Excitation threshold and gyroharmonic suppression of artificial E region field-aligned plasma density irregularities

Authors


Abstract

[1] Ionospheric modification experiments have been carried out using the HAARP facility along with a 30 MHz coherent scatter radar imager in Alaska to examine properties of artificial E region field-aligned plasma density irregularities (FAIs). In one set of experiments, the RF emission power was varied gradually in order to determine the threshold electric field for irregularity generation. A threshold O mode peak electric field amplitude of 170–195 mV/m at an altitude of 99 km and a heating frequency of 2.7 MHz was identified based on the full-wave formalism of Thidé and Lundborg (1986). In another, the pump frequency was varied gradually to investigate the suppression of the FAIs at frequencies near the second electron gyroharmonic frequency (2Ωe). Coherent echoes were found to be suppressed for pump frequencies in an asymmetric band 40–50 kHz wide around 2Ωe but only for irregularities driven marginally above threshold. Theoretical context for these results is provided.

1. Introduction

[2] Visible to coherent scatter radars, E and F region field-aligned plasma density irregularities (FAIs) provide incisive diagnostics of ionospheric modification experiments. A number of reviews have been made of the experimental database and of what can be inferred about the underlying plasma instabilities at work [see Robinson, 1989; Frolov et al., 1997; Gurevich, 2007]. That irregularities are produced near the upper hybrid resonance level in the plasma rather than at the critical height points to two instability processes. These are the closely related thermal parametric (TPI) and thermal oscillating two-stream (TOTSI) instabilities [Grach et al., 1978; Das and Fejer, 1979; Fejer, 1979; Kuo and Lee, 1982; Dysthe et al., 1983; Mjølhus, 1990], and the resonance instability [Vas'kov and Gurevich, 1977; Inhester et al., 1981; Grach et al., 1981; Dysthe et al., 1982; Lee and Kuo, 1983; Mjølhus, 1993]. In the TPI, the pump electromagnetic wave is resonantly converted in the presence of field-aligned plasma density irregularities into an upper hybrid HF sideband wave which heats the plasma collisionally and intensify the irregularities through differential heating. Two HF sidebands (stokes and antistokes) are present in the TOTSI. When the amplitude of the irregularities (striations) becomes large, upper hybrid waves may be trapped, causing additional mode conversion, heating, and trapping in union with the generation of thermal cavitons. This describes the resonance instability, which is characterized by explosive wave growth. Coherent scatter is telltale of plasma striations created by these processes [e.g., Stubbe, 1996].

[3] The complexity of the artificial FAI problem, which involves inhomogeneous, anisotropic, dissipative, hot plasmas supporting coupled electromagnetic and electrostatic waves, imposes approximations and assumptions on the theories developed for it, which differ in their details. For example, Gustavsson et al. [2009] recently pointed out how different theoretical predictions for the TOTSI threshold for excitation scale differently with temperature and collision frequency. Precise measurements are needed for refining TOTSI and resonance instability theory.

[4] The central role of upper hybrid waves in FAI generation implies that the process could be interrupted at pump frequencies close to electron gyroharmonic frequencies, i.e., where ωωuhnΩ. As pointed out by Leyser et al. [1990], upper hybrid waves with finite parallel wave numbers experience cyclotron damping at gyroharmonic frequencies. Furthermore, Mjølhus [1993] have argued that upper hybrid wave trapping should be suppressed at frequencies at and just below gyroharmonic frequencies with n ≥ 3 on the basis of a geometric optics argument applied to the shape of the wave dispersion curves in this limit. The theory has been expanded by Huang and Kuo [1994], Gurevich et al. [1996], and Grach et al. [2004]. Istomin and Leyser [2003] further argued that striations should be intensified at frequencies just above gyroharmonic frequencies. Finally, Rao and Kaup [1990] have shown that upper hybrid waves at n ≥ 3 gyroharmonic frequencies can be damped through coupling to electron Bernstein waves. Experiments in the F region using gyroharmonic pump frequencies with n ≥ 3 have indeed shown reduced anomalous absorption [Stocker et al., 1993; Stubbe et al., 1994], the persistence of Langmuir turbulence and associated effects [Honary et al., 1999], airglow suppression and overshoot [Kosch et al., 2002; Gustavsson et al., 2002; Kosch et al., 2005], modified stimulated electromagnetic emission (SEE) effects [Stubbe et al., 1994; Honary et al., 1995], and suppressed coherent scatter [Honary et al., 1999; Ponomarenko et al., 1999; Kosch et al., 2002] at these frequencies.

[5] Ionospheric modifications at the second electron gyroharmonic frequency differ fundamentally from the n ≥ 3 cases (see, for example, Grach [1979] for basic theory). Mjølhus [1993] were the first to point out that wave trapping might be prohibited entirely at pump frequencies below the second electron gyroharmonic frequency, although the threshold for excitation of thermal parametric instability may also be reduced in the vicinity of the second electron gyroharmonic frequency [Grach, 1979]. Experimentally, coherent scatter is observed at pump frequencies near 2Ωe, and enhancements have been reported at frequencies just above 2Ωe [Fialer, 1974; Minkoff et al., 1974; Kosch et al., 2007]. Airglow intensifications are also seen at pump frequencies slightly above 2Ωe [Haslett and Megill, 1974; Djuth et al., 2005; Kosch et al., 2005, 2007]. It is unclear if the DM (downshifted maximum) and 2DM lines in SEE spectra are suppressed when pumping near 2Ωe, as they are at higher gyroharmonic frequencies [Djuth et al., 2005].

[6] The availability of a VHF coherent scatter radar situated near the HAARP ionospheric modification facility in Alaska affords an opportunity to test and expand the theoretical framework surrounding heater-induced FAIs as they pertain to E region modification. Since the E region follows a very regular, predictable diurnal pattern during geomagnetically quiet periods, and since ionospheric refraction is unnecessary for satisfying the condition for field-aligned backscatter from E region targets at high latitudes, E region FAI experiments can be accurately quantified at HAARP. The closed feedback design of HAARP moreover allows precise control of the heater power, gain, and frequency, making laboratory-grade experiments on E region FAIs possible.

[7] Heater-induced E region FAIs have been observed in experiments incorporating coherent scatter radars by Fialer [1974] at Platville, Coster et al. [1985] at Arecibo, and Hibberd et al. [1983], Djuth et al. [1985], Hoeg [1986], and Noble et al. [1987] at Tromsø. Recently, Nossa et al. [2009] reported observations of E region FAIs excited at pump frequencies slightly above and below the second electron gyroharmonic frequency, and Hysell and Nossa [2009] accounted for this possibility theoretically by including the effects of finite parallel wave numbers in the upper hybrid waves involved, which can restore the lower cutoff frequency in the dispersion relation of the waves.

[8] Below, we describe additional experiments designed to test two specific theoretical predictions for FAI production through ionospheric modification. One of these is the threshold condition for TOTSI onset, and the other is the effect of heating at frequencies near the second electron gyroharmonic frequency. Evidence for irregularity preconditioning, which is telltale of wave trapping and resonance instability, will also be presented. Note that the E region critical frequency during undisturbed periods is too low to test FAI generation with pump frequencies at the third or higher gyroharmonic frequency.

2. Observations

[9] The Ionospheric Research Instrument (IRI) at the High Frequency Active Auroral Research Program (HAARP) (62.39N, 145.15W) was used to generate artificial E region field-aligned density irregularities (FAIs) with its planar array of 15 × 12 low-band dipole elements. Experiments were performed using O mode emissions, vertical pointing, and finely graduated power levels and frequencies (see below). At the same time, the ionosphere over HAARP was monitored with a coherent scatter radar interferometer operating at 30 MHz and located at the NOAA Kasitsna Bay Laboratory (KBL) (59.47N, 151.55W) near Homer, Alaska. This radar has its locus of perpendicularity at precisely 100 km altitude over HAARP, making it suitable for observing artificial E region FAIs there. The imaging radar is capable of resolving two-dimensional fine structure in backscatter from the common volume with kilometric resolution. It employs a transmitter with a peak power of 12 kW and digital receivers which sample six spaced antenna groups.

[10] For our experiments, we utilized a 13 baud Barker coded pulse with a 10 μs baud length. The interpulse period for the radar experiments was 2.46 ms or 370 km. Doppler velocities as large as ∼1000 m/s can be measured without frequency aliasing, which is necessary for observing natural auroral irregularities, although the Doppler shifts encountered during ionospheric modification experiments are typically an order of magnitude smaller than this. Additional specifications for the radar and its operating mode were given by Nossa et al. [2009]. The HAARP ionosonde and riometer were also operating during the study.

[11] Heating experiments took place at the HAARP facility from 5 to 14 August 2009, around midday when the E region critical frequency was the highest. The experiments were performed during geomagnetically quiet periods. Figure 1 shows the E region critical frequency (FoE) measured by the HAARP Digisonde throughout the experiments and exemplifies the regular diurnal behavior of the background E region density under photochemical control. Apparent irregularities in the measurements around midday are mainly an artifact associated with the operation of the HF facility itself. The daily peak FoE was about 3.2 MHz, and the F10.7 solar flux index was nearly constant at 69. All of the experiments involved O mode emission and vertical pointing.

Figure 1.

Measured E region critical frequency versus universal time for the experimental period in question. Note that LT = UT + 9 h.

[12] Figure 2 shows an estimate of the midday plasma number density profile over the HAARP site for the experimental period in question based on the International Reference Ionosphere (IRI) 2007 model [Bilitza and Reinisch, 2007]. For the purposes of the calculations to follow, the model profile can be represented by the sum of three Chapman functions centered in the D, E, and F1 regions, respectively. This representation is depicted by the dashed line in Figure 2. The absorption at the HAARP riometer frequency can be predicted on the basis of this model and used, along with FoE predictions, as a rudimentary means of validation. The result, −0.15 dB, is consistent with the absorption typically measured at midday during the campaign. According to this model profile and the IGRF reference magnetic field model, the upper hybrid interaction height for our experiments at 2.7 MHz was 99 km.

Figure 2.

Ionospheric plasma density profile predicted by the IRI model (solid curve). Approximation to the model composed of the sum of three Chapman functions (dashed curve).

2.1. Pump Threshold for Instability

[13] Ionospheric modification experiments geared at assessing the threshold ionospheric electric field for instability were performed at a frequency of 2.7 MHz, the lowest possible at HAARP. At this frequency and for vertical pointing, the HAARP IRI has a directivity of 20.9 dBi. (This estimate assumes a uniform linear array of short dipoles over an infinite ground plane and is a more accurate figure than the one given by Nossa et al. [2009], which was based on a physical area calculation. It is also consistent with validation measurements.) Given a nominal radiated power of 3.18 MW at this frequency, the maximum effective radiated power would be 390 MW. The peak incident electric field at a reference height of 70 km, below the ionosphere, would be 2.2 V/m at this power level.

[14] We have used the full-wave formalism of Thidé and Lundborg [1986] to estimate the pump electric field in the E region ionosphere, taking into account the effects of Airy swelling, the finite magnetic dip angle, background absorption, and the dependence on propagation distance. The calculations incorporates the aforementioned plasma density profile and assumes an electron neutral collision frequency of 4 × 104 s−1 at 99 km altitude, decreasing in altitude with a 6 km scale height. The results are depicted in Figure 3. According to the figure, the horizontal pump electric field amplitude at an altitude close to 99 km, the nominal upper hybrid interaction height, would have been between 0.44 times the field amplitude at 70 km altitude or about 970 mV/m, assuming full-power emission and neglecting anomalous absorption.

Figure 3.

Electric field amplitude for a pump wave at 2.7 MHz propagating through the ionosphere given by Figure 2. A magnetic declination of 14° is assumed. The reflection height in this case is 99.86 km. The perpendicular east (magnetic), perpendicular north (magnetic), and parallel components of the electric field are depicted in blue, red, and green, respectively. Amplitudes as a fraction of the amplitude at a 70 km reference altitude are represented.

[15] Notice that Airy swelling is nearly absent in the horizontal field components. This is a consequence of normal absorption, which attenuates the reflected wave to the point that a standing-wave pattern is suppressed back at the upper hybrid resonance height. There, the reflected wave amplitude is about one fifth the amplitude of the upgoing wave. This prediction has important implication for E region FAI generation. The plasma interaction region occupies a narrow band of altitudes surrounding the upper hybrid resonance height no more than a few tens of meters deep (see section 3). About this height, wave heating is antisymmetric, such that plasma depletions above (below) it experience a surplus (deficit) of heating. The net differential heating of the field-aligned depletion with respect to background would be zero if the symmetry were not broken [e.g., Das and Fejer, 1979]. While a number of factors contribute to symmetry breaking [Dysthe et al., 1983], the most important is the standing wave pattern. We can expect FAI generation to be the most efficient when the upper hybrid interaction height coincides with a node in the pattern and when the pattern itself is distinct. The finite width of the interaction region, which increases with the electron-neutral collision frequency, limits the efficiency further and is another factor potentially inhibiting FAI generation in the E region.

[16] Heating experiments were performed at reduced power in an attempt to identify the threshold for instability onset. Pump power was varied discretely over a series of steps lasting 10 s each. This figure is long compared to the neutral-electron collision time, (νenm/M)−1, which is a characteristic time scale for instability and about 1 s in the E region. The power steps followed a quadratic progression so that the pump field increased and decreased linearly. Heater power increased from zero for 2 min to a maximum and then decreased for 2 min, with a 1 min emission gap completing each 5 min heating cycle.

[17] Figure 4 shows coherent echoes received by the 30 MHz radar in Homer from E region field-aligned plasma density irregularities in the modified volume over HAARP. Similar experiments were run on 6 and 7 August 2009, producing comparable results. We focus here and in subsequent examples on events when some of the strongest echoes were received for a given incident heater power level (see below).

Figure 4.

Range-time Doppler intensity (RTDI) plot of backscatter from artificial E region FAIs over HAARP observed on 7 August 2009. Here the brightness, hue, and saturation of the pixels denote echo signal-to-noise ratio (SNR), Doppler shift, and spectral width, according to the legend shown. Note that the echoes from heater-induced FAIs are range aliased and that their true range is greater than their apparent range by 370 km. The average signal-to-noise ratio for apparent ranges between 80 and 130 km is plotted beneath the RTDI plot. Variations in the line plot reflect both changes in the size of the modified volume and in the scattering intensity of regions within the volume. Echoes from meteor trails are also visible. The incoherent integration time is about 3 s. Figure 4 depicts 12 distinct cycles lasting 5 min each.

[18] Figure 4 conveys information about the signal-to-noise ratio, Doppler shift, and spectral width of the coherent echoes detected at Homer. We concentrate here on the variation of echo power with pump electric field, which varied in steps lasting 10 s, starting at 2125, following the progression specified in Figure 5, and repeating every 5 min. The maximum pump power in each cycle was 18% of IRI maximum, and the minimum was just 2.25%. In view of the number of independent power estimates that enter into the calculation of the curve at the bottom of Figure 4, which reflect averages over time, range, spaced antennas, and Doppler frequencies, registered signal-to-noise ratios as small as −15 dB are statistically significant (have RMS relative errors less than 50%), although care must be taken to distinguish echoes due to meteors and other clutter. Close inspection of the figure shows that echoes above this threshold appear between 30 and 55 s into each heating cycle.

Figure 5.

Heating power schedule for instability threshold experiments depicted in Figures 4 and 6. The top row shows the time in seconds into the heating cycle when a pump power transition occurred. The middle and bottom rows show the pump electric field and pump power as fractions of the maximum possible. No power was emitted in the final minute of each 5 min heating cycle.

[19] Slow, secular variations in the peak backscatter power evident in Figure 4 suggest that background conditions were changing such as to vary the conditions for instability onset. The threshold condition for instability is influenced by the plasma density scale height and electron mean free path at the upper hybrid interaction height, and both of these may undergo natural and heater-induced variations. More important, the threshold condition is strongly influenced by the interaction height relative to the RF standing wave pattern. Our strategy is to focus on the strongest echo events with the lowest electric field thresholds, reasoning that such events occurred under optimal FAI generation conditions. Subsequent analysis will then assume those conditions.

[20] Figure 6 highlights one of the strongest echo events observed in the campaign when instability onset was achieved earliest. In this case, instability was detected at 30 s, precisely at the moment the pump electric field transitioned from 17.5% to 20% of its predicted 970 mV/m maximum. This finding brackets the threshold pump electric field for instability to 170–195 mV/m.

Figure 6.

Range-time Doppler intensity (RTDI) plot of backscatter from artificial E region FAIs over HAARP observed on 7 August 2009, during a relatively strong echo event. Heating commenced 10 s after 2155 UT, peaked at 2157 UT, and ceased at 2159 UT.

2.2. Preconditioning

[21] The heating profiles in Figure 4 and Figure 6 are asymmetric in time in the sense that the echoes observed on the power downramp are stronger than those on the upramp given equivalent pump power levels. Coherent backscatter remained detectable at the end of the heater-on intervals, demonstrating that irregularities can be sustained at pump power levels well below the onset threshold. Nossa et al. [2009] reported on similar observations and interpreted the apparent hysteresis as evidence of striation formation in the modified volume and of resonance instability. Similar hysteresis phenomena have been reported for F region artificial FAIs generated by the EISCAT and SPEAR facilities, respectively [Wright et al., 2006, 2009].

[22] In the August experiments, we pursued this evidence further using a modified version of the experiment described above. This time, pairs of power ramps, which individually followed the schedule shown in Figure 7, were separated by a 2 min heating gap. In this way, the second ramp in each pair followed a period when irregularities were already present whereas the first ramp did not. Note that the power steps were somewhat coarser in this experiment than in the previous one, and that the maximum heater power was greater.

Figure 7.

Heating power schedule for instability threshold experiments depicted in Figures 8 and 9. The top row shows the time in seconds into the heating cycle when a pump power transition occurred. The middle and bottom rows show the pump electric field and pump power as fractions of the maximum possible. This pattern was repeated twice, followed by a 2 min heating gap, giving an overall cycle time of 10 min.

[23] Figure 8 shows results from experiments on 14 August 2009. The coherent echoes are clearly stronger than those observed on 6 and 7 August from Homer. These and other experiments indicate a marginal increase in echo intensity with increased heater power over the entire HAARP radiated power range [see also Nossa et al., 2009]. A gradual secular variation in echo intensity is also evident in these data. The shortest time to echo onset in the heating cycles was just over 30 s, here and in observations made on 13 August, which is consistent with the threshold electric field for onset established above.

Figure 8.

Range-time Doppler intensity (RTDI) plot of backscatter from artificial E region FAIs over HAARP observed on 14 August 2009. The figure depicts eight distinct cycles lasting 10 min each.

[24] Figure 9 focuses on the strongest echoes observed on 14 August. Figure 9 demonstrates not only hysteresis, signified by the asymmetry in the coherent scatter between the power upramps and downramps, but also preconditioning, signified by differences between the first and second event. Note how readily irregularities could be generated in the second event. Close examination of the figure shows that coherent scatter onset began just 15 s into the second heating cycle, 5 s after heating commenced, at an electric field strength of 10% of maximum or about 100 mV/m. Irregularities moreover emerged over a 30 km wide span of ranges nearly simultaneously. This phenomenon cannot be due to elevated temperatures within the modified volume, since the threshold for irregularity onset increases with temperature. We interpret such preconditioning behavior as evidence of plasma striations which permit wave trapping and suppress the threshold electric field for instability considerably. The striations evidently survived 10 s without heating but not 2 min.

Figure 9.

Range-time Doppler intensity (RTDI) plot of backscatter from artificial E region FAIs over HAARP observed on 14 August 2009. The earlier heating event in the pair was preceded by a 2 min heating gap. The latter event followed the former after a 10 s heating gap.

2.3. Gyroharmonic Suppression

[25] Measuring the threshold electric field for onset is one way of quantifying the theory of the thermal oscillating two-stream instability, and testing for preconditioning is a way of identifying resonance instability. Upper hybrid waves play a central role in both instabilities, and examining FAI behavior for pump wave frequencies close to harmonics of the electron gyrofrequency is a third way to validate and expand instability theories and models. The double resonance condition for the second electron gyroharmonic can be met routinely in E region ionospheric modification experiments in summer months around midday.

[26] Experiments were performed where the pump mode frequency was varied from 2.9 MHz to 3.1 MHz and back to 2.9 MHz over a 4 min period, with a 1 min gap between heating cycles. The frequency span included 2Ωe which is close to 3 MHz in the E region over HAARP. The frequency was varied over 500 discrete steps separated by 400 Hz and lasting 240 ms each. Heating occurred using vertical pointing and full-power emission.

[27] Figure 10 shows the Homer radar results for experiments conducted on 8 August 2009. The figure demonstrates the sensitivity of echo intensities, range extents, and Doppler shifts to pump frequency. As the frequency increases, the interaction height and the radar range to the interaction region also increase. Steep neutral wind shears are known to be prevalent in the lower thermosphere [see, e.g., Larsen et al., 1989]. Variations in neutral wind forcing, combined with the rapid change in the ion mobility with altitude, make the Doppler shift of the coherent echoes strongly dependent on echo height.

Figure 10.

Range-time Doppler intensity (RTDI) plot of backscatter from artificial E region FAIs over HAARP observed on 8 August 2009. Each heating cycle depicted represents a pump mode frequency sweep from 2.9 to 3.1 MHz and back to 2.9 MHz, with sweeping occurring at a uniform rate. The plotted points in the bottom plot reflect the average signal-to-noise ratio in apparent ranges between 130 and 140 km. Vertical lines indicate times when the pump frequency was twice the electron gyrofrequency.

[28] It is important to note that the decrease in echo power at the highest pump frequencies (midway through Figures 10, 11, and 12 and the figures that follow) is due to the fact that those frequencies approached or exceeded FoE. While this behavior is clearly evident in the 5 and 8 August experiments described here and below, it is not characteristic of our experiences with data from the Homer radar, which have exhibited strong echoes on other occasions under comparable ionospheric conditions using pump frequencies as high as 3.26 MHz. Nonetheless, decreasing echo intensity near the horizontal center of Figures 10, 11, and 12 and the figures that follow should not be mistaken for gyroharmonic heating effects.

Figure 11.

Range-time Doppler intensity (RTDI) plot of backscatter from artificial E region FAIs over HAARP observed on 5 August 2009. Each 4 min heating cycle depicted represents a pump mode frequency sweep from 2.9 to 3.1 MHz and back to 2.9 MHz, with sweeping occurring at a uniform rate. The plotted points in the bottom plot reflect the average signal-to-noise ratio in apparent ranges between 80 and 95 km. Vertical lines indicate times when the pump frequency was twice the electron gyrofrequency.

Figure 12.

Coherent echo signal-to-noise ratio versus true range and time on 5 August 2009. These results are derived from imaging analysis from a single azimuth bin passing the modified volume to the west. The bottom plot shows the SNR averaged over groups of ranges indicated by the colored lines; dashed vertical lines reflect the second electron gyroharmonic frequency representative for the cut. (2Ωe is lower on the nearside than on the far side.) The plot at right gives a plan view of the experiments as viewed from the Homer site.

[29] Note next, however, that echoes from the most distant ranges in Figure 10 weakened when the pump frequency passed near the second electron gyroharmonic frequency. Figure 10 (bottom) shows the average signal-to-noise ratio for echoes at apparent ranges between 130 and 140 km. Vertical lines drawn through both the top and bottom frames of Figure 10 indicate times when the pump frequency was precisely 3.025 MHz, which is f = 2Ωe calculated for the far side of the modified ionospheric volume at an altitude of 100 km, according to the IGRF. Valleys in the backscatter power centered on this frequency are evident. (What appear to be peaks in the power at frequencies above f = 2Ωe merely reflect the fact that more echoes fall into the 130–140 km zone as pump frequency, target altitude, and target range increase together.) The broad null surrounding f = 2Ωe is tens of kHz wide and is asymmetric, exhibiting a steeper shoulder on the high-frequency side than the low-frequency side. Note also that the reduction in echo power near the second electron gyroharmonic frequency is only evident in the peripheral ranges and not in the center of the modified volume.

[30] Figure 11 shows comparable data taken on 5 August 2009. An expanded time scale is used this time for more detail. In these data, the most significant variation in echo intensity is seen in the shortest range gates corresponding to the nearside of the modified volume. Here, f = 2Ωe is 3.015 MHz at 100 km altitude according to IGRF. Vertical lines in Figure 11 indicate times when the pump frequency matched this frequency. Figure 11 (bottom) shows the signal-to-noise ratio in the apparent range bins between 85–100 km. Echo suppression precisely at the second electron gyroharmonic frequency is again evident in these range bins, where irregularities are driven just marginally above threshold. The suppression band extends both below and above 2Ωe, albeit asymmetrically, and a small overshoot above 2Ωe is suggested.

3. Analysis

[31] The pump electric field threshold for onset should be a signature for the instability responsible for producing FAIs in ionospheric modification experiments. We estimate the threshold to be as little as 170 mV/m for E region FAIs at 99 km altitude. This is roughly half the value estimated by Nossa et al. [2009] using the same apparatus and under similar ionospheric conditions. The main shortcoming of the previous experiments was that the heater power was varied rapidly and continuously. This procedure effectively conflated two issues: the threshold for instability excitation and the latency period for producing irregularities intense enough to be visible to the radar. By varying the power in gradual steps, we were able to more accurately isolate and bracket the threshold electric field. The 10 s dwells employed in these experiments may not fully have resolved the latency issue, however, as some of the weakest echoes observed by the Homer radar on the periphery of the modified region sometimes take more than 10 s to appear [Nossa et al., 2009]. Consequently, our estimate of the threshold electric field is likely still an overestimate.

[32] While the theoretical focus has been on F region FAIs, the role of ions (which merely provide a neutralizing background) is limited in either case, and so the theories described in the introduction are readily adaptable. The theory developed by Dysthe et al. [1983] includes a detailed treatment of magnetoionic effects and so is particularly applicable to the E region problem. It includes the combined effects of pump mode and upper hybrid wave electric fields on differential heating along a field line, mediated by the full conductivity tensor, and balances heating against cooling by electron-neutral collisions and transport via parallel and perpendicular diffusion and conduction. Limits for weakly and strongly ionized gasses are considered, the former being relevant for the E region. The predicted threshold electric field depends most strongly on the parallel electron thermal conductivity, the electron collisional cooling rate, the electron mean free path, the magnetic declination, the Y ≡ Ωe/ω parameter, and the vertical plasma density scale length.

[33] We adapt the theory for the E region with two modifications. The first is to allow for an interaction height range which is thick compared to ripples in the Airy pattern. The thickness of the interaction region, measured as a ratio of the vertical plasma density scale length L, is set by the imaginary part of the longitudinal projection of the dielectric tensor for the upper hybrid wave, δ = Z(1 + Y2)/(1 − Y2). The differential heating rate can be shown consequently to be proportional to exp(−2kLδ), where k is the pump wave number. Dysthe et al. [1983] took this factor to be unity. For our experiments, taking L ∼ 5 km, the factor is about 0.067. The effect of this rather low heating efficiency factor is to increase the threshold electric field for instability onset by about a factor of 4.

[34] The second modification is a provision for cooling via inelastic collisions between electrons and neutrals. We replace the electron cooling term employed by Dysthe et al. [1983], which is characterized by the dimensionless coefficient δT (m/M), by the expression δe = 4.8 × 10−3 (185/Te)3/2 (Te here in Kelvin units), which has been adapted from Gurevich [1978]. This expression is expected to be valid at low electron temperatures and is appropriate only for threshold conditions. It has been used successfully to predict the effective ratio of specific heats for the electrons in the context of Farley Buneman waves in the electrojet [Hysell et al., 2007].

[35] Taking T = 207 K and incorporating the aforementioned modifications and assumed model plasma density and collision frequency profiles, the Dysthe et al. [1983] theory predicts a threshold electric field of 180 mV/m for our experimental conditions. This agrees rather closely with the experimental results, although the significance of the agreement should not be overstated. The threshold prediction rests upon a number of approximately specified parameters, the electron density and collision frequency profiles near the upper hybrid resonance height and the shape of the standing wave pattern chief among them.

[36] That the threshold electric field was reduced by a factor of 2 or more for a time after heating was discontinued is evidence of remnant striations, wave trapping, and resonance instability. On the basis of Figure 9, we can argue that the lifetime of the dominant striations in that experiment was between 10 and 100 s. Given a transverse ambipolar diffusion coefficient of 8.4 m2/s, the length scale of those striations must therefore have been between 10 and 30 m.

[37] Coherent echo suppression at pump frequencies close to the second electron gyroharmonic frequency is further evidence of the role of upper hybrid waves in artificial FAI generation. Suppression occurs over a band of pump frequencies tens of kHz wide. The band is asymmetric and wider below 2Ωe than above it. Figures 10 and 11 also suggest enhancements in echo intensity at frequencies just above 2Ωe, although this is unclear without some specification of the baseline echo dependence on frequency.

[38] Echo suppression occurs only at the periphery of the modified region, and pumping at the second electron gyroharmonic frequency has no observable effect near the center of the region where the FAIs are strongest. The horizontal extent of the modified region is known to be expanded significantly by the IRI side lobes, which peak at about 13.5 dB below the main lobe. In view of the threshold electric field measurements, we know that the side lobe emissions are just above threshold for exciting FAIs. Figures 10 and 11 suggest that the main effect of gyroharmonic pumping is to extinguish the irregularities in the IRI side lobes and at the extreme periphery of the main lobe.

[39] The frequency bands where echoes are suppressed in Figures 10 and 11 are broadened by the heterogeneity of the magnetic induction across the modified volume, which varies by about 10 kHz between extreme observing azimuths. We can compensate for this effect by incorporating imaging techniques in the coherent scatter radar data analysis. Figure 12 shows the backscatter signal-to-noise ratio for echoes sorted against true range and time. Imaging has been used to isolate the echoes coming from one bearing, offset slightly from the center of the modified volume as indicated in Figure 12 (top right). This bearing passes to the west of the ionospheric volume illuminated by HAARP's main beam and to the east of a side lobe. In this way, the data reflect echoes from parts of the ionosphere heated marginally above threshold. The angular width of the sector probed here is 0.83°. Across that width, variations in the geomagnetic field can be neglected.

[40] Figure 12 shows precisely how irregularities generated by heating just above the TOTSI threshold are suppressed by heating near 2Ωe. The width of the suppressed zone is about 15 (30) kHz above (below) 2Ωe. There is now a clearer indication of echo enhancement at frequencies just above 2Ωe, although the significance of this trend is still difficult to assess for lack of a specification of the baseline trend. Similar analysis for the radar bearing passing through the center of the main modified region shows no gyroharmonic suppression except in the nearest and farthest radar ranges.

[41] Mjølhus [1993] explained FAI suppression at gyroharmonic frequencies in terms of the topology of the dispersion relation for upper hybrid waves and the requirement for a separation between the lower and upper cutoff frequencies for wave trapping to occur. Suppression is predicted at frequencies just below gyroharmonic frequencies under this mechanism. The same mechanism should prohibit wave trapping at pump frequencies below 2Ωe entirely. Hysell and Nossa [2009] argued that wave trapping below the second gyroharmonic frequency can occur if finite parallel wave numbers are allowed for the upper hybrid waves, since finite kì has the effect of introducing a lower cutoff frequency below 2Ωe. The same principle should also permit wave trapping near gyroharmonic frequencies. Because of this, because FAI suppression is observed both below and above gyroharmonic frequencies, and because suppression is only observed for irregularities driven marginally above threshold where the resonance instability is not in clear evidence, the wave trapping argument cannot account for the echo suppression observed in our experiments.

[42] Cyclotron damping also fails to offer an explanation. The condition for significant cyclotron damping is that ∣ωnΩ∣ and kìvt, where vt is the electron thermal velocity. Cyclotron damping is negligible compared to collisional damping in the E region for offset frequencies Δω = ∣ωnΩ∣ greater than a few times kìvt. Whether we associate kì with the pump mode wave number or the finite altitude span of the interaction region, estimates greater than about 2π/100 m−1 are difficult to justify here. Consequently, the bandwidth for significant cyclotron damping about gyroharmonic frequencies in E region ionospheric modification experiments is predicted to be of the order of a kilohertz, 1–2 orders of magnitudes narrower than the bandwidth observed. (Note, however, that cyclotron damping could well be more significant in the F region, where the interaction region is shallower so that kì could be greater. Also, cyclotron damping does not have to compete with significant collisional damping in the F region.)

[43] We therefore examine the mechanism proposed by Rao and Kaup [1990] whereby upper hybrid waves are damped near gyroharmonic frequencies by mode conversion into nonpropagating electron Bernstein waves. Rao and Kaup [1990] discounted the viability of this mechanism near the second electron gyroharmonic frequency, but we can obtain comparable results for the n = 2 and n ≥ 3 gyroresonances by including the effects of finite parallel wave numbers, which introduce dispersion in the long-wavelength limit.

[44] Hysell and Nossa [2009] derived the following dispersion relation which includes upper hybrid and electron Bernstein waves [see also Grach, 1979]:

equation image

where k is the transverse wave number, ρ is the electron gyroradius and χ2 = k2ρ2 is considered to be a small quantity, In is the modified Bessel function of the first kind, and where electron-neutral collisions have been neglected for simplicity and to follow the form of the original Rao and Kaup [1990] work. For small arguments, the leading behavior of In is given by In(z) ≈ (z/2)n/n!. Following the form of Rao and Kaup [1990], we break out the n = 1 term from the sum (but not the n = 2) and rewrite the dispersion relation in the limit of ω2ωuh2ωeb2, with ωuh2 ≡ (k2/k2)ωp2 + Ω2 and ωeb2m2Ω2 for the mth gyroresonance, with m ≥ 2:

equation image

or equivalently:

equation image

Here we regard ωuh and ωeb as slowly varying functions of position and perpendicular wave number. Equation (1) makes it clear how upper hybrid and electron Bernstein waves are coupled by thermal effects, which stronger coupling implied for lower m. For efficient coupling, the wave frequencies must match somewhere in xk space, in the mode conversion region. Matching is facilitated by inhomogeneity in the plasma and by dispersion. In (1) and (2), dispersion is incorporated into ωuh through the kì term, and inhomogeneity into ωeb through inhomogeneity in the background magnetic field.

[45] The relative amplitude of the upper hybrid wave on the incoming and outgoing side of the conversion region can be characterized by a transmission coefficient which describes the coupling efficiency across the region [see Rao and Kaup, 1990, and references therein]

equation image

where LB is the spatial scale length of variations in the magnetic field and where, for this problem, μ can be shown to be

equation image

which has been derived with the assumption k2k2. The precise relationship between k and kì is given by enforcing ωuh = ωeb. Evaluating mu for the m = 2 gyroresonance with λ = 5 m and k/kì = 20 gives μ ∼ 3.5 × 10−2 m−1. This is comparable to the value estimated by Rao and Kaup [1990] for F region heating experiments involving the m = 3 gyroresonance. For any reasonable estimate of the spatial length scale of inhomogeneity in the magnetic field, this implies a transmission coefficient that is essentially zero, or equivalently, an absorption coefficient of unity. Mode conversion from upper hybrid to electron Bernstein waves should therefore proceed efficiently at the m = 2 gyroresonance.

[46] We can estimate the bandwidth of the effect approximately from equation (2) by equating the right side with the mean squared frequency offset 〈∣Δω2〉. For our experimental conditions, this gives 2ΔfRMS ∼ 16 kHz. This is comparable to if about a factor of 2 less than the observed m = 2 echo suppression bandwidth.

4. Conclusions

[47] Experiments at HAARP have shown that E region FAIs can be generated with peak pump mode electric field intensities of about 170 mV/m and maintained with much smaller intensities. This figure is consistent with estimates based on the fluid-theory formulation given by Dysthe et al. [1983] if the finite interaction region depth and inelastic electron collisions are taken into consideration. Their prediction depends mainly on the electron cooling rate, the parallel thermal conductivity, the electron mean free path, and the vertical density gradient scale length at the upper hybrid interaction height. Other transport coefficients are predicted to have only minor effects, but this may require further investigation in the context of E region FAIs.

[48] The experiments have also produced evidence of striation formation, preconditioning, and resonance instability in the modified ionospheric volume driven with pump mode intensities well above threshold. The dominant striation transverse scale length has been roughly estimated to be 10–30 m. It should be possible to narrow this range with more targeted ground- and space-based experiments in the future.

[49] Our experiments have shown that FAIs can be suppressed at the double resonance, where the pump frequency, upper hybrid frequency, and second electron gyroharmonic frequency nearly match. Suppression is only evident for irregularities driven marginally above threshold, where the resonance instability is not in evidence. The suppression is asymmetric in frequency, with an overall bandwidth of 40–50 kHz. A slight echo enhancement seems to occur at the top of this band, although the background trend is unclear.

[50] The suppression cannot be explained in terms of cyclotron damping or wave trapping effects near electron gyroharmonic frequencies but may be related to mode conversion of upper hybrid waves into nonpropagating electron Bernstein waves. The theory is provisional, and the precise damping mechanism and damping rate remain to be estimated. In any event, echo suppression at the second electron gyroharmonic frequency appears to be a minor effect compared to what is observed at the n ≥ 3 harmonics.

Acknowledgments

[51] The authors are grateful for help received from the NOAA Kasitsna Bay Laboratory, its director Kris Holderied, lab manager Mike Geagel, and lab director Connie Geagel. This project was supported by DARPA through contract HR0011-09-C-0099. Additional support came from the High-Frequency Active Auroral Research Program (HAARP) and from the Office of Naval Research and the Air Force Research Laboratory under grant N00014-07-1-1079 to Cornell.