Excitation threshold and gyroharmonic suppressionof artificial E region field‐aligned plasma density irregularities

D. L. Hysell,1 E. Nossa,1 and M. McCarrick2

Received 14 January 2010; revised 26 May 2010; accepted 8 July 2010; published 12 November 2010.

[1] Ionospheric modification experiments have been carried out using the HAARP facilityalong with a 30 MHz coherent scatter radar imager in Alaska to examine propertiesof artificial E region field‐aligned plasma density irregularities (FAIs). In one set ofexperiments, the RF emission power was varied gradually in order to determine thethreshold electric field for irregularity generation. A threshold O mode peak electric fieldamplitude of 170–195 mV/m at an altitude of 99 km and a heating frequency of 2.7 MHzwas identified based on the full‐wave formalism of Thidé and Lundborg (1986). Inanother, the pump frequency was varied gradually to investigate the suppression of theFAIs at frequencies near the second electron gyroharmonic frequency (2We). Coherentechoes were found to be suppressed for pump frequencies in an asymmetric band40–50 kHz wide around 2We but only for irregularities driven marginally above threshold.Theoretical context for these results is provided.

Citation: Hysell, D. L., E. Nossa, and M. McCarrick (2010), Excitation threshold and gyroharmonic suppression ofartificial E region field‐aligned plasma density irregularities, Radio Sci., 45, RS6003, doi:10.1029/2010RS004360.

1. Introduction[2] Visible to coherent scatter radars, E and F region

field‐aligned plasma density irregularities (FAIs) provideincisive diagnostics of ionospheric modification experi-ments. A number of reviews have been made of theexperimental database and of what can be inferred aboutthe underlying plasma instabilities at work [see Robinson,1989; Frolov et al., 1997; Gurevich, 2007]. That irregu-larities are produced near the upper hybrid resonancelevel in the plasma rather than at the critical height pointsto two instability processes. These are the closely relatedthermal parametric (TPI) and thermal oscillating two‐stream (TOTSI) instabilities [Grach et al., 1978; Das andFejer, 1979; Fejer, 1979; Kuo and Lee, 1982; Dystheet al., 1983; Mjølhus, 1990], and the resonance instability[Vas’kov and Gurevich, 1977; Inhester et al., 1981; Grachet al., 1981; Dysthe et al., 1982; Lee and Kuo, 1983;Mjølhus, 1993]. In the TPI, the pump electromagnetic waveis resonantly converted in the presence of field‐alignedplasma density irregularities into an upper hybrid HF

sideband wave which heats the plasma collisionally andintensify the irregularities through differential heating. TwoHF sidebands (stokes and antistokes) are present in theTOTSI.When the amplitude of the irregularities (striations)becomes large, upper hybridwavesmaybe trapped, causingadditional mode conversion, heating, and trapping in unionwith the generation of thermal cavitons. This describes theresonance instability, which is characterized by explosivewave growth. Coherent scatter is telltale of plasma striationscreated by these processes [e.g., Stubbe, 1996].[3] The complexity of the artificial FAI problem, which

involves inhomogeneous, anisotropic, dissipative, hotplasmas supporting coupled electromagnetic and electro-static waves, imposes approximations and assumptions onthe theories developed for it, which differ in their details.For example,Gustavsson et al. [2009] recently pointed outhow different theoretical predictions for the TOTSIthreshold for excitation scale differently with temperatureand collision frequency. Precise measurements are neededfor refining TOTSI and resonance instability theory.[4] The central role of upper hybrid waves in FAI

generation implies that the process could be interrupted atpump frequencies close to electron gyroharmonic fre-quencies, i.e., where w ∼ wuh ∼ nW. As pointed out byLeyser et al. [1990], upper hybrid waves with finiteparallel wave numbers experience cyclotron damping atgyroharmonic frequencies. Furthermore, Mjølhus [1993]have argued that upper hybrid wave trapping should be

1Earth and Atmospheric Sciences, Cornell University, Ithaca,New York, USA.

2Marsh Creek, LLC, Gakona, Alaska, USA.

Copyright 2010 by the American Geophysical Union.0048‐6604/10/2010RS004360

RADIO SCIENCE, VOL. 45, RS6003, doi:10.1029/2010RS004360, 2010

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suppressed at frequencies at and just below gyroharmonicfrequencies with n ≥ 3 on the basis of a geometric opticsargument applied to the shape of the wave dispersioncurves in this limit. The theory has been expanded byHuang and Kuo [1994], Gurevich et al. [1996], andGrach et al. [2004]. Istomin and Leyser [2003] furtherargued that striations should be intensified at frequenciesjust above gyroharmonic frequencies. Finally, Rao andKaup [1990] have shown that upper hybrid waves atn ≥ 3 gyroharmonic frequencies can be damped throughcoupling to electron Bernstein waves. Experiments inthe F region using gyroharmonic pump frequencies withn ≥ 3 have indeed shown reduced anomalous absorp-tion [Stocker et al., 1993; Stubbe et al., 1994], the per-sistence of Langmuir turbulence and associated effects[Honary et al., 1999], airglow suppression and over-shoot [Kosch et al., 2002; Gustavsson et al., 2002; Koschet al., 2005], modified stimulated electromagnetic emis-sion (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] atthese frequencies.[5] Ionospheric modifications at the second electron

gyroharmonic frequency differ fundamentally from then ≥ 3 cases (see, for example, Grach [1979] for basictheory). Mjølhus [1993] were the first to point out thatwave trapping might be prohibited entirely at pump fre-quencies below the second electron gyroharmonic fre-quency, although the threshold for excitation of thermalparametric instability may also be reduced in the vicinityof the second electron gyroharmonic frequency [Grach,1979]. Experimentally, coherent scatter is observed atpump frequencies near 2We, and enhancements havebeen reported at frequencies just above 2We [Fialer,1974; Minkoff et al., 1974; Kosch et al., 2007]. Airglowintensifications are also seen at pump frequencies slightlyabove 2We [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 spectraare suppressed when pumping near 2We, as they are athigher gyroharmonic frequencies [Djuth et al., 2005].[6] The availability of a VHF coherent scatter radar

situated near the HAARP ionospheric modificationfacility in Alaska affords an opportunity to test andexpand the theoretical framework surrounding heater‐induced FAIs as they pertain to E region modification.Since the E region follows a very regular, predictablediurnal pattern during geomagnetically quiet periods, andsince ionospheric refraction is unnecessary for satisfyingthe condition for field‐aligned backscatter from E regiontargets at high latitudes, E region FAI experiments can beaccurately quantified at HAARP. The closed feedbackdesign of HAARP moreover allows precise control of theheater power, gain, and frequency, making laboratory‐grade experiments on E region FAIs possible.

[7] Heater‐induced E region FAIs have been observedin experiments incorporating coherent scatter radars byFialer [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 regionFAIs excited at pump frequencies slightly above andbelow the second electron gyroharmonic frequency, andHysell and Nossa [2009] accounted for this possibilitytheoretically by including the effects of finite parallelwave numbers in the upper hybrid waves involved,which can restore the lower cutoff frequency in the dis-persion relation of the waves.[8] Below, we describe additional experiments designed

to test two specific theoretical predictions for FAI pro-duction through ionospheric modification. One of these isthe threshold condition for TOTSI onset, and the other isthe effect of heating at frequencies near the second elec-tron gyroharmonic frequency. Evidence for irregularitypreconditioning, which is telltale of wave trapping andresonance instability, will also be presented. Note that theE region critical frequency during undisturbed periods istoo low to test FAI generation with pump frequencies atthe 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 generateartificial E region field‐aligned density irregularities(FAIs) with its planar array of 15 × 12 low‐band dipoleelements. Experiments were performed using O modeemissions, vertical pointing, and finely graduated powerlevels and frequencies (see below). At the same time, theionosphere over HAARP was monitored with a coherentscatter radar interferometer operating at 30 MHz andlocated at the NOAA Kasitsna Bay Laboratory (KBL)(59.47N, 151.55W) near Homer, Alaska. This radar hasits locus of perpendicularity at precisely 100 km altitudeover HAARP, making it suitable for observing artificialE region FAIs there. The imaging radar is capable ofresolving two‐dimensional fine structure in backscatterfrom the common volume with kilometric resolution. Itemploys a transmitter with a peak power of 12 kW anddigital receivers which sample six spaced antennagroups.[10] For our experiments, we utilized a 13 baud Barker

coded pulse with a 10 ms baud length. The interpulseperiod for the radar experiments was 2.46 ms or 370 km.Doppler velocities as large as ∼1000 m/s can be mea-sured without frequency aliasing, which is necessary forobserving natural auroral irregularities, although theDoppler shifts encountered during ionospheric modifi-cation experiments are typically an order of magnitude

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smaller than this. Additional specifications for the radarand its operating mode were given by Nossa et al.[2009]. The HAARP ionosonde and riometer were alsooperating during the study.[11] Heating experiments took place at the HAARP

facility from 5 to 14 August 2009, around midday whenthe E region critical frequency was the highest. Theexperiments were performed during geomagneticallyquiet periods. Figure 1 shows the E region critical fre-quency (FoE) measured by the HAARP Digisondethroughout the experiments and exemplifies the regulardiurnal behavior of the background E region densityunder photochemical control. Apparent irregularities inthe measurements around midday are mainly an artifactassociated with the operation of the HF facility itself. Thedaily peak FoE was about 3.2 MHz, and the F10.7 solarflux index was nearly constant at 69. All of the experi-ments involved O mode emission and vertical pointing.[12] Figure 2 shows an estimate of the midday plasma

number density profile over the HAARP site for theexperimental period in question based on the Interna-tional Reference Ionosphere (IRI) 2007 model [Bilitzaand Reinisch, 2007]. For the purposes of the calcula-tions to follow, the model profile can be represented bythe sum of three Chapman functions centered in the D, E,and F1 regions, respectively. This representation isdepicted by the dashed line in Figure 2. The absorptionat the HAARP riometer frequency can be predicted onthe basis of this model and used, along with FoE predic-tions, as a rudimentary means of validation. The result,−0.15 dB, is consistent with the absorption typicallymeasured at midday during the campaign. According tothis model profile and the IGRF reference magneticfield model, the upper hybrid interaction height for ourexperiments at 2.7 MHz was 99 km.

2.1. Pump Threshold for Instability

[13] Ionospheric modification experiments geared atassessing the threshold ionospheric electric field forinstability were performed at a frequency of 2.7 MHz, thelowest possible at HAARP. At this frequency and for

Figure 1. Measured E region critical frequency versus universal time for the experimental periodin question. Note that LT = UT + 9 h.

Figure 2. Ionospheric plasma density profile predictedby the IRI model (solid curve). Approximation to themodel composed of the sum of three Chapman functions(dashed curve).

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vertical pointing, the HAARP IRI has a directivity of20.9 dBi. (This estimate assumes a uniform linear arrayof short dipoles over an infinite ground plane and is amore 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 thisfrequency, the maximum effective radiated power wouldbe 390 MW. The peak incident electric field at a refer-ence height of 70 km, below the ionosphere, would be2.2 V/m at this power level.[14] We have used the full‐wave formalism of Thidé

and Lundborg [1986] to estimate the pump electricfield in the E region ionosphere, taking into account theeffects of Airy swelling, the finite magnetic dip angle,background absorption, and the dependence on propa-gation distance. The calculations incorporates the afore-mentioned plasma density profile and assumes an electronneutral collision frequency of 4 × 104 s−1 at 99 km altitude,decreasing in altitude with a 6 km scale height. Theresults are depicted in Figure 3. According to the figure,the horizontal pump electric field amplitude at an altitudeclose to 99 km, the nominal upper hybrid interactionheight, would have been between 0.44 times the fieldamplitude at 70 km altitude or about 970 mV/m,assuming full‐power emission and neglecting anomalousabsorption.[15] Notice that Airy swelling is nearly absent in the

horizontal field components. This is a consequence ofnormal absorption, which attenuates the reflected wave tothe point that a standing‐wave pattern is suppressed back

at the upper hybrid resonance height. There, the reflectedwave amplitude is about one fifth the amplitude of theupgoing wave. This prediction has important implicationfor E region FAI generation. The plasma interactionregion occupies a narrow band of altitudes surroundingthe upper hybrid resonance height no more than a fewtens of meters deep (see section 3). About this height,wave heating is antisymmetric, such that plasma deple-tions above (below) it experience a surplus (deficit) ofheating. The net differential heating of the field‐aligneddepletion with respect to background would be zero if thesymmetry were not broken [e.g., Das and Fejer, 1979].While a number of factors contribute to symmetrybreaking [Dysthe et al., 1983], the most important is thestanding wave pattern. We can expect FAI generation tobe the most efficient when the upper hybrid interactionheight coincides with a node in the pattern and when thepattern itself is distinct. The finite width of the interactionregion, which increases with the electron‐neutral colli-sion frequency, limits the efficiency further and isanother factor potentially inhibiting FAI generation in theE region.[16] Heating experiments were performed at reduced

power in an attempt to identify the threshold for insta-bility onset. Pump power was varied discretely over aseries of steps lasting 10 s each. This figure is long com-pared to the neutral‐electron collision time, (nen m/M)−1,which is a characteristic time scale for instability andabout 1 s in the E region. The power steps followed aquadratic progression so that the pump field increasedand decreased linearly. Heater power increased from zero

Figure 3. Electric field amplitude for a pump wave at 2.7 MHz propagating through the iono-sphere given by Figure 2. A magnetic declination of 14° is assumed. The reflection height inthis case is 99.86 km. The perpendicular east (magnetic), perpendicular north (magnetic), andparallel components of the electric field are depicted in blue, red, and green, respectively. Amplitudesas a fraction of the amplitude at a 70 km reference altitude are represented.

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for 2 min to a maximum and then decreased for 2 min,with a 1 min emission gap completing each 5 min heatingcycle.[17] Figure 4 shows coherent echoes received by the

30 MHz radar in Homer from E region field‐alignedplasma density irregularities in the modified volumeover HAARP. Similar experiments were run on 6 and7 August 2009, producing comparable results. We focushere and in subsequent examples on events when some of

the strongest echoes were received for a given incidentheater power level (see below).[18] Figure 4 conveys information about the signal‐to‐

noise ratio, Doppler shift, and spectral width of thecoherent echoes detected at Homer. We concentrate hereon 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, andrepeating every 5 min. The maximum pump power ineach cycle was 18% of IRI maximum, and the minimum

Figure 4. Range‐time Doppler intensity (RTDI) plot of backscatter from artificial E region FAIsover HAARP observed on 7 August 2009. Here the brightness, hue, and saturation of the pixelsdenote echo signal‐to‐noise ratio (SNR), Doppler shift, and spectral width, according to the legendshown. Note that the echoes from heater‐induced FAIs are range aliased and that their true range isgreater than their apparent range by 370 km. The average signal‐to‐noise ratio for apparent rangesbetween 80 and 130 km is plotted beneath the RTDI plot. Variations in the line plot reflect bothchanges in the size of the modified volume and in the scattering intensity of regions withinthe volume. Echoes from meteor trails are also visible. The incoherent integration time is about3 s. Figure 4 depicts 12 distinct cycles lasting 5 min each.

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was just 2.25%. In view of the number of independentpower estimates that enter into the calculation of the curveat the bottom of Figure 4, which reflect averages over time,range, spaced antennas, andDoppler frequencies, registeredsignal‐to‐noise ratios as small as −15 dB are statisticallysignificant (have RMS relative errors less than 50%),although care must be taken to distinguish echoes due tometeors and other clutter. Close inspection of the figureshows that echoes above this threshold appear between 30and 55 s into each heating cycle.[19] Slow, secular variations in the peak backscatter

power evident in Figure 4 suggest that backgroundconditions were changing such as to vary the conditionsfor instability onset. The threshold condition for insta-bility is influenced by the plasma density scale height andelectron mean free path at the upper hybrid interaction

height, and both of these may undergo natural andheater‐induced variations. More important, the thresholdcondition is strongly influenced by the interaction heightrelative to the RF standing wave pattern. Our strategy isto focus on the strongest echo events with the lowestelectric field thresholds, reasoning that such eventsoccurred under optimal FAI generation conditions. Sub-sequent analysis will then assume those conditions.[20] Figure 6 highlights one of the strongest echo

events observed in the campaign when instability onsetwas achieved earliest. In this case, instability was detectedat 30 s, precisely at the moment the pump electric fieldtransitioned from 17.5% to 20% of its predicted 970mV/mmaximum. This finding brackets the threshold pumpelectric field for instability to 170–195 mV/m.

Figure 6. Range‐time Doppler intensity (RTDI) plot of backscatter from artificial E region FAIsover HAARP observed on 7 August 2009, during a relatively strong echo event. Heating com-menced 10 s after 2155 UT, peaked at 2157 UT, and ceased at 2159 UT.

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2.2. Preconditioning

[21] The heating profiles in Figure 4 and Figure 6 areasymmetric in time in the sense that the echoes observedon the power downramp are stronger than those on theupramp given equivalent pump power levels. Coherentbackscatter remained detectable at the end of the heater‐on intervals, demonstrating that irregularities can be sus-tained at pump power levels well below the onset threshold.Nossa et al. [2009] reported on similar observations andinterpreted the apparent hysteresis as evidence of striationformation in the modified volume and of resonanceinstability. Similar hysteresis phenomena have beenreported for F region artificial FAIs generated by theEISCAT and SPEAR facilities, respectively [Wrightet al., 2006, 2009].

[22] In the August experiments, we pursued this evi-dence further using a modified version of the experimentdescribed above. This time, pairs of power ramps, whichindividually followed the schedule shown in Figure 7,were separated by a 2 min heating gap. In this way, thesecond ramp in each pair followed a period when irreg-ularities were already present whereas the first ramp didnot. Note that the power steps were somewhat coarser inthis experiment than in the previous one, and that themaximum heater power was greater.[23] Figure 8 shows results from experiments on

14 August 2009. The coherent echoes are clearly strongerthan those observed on 6 and 7 August from Homer.These and other experiments indicate a marginal increasein echo intensity with increased heater power over the

Figure 8. Range‐time Doppler intensity (RTDI) plot of backscatter from artificial E region FAIsover HAARP observed on 14 August 2009. The figure depicts eight distinct cycles lasting 10 mineach.

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entire HAARP radiated power range [see also Nossaet al., 2009]. A gradual secular variation in echo inten-sity is also evident in these data. The shortest time to echoonset in the heating cycles was just over 30 s, here and inobservations made on 13 August, which is consistent withthe threshold electric field for onset established above.[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 scatterbetween the power upramps and downramps, but alsopreconditioning, signified by differences between thefirst and second event. Note how readily irregularitiescould be generated in the second event. Close examina-tion of the figure shows that coherent scatter onset beganjust 15 s into the second heating cycle, 5 s after heatingcommenced, at an electric field strength of 10% of

maximum or about 100 mV/m. Irregularities moreoveremerged over a 30 km wide span of ranges nearlysimultaneously. This phenomenon cannot be due toelevated temperatures within the modified volume, sincethe threshold for irregularity onset increases with tem-perature. We interpret such preconditioning behavior asevidence of plasma striations which permit wave trappingand suppress the threshold electric field for instabilityconsiderably. The striations evidently survived 10 swithout heating but not 2 min.

2.3. Gyroharmonic Suppression

[25] Measuring the threshold electric field for onset isone way of quantifying the theory of the thermal oscillatingtwo‐stream instability, and testing for preconditioning is

Figure 9. Range‐time Doppler intensity (RTDI) plot of backscatter from artificial E region FAIsover HAARP observed on 14 August 2009. The earlier heating event in the pair was preceded by a2 min heating gap. The latter event followed the former after a 10 s heating gap.

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a way of identifying resonance instability. Upper hybridwaves play a central role in both instabilities, andexamining FAI behavior for pump wave frequenciesclose to harmonics of the electron gyrofrequency is athird way to validate and expand instability theories andmodels. The double resonance condition for the secondelectron gyroharmonic can be met routinely in E regionionospheric modification experiments in summer monthsaround midday.[26] Experiments were performed where the pump

mode frequency was varied from 2.9 MHz to 3.1 MHzand back to 2.9 MHz over a 4 min period, with a 1 mingap between heating cycles. The frequency span included

2We which is close to 3 MHz in the E region overHAARP. The frequency was varied over 500 discretesteps separated by 400 Hz and lasting 240 ms each.Heating occurred using vertical pointing and full‐poweremission.[27] Figure 10 shows the Homer radar results for

experiments conducted on 8 August 2009. The figuredemonstrates the sensitivity of echo intensities, rangeextents, and Doppler shifts to pump frequency. As thefrequency increases, the interaction height and the radarrange to the interaction region also increase. Steep neutralwind shears are known to be prevalent in the lowerthermosphere [see, e.g., Larsen et al., 1989]. Variations

Figure 10. Range‐time Doppler intensity (RTDI) plot of backscatter from artificial E region FAIsover HAARP observed on 8 August 2009. Each heating cycle depicted represents a pump modefrequency sweep from 2.9 to 3.1 MHz and back to 2.9 MHz, with sweeping occurring at a uniformrate. The plotted points in the bottom plot reflect the average signal‐to‐noise ratio in apparentranges between 130 and 140 km. Vertical lines indicate times when the pump frequency was twicethe electron gyrofrequency.

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in neutral wind forcing, combined with the rapid changein the ion mobility with altitude, make the Doppler shiftof the coherent echoes strongly dependent on echoheight.[28] It is important to note that the decrease in echo

power at the highest pump frequencies (midway throughFigures 10, 11, and 12 and the figures that follow) is dueto the fact that those frequencies approached or exceededFoE. While this behavior is clearly evident in the 5 and8 August experiments described here and below, it is notcharacteristic of our experiences with data from theHomer radar, which have exhibited strong echoes onother occasions under comparable ionospheric conditions

using pump frequencies as high as 3.26 MHz. Nonethe-less, decreasing echo intensity near the horizontal centerof Figures 10, 11, and 12 and the figures that followshould not be mistaken for gyroharmonic heating effects.[29] Note next, however, that echoes from the most

distant ranges in Figure 10 weakened when the pumpfrequency passed near the second electron gyroharmonicfrequency. Figure 10 (bottom) shows the average signal‐to‐noise ratio for echoes at apparent ranges between130 and 140 km. Vertical lines drawn through both thetop and bottom frames of Figure 10 indicate times whenthe pump frequency was precisely 3.025 MHz, which isf = 2We calculated for the far side of the modified iono-

Figure 11. Range‐time Doppler intensity (RTDI) plot of backscatter from artificial E region FAIsover HAARP observed on 5 August 2009. Each 4 min heating cycle depicted represents a pumpmode frequency sweep from 2.9 to 3.1 MHz and back to 2.9 MHz, with sweeping occurring ata uniform rate. The plotted points in the bottom plot reflect the average signal‐to‐noise ratio inapparent ranges between 80 and 95 km. Vertical lines indicate times when the pump frequencywas twice the electron gyrofrequency.

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spheric volume at an altitude of 100 km, according to theIGRF. Valleys in the backscatter power centered on thisfrequency are evident. (What appear to be peaks in thepower at frequencies above f = 2We merely reflect the factthat more echoes fall into the 130–140 km zone as pumpfrequency, target altitude, and target range increasetogether.) The broad null surrounding f = 2We is tens ofkHz wide and is asymmetric, exhibiting a steepershoulder on the high‐frequency side than the low‐frequency side. Note also that the reduction in echopower near the second electron gyroharmonic frequencyis only evident in the peripheral ranges and not in thecenter of the modified volume.[30] Figure 11 shows comparable data taken on

5 August 2009. An expanded time scale is used this timefor more detail. In these data, the most significant varia-tion in echo intensity is seen in the shortest range gatescorresponding to the nearside of the modified volume.

Here, f = 2We is 3.015 MHz at 100 km altitude accordingto IGRF. Vertical lines in Figure 11 indicate times whenthe pump frequency matched this frequency. Figure 11(bottom) shows the signal‐to‐noise ratio in the apparentrange bins between 85–100 km. Echo suppression pre-cisely at the second electron gyroharmonic frequency isagain evident in these range bins, where irregularities aredriven just marginally above threshold. The suppressionband extends both below and above 2We, albeit asym-metrically, and a small overshoot above 2We is suggested.

3. Analysis[31] The pump electric field threshold for onset should

be a signature for the instability responsible for produc-ing FAIs in ionospheric modification experiments. Weestimate the threshold to be as little as 170 mV/m forE region FAIs at 99 km altitude. This is roughly half the

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 modifiedvolume to the west. The bottom plot shows the SNR averaged over groups of ranges indicatedby the colored lines; dashed vertical lines reflect the second electron gyroharmonic frequency rep-resentative for the cut. (2We is lower on the nearside than on the far side.) The plot at right gives aplan view of the experiments as viewed from the Homer site.

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value estimated by Nossa et al. [2009] using the sameapparatus and under similar ionospheric conditions. Themain shortcoming of the previous experiments was thatthe heater power was varied rapidly and continuously.This procedure effectively conflated two issues: thethreshold for instability excitation and the latency periodfor producing irregularities intense enough to be visibleto the radar. By varying the power in gradual steps, wewere able to more accurately isolate and bracket thethreshold electric field. The 10 s dwells employed inthese experiments may not fully have resolved thelatency issue, however, as some of the weakest echoesobserved by the Homer radar on the periphery of themodified region sometimes take more than 10 s to appear[Nossa et al., 2009]. Consequently, our estimate of thethreshold 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 neutral-izing background) is limited in either case, and so thetheories described in the introduction are readily adapt-able. The theory developed by Dysthe et al. [1983]includes a detailed treatment of magnetoionic effectsand so is particularly applicable to the E region problem.It includes the combined effects of pump mode and upperhybrid wave electric fields on differential heating along afield line, mediated by the full conductivity tensor, andbalances heating against cooling by electron‐neutralcollisions and transport via parallel and perpendiculardiffusion and conduction. Limits for weakly and stronglyionized gasses are considered, the former being relevantfor the E region. The predicted threshold electric fielddepends most strongly on the parallel electron thermalconductivity, the electron collisional cooling rate, theelectron mean free path, the magnetic declination, theY ≡ We/w parameter, and the vertical plasma density scalelength.[33] We adapt the theory for the E region with two

modifications. The first is to allow for an interactionheight range which is thick compared to ripples in theAiry pattern. The thickness of the interaction region,measured as a ratio of the vertical plasma density scalelength L, is set by the imaginary part of the longitudinalprojection of the dielectric tensor for the upper hybridwave, d = Z(1 + Y2)/(1 − Y2). The differential heating ratecan be shown consequently to be proportional to exp(−2kLd), 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 ofthis rather low heating efficiency factor is to increase thethreshold electric field for instability onset by about afactor 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 byDysthe et al. [1983], which is characterized by the

dimensionless coefficient dT (m/M), by the expressionde = 4.8 × 10−3 (185/Te)

3/2 (Te here in Kelvin units),which has been adapted from Gurevich [1978]. Thisexpression is expected to be valid at low electron tem-peratures and is appropriate only for threshold condi-tions. It has been used successfully to predict theeffective ratio of specific heats for the electrons in thecontext of Farley Buneman waves in the electrojet[Hysell et al., 2007].[35] Taking T = 207 K and incorporating the afore-

mentioned modifications and assumed model plasmadensity and collision frequency profiles, the Dysthe et al.[1983] theory predicts a threshold electric field of180 mV/m for our experimental conditions. This agreesrather closely with the experimental results, although thesignificance of the agreement should not be overstated.The threshold prediction rests upon a number of approx-imately specified parameters, the electron density andcollision frequency profiles near the upper hybrid reso-nance height and the shape of the standing wave patternchief among them.[36] That the threshold electric field was reduced by a

factor of 2 or more for a time after heating was dis-continued is evidence of remnant striations, wave trap-ping, and resonance instability. On the basis of Figure 9,we can argue that the lifetime of the dominant striationsin that experiment was between 10 and 100 s. Given atransverse ambipolar diffusion coefficient of 8.4 m2/s, thelength scale of those striations must therefore have beenbetween 10 and 30 m.[37] Coherent echo suppression at pump frequencies

close to the second electron gyroharmonic frequency isfurther evidence of the role of upper hybrid waves inartificial FAI generation. Suppression occurs over a bandof pump frequencies tens of kHz wide. The band isasymmetric and wider below 2We than above it. Figures 10and 11 also suggest enhancements in echo intensity atfrequencies just above 2We, although this is unclearwithout some specification of the baseline echo depen-dence on frequency.[38] Echo suppression occurs only at the periphery of

the modified region, and pumping at the second electrongyroharmonic frequency has no observable effect nearthe center of the region where the FAIs are strongest. Thehorizontal extent of the modified region is known to beexpanded significantly by the IRI side lobes, which peakat about 13.5 dB below the main lobe. In view of thethreshold electric field measurements, we know that theside lobe emissions are just above threshold for excitingFAIs. Figures 10 and 11 suggest that the main effect ofgyroharmonic pumping is to extinguish the irregularitiesin the IRI side lobes and at the extreme periphery of themain lobe.[39] The frequency bands where echoes are suppressed

in Figures 10 and 11 are broadened by the heterogeneity

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of the magnetic induction across the modified volume,which varies by about 10 kHz between extreme observ-ing azimuths. We can compensate for this effect byincorporating imaging techniques in the coherent scatterradar data analysis. Figure 12 shows the backscattersignal‐to‐noise ratio for echoes sorted against true rangeand time. Imaging has been used to isolate the echoescoming from one bearing, offset slightly from the centerof the modified volume as indicated in Figure 12 (topright). This bearing passes to the west of the ionosphericvolume illuminated by HAARP’s main beam and to theeast of a side lobe. In this way, the data reflect echoesfrom parts of the ionosphere heated marginally abovethreshold. The angular width of the sector probed here is0.83°. Across that width, variations in the geomagneticfield can be neglected.[40] Figure 12 shows precisely how irregularities

generated by heating just above the TOTSI threshold aresuppressed by heating near 2We. The width of the sup-pressed zone is about 15 (30) kHz above (below) 2We.There is now a clearer indication of echo enhancement atfrequencies just above 2We, although the significance ofthis trend is still difficult to assess for lack of a specifi-cation of the baseline trend. Similar analysis for the radarbearing passing through the center of the main modifiedregion shows no gyroharmonic suppression except in thenearest and farthest radar ranges.[41] Mjølhus [1993] explained FAI suppression at

gyroharmonic frequencies in terms of the topology of thedispersion relation for upper hybrid waves and therequirement for a separation between the lower and uppercutoff frequencies for wave trapping to occur. Suppres-sion is predicted at frequencies just below gyroharmonicfrequencies under this mechanism. The same mechanismshould prohibit wave trapping at pump frequencies below2We entirely. Hysell and Nossa [2009] argued that wavetrapping below the second gyroharmonic frequency canoccur if finite parallel wave numbers are allowed for theupper hybrid waves, since finite kì has the effect ofintroducing a lower cutoff frequency below 2We. Thesame principle should also permit wave trapping neargyroharmonic frequencies. Because of this, because FAIsuppression is observed both below and above gyro-harmonic frequencies, and because suppression is onlyobserved for irregularities driven marginally abovethreshold where the resonance instability is not in clearevidence, the wave trapping argument cannot account forthe echo suppression observed in our experiments.[42] Cyclotron damping also fails to offer an explana-

tion. The condition for significant cyclotron damping isthat ∣w − nW∣ and kìvt, where vt is the electron thermalvelocity. Cyclotron damping is negligible compared tocollisional damping in the E region for offset frequenciesDw = ∣w − nW∣ greater than a few times kìvt. Whether weassociate kì with the pump mode wave number or the

finite altitude span of the interaction region, estimatesgreater than about 2p/100 m−1 are difficult to justify here.Consequently, the bandwidth for significant cyclotrondamping about gyroharmonic frequencies in E regionionospheric modification experiments is predicted to beof the order of a kilohertz, 1–2 orders of magnitudesnarrower than the bandwidth observed. (Note, however,that cyclotron damping could well be more significant inthe F region, where the interaction region is shallower sothat kì could be greater. Also, cyclotron damping does nothave to compete with significant collisional damping inthe F region.)[43] We therefore examine the mechanism proposed by

Rao and Kaup [1990] whereby upper hybrid waves aredamped near gyroharmonic frequencies by mode con-version into nonpropagating electron Bernstein waves.Rao and Kaup [1990] discounted the viability of thismechanism near the second electron gyroharmonic fre-quency, but we can obtain comparable results for then = 2 and n ≥ 3 gyroresonances by including the effects offinite parallel wave numbers, which introduce dispersionin the long‐wavelength limit.[44] Hysell and Nossa [2009] derived the following

dispersion relation which includes upper hybrid andelectron Bernstein waves [see also Grach, 1979]:

0 ¼ 1� 2!2p

k2?k2

e��2

�2

X1

n¼1

n2Inð�2Þ!2 � n2W2 ð1Þ

where k? is the transverse wave number, r is the electrongyroradius and c2 = k?

2 r2 is considered to be a smallquantity, In is the modified Bessel function of the firstkind, and where electron‐neutral collisions have beenneglected for simplicity and to follow the form of theoriginal 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 breakout the n = 1 term from the sum (but not the n = 2) andrewrite the dispersion relation in the limit of w2 ∼ wuh

2 ∼web2 , with wuh

2 ≡ (k?2 /k2)wp

2 +W2 and web2 ≡m2W2 for themth

gyroresonance, with m ≥ 2:

!2 � !2uhðk 2

?; x� �

!2 � !2ebðk 2

?; x� �

¼ m2ðm2 � 1Þ2m�1m!

W2ðk 2?=k

2Þ!2p�

2ðm�1Þ ð2Þ

or equivalently:

!� !uhðk 2?; xÞ

� �!� !ebðk 2

?; x� �

¼ m2 � 1

2mþ1m!ðk 2

?=k2Þ!2

p�2ðm�1Þ : ð3Þ

Here we regard wuh and web as slowly varying functions ofposition and perpendicular wave number. Equation (1)

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makes it clear how upper hybrid and electron Bernsteinwaves are coupled by thermal effects, which strongercoupling implied for lower m. For efficient coupling, thewave frequencies must match somewhere in x − k? space,in the mode conversion region. Matching is facilitated byinhomogeneity in the plasma and by dispersion. In (1) and(2), dispersion is incorporated into wuh through the kìterm, and inhomogeneity into web through inhomogeneityin the background magnetic field.[45] The relative amplitude of the upper hybrid wave

on the incoming and outgoing side of the conversionregion can be characterized by a transmission coefficientwhich describes the coupling efficiency across the region[see Rao and Kaup, 1990, and references therein]

T ¼ exp ��LBð Þwhere LB is the spatial scale length of variations in themagnetic field and where, for this problem, m can beshown to be

� ¼ �ðm2 � 1Þ2mm!

�2ðm�1Þðk=kkÞ2k? ð4Þ

which has been derived with the assumption k?2 � kk

2.The precise relationship between k? and kì is given byenforcing wuh = web. Evaluating mu for the m = 2 gyro-resonance with l = 5 m and k?/kì = 20 gives m ∼ 3.5 ×10−2 m−1. This is comparable to the value estimated byRao and Kaup [1990] for F region heating experimentsinvolving the m = 3 gyroresonance. For any reasonableestimate of the spatial length scale of inhomogeneity inthe magnetic field, this implies a transmission coefficientthat is essentially zero, or equivalently, an absorptioncoefficient of unity. Mode conversion from upper hybridto electron Bernstein waves should therefore proceedefficiently at the m = 2 gyroresonance.[46] We can estimate the bandwidth of the effect

approximately from equation (2) by equating the rightside with the mean squared frequency offset h∣Dw∣2i. Forour experimental conditions, this gives 2D fRMS ∼ 16 kHz.This is comparable to if about a factor of 2 less thanthe 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 electricfield intensities of about 170 mV/m and maintained withmuch smaller intensities. This figure is consistent withestimates based on the fluid‐theory formulation given byDysthe et al. [1983] if the finite interaction region depthand inelastic electron collisions are taken into consider-ation. Their prediction depends mainly on the electroncooling rate, the parallel thermal conductivity, the elec-

tron mean free path, and the vertical density gradientscale length at the upper hybrid interaction height. Othertransport coefficients are predicted to have only minoreffects, but this may require further investigation in thecontext of E region FAIs.[48] The experiments have also produced evidence of

striation formation, preconditioning, and resonanceinstability in the modified ionospheric volume drivenwith pump mode intensities well above threshold. Thedominant striation transverse scale length has beenroughly estimated to be 10–30 m. It should be possible tonarrow 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 pumpfrequency, upper hybrid frequency, and second electrongyroharmonic frequency nearly match. Suppression isonly evident for irregularities driven marginally abovethreshold, where the resonance instability is not in evi-dence. The suppression is asymmetric in frequency, withan overall bandwidth of 40–50 kHz. A slight echoenhancement 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 electrongyroharmonic frequencies but may be related to modeconversion of upper hybrid waves into nonpropagatingelectron Bernstein waves. The theory is provisional, andthe precise damping mechanism and damping rate remainto be estimated. In any event, echo suppression at thesecond electron gyroharmonic frequency appears to be aminor effect compared to what is observed at the n ≥ 3harmonics.

[51] Acknowledgments. The authors are grateful for helpreceived from the NOAA Kasitsna Bay Laboratory, its director KrisHolderied, 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 ActiveAuroral Research Program (HAARP) and from the Office of NavalResearch and the Air Force Research Laboratory under grantN00014‐07‐1‐1079 to Cornell.

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