Observations of backscatter autocorrelation functions from

1.07-m ionospheric irregularities generated by the European

Incoherent Scatter Heater Facility

E. Nielsen and M. T. RietveldMax-Planck-Institut fur Aeronomie, Katlenburg-Lindau, Germany

Received 17 June 2002; revised 4 December 2002; accepted 14 January 2003; published 2 May 2003.

[1] During an ionospheric heating experiment using the European Incoherent ScatterHeater Facility on 10 July 1999, artificial backscatter was detected by the ScandinavianTwin Auroral Radar Experiment (STARE) 140 MHz coherent radar system. The STAREradar operations included for the first time multipulse observations. The autocorrelationfunction and power spectrum of the backscattered radar signal were observed to becharacterized by a half-power correlation time 13 ± 1 ms or by a corresponding spectralwidth 47 ± 4 Hz. This spectral width is comparable to the width observed at much lowerfrequencies, at 46.9 MHz and 21.4 MHz. The spectral width may, in part, result from thespatial extent of the heated region and from the spatial resolution of the radar inconnection with spatial gradients in the background electric field. An upper value of theturbulent diffusion coefficient derived from the observations is 4.5 m2/s. It is up to a factorof 10 larger than the classical coefficient. Apart from spatial effects the increase may becaused by increased electron scattering in the plasma waves excited by the heateractivity. INDEX TERMS: 2471 Ionosphere: Plasma waves and instabilities; 2403 Ionosphere: Active

experiments; 2407 Ionosphere: Auroral ionosphere (2704); 2439 Ionosphere: Ionospheric irregularities;

KEYWORDS: ionosphere, RF heating, plasma instabilities, coherent radar

Citation: Nielsen, E., and M. T. Rietveld, Observations of backscatter autocorrelation functions from 1.07-m ionospheric

irregularities generated by the European Incoherent Scatter Heater Facility, J. Geophys. Res., 108(A5), 1166,

doi:10.1029/2002JA009537, 2003.

1. Introduction

[2] Small-scale spatial fluctuations in the electron densityoccur when the ionospheric electric field in the E regionexceeds the threshold at which the two-stream plasmainstability is excited as the electron gas streams throughthe slower moving ion gas [see, e.g., Nielsen et al., 2002].Such density fluctuations are aligned with the geomagneticfield, and they are therefore detectable by radar when theradar k-vector is perpendicular to the magnetic field direc-tion. It is well known that small-scale spatial densityfluctuations can also be excited by artificial means. Thisis done by transmitting high-frequency electromagneticradiation into the ionosphere. The radiation excites variousinstabilities leading to electrostatic plasma waves, which aredamped resulting in electron heating [Stubbe, 1996; Nobleet al., 1987; Hoeg et al., 1986; Hibberd et al., 1983]. Theheater-induced electron density fluctuations occur alsowhen the electric field in the ionosphere is <15 mV/m,i.e., less than required for the two-stream instability tooperate. The current understanding of the generation ofthese density irregularities by heating lies within the frame-work of excitation of the thermal resonance instability at theupper hybrid level [Dysthe et al., 1982; Inhester, 1982;Vas’kov and Gurevich, 1977]. The irregularities are excited

preferentially when the high-frequency heater wave is trans-mitted in the O mode and when its frequency is less than theupper hybrid frequency in the E region. The e-foldinggrowth times vary between 2 s and 15 s, with the smallervalues being the typical ones. The altitude of the irregu-larities is variable; it has been determined as being largerthan 100 km. The actual altitude presumably depends on thedetailed vertical electron density variations in the E regionand on the spatial extent of the irregularities along themagnetic field direction, i.e., on how field aligned theirregularities really are. Spectral observations of the back-scatter signal from heater-generated irregularities have pre-viously been made at 46.9 MHz [Djuth et al., 1985] and at21.4 MHz [Noble et al., 1987] for the same event.[3] The characteristics of radio waves backscattered from

artificial 1.07 m irregularities generated by the EISCAT(European Incoherent Scatter) Heater Facility [Rietveld etal., 1993] have been studied with the STARE (ScandinavianTwin Auroral Radar Experiment) 140 MHz VHF radarsystem [Nielsen et al., 1999]. During earlier observationsthe STARE radar was operated in a single pulse/doublepulse mode. Those observations therefore only determinedtwo points on the autocorrelation function of the back-scattered radar signal, and may therefore provide only acrude hint of the complexities of the actual autocorrelationfunction, and thus give a simplified impression of theplasma physics processes in the backscatter region.

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 108, NO. A5, 1166, doi:10.1029/2002JA009537, 2003

Copyright 2003 by the American Geophysical Union.0148-0227/03/2002JA009537

SIA 2 - 1

[4] In this paper we present new multipulse observationsof radar auroral backscatter. The measurements provide 13points on the autocorrelation function. This corresponds to amaximum correlation time of 2.6 ms. These measurementsare not detailed enough to reveal all details of a realisticpower spectrum of the backscattered signal. The correlationtime of the waves is much larger than 2.6 ms, and thespectra are therefore much more narrow than the resolutionof the experiment.

2. Experiments

[5] The EISCAT heating facility is used to modify theionosphere [Rietveld et al., 1993]. During the observationsthe heater operated at 4.04 MHz. The effective radiatedpower was kept constant at 180 MW during the experiment.The dimensions of the antenna expressed in units of wave-length of the heater radio waves: distance between rows is0.61, the dipole length is 0.86, and the antenna height aboveground is 0.21. The width of the vertical antenna main lobefor this experiment is therefore at �3 dB 14.5� and at �6dB 19.6�. These angles correspond to horizontal dimensionsof 28 and 38 km at 110-km altitude. Sixty-one percent of theenergy is radiated inside the �3-dB contour, and 77% isradiated inside the �6-dB contour.[6] STARE is a 140-MHz coherent radar system with a

large field of view over northern Scandinavia nearly cen-tered on the location of the Heater Facility. The radar systemconsists of two radar stations, one near Trondheim(10.73�E, 63.40�N), Norway, and one in Hankasalmi(26.85�E, 62.25�N), Finland. The radar antennas are point-ing poleward at low elevation angles, with the radar k vectorbeing within one degree of perpendicular to the geomag-netic field in the E region over the Heater Facility. The radarantennas have good gain between 5� and 12� elevationcorresponding to ranges to the E region from �500 to�1200 km. The radar used 100 ms-pulse width, yielding arange resolution of 15 km. The transmitter antenna is widelobed with a half width of �50�. The receiver antenna haseight narrow lobes each with a half width of 3.6�. Thus, inaddition to the good range resolution the receiving antennaensures a good azimuthal resolution of the observations.[7] Figure 1 shows the spatial relationship between the

Norwegian radar lobe/range coverage and the heater anten-na’s �3 and �6-dB radiation diagram contours in theionosphere at an altitude of 110 km. The heater is locatedin lobe 8 of the radar receiver antenna diagram at a range of795 km. The �3 and �6-dB contours intersect mainly tworadar range intervals, ‘‘bin 10’’ and ‘‘bin 11.’’[8] The radar was operated with three different pulse

patterns, executed in sequence within a cycle. The cycle isexecuted about 200 times (= Ncyc) within the integrationtime of 20 s.

2.1. Single Pulse Mode

[9] A single pulse is transmitted and received over arange interval which includes the heater location. This modeprovides the backscattered power versus range. The poweras a function of range along a lobe, say lobe 8, is Pi, wherethe index i is the bin number (range number). Let thequadrature receiver output for this pulse be zi = xi + iyi.The average received power averaged over an integration

time, Ncyc, corrected for noise, and normalized to theaverage noise power level, Ni,ave, is

Pi;ave ¼1

Ncyc

XNcyc

k¼1

ZikZik*� Ni;ave

" #=Ni;ave ð1Þ

2.2. Double Pulse Mode

[10] Two pulses are transmitted with a time separation,Tp, of 200 ms between their leading flanks. This modeallows derivation of Doppler velocities as a function ofrange along the lobes, Vi,DP. The Doppler velocity isexpressed by the value of the autocorrelation function(ACF) of the backscattered signal at a time delay equal tothe separation between the double pulses,

ACFi Tp� �

¼XNcyc

k¼1

ZikZjk*

" #=Ni;ave ¼ Ri Tp

� �þ iIi Tp

� �ð2Þ

and, with Tp measured in ms,

j ¼ iþ Tp=100 ð3Þ

and thus

Vi;DP ¼ l8Tp

atanIi Tp� �

Ri Tp� �

" #=90 ð4Þ

where l is the radar wavelength.

2.3. Multipulse Mode

[11] Six pulses are transmitted in a time pattern expressedas 1:3:6:2:5. One time delay is 200 ms. There are 13 time

Figure 1. Geographic map showing the spatial coverageand resolution of the STARE Norwegian radar over theEISCAT Heater Facility. Radar measurements are spatiallyaveraged over each ‘‘bin.’’ The two circles indicate thespatial coverage of the vertical heater antenna lobe; theycorrespond to the �3-dB and �6-dB levels of the antennaradiation diagram.

SIA 2 - 2 NIELSEN AND RIETVELD: ACFs OF 1.07-m HEATER-GENERATED PLASMA WAVES

lags (correlation times) observed using this pulse pattern. Ifthere is a spatially wide backscatter region in the iono-sphere, then, of course, the signal arriving at the radar at agiven time, will be the sum of signals from all pulsesbackscattered from different ranges. Unlike the single pulsemeasurements, the signal received at a given time duringmultipulse measurements does not correspond to a givenrange, but is the sum of signals backscattered from manyranges. However, the pulse pattern is chosen in such a waythat two signals received with a time interval �t containsthe signal from one, and only one, common range. This isthe case when �t is equal to the time separation betweenany pair of pulses (= lag). Cross correlating the signalsreceived with the time interval �t yield therefore the valueof the ACF at the common range for that time interval(= lag = correlation time). The ACF is calculated usingequation (2). The time interval (correlation time or timedelay) between two pulses with lag number, lag#, is T 0

p =Tp * lag#. Replacing Tp with T 0

p in equation (2) yields theassociated value of the ACF. The ACF is measured as afunction of range and of correlation time up to a maximumof Tp,max = 13 � 200 ms = 2.6 ms. This truncation of theACF implies that the spectral resolution of the observationsare limited to 1/Tp,max � 385 Hz (at a level of 4 dB belowthe spectral maximum). A backscatter spectrum with theform of a delta function centered at the frequency wo wouldtherefore appear in the radar observations as a single peakspectrum with a width of 385 Hz and have the form

P ¼sin wo � wð Þ Tp;max

2

wo � w

!2

ð5Þ

[12] In the general case the radar will receive signals atany given time from all the six pulses. Since the signal fromthe wanted range arise from only one of the six pulses, the

(useful) signal is only 1/6 of the total signal received. Therest (5/6) of the signal is noise, referred to as clutter [Farley,1972]. In the general case for ACF measurements thesignal-to-noise Ratio (SNR) is therefore only 1/5. If thesignal from the wanted range is weaker than from the otherrange(s), then the SNR is even smaller. If the signal from thewanted range is stronger than from the other range(s), thenthe SNR is larger. If there is no backscatter from otherranges than the wanted range, then there is no clutter, andthe SNR is determined only by the intensity of the signalbackscattered from the wanted range. The latter is the casefor the heater-induced backscatter considered here; there isbackscatter from only one range, and the SNR relevant tothe ACF measurements is controlled by the backscattergenerated by the heater.

3. Observations

[13] On 10 July 1999, between 0010 and 0055 UT theHeater Facility radiated O-mode waves during an experi-ment to measure the effect on Polar Mesospheric SummerEchoes using the EISCAT 224-MHz radar [Chilson et al.,2000]. The heater was transmitting in a sequence 20 s on, 20s off, synchronized to the start (zero second) of the minute.The SNR of the backscattered power from the single pulsemode received in the Norwegian radar’s lobe 8 receiverchannel is shown in Figure 2 as a function of range andtime. Far to the north is a region of weak natural backscatter.The backscattered signal over the heater is appearing andthen disappearing in 20-s intervals. A closer analysis con-firms the signal to appear when the heater is on. The SNR ofthe signal backscattered over the heater increases from �10dB to �18 dB during the event. The SNR in bin 10 and bin11 is 8 to 10 dB stronger than in the nearest neighbor bins.The backscatter in direction of the Finnish STARE radarremained below the radar threshold during the whole event.

Figure 2. Radar backscatter power expressed as signal-to-noise ratio (SNR) as a function of time andrange in lobe 8 passing over the heater. The heater-induced backscatter is characterized by the 20-s on/offpattern dictated by the heater cycle. To the north is a region of weak natural backscatter. See color versionof this figure at back in the HTML.

NIELSEN AND RIETVELD: ACFs OF 1.07-m HEATER-GENERATED PLASMA WAVES SIA 2 - 3

Thus, in the following, only Norwegian STARE observa-tions are shown.[14] The double-pulse Doppler velocity over the heater

shows no detectable variation with time; its average valueduring the event is �7 m/s.[15] A time series of typical ACFs of the radar signal

backscattered from the region over the heater is shown inFigure 3. Data are only plotted for a single pulse SNR > 0.The real/imaginary/magnitude components of the ACF areplotted with solid/dashed/dotted lines. The magnitude is thesquare root of the sum of the squares of the real andimaginary components. The components are weaklydecreasing over the 13 lags. The real/imaginary componentsdecrease over 13 lags (2.6 ms) by �0.04/�0.15 in units of‘‘normalized power.’’ With reference to equation (4) thiscorresponds to mean Doppler velocities of �10 m/s, con-sistent with the result based on the double-pulse experiment.The magnitude decreases by 4% ± 1% over 13 lags, where1% represents the standard deviation of the data points fromthe fitted curve. This result will be used later to estimate theactual width of the backscattered power spectrum.[16] The power spectrum is the Fourier transform of the

ACF. The mean frequency of a power spectrum, S( f ), isgiven by

fh i ¼Z

fS fð Þdf ð6Þ

[17] However, using a double-pulse technique, one meas-ures not h f i but fo given by

Zsin 2pT f � foð Þð Þdf ¼ 0 ð7Þ

One can show that for a symmetric spectrum or for a narrowspectrum, fo = h f i. This is confirmed by the observedspectra. Figure 4 shows a typical spectrum with values ofthe variously defined Doppler velocities characterizing thespectra. Averaged over all the data obtained during theheater experiment, the calculated double-pulse velocity is�17 m/s. This is not statistically different from theexperimentally determined value of �7 m/s obtained usingequation (6). The spectral width is determined using linearinterpolation between the powers at the observed frequencypoints. The mean width of the spectra at the �4 dB powerlevel is �380 Hz, which is statistically consistent with the385-Hz width predicted for an ideal delta function back-scatter spectrum. This implies directly that the spectralwidth of the actual spectrum must be very small comparedto 385 Hz.

4. Discussion

[18] The ACFs of 1.07-m irregularities in the E regiongenerated by heater O-mode radiation have been observedwith a single-, double-, and multipulse (six pulses) radarexperiment up to a correlation time of 2.6 ms. The 1.07-mdensity fluctuations were produced over the heater site. TheSNR in bin 10 and bin 11, i.e., in two bins over the heatersite each 15-km wide, is 8 to 10 dB stronger than in theneighboring bins. This is consistent with a horizontal spatialscale of 25/28 km at 100-/110-km altitude (this correspondsto the �3-dB contour of the heater antenna radiationdiagram). The backscattered power from the region overthe heater increased from 10 dB to 18 dB during the 50-minduration of the experiment. This probably indicates localchanges in the background parameters controlling the back-

Figure 3. Autocorrelation functions observed in lobe 8/bin 10 (over the heater) versus time. The real(solid)/imaginary (dashed) components are weakly decreasing/increasing with lag time, corresponding toa mean Doppler velocity of �10 m/s. The magnitude (dotted) is decreasing 4% (with an uncertainty of±1%) over 2.6 ms. The SNR is noted in each panel; measurements are only shown for SNR > 0.

SIA 2 - 4 NIELSEN AND RIETVELD: ACFs OF 1.07-m HEATER-GENERATED PLASMA WAVES

scatter volume. The average velocity of the irregularitiesexcited by the heater derived from the double-pulse meas-urements and from the ACF is about �10 m/s.[19] The backscattered signals have, within the spectral

resolution, simple single-peaked spectra. This observationalresult confirms earlier assumptions underlying interpreta-tions of single-pulse/double-pulse observations. Some ofthese earlier conclusions are also directly confirmed by theobservations presented here.[20] That the Norwegian radar observes a signal, but not

the Finnish radar does not, has been interpreted as evidencethat the heated region is near 100-km altitude. In thisaltitude the Norwegian radar k vector is close to beingperpendicular to the geomagnetic field, while the Finnishradar k vector is �1� off perpendicular. The signal at theFinnish radar is therefore expected to be weaker than thesignal at the Norwegian radar, by �10 dB owing to aspectangle effects. If this was the only effect, the radar in Finlandshould have observed backscatter late in the evening, whenthe SNR in Norway was 18 dB. The flow angle alsoinfluences the signal intensity and may contribute to theweaker signal in Finland. The appearance of backscatterover the heater occurs in close synchronization with theheater on/off cycle. This is consistent with an average e-folding growth time for heater irregularity excitation to be<20 s, the time resolution of the observations.[21] Attenuation of the ACF magnitude with correlation

time contains information about the spectral width of thebackscattered signal and about the diffusion coefficient inthe backscatter volume. The average slope of the magnitudeof the normalized power versus lag number corresponds to adecrease of the ACF magnitude of �4% over a correlation

time of 2.6 ms. We introduce the following expression forthe ACF magnitude [see, e.g., Jackel, 2000]

r tð Þ ¼ exp � tte

nt

: ð8Þ

[22] The expression separates the shape of the ACF,determined by the parameter nt, from the width of theACF, determined by the parameter te, the ‘‘correlationtime.’’ Here t is the lag time. A measure of the width ofthe ACF is given by t = te, i.e., the width is equal to the lagtime for which the ACF magnitude has decreased to equal1/e of its maximum (corresponding to a �4 dB decrease).For nt = 2, the Gaussian case, the e-folding correlation time,te, has been derived from the measurements by a linear leastsquares fit to the logarithm of the ACF amplitude: te = 13ms. For a realistic decrease of the ACF amplitude over 13lags from 3% to 5% (= 4% ± 1%) the estimated correlationtime is between 12 and 14 ms. The mean correlation time islisted in Table 1.[23] Hanuise et al. [1993] and Villain et al. [1987]

showed that HF Doppler spectra of natural backscatter hasa shape that depends on the size of the correlation length ofthe plasma turbulent motion, Lc, compared to the observedfluctuation wavelength, l. The latter is for the STAREsystem equal to 1.07 m. When Lc � l, then the Dopplerspectrum has a Gaussian shape. When Lc � l, then theDoppler spectrum has a Lorentzian shape. Finally, anintermediate case occurs when Lc � l. In that case theautocorrelation function of the backscattered signal starts asa Gaussian (for correlation times, t, much smaller than theplasma correlation time, te) and ends as a Lorentzian fort� te. Villain et al. [1987] determined the value of Lc to beclose to 1 m and the value of te to be �15 ms. Thus theplasma correlation length is comparable with our observa-tion scale length, and the maximum lag time of ourobservations is much smaller than the plasma correlationtime. This means that the Doppler spectrum of the STAREobservations should have a Gaussian shape.[24] The spectrum and the ACF have the form

S2 ¼ C3 exp � w� w0ð Þ2

2s2

!ð9Þ

A2 ¼ C4 exp � 1

2s2t2

ð10Þ

[25] Equations (9) and (10) have been used to estimate thespectral width, W, of the signal backscattered from theheater-induced plasma waves: s = 21/2 1000/13 = 21/2

76.9 = 109 Hz. At half power the total width is 1.17 �2 � s = 2.34 s and at the 1/e - level we have W = 2.7 s. At

Table 1. Estimates of Autocorrelation Function/Spectral Widths

(for 4% Decrease Over 13 Lags) and Diffusion Coefficient

Spectral Shape, Gaussian nt = 2

ACF width te, ms 13Spectral width W, Hz 47Diffusion coefficient D, m2/s 4.5

Figure 4. A spectrum with several different Dopplervelocities noted: the Doppler velocity experimentallydetermined using the 200-ms double pulse (24 m/s); thedouble-pulse velocity calculated from the spectrum usingequation (6) (�10 m/s); the mean Doppler velocitycalculated from the spectrum using equation (5) (�10 m/s);the frequency point at which the observed power is maximum(0 m/s); and the width at �4 dB-level calculated from thespectrum (379 Hz).

NIELSEN AND RIETVELD: ACFs OF 1.07-m HEATER-GENERATED PLASMA WAVES SIA 2 - 5

the �4 dB level the total spectral width is s/2p or W � 47Hz. For a decrease of the ACF amplitude over 13 lags from3% to 5%, the estimated spectral width is in the range from43 to 51 Hz (corresponding to the correlation times, 12 and14 ms). The mean width is listed in Table 1.[26] Owing to truncation of the observations in the time

domain an observed spectrum would have a width of 385Hz if the actual spectrum had the form of a delta function orif the actual spectrum was much narrower than 385 Hz. Theobserved spectra have an average width of �385 Hz. Thisimplies that the actual backscattered spectrum has a widthmuch smaller than 385 Hz. This is confirmed by theestimated actual spectral width in Table 1, which showsthe estimate is a factor 8 less than 385 Hz.[27] Villain et al. [1996] developed a theory that allows

an estimate of the diffusion coefficient, D. They introduceda Lagrangian description of the plasma turbulent motion andshowed that for small t: s = (D/T)1/2 � k, where D is thediffusion coefficient, T is the plasma correlation time, and kis the plasma wave k vector, 2p/1.07. The spectral width isdetermined by both the diffusion coefficient and by thecorrelation time. For small t, D = 344 � T m2/s. If for Tweuse the observed value of te = 13 ms (see Table 1), then D =4.5 m2/s. Thus the derived diffusion coefficient is an orderof magnitude larger than the classical value. The value ofthe diffusion coefficient is listed in Table 1.[28] The diffusion coefficient is closely associated with

the electron collision frequency, ne. An increase in thediffusion coefficient can be expressed as an increasedanomalous electron collision frequency, n*e. Such anincrease could be due to momentum transfer betweenelectrons and plasma waves excited by the heater experi-ment or by naturally excited waves [Sudan, 1983; Robinson,1986]. The observed ratio n*e/ne covers a large magnituderange [Gagnepain et al., 1977; Ogawa et al., 1980; Rein-leitner and Nielsen, 1985; Nielsen, 1986; Primdhal, 1986;Igarashi and Schlegel, 1987; St.-Maurice, 1987; Haldoupis,1989]. Many values are commonly between 5 and 10, butthere are also larger values, up to 2 orders of magnitude ormore. Thus, for the artificial heater-generated backscatterthe diffusion coefficient for the Gaussian case is in a rangethat is realistic for normal conditions. However, the uncer-tainties in the actual electron temperature, collision fre-quency, and the correlation time prevents a closer analysis.[29] The new results of these measurements of the auto-

correlation function of the signal backscattered from heater-generated ionospheric electron density fluctuations are (1)the ACF has an e-folding correlation time of 13 ms, (2) thespectral peak has a width at �4 dB estimated to be 47 Hz,and (3) the diffusion coefficient for the Gaussian case isequal to or larger than the classical coefficient, possibly upto a factor of 10 larger.[30] Djuth et al. [1985] observed backscatter spectra at

46.9 MHz from the EISCAT heating experiment. Theyfound the half-power width of the spectral peaks to rangebetween 12 and 20 Hz. This corresponds to Dopplervelocities from 38 to 64 m/s. That range is equivalent to aspectral width of 35 to 60 Hz at 140 MHz. Noble et al.[1987] also measured spectral widths of 5 to 11 Hz at 21.4MHz (corresponding to 35 and 77 m/s) for the same event.That range is equivalent to a spectral width of 33 to 72 Hz at140 MHz. The spectral widths measured at these lower

frequencies are consistent with the widths of the spectrafound in this study (43/51, 35/60, and 33/72 Hz). Thisimplies that the spectral widths measured at 21.4 MHz, at46.9 MHz, and at 140 MHz are comparable when expressedin Doppler velocities (46/55, 38/64, and 35/77 m/s), whichreflect the actual spread of phase velocity of the plasmawaves in the ionosphere.[31] The Doppler velocities observed during this experi-

ment are close to zero. During other STARE/heating experi-ments, velocities with values between zero and 700 m/swere observed. The average Doppler velocity of artificialirregularities amounted to 175 m/s [Hoeg et al., 1986].[32] The spectral broadening is influenced by the width in

range and in azimuth and elevation of the radar receivingantenna lobe. Since no natural backscatter is observed overthe Heater Facility, the electron drift velocity is less than thethreshold for plasma wave excitation, i.e., less than �300m/s. For a heated region 40 km across at a distance of 795km, a uniform cross lobe drift of <300 m/s would produce<15 m/s Doppler velocity variation across the lobe. Thiscorresponds to a spectral broadening of <14 Hz. Thespectral peak would be further broadened if the line-of-sightdrift velocity has a gradient across the heated region. If thegradient were assumed to be 1 m/s per kilometer (a notunreasonable gradient in the auroral zone ionosphere), thenthe spectral broadening would amount to 15 Hz. Thecombined spectral broadening owing to the spatial extentof the heated region and the spatial resolution of the radarthus could amount to �30 Hz, a value consistent with theobservations. Thus simple arguments based on spatialrelations can account for the observed spectral width. Thedifferences in spectral widths observed for the three fre-quencies may reflect the changes in spatial variations duringthe events. The implication of these spatial effects is that thededuced spectral width is an upper estimate of the width ofthe spectrum associated with the heater-generated irregu-larities.[33] According to present theoretical thinking the proper-

ties of 1-m irregularities appear to be understandable withinthe framework of the thermal resonance theory [Stubbe,1996, and references therein]. This is a theory that assumesthe plasma fluctuations that cause backscatter of the radarsignal are excited in a two-step process. The pumping HFwave is scattered in existing field-aligned density fluctua-tions, resulting in excitation of upper hybrid electrostaticwaves propagating almost perpendicular to the magneticfield. These electrostatic waves heat the plasma in regionsof depleted electron density. This secondary heating byelectrostatic waves is most efficient where the frequencyof the pump wave is close to resonance with the upperhybrid frequency. It has been proposed for natural plasmawave instabilities that they lead to increased scattering ofelectrons in the plasma wave electric field. This is equiv-alent to an increase of the diffusion coefficient of theelectrons and a broadening of the plasma wave phasevelocity spectrum. The increased scattering and increaseddiffusion coefficient results in a broadening of the spectrumof the backscattered radar signal. The theory developed fornatural radar aurora to account for experimental results hasbeen applied to the heater-generated irregularities to derivethe magnitude of the diffusion coefficient. When the plasmacorrelation length is comparable to the observation fluctua-

SIA 2 - 6 NIELSEN AND RIETVELD: ACFs OF 1.07-m HEATER-GENERATED PLASMA WAVES

tion wavelength (for these observations both scales are�1 m), the theory predicts a Gaussian shape of the Dopplerspectrum for correlation time that is small compared to theplasma turbulence correlation time, as is the case for theseobservations (2.6 ms � 15 ms). Applying the theory wefound, a correlation time of 13 ms, a spectral width of 47 Hz,and a diffusion coefficient a factor 1 to 10 larger than theclassical coefficient. The estimated spectral width (at140 MHz) is comparable to the spectral width determinedexperimentally at 21.4 MHz and 46.9 MHz. However, thespectral widths can, partly or wholly, be accounted for byspatial gradients in the ionospheric electron drift velocity orelectric fields. Considering the possibility of ‘‘spatial con-tamination’’ of the spectra, the derived spectral widths andthe associated estimates of the diffusion coefficient must beconsidered upper estimates.

[34] Acknowledgments. The STARE system was operated jointly bythe Max Planck Institute for Aeronomie, Germany, and by the FinnishMeteorological Institute, Finland, in cooperation with SINTEF, Universityof Trondheim, Norway. The EISCAT heater is an international facilitysupported by Finland, France, Germany, Japan, Norway, Sweden, and theU.K.[35] Arthur Richmond thanks the reviewer for assistance in evaluating

this paper.

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�����������������������E. Nielsen and M. T. Rietveld, Max-Planck-Institut fur Aeronomie,

37191 Katlenburg-Lindau, Germany. (nielsen@linmpi.mpg.de; rietveld@linmpi.mpg.de)

NIELSEN AND RIETVELD: ACFs OF 1.07-m HEATER-GENERATED PLASMA WAVES SIA 2 - 7