially as it was measured by the signal analysis system but in the frequency–time domain. The pump is seen as an intense (−15 dBm), few kHz narrow, region starting its cycle at 5380 kHz at time 0 s. As time goes on the pump increases, what on this scale appears to be, linearly in frequency until 4.25 s after which the frequency decreases down to the same frequency as at the start of the cycle. This cycle is then repeated indefinitely. On either side of the pump we can identify the SEE components. The large arrow-head shaped region above the pump is the BUM feature and running parallel just 10 kHz below the pump is the DM.

Figure 2.

Dynamic spectrum of one full sweep cycle. The pump signal is seen at frequency 5380 kHz starting at time 0 s, then increases in frequency until 4.25 s at which time the pump frequency decreases until time 8.5 s at which point the pump frequency is again 5380 kHz as it was at the beginning at time 0 s. The SEE features are seen in the sidebands of the pump and clearly vary in intensity which follows the variation of the pump frequency.

Figure 3.

(a) The stack of five plots showing SEE spectra for the five different pump frequencies marked on the vertical axis in the middle of the figure. The standard SEE spectral features and the pump are labeled. These spectra are cross sections of the pump relative spectra versus pump frequency two-dimensional plot in Figure 3b. (b) The position of the cross sections are marked with dashed, magenta lines. The estimated range of the local fourth gyroharmonic is shown as a hatched region on the pump frequency axis.

[11] The absolute dynamic spectrum of Figure 2 is useful for illustrating the sweep experiment but the SEE itself is more conveniently viewed as spectra relative to the pump frequency. By shifting the spectra in Figure 2 so that the swept pump frequencies are all placed at relative frequency 0 Hz as a function of the absolute pump frequency and averaging over several sweeps we obtain the data plotted in Figures 3 and 4.Figure 3a shows how usual SEE spectra relate to the sweep spectrogram in Figures 3b and 4: Any horizontal slice through the sweep spectrogram is a pump relative SEE spectrum.

Figure 4.

Contour plot of received power as a function of pump relative frequency and actual pump frequency, averaged over four up and four down sweeps. The power contour levels are marked in units of dBm. The dashed black line shows a linear fit to BUM peak positions for the highest pump frequencies extrapolated down to where it intercepts the pump signal. The horizontal and vertical axis are scaled equally so constant absolute frequencies are lines inclined at −45°. Such lines are seen in the plot and are caused by monochromatic radio interference.

[12] Figure 4 is useful for getting an overview of the sensitive dependence on pump frequency of the SEE, and its features, around the fourth gyroharmonic. The pump is seen as the heavy vertical line-like structure at 0 kHz throughout the whole sweep range. The DM family, namely, DM, 2DM, and 3DM, are seen most clearly for the lowest pump frequencies and at −9, −18 and −27 kHz, respectively, relative to the pump frequency; see also Figure 3. They are most intense for the lowest pump frequencies for which their peak intensities are −74, −86, and −100 dBm, respectively.

[13] Roughly speaking, the upshifted maximum (UM) is the upshifted counterpart to the DM but much weaker and at a slightly different frequency shift. The UM is seen at a frequency relative pump of +8 kHz but only for pump frequencies in the range 5380–5390 kHz after which the BUM power level effectively swamps the UM frequency range. There are indications in the data that the UM experiences a suppression similar to the DM suppression. Unfortunately, it is difficult, without access to other radiation parameters such as the state of polarization, to establish the qualitative details of the UM suppression from the data set since the UM has frequencies in common with the lower sideband of the BUM for some pump frequencies.

[14] In Figure 4, the BUM is seen as the large wedge-shaped structure in the upper sideband ranging from 10–150 kHz at the high-frequency edge of the pump sweep interval and disappearing altogether at the lower frequency edge of the pump sweep interval. In Figure 4 the dependence of the BUM structure as a whole on pump frequency is visualized. The structure itself may be roughly divided into two regions: one is the BUM cutoff region which broadly speaking is the trough between the pump and the BUM. For pump frequencies above about 5430 kHz, the BUM peak lies on a line marked by a dashed black line which has been extrapolated to the 0 kHz relative pump line. The intercept corresponds to a pump frequency of 5410 kHz. This is seen to agree with equation (1) and the value 5410 kHz is the same as was used before the start of the sweep as an estimate of the electron gyroharmonic.

[15] Another SEE feature which can be seen is a −100 dBm weak, 10 kHz broad power maximum at roughly −30 kHz below the pump for pump frequencies in the range 5425–5440 kHz, i.e., above the gyroharmonic. It has a symmetric dependence on pump frequency and absolute frequency offset from pump as the BUM peak. This feature is probably the broad downshifted maximum (BDM) mentioned by Stubbe et al. [1984]. It mirrors the BUM dependence on the pump in the lower sideband but at much lower intensity.

[16] Besides the BUM and the DM family, which are clearly seen within the pump frequency range, there are a few SEE components which are not as well developed, namely, the narrow continuum (NC), the down shifted peak (DP), and the broad continuum (BC), see Leyser et al. [1993]. The NC, for instance, which appears as a slight broadening in the lower sideband of the pump out to a few kHz, but only for pump frequencies in the higher half the sweep interval. It appears to broaden slightly with increasing pump frequency. The DP component cannot be found at any pump frequency in the sweep range. More support of these facts will be given in the section on the detailed analysis of the DM. Finally, the BC does not appear at all for this pump frequency range.

[17] Finally, there is one spectral feature which is not easily attributable to known SEE features. This is the very wide and weak feature in the upper sideband extending from about +20 kHz to +150 kHz for pump frequencies about 5380 kHz up to 5400 kHz. It is seen as an upward pointing triangular region in the lower right-hand corner of Figure 4. This feature has a maximum at about +135 kHz. The relative frequency of the maximum does not vary with pump frequency but its intensity diminishes as the pump frequency approaches the middle of the sweep interval and ranges from −105 dB, down to the noise floor at −110 dB. This peak is superimposed on a wider “continuum” structure which seems to move toward the pump as the pump frequency is increased until it is overlapped by the BUM and no longer visible. This structure may be related to the broad dynamic (BD) emission observed by Leyser et al. [1993].

3.2. The DM Family Close to the Fourth Gyroharmonic

[18] One of the more interesting SEE phenomena is the suppression of the DM for pump frequencies close to local ionospheric electron gyroharmonics. Different stages of this suppression can be seen in Figure 5 which shows overlayed lower sideband spectra for two ranges of pump sweep frequencies f0: the lower panel shows spectra for f0 < 5406 kHz and the upper panel shows the spectra for f0 > 5415 kHz. As the pump frequency is increased from the lowest frequency 5380 kHz to the highest frequency 5441 kHz, the DM is seen to weaken steadily in the lower panel and then to grow slowly in the upper panel as the pump frequency is increased further. For pump frequencies in between these two panels the DM is almost indistinguishable from the noise floor and this we will call the suppression maximum of the DM.

Figure 5.

Close-up of a series of spectra of the DM peak. Each spectrum has a unique color which corresponds to a pump frequency step (step size 1 kHz) in the sweep. The color scale goes from dark red for the lowest sweep frequency (5380 kHz) up to dark blue for the highest frequency (5441 kHz). (a) Spectra obtained with pump frequency above f0 = 5415 kHz and (a) spectra for pump frequencies below f0 = 5406 kHz.

[19] A qualitatively similar behavior is exhibited by the 2DM. Inspection shows that the shape as well as intensity of the DM changes systematically as the pump frequency is stepped. Particulary, the high-frequency flank of the DM fDMhf has the same frequency offset from f0, for all spectra, that is f0fDMhf ≈ 7.5 kHz, while as the DM approaches the suppression maximum, its peak diminishes and shifts toward higher frequencies. Such a value of f0fDMhf corresponds to the lower hybrid frequency in the ionosphere, flh = (fcefci)1/2. This confirms results by Leyser et al. [1990, 1994]. It is also seen that the peak and the high-frequency flank of the DM is much more pronounced for the pump frequencies below the suppression maximum. This is most probably related to the fact that the NC feature is much more developed for pump frequencies above the suppression maximum. The analysis of the DM family spectra below the suppression maximum has shown also that for all spectra fDMf2DMhf = const ≈ 7.5 kHz, which is approximately equal to flh and f0fDM = fDMf2DM. This also confirms results by Leyser et al. [1994] obtained for pump frequency ranges f0 > 5fce and f0 > 7fce.

[20] The resonance-like behavior of the DM near the gyroharmonic becomes clear if the integrated power of the whole DM feature is plotted as a function of the pump frequency as is shown in Figure 6. To simplify the further discussion we call the curves shown in Figure 6, suppression curves. The first noticeable feature of the DM suppression curve in Figure 6 is that it is asymmetric. As the pump tends toward lower pump frequencies, the curve flattens out, while for the highest pump frequencies in the sweep range the curve is almost linear with a slope of about +0.5 dB/kHz. The curve minimum, or DM suppression maximum, is estimated to be at the pump frequency 5409 ± 1 kHz which is unfortunately obscured by a radio interference at absolute frequency 5400 kHz. The interference shows up here because the DM peak is about 9 kHz below the pump.

Figure 6.

Integrated power of the DM and 2DM versus pump frequency showing the suppression of the DM family close to the gyroharmonic. We call these curves the suppression curves of the DM family. The power here correspond to the power integrated in the frequency bands [−8, −9.5] kHz (relative to the pump) for the DM and [−18, −16.5] kHz for the 2DM. The error bars on the curve shows the statistical variance of the measurement over eight sweeps. The upper and lower bounds of the half minimum of the suppression curves are marked. Note that the lower bounds of the DM and 2DM are very close to each other while the upper bound of the 2DM is 10 kHz higher than the upper bound of the DM.

[21] To characterize the suppression curves we introduce a few quantities: f0(DMsup) is the pump frequency for which the DM is maximally suppressed, f0(DMlbsup) is the pump frequency less than f0(DMsup) for which the DM is 3 dB above the DM suppression maximum, similarly, f0(DMubsup) is the pump frequency greater than f0(DMsup) for which the DM is 3 dB above the DM suppression maximum. Obvious analogue notation is used for the 2DM. We then define the width of the DM suppression maximum Δf0(DMsup) to be the frequency difference f0(DMubsup) − f0(DMlbsup). The experimental values for these characteristics of the suppression curves are found in Table 1.

Table 1. Observed Characteristics of the DM Suppression Curves

[22] The depth of the suppression curve was not possible to estimate satisfactorily in this experiment since the suppression curve did not flatten out in the pump sweep interval used here but must be more than 25 dB for the DM and more than 20 dB for 2DM.

[23] We tested numerically the hypothesis that the DM suppression curve data was consistent with linear harmonic resonance models. The results were negative. It was found that an iterative least squares fit of Lorentzian or Gaussian models to the DM suppression curve did not converge to sufficient statistical confidence. The DM curve was too broad compared to its depth to fit the Lorentzian and too asymmetric to fit the Gaussian.

[24] Also the 2DM and 3DM exhibit suppression curves. The 2DM is shown in the same plot as the DM suppression curve (Figure 6). As can be seen, the DM and 2DM are quite similar in the low-frequency half of the suppression curve while in the high-frequency half of the curve they deviate from each other. More quantitatively, consider the 3 dB points of the DM, the 2DM and the 3DM curves which are marked in the figure or tabulated in Table 1. What is noticeable is that the low-frequency edge of the DM minimum, 2DM minimum and 3DM minimum are roughly the same, but the high-frequency edge of the respective minimums clearly vary. The difference between f0(DMubsup) and f0(2DMubsup) is 10 kHz and the difference between f0(2DMubsup) and f0(3DMubsup) is at least 11 kHz. Note that these values are approximately equal to the DM frequency relative to the pump.

3.3. Detailed Analysis of the BUM Around the Fourth Gyroharmonic

[25] It is well known that the BUM is generated, roughly speaking, when the pump frequency is just above a gyroharmonic. Spectra of the BUM for different pump frequencies close to the harmonic are shown in Figure 7. For clarity, we display the spectra in two distinct regions shown Figures 7a and 7b. Figure 7a shows that the BUM structure is shifted toward the pump as the pump frequency is decreased. This is in agreement with the formula (1). In Figure 7b, however, the BUM structure does not seem to shift toward the pump any longer but simply diminishes in strength until it is indistinguishable from the noise floor for the lowest pump frequencies. The phenomenon that, seemingly, the BUM cannot be brought arbitrarily close to the pump is expressed by saying that the BUM exhibits a cutoff. The BUM cutoff frequency, defined as the pump relative frequency for which the low-frequency flank of the BUM spectra visible in Figure 7b meets the noise floor, is about 9–11 kHz. The pump frequency below which the BUM exhibits a cutoff is 5419 kHz, which was the frequency used in the division between Figures 7a and 7b.

Figure 7.

Close-up of a series of spectra of the BUM structure. The color coding is the same as in the DM close-up plots. (a) Spectra obtained with pump frequencies ranging from 5420–5441 kHz and (b) spectra for pump frequencies 5380–5419 kHz.

[26] From Figures 7 and 4, we find that the BUM is only generated for f0 ≥ 5387 kHz and that for f0 = 5387 kHz the peak of the BUM at about 11 kHz is barely above the noise floor. In terms of absolute frequency the lowest detectable BUM frequency is 5398 kHz. These data clearly show that the BUM is generated for pump frequencies below the DM suppression maximum. These results confirm the observations made by Frolov et al. [1998].

[27] As mentioned above concerning the BUM cutoff, a casual observation seems to indicate that there is a minimum frequency offset above the pump for the components of the BUM spectrum. Examination of the close-up of the BUM cutoff in Figure 8 shows however that while the major bulk of the BUM structure is clearly upshifted from the BUM cutoff in agreement with previous observation, there is also some emission below the cutoff and in addition this emission obeys the empirical formula (1) for the BUM peak. Spectra of this emission can just barely be seen looking back at Figure 7: the lightest blue spectrum in the upper panel has a slightly higher intensity at the lowermost edge of the main BUM structure compared to the other spectra. This “sub-cutoff emission” is only observable for a narrow range of pump frequencies, namely, about 5 kHz. It is also very weak, peak power of at most −90 dBm which is 12 dBm below the BUM peak power. The very narrow range of pump frequencies for which it exists and its weakness compared to the BUM, factors which are easily overcome by the sweep technique used here, might explain why this emission has not been observed earlier.

Figure 8.

Low-frequency edge of BUM spectra versus pump frequency. The UM feature is also shown.

3.4. Sweep Hysteresis Effect

[28] Detailed comparison of SEE spectra during up sweeps and down sweeps recorded for τstep = 0.07 s, reveals a clear and systematic difference between the two. The difference between up and down sweeps is hardly noticeable in the normal spectra, as is evidenced by the similarity between Figures 9a and 9b, which show contour plots of spectra versus pump frequency for up sweep and down sweep in Figures 9a and 9b, respectively. Each contour plot is an average over four successive sweeps recorded after numerous sweeps had already been completed. The variation among up sweeps (and down sweeps) was found to be very small. The differences between sweep direction are brought out by considering the relative difference in intensity between the sweep directions

equation image

This relative difference quantity is shown in Figure 9c. One can see the portions of SEE sensitive to the pump sweep direction the high-frequency flank of the BUM, the low-frequency flank of the BUM with maximum at the BUM cutoff, the DM feature just above its suppression maximum and the UM. All regions with the greatest hysteresis effect are seen to be above 5400 kHz in absolute frequency. It is interesting to note that there is a “corridor” in the BUM structure between 60 and 70 kHz above the pump, splitting the BUM into two parts which does not exhibit hysteresis.

Figure 9.

Pump relative spectra versus pump frequency for (a) upgoing sweeps, (b) downgoing sweeps, and (c) relative difference on a logarithmic scale between upgoing and downgoing sweeps. The biggest differences can be seen to be at the cutoff region and the high-frequency flank of the BUM and the DM peak just above the DM suppression maximum.

[29] The systematic nature of the sweep hysteresis effect is clear if we look at how the total DM and BUM intensity varies with pump frequency and sweep direction as shown in the upper and lower panels of Figure 10, respectively. It is seen that in both cases the up sweep has consistently higher SEE intensity than the down sweep. As the direction is changed the intensity level is also changed. A similar behavior was also seen for sweep rates slower than τstep = 0.07 s but in these cases the magnitude of the intensity difference was less. Finally, it is clear here that the error for the upper bound of the DM suppression half maximum is mainly due the hysteresis differences and is of the order Δf ∼ 3 kHz.

Figure 10.

Hysteresis of integrated BUM power and integrated DM power versus pump frequency.

[30] It is interesting to note that the monochromatic radio interference, especially the one at 5400 kHz, also exhibits an hysteresis effect. It is conceivable that these radio signals are high angle and have propagated through the overhead pump plasma interaction region before being measured by our receiving equipment.

4. Discussion

[31] It is now commonly accepted that the DM, the BUM, and the BC features of SEE are closely related to the upper hybrid (UH) and electron Bernstein (EB) HF plasma waves and small scale magnetic field aligned irregularities (N) or striations. Such an excitation occurs due to the development of the thermal parametric instability Grach et al. [1981] and in the well developed stage due to resonance instabilities [Vas'kov and Gurevich, 1977] near the upper hybrid resonance height of the pump wave where

equation image

where fuh is the local upper hybrid frequency and fpe is the local electron plasma frequency. Formation of these SEE features occurs due to the different types of nonlinear interactions between HF plasma waves responsible for their spectrum formation and subsequent plasma wave transformation off the striations into electromagnetic waves detectable as SEE on the ground.

[32] In the case when the pump frequency f0 and, therefore, the HF plasma frequency fUH/EB is close to both the upper hybrid frequency fuh and a harmonic of the electron cyclotron frequency nfce

equation image

a condition also known as the double resonance condition, the efficiency of the UH/EB wave excitation decreases essentially, and the SEE generation is suppressed. The physical reasons for such a suppression as well as its frequency width are defined by the plasma wave dispersion properties in an inhomogeneous ionosphere and discussed by Grach et al. [1994] and Leyser et al. [1994].

[33] The experimental data clearly show that the SEE spectral structure changes dramatically if f0 passes nfce. Naturally occurring variations of the ionosphere during the experiments could easily destroy the resonance conditions presenting difficulties for the diagnostics of nonlinear plasma processes in the ionosphere. One basic idea of the experiment described here was to avoid the influence by such a variability by quickly sweeping the pump frequency and thereby obtain an minimally disturbed measurement of the SEE dependence on the f0 close to nfce. To do this it was necessary to put the ionosphere into a preconditioned state with well developed striations in the background ionosphere before the start of the sweep. A precondition state is needed because the SEE spectrum formation in a preconditioned ionosphere takes only a few ms, (which is much less than the τstep used), while the characteristic time for striation development in an ionosphere which has not been conditioned is 0.5–5 s and can take up to a few tens of seconds when f0nfce. Quantitative estimates of the variability of parameters which can destroy the regular double resonance mechanism of the SEE generation mechanism of the SEE features were derived by Leyser et al. [1994]. Here we mention only that the sweep parameters used (see section 2) in our experiment allows us to consider the ionosphere as stationary over several sweeps.

4.1. Consequences of the Suppression Curves on DM Family Models

[34] The favored models for the generation of the DM family are the so-called cascade models, which have been used, in particular, to explain the constant high-frequency flanks of the DM family members; see section 3.2. In this section we discuss the consequences of the family of suppression curves shown in Figure 6 for the cascade models. One of the more popular cascade models has been discussed by Zhou et al. [1994], Istomin and Leyser [1998], and Shvarts and Grach [1997]. This model can be summarized in the following scheme:

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The model can be described as follows: First, the process (5) corresponds to the pump wave transformation or scattering into UH/EB waves off striations (N); then according to (6), UH/EB waves decay iteratively to daughter UH/EB' waves with lower and lower frequencies and lower hybrid (LH) waves as decay products; and finally the plasma waves are transformed off the striations into electromagnetic waves (EM), which are then identified on the ground as the DM family according to (8) and (9).

[35] An alternative cascade model is obtained by replacing the processes (5) and (6) with the process

equation image

and retain the rest of the processes in the hierarchal chain above (79). The first step (10) of this model, namely, the direct decay of the pump wave into the UH/EB and LH waves, was discussed by Vas'kov and Bud'ko [1993a, 1993b], Istomin and Leyser [1995], and Shvarts and Grach [1997]. To distinguish between these two models we will refer to the equations by which they differ, namely, equations (5), (6), and (10).

[36] Inspection of the schemes for the equations (5) and (6) model reveals that the nDM depends on (n + 1) UH/EB mother waves with frequencies f0mflh (m = 0…n) respectively. If we assume that the UH/EB waves are suppressed exactly at electron cyclotron harmonics gfce (g = 1, 2, 3…), then the DM will be quenched when f0 = gfce + mflh where m = 0, 1, that is twice for each harmonic. Similarly, the 2DM will be quenched when m = 0, 1, 2, that is three times for each harmonic, and the 3DM will be quenched when m = 0, 1, 2, 3, that is four times for each harmonic and so on. Therefore we would expect all nDM to be quenched twice, namely, when the pump is equal to gfce and when it is equal to gfce + flh, but the 2DM and the 3DM will in addition be quenched at gfce + 2flh and the 3DM will be quenched at gfce + 3flh and so on.

[37] In the equation (10) model the suppression conditions have a distinct difference owing to the fact that it does not require the existence of a UH/EB wave with the same frequency as the pump. Therefore this model predicts that all DM are suppressed when f0 = gfce + flh but not at f0 = gfce, so nominally this direct model will be equivalent to the equations (5) and (6) model in terms of suppression maximum if we discard the m = 0 case in the above discussion.

[38] Clearly, the hierarchal structure of the cascade models explains the data in Table 1 in which all the DM suppression curves have their low-frequency bounds at roughly the same frequency while the upper frequency bounds, on the other hand, increase cumulatively in multiples of roughly flh with increasing DM number. The suppression curves must however be interpreted differently depending on which particular cascade model is taking place.

[39] Considering first the equations (5) and (6) model, it specifies that the DM suppression curve should have two minima. Even though the curve appears to have only one minimum, it is possible to fit two minima reasonably at the pump frequencies 5404 and 5413 kHz if we assume that the width of each minimum is about 5 kHz and that each minimum has a finite depth. In contrast, the equation (10) model can easily be fitted to the curve by placing its single minimum at the minimum of the curve, namely, 5409 kHz. Also the 2DM curve can be considered. It could reasonably fit either the three minima of the equations (5) and (6) model at 5404, 5413, and 5421 kHz, or it could also fit the two minima of the equation (10) model at 5409 and 5418 kHz. In conclusion then the fourth gyroharmonic suppression curves could reasonably fit either of the two cascade models considered here but they infer different gyroharmonic estimates, namely, the equations (5) and (6) model puts 4fce ≈ 5404 kHz while the equation (10) model puts 4fce ≈ 5400 kHz. These values are compared with the gyroharmonic estimate based on BUM data in section 4.3.

[40] In the discussion above we have considered the two proposed cascade models as occurring separately but it also possible to consider them as concurrent processes. If such were the case, the low-frequency minimum of the equations (5) and (6) model occurring when f0 = gfce can be detected since the DM can still be generated by way of the equation (10) model. Such a situation therefore can not be ruled out from the data. Also, even though multiple minima in the DM suppression curve could be resolved at the fourth harmonic, this may be possible at higher cyclotron harmonics where the suppression curves are known to be more narrow [Leyser et al., 1992].

4.2. BUM Related Emissions Below BUM Cutoff

[41] It was shown in a previous section that there existed weak SEE emissions which obeyed the empirical BUM peak law (1) and yet had frequencies that were lower than the so-called BUM cutoff. There are three possible explanations for this: either the BUM actually consists of two emission components, or that the BUM is strongly, but not completely, suppressed for frequencies shifts below the cutoff frequency, or the BUM is excited in an extended altitude region with the condition f0 = nfce in the lower region while f0 > fce at higher altitudes [Leyser et al., 1990]. In any case the existing BUM generation models, such as the four-wave nonlinear interactions [Bud'ko and Vaskov, 1992; Goodman et al., 1993; Tripathi and Liu, 1993; Huang and Kuo, 1994] or the accelerated electrons models [Ermakova and Trakhtengerts, 1995; Grach, 1999], do not immediately explain this behavior and therefore need to be revised. In the case of the four-wave model this could be accomplished by allowing not only for the participation of a lower hybrid wave in the interaction but also some other lower frequency plasma wave such as an ion-acoustic. As for the two component nature of the BUM, there exists other data in support of such an interpretation; see Frolov et al. [1996, 1998] and Sergeev et al. [2001].

4.3. Comparison of SEE Estimates of the Electron Cyclotron Frequency

[42] One important unresolved issue about SEE is the exact quantitative role the gyroharmonic has in SEE generation. In particular two quantitative aspects of the gyroharmonic in SEE generation has been proposed: as the suppression condition for the DM and as the intercept frequency for the BUM frequency shift.

[43] As mentioned in section 4.1, the cascade models if invoked separately give two different estimates of the fourth gyroharmonic when fitted to the data, namely, 5404 kHz, according to the equations (5) and (6) model, and 5400 kHz, according to the equation (10) model. On the other hand, in section 3.3 it was found that the linear fit of the BUM peak using formula (1) puts the fourth gyroharmonic at 5410 kHz. Thus we find that even though the minimum in the DM suppression curve matches the BUM formula (1) to within the 1 kHz resolution, neither of the fce estimates from the DM models fit the fce estimate from the BUM formula (1).

[44] Due to the incompatible estimates of the gyroharmonic we conclude that it is necessary to revise or refine either the model for the suppression of the DM or the empirical BUM formula (1). In the BUM formula, for instance, an additional term could easily be added, say for the sake of discussion fLH, without upsetting the empirical evidence to date.

4.4. The Sweep Hysteresis Effect

[45] As was evidenced in section 3.4, the SEE intensity was sensitive to the direction of the sweep of the pump frequency. One explanation could stem from the differences in the generation of striations, and the associated anomalous absorption (AA) of the SEE, just above and just below a gyroharmonic [Ponomarenko et al., 1999; Stubbe et al., 1994; Grach et al., 1997; Grach, 1985; Grach et al., 1998]. The argument is that the 8 s sweep cycle is not slow enough to establish an “adiabatic” transition between above and below the fourth gyroharmonic. That AA is involved in the hysteresis is supported by the fact that even some of the intensity of monochromatic interferences, which happened to be in measured frequency band, were consistently different for up sweeps compared down sweeps. In any case more sweep experiments in which the dependence of hysteresis on the range of sweep frequencies, the duration of the sweep, and the preconditioning are called for.

4.5. Sweep as an Ionospheric Diagnostic

[46] It has been proposed that SEE could be used in different ways as a diagnostic for ionospheric parameters. For example, the diagnostic SEE (DSEE) technique [Sergeev et al., 1997] can provide several diagnostics of the heated plasma volume where other methods fail. Another possible diagnostic is a high-resolution measurement of the local ionospheric cyclotron frequency determined from the frequency of the DM suppression maximum. To determine the DM suppression in practice, we suggest the automated sweep through a gyroharmonic introduced in this paper. It is clear from the results of this experiment that one can obtain the DM suppression minimum at the fourth gyroharmonic to within 1 kHz frequency resolution in less than 10 s. These values are in other words the upper limits on the performance of such a SEE diagnostic. For long term, continuous measurements of the DM suppression, the automated sweep could be fitted with a feedback mechanism, in which the DM suppression maximum frequency is determined after each sweep and if it is found not to be at the center of the current sweep interval, the sweep interval is modified so as to put the DM minimum at the center of the next sweep interval. In this way changes or fluctuations of the DM suppression, and hence the local magnetic field strength, could be monitored and measured.

[47] The technique can easily be adapted for measurements at higher (n = 5, 6) gyroharmonics where the width of the DM suppression Δf0(DMsup are about 3 kHz for n = 5 and 1 kHz for n = 6. At n = 7, where Δf0(DMsup ≈ 0.2 kHz [Leyser et al., 1992, 1994], sweep measurements could provide an accuracy of magnetic field measurements of about 2 · 10−5 or, according to (4), plasma density measurements with an accuracy about 10−3. Ultimately one could sweep through all the harmonics of the local electron cyclotron frequencies below the critical frequency of the ionosphere. Such measurements would give diagnostic information on the structure of the ionosphere alternative to ionosondes.

5. Conclusions

[48] It has been found that the novel technique presented in this paper, consisting of computer controlled sweep of the HF pump frequency generated detailed information on spectral dependence of SEE on the pump frequency. The resolution and the detail of the technique allowed new discoveries on the nature of SEE.

[49] Detailed measurement of the DM suppression curve shows that it does not fit a Lorentzian or Gaussian model for a harmonically damped resonance absorption. It was observed that the low-frequency edge of the DM, the 2DM and the 3DM suppression curves were all the same but that the upper frequency edge of the 2DM was roughly 10 kHz higher than the DM and the 3DM was roughly 20 kHz higher than the DM. This is consistent with a parametric cascading model of the DM family.

[50] The fourth harmonic of the local electron cyclotron frequency estimates obtained using the DM suppression curves were slightly different for the two proposed cascade models of the DM family. Furthermore, these estimates also found to be incompatible with the estimate obtained from BUM peak and the relation (1). Therefore either the BUM relation (1) or the models of the suppression of the DM must be reconsidered.

[51] Emissions were found that exhibited the same dependence on pump frequency as the BUM peak but at pump offset frequencies lower than the BUM cutoff where it was previously conceived that the BUM structure could not exist.

[52] It was found that the SEE exhibits a hysteresis effect which manifests itself as a dependence of SEE intensity on the direction of the pump frequency sweep. It is suggested that this effect is due to the short sweep cycle period of 8 s and differences in the anomalous absorption of the pump wave and escaping SEE for f0 < 4fce compared to f0 > 4fce.

[53] A SEE feature not previously reported was observed during the experiment. It appeared as a broad structure in the 20–150 kHz range with a peak at 135 kHz. It was about 20 dB weaker than the BUM maximum power and existed for frequencies below the assumed gyrofrequency.

[54] The data demonstrates the feasibility and practical performance of using the DM suppression as an ionospheric diagnostic. During the fastest pump sweep measurements achieved in the experiment, the DM minimum could be determined to within a few kHz every 10 s.


[55] This work was financially supported by the Swedish Natural Science Research Council (NFR) and the Russian Foundation for Basic Research (RFBR) grants 00-02-17433 and 01-02-16752. The 1998 experiment was supported by the International Center for Advanced Studies in Nizhniy Novgorod (INCAS) grant 97-2-02.

[56] Michel Blanc thanks Peter Stubbe for his assistance in evaluating this paper.