Interferometric phase velocity measurements in the auroral electrojet

Planer Printed

W32 0633/t% 5300+0.00 ,!‘i 1986 Pergmon Journals Ltd.

Spacv Srr., Vol. 34, No. 12, pp, 1285 1297, 1986 m Great Britain

INTER F~RO~ETRIC PHASE VELOCITY MEASUREMENTS IN THE AURORAL ELECTROJET J. LABELLE’, P. M. KINTNER and M. C. KELLEY School of Electrical Engineering, Cornell University, Ithaca, NY 14853, U.S.A.

(Reeeiwd 23 June 1986) Abstract-A double-probe electric field detector and two spatially separated fixed-bias Langmuir probes were flown on a Taurus-Tomahawk sounding rocket launched from Poker Fiat Research Range in March 1982. Interesting wave data have been obtained from about 10s of the downleg portion of the Right during which the rocket passed through the aurora1 electrojet. Here the electric field receiver and both density fluctuation (&+I) receivers responded to a broad band of turbulence centered at 105 km altitude and at frequencies generally below 4 kHz. Closer examination of the two Gn/n turbulent waveforms reveals that they are correlated, and from the phase difference between the two signals, the phase velocity of the waves in the rocket reference frame is inferred. The magnitude and direction of the observed phase velocity are consistent either with waves which travel at the ion sound speed (C,) or with waves which travel at the electron drift velocity. The observed phase velocity varies by about 50% over a 5 km altitude rangean effect which probably results from shear in the zonal neutral wind, although unfortunately no simultaneous neutral wind measurements exist to confirm this.

1.

Introduction

In this paper, we present rocket measurements of the phase velocity of electrostatic waves observed in the aurora1 electrojet, using a technique which involves a cross-correlation of data coIlected from two spatially separated probes. Several previous rocket observations of aurora1 E-region irregularities have been reported (see, for example, Keiley and Mozer, 1973; Holtet, 1973; Olesen et al., 1976; Bahnsen et al., 1978; Pfaff et al., 1984), but with one exception (Bahnsen et al., 1978; Primdahl and Bahnsen, 1985) these experiments have not included measurements of the phase velocity of the waves. The primary reason for this shortcoming is the difficulty of interpreting the power spectrum computed by Fourier analysis of the data collected by rocket-borne probes, since such probes in moving through the ionosphere respond to both temporal and spatial variations in the plasma. The problem of interpretation of power spectra measured by in situ probes has been investigated theoretically by Fredricks and Coroniti (1976). They find that for purely spatial, isotropic turbulence, a power-law form for the spectrum of irregularities is preserved in the Fourier analysis of the probe dataalthough the interpretation of the slope of the spectrum depends on whether the observed turbulence is

*Present address: Astrophysik, Institut Garching. F.R.G.

Max-Planck-Institut fiir extraterrestrische

fiir Phvsik und Physik, 8046

one-, two- or three-dimensional. However, even in cases when the spectral forms are preserved, there exists no unique conversion between the frequency in the rocket frame and the wavenumber of the observed plasma irregularities. Physically, this implies that the same wavenumber, associated with wave vectors in different directions, maps to different frequencies in the rocket frame, and conversely, different wavenumbers may map to the same frequency. Because in general it is not possible to unambiguously associate frequencies in the Fourier analysis of probe data with wavenumbers in the rest frame, experimenters have devised alternate techniques for deducing wavelengths of structures observed with in situ probes. The experiment reported below is very similar to three previous experiments which have involved measurements of waves in the aurora1 ionosphere using two spatially separated electric field detectors (Kelley et al., 1970; Bahnsen et al., 1978; Kintner ef at., 1984). Kelley et al. (1970) pass their electric field data through a variety of band-pass filters and cross-correlate the filtered waveforms. They find that the correlation coefficient is elevated at the boundaries of an aurora1 arc which is traversed by the rocket, and from the time delay between the two signals they infer a wave phase velocity. Bahnsen et ul. (1978) observe “regular” (monochromatic) waves in the aurora1 electrojet on both the upleg and downleg of their experiment, and from the crosscorrelation of the waveforms detected by the two electric field detectors, they associate a phase velocity

1285

1286

J.

,LABELLE et a/.

34008 Poker Flat, Alaska 15 March 1982 8:30 PM (local tlme)

Electric Fieldprobes

-l5M-

I

----3OM FIG. 1. THE

CONFIGURATION

TAURUS-TOMAHAWK

OF PROBES FLOWN

ROCKETDENOTED MARCH 1982.

34.008,

ON THE

LAUNCHED

15

with these waves. Kintner et al. (1984) report observations of lower hybrid waves generated by an artificial ion beam in which simultaneous data from two spatially separated probes have been cross-spectrally analyzed to determine the wavelength and phase velocity of the waves. In laboratory experiments, the use of cross-correlational or cross-spectral analysis to resolve spatial structures in plasma turbulence is somewhat more common (see, for example, Harker and Ilic, 1974; Iiic et a[., 1975; Gresillon and Doveil, 1975; Gresillon et al., 1975; Bessem and Stevens, 1984).

2. AN EXPERIMENT PHASE VELOCITIES

TO MEASURE

IRREGULARITY

IN THE AURORAL

ELECTROJET

The configuration of probes illustrated in Fig. 1 flew aboard a Taurus-Tomahawk sounding rocket launched on 15 March 1982, from Poker Flat Research Range near Fairbanks, Alaska. The payload achieved an apogee of about 460 km, and its primary mission was to provide observations of plasma phenomena associated with a radial-shaped charge detonated near apogee. Details of these other experiments as well as descriptions of the launch conditions are discussed by Wescott et al. (1985). The two cylindrical Langmuir probes consisted of exposed metallic surfaces measuring 5cm in length and 1.3cm in diameter, which were separated by 1.5m

and hence provided a two-point measurement in the ionospheric plasma. The line defined by the centers of these two probes is hereafter referred to as the interferometer axis. The probes are labeled 6nl and 6n2 because they were operated in the fixed-bias mode in which fluctuations in the collected current are usually related to fluctuations in the plasma densityalthough under certain conditions such probes are also sensitive to electric field fluctuations as in the experiment reported by Kintner et al. (1984). On the same booms, two spherical Langmuir probes at the floating potential were sensitive to the component of the electric field along the interferometer axis. The interferometer axis itself rotated in the horizontal plane with the rocket spin frequency of 4.5 Hz. The electric field measurements and the 6nl and 6112signals were telemetered from the payload to the ground station by an FM radio link. The data were recorded in analog form during the experiment but were later digitized at Wallops Flight Facility, enabling the use of digital signal processing techniques in the data analysis. The payload penetrated a region of intense electrostatic turbulence associated with the aurora1 electrojet during both upleg and downleg. However, due to the concern that the simultaneous operation of two fixedbias Langmuir probes would adversely affect the vehicle potential, one of the cylindrical Sn probes was not turned on until after the release, and therefore no interferometric measurements were possible during the upleg. The discussion below concentrates on a 15 s interval centered at approximately 105 km altitude during the rocket’s descent. A Fast-Fourier Transform algorithm has been employed to spectrally analyze the density fluctuations and the electric field fluctuations observed with the rocket-borne probes, and Fig. 2 shows the evolution of these spectra during the downleg portion of the trajectory between the altitudes of 125 and 90km. In this example, individual spectra of the density and electric field fluctuations are computed 32 times per second, frequency and time form the vertical and horizontal axes, respectively, and the power in each spectrum is reflected in the gray scale. Altitudes corresponding to the flight times are indicated in the top panel. At the time depicted in Fig. 2, the rocket velocity is approximately 2.5 km s- I. Because of the high vehicle velocity, it is tempting to associate frequencies in the rocket reference frame with wavelength through the simple Doppler shift formula. However, in the present example, the rocket’s velocity is mostly downward in a region where the Earth’s magnetic field is vertical. Furthermore, the rocket was launched magnetically

6i0

FIG.

2.

115 L

FROM

Altitude

Ftight THE DOUBLE-PROBE

FIELD

FROM DETECTOR

OBTAINED

(BOTTOM

PANEL).

PROBE

630

T = 0) THE FIXED-BIAS

after

628

(TOP PANEL)

i km) 105 100 I_. f_-___ --- _._A_ -

(seconds ELECTRIC

TURBULENCE

time

626

II0 t -. .- --A,,---

OF THE ELEmRoJET

624

electrojet

SPECTROGRAMS

622

120 1

34.008 downleg spectrograms

AND

632

95 1 -. -

634

90 .I I

-6O’-

80 ,

Flight

I

626 Time (seconds

I

Altitude (km) 110

after

/ I

627 T=O)

,

117.5

to its own peak value.

FIG.~.(~) THE~OMPONENTOFTHEELECTRICFIEI.DPARALLELTOTHBINTERFEROMETERAXIS,MEASUREDIN THE ROCKET REFERENCE FRAME. @) A GRAY-SCALE REPRESENTATION OF THE XCF COMPUTED FROM THE TWO ~N/N SIGNALS.Each cross-correlation has been normalized such that the darkest gray level corresponds

1

625

1

112.5

624

1

115

628

105

1

I

00

LG

Phase velocity measurements in aurora1 electrojet northward which implies that on the downleg the relatively small horizontal rocket velocity (a few hundred meters per second) is directed such that the total rocket velocity was almost parallel to the magnetic field near 100 km altitude. Thus, if we expect to observe waves which are field-aligned or nearly field-aligned, the effective rocket velocity for Doppler shifting such waves is very small, possibly smaller than the wave phase velocities (E.pr
1289

more, if the fluctuations observed are indeed electric fields, the interpretation of the cross-correlation function changes considerably, and in this particular experiment such an interpretation implies results which are not physically reasonable, as discussed below. No spectral features can be readily identified in either of the spectrograms of Fig. 2. The once- or twice-per-spin modulation at the lowest frequencies which occurs at all altitudes including those above the turbulent layer is not believed to be geophysical and probably results from the vehicle wake.

3. CROSS CORRELATION

ANALYSIS

Although the turbulence in Fig. 2 diplays no distinguishable features in the frequency-time spectrogram, the data include dual-probe measurements of the density fluctuations which can be analyzed by cross-correlational analysis. The fundamental function in this regard is the correlation function, defined by P( X?r) =

V(x, t) V(x + x, r + r) dxdt Jjj

(1)

in which V(x, t) is the signal (h/n) which can in principle be observed at time t by a probe located at x. For a one-dimensional space, the correlation function defines a surface. The function has a maximum value at the point (x = 0,~ = 0) and generally diminishes in amplitude for larger values of 1 and t, though typically it exhibits local maxima and minima away from the origin, known as “side bands“. In this experiment only two points in space are measured, not an infinite number as would be required to determine the entire surface. Thus, we physically can measure only two cross-sections of the correlation function: the auto-correlation function (ACF), defined by ACF =

V(x, t) f’(x, t + r)dt, s

and the cross-correlation

function

(XCF), defined

V(x, t) f’(x + d, t + r)dt,

XCF = s

(2) by (3)

where d is the separation distance between the probes. Physically, both the ACF and the XCF are measurements of the degree of correlation between the irregularities observed in the plasma at different times or different locations. The ACF is in some sense more sensitive to the temporal coherence of the irregularit-

J. LABELLEet al.

1290

ies-the degree to which an observed irregular waveform resembles that observed a short time earlier at the same location. Of course, since in general irregularities have a drift velocity with a finite component along the interferometer axis, the auto-correlation function will inevitably be related to the degree of spatial correlation, too. Likewise, the cross-correlation function is sensitive to both spatial and temporal changes in the observed waveform. From the ACF and the XCF, we can define characteristic parameters which in turn are related to the phase velocity of the irregularities. With two probes, it is not possible to measure the actual threedimensional phase velocity since the two-probe system is only sensitive to the component of the wave-vector k along the interferometer axis. Futhermore, the velocity observed by the rocket-borne interferometer is shifted up or down due to the projection of the rocket velocity along the wave vector. If the wavevector is given by

where P(&, 0) = P(0, r,).

(10)

Note that both the “apparent drift velocity” and the “fading velocity” can be deduced from the measured XCF and ACF. We now turn to the sounding rocket data. The two digitized (&r/n) signals form the two sequences, x(n) and y(n), and the non-nomalized XCF are computed digitally from these two sequences using the relation XCF(m) =

: x(n). y(n + m). n= -N

(11)

(8)

Figure 3 illustrates two examples of the cross-correlation function computed from the two h/n signals. Each computation corresponds to 32ms of data, and the two examples are sampled 1OOms apartapproximately half a spin cycle. In both cases the XCF is highly peaked, but the right-hand panels indicate that the position of the peak varies in time. At t = 624.800, 6nl leads 6n2 by about l.Oms, but 1OOms later, 6n2 leads 6nl by the same amount. In order to track changes in the leg for optimum cross-correlation, a gray scale representation of the XCF is displayed in Fig. 4b. The vertical axis expresses the time by which Snl leads to 6n2; the altitude and the corresponding flight time appear on the horizontal axis, and the gray scale expresses the relative power in the cross-correlation function. Each cross-correlation is normalized independently such that its peak value corresponds to the darkest gray scale level. Furthermore, the raw data for each channel is digitally filtered prior to the computation of the cross-correlation function, using a 1OOHz wide band-pass with a lower cutoff of 25 Hz and an upper cutoff of 125 Hz. The most striking feature in Fig. 4b is that for a portion of the electrojet beginning at about 113 km altitude and ending at 105 km, the lag for optimum cross-correlation varies sinusoidally at the rocket spin frequency. This is exactly the response expected from the cross-correlation of two probes spinning in a plane roughly perpendicular to the magnetic field and simultaneously moving through a region of fieldaligned density irregularities propagating in one direction: at one moment, Snl receives a signal phase advanced relative to Sn2, while one-half spin period later, 6nl and 6n2 have effectively switched places so that the signal at 6nl is phase-retarded relative to

The “fading velocity” (V,‘) is defined to be the ratio of space-shift to time-shift required to produce an equal reduction in the correlation function:

Figure 4b also shows a tendency of the lag for optimum cross-correlation to increase with decreasing altitude. For example, comparing the maximum lags

c = (k,)% + (k,)Q + (k&,

(4)

the rocket velocity by 0, = (1/,)2 + (v,)S + (K)k

(5)

and the 2 coordinate is parallel to the interferometer axis, then the “phase velocity” to which the two-probe system is sensitive is given by V= (Wlk,) - t’,,

(6)

hereafter referred to as the “appropriate phase velocity”. Briggs et al. (1950) deduce the relationship between the drift velocity of ionospheric irregularities and the fading of radio signals observed by spaced receivers. The result is a formula for the appropriate drift velocity: 1/V’ = ( kg2 ,

(7)

where V is the appropriate drift velocity. In this equation, the “apparent drift velocity” (V’) is defined to be the quotient of the distance between the probes (d) and the lag for optimum cross-correlation (r,), the latter of which is defined as the value of 7 for which the XCF is maximum: f” = (d/z,,).

Sn2.

Phase velocity measurements

in aurora1

electrojet

-6

Laqtime

FIG. 3. TWOEXAMPLESOFTHECROSS-CORRELATIONFUNCTIONCOMPUTEDFROMTHETWO

two panels correspond to a time 1OOms earlier than the bottom at right show that the lag for optimum cross-correlation

observed during each spin period, we observe that the lag increases by approximately a factor of two between 112 and 107 km. Note, however, that the change in the lag can equally well be interpreted as temporal rather than spatial, which implies that the 100% increase occurs within 2s. Figure 4a shows the electric field in the rocket reference frame as detected by the two spherical Langmuir probes which were operated at their floating potentials. This measurement technique is sensitive to the component of the electric field parallel to the interferometer axis. We may compare Fig. 4a with the lag for optimum cross-correlation between the two (&a/n) signals (Fig. 4b), since both measurements are made in the rocket reference frame. Both quantities vary sinusoidally with the rocket spin frequency, but the electric field, considered positive when it points from 6nl toward 6n2, lags the spin dependence of the lag for optimum cross-correlation by 90”. This result, along with the direction of the magnetic field and the direction of the spin of the vehicle, implies that the observed appropriate phase velocity is consistent in direction with a wave whose E vector is parallel to

3

0

-3

-3

upper

1291

c

(ms)

0

Lagtlme

6

(ms 1 6n/n SIGNALS.The

two panels. The expanded changes in time.

views

e x B. We return to this comparison in the discussion section below. If the spin modulation in the XCF results from an electrostatic wave being observed in the rocket reference frame, equations (7) and (8) imply that z, = d(V/C) in which TV is the lag for optimum cross-correlation, d is the separation of the probes, Vis the appropriate phase velocity of the wave, and Vd is the fading velocity defined by equations (9) and (10). To determine the fading velocity (V,‘) requires the autocorrelation function which has been computed using the 6nl signal. (The ACF as computed from 6n2 takes on a very similar form.) For both the ACF and the XCF, the central peak in the function can be fitted to a Gaussian which is characterized by three parameters: the width, the position of the peak, and the relative power of the peak. Figure 5 illustrates the evolution in time of these three parameters for both the XCF (Fig. 5a) and the ACF (Fig. 5b). From 624 to 627, the sinusoidal variation of the lag for optimum cross-correlation

J.LABELLE et al.

1292

Cross-Correlation

Function

6250

(XCF)

6300 Fliyhl

Time

6350

(set)

FIG, 5 (a).THE EVOLUTION INTIME OF THECROSS-CORRELATION

FUNCTION COMPUTED

USINCTHE&I~

AND

6n2 SIGNALS. The peak in the function is fitted to a Gaussian using three parameters: the position of the peak (lag), the width of the peak, and the amplitude of the peak (power). The variation of these three parameters is illustrated in the three panels.

Auto- Correlation

Function

( ACF 1

4

:: UJ E

2

0 Power 400

6250

630.0 Flight

FIG 5(b). ~HEEVOLIJT~ONINT~MEOFTHE

Time

AUTO-CORRELATION FUNCTIONCOMPUTEDFROMTHE

The format

6350

(set)

is the same as in Fig. 5 (a).

6nl SIGNAL

Phase velocity measurements in aurora1 electrojet appears with the same features noted above. At the same time, the width of the XCF steadily increases; however, the width of the ACF is comparable to that of the XCF and also increases with time at about the same rate. Also, the peak power of both the ACF and the XCF increases between 624 and 627, but the ratio of the two is approximately constant and is of the order of 0.5. From equations (9) and (10) we note that the fading velocity (v,‘) is estimated from the XCF and the ACF by determining the minimum time lag for which the value of the ACF equals the value of the XCF at zero lag. This time lag can be determined using the Gaussian parameters plotted in Fig. 5. From equation (8) we can compute the apparent drift velocity (V’) from the lag for optimum cross-correlation, also among the parameters of Fig. 5a. The appropriate phase velocity is then given by equation (7). Thus, the data in Fig. 5 yield a plot of the appropriate phase velocity vs flight time (Fig. 6). In this analysis only two points per spin period are plotted, corresponding to the two times each spin when the interferometer axis is most nearly aligned with the phase velocity-i.e. the two minimum values of the appropriate phase velocity which are achieved each spin cycle. The values thus obtained for the appropriate phase velocity overestimate the actual phase velocity, which in general lies outside the plane defined by the spinning interferometer axis. As mentioned above, the interpretation of Fig. 4 changes significantly if it is assumed that the probes respond to electric field fluctuations rather than density fluctuations. In such a case, it is necessary to multiply one of the (6n/n) signals by (- 1) before computing the cross-correlation function, since the two electric field dipoles respond to the electric field in the opposite sense. Furthermore, the effective probe separation distance is effectively halved, since the electric field measurements are centered half-way between the probe and the rocket body. (Both of these effects are discussed in more detail by Kintner et al., 1984.) As a consequence, the inferred phase velocity would be half of the value indicated in Fig. 6, or about 250 ms-‘, and the direction of f, obtained from comparison with the DC electric field, would be opposite to the B x B direction. The fact that such results seem physically less reasonable than those implied by Figs 4, 5 and 6 lends support to the other evidence mentioned above which indicates that for these low-frequency fluctuations the fixed-bias Langmuir probes responded primarily to density irregularities rather than electric field fluctuations. The altitude variation in the lag for optimum cross-correlation translates into a decrease in the

1293 Altitude

1150

01 624

(km)

II2 5

1100

I

1000

I/

I,

,,I

625 Flight

I,,,,,,

626 Tome (WC)

107 5

I 627

FIG.~. THEAPPROPRIATEPHASEVELOCITYASINFERREDFROM THE DATA OF FIG. 5, COMBINED WITH EQUATIONS (7), (8), (9) AND (10). The observed phase velocity decreases with decreasing altitude.

appropriate phase velocity with decreasing altitude. In Fig. 6, V varies from 600m s- ’ at 112 km to 300m s- ’ at 107 km. The lag for optimum crosscorrelation observed at 112 km is about 1.7 ms which implies an apparent drift velocity of 600 m s - I, comparable to the value of Vobserved at the same altitude. Thus, the analysis of this experiment indicates that V, V’ and VA are of comparable magnitude so that the apparent drift velocity is a good estimate of the appropriate phase velocity in this case. When Fig. 4b is extended to larger values of time lag, sidebands are visible in the cross-correlation function. These are apparent in both the top and bottom panels of Fig. 3. These sidebands arise when the part of the signal which is well-correlated between the two probes is also relatively monochromatic. In such a case, the two signals are strongly correlated for time lags which satisfy 7 = 7 + nt,,where (l/t,) is the frequency of the correlated signal in the rocket frame, and n is an integer. The sidebands in Fig. 3 are spaced by about 20ms, implying a frequency of 50 Hz. The frequency can in turn be combined with the observed appropriate phase velocity to obtain one component of r(, through the relation: k, = 2rflflv: From this equation we find k, = 0.682m-’ in this experiment, equivalent to a wavelength of 10m. A wavelength greater than the probe separation distance is an assumption implicit in the analysis presented above. Ambiguity results if the wavelength is smaller than the probe separation distance because the phase difference between the two signals passes through the value 27~ one or more times each spin period-whenever the projection of the probe separation vector onto the wave vector equals a multiple

1294

J.

LABELLEet al.

of the wavelength. In some cases the signature of this ambiguity can be difficult to recognize, as in the example discussed by Pfaff (1985). However, in the present experiment, the time resolution in the crosscorrelation functions seems sufficient to show that the lag for optimum cross-correlation does not “wrap around” each spin period. Therefore, the interpretation that the wavelength is somewhat longer than the probe separation distance of 1.5 m seems safe. In addition to the rotation which produces the sinusoidal variation observed in the lag for optimum cross-correlation, the rocket payload in general executes a coning motion about a roughly vertical fixed axis. The rocket’s coning is usually much slower than the spin, and therefore the angle between the wave phase velocity and the plane defined by the rotating interferometer axis is well defined and varies approximately sinusoidally with the coning frequency; in effect, the appropriate phase velocity to which the interferometer is sensitive varies according to the coning period, even if the wave phase velocity is constant. If the coning motion is severe enough, it could produce a time variation in the measured velocity similar to the trend seen in Fig. 6. To evaluate the effect of the coning in this experiment, we have examined the vector mangetic field which was measured by a flux-gate magnetometer mounted in the payload. The magnetometer data indicate that the coning frequency is approximately 24s and the angle between the rocket axis and the Earth’s magnetic field never exceeds 15”. If the observed electrostatic waves are field-aligned to within lo”, then the most severe change in the measured phase velocity occurs if the plane defined by the spinning interferometer axis contains fc during one portion of the coning period and differs from k by 25” one-half coning period later. In this case, during a 12s interval, the measured phase velocity varies [ V,,,,,/cos(25”)]. Since between ( Vphase) and cos(25”) = (0.91), a 10% change in 12 scan be explained by the coning effect-equivalent approximately to a 2.5% change in 3 s. Recall that the data (Fig. 6) implies a change of almost 50% between t = 624 and t = 627. Thus, the analysis of the magnetometer data shows that the rocket’s coning motion falls at least a factor of 10 short of explaining the observed change in the phase velocity. As mentioned above, the interferometric technique overestunates the wave phase velocity since in general the interferometer axis is not parallel to k for any part of the rocket spin cycle. The magnetometer data allows us to estimate this error, provided that the observed waves are field-aligned. In this case, the plane defined by the spinning interferometer axis,

which is perpendicular to the rocket axis, at no time differs from r( by more than 15”. Therefore, the wave phase velocity is overestimated by at most a factor of [(l/cos(l5”)], or about 5%.

4. DISCUSSION

The observed phase velocity, as pointed out in Fig. 6, is 300-600 m s-i in the rocket reference frame, but is perhaps overestimated by as much as 5% due to the attitude of the rocket with respect to the geomagnetic field. From comparison with the electric field observations in the rocket frame (Fig. 4a), we have inferred that the direction of the phase velocity is consistent with the direction defined by I? x 8. The ambient e is typically northward, which implies that I? x fi is westward; careful comparison with the magnetometer data is also consistent with f in the magnetic East-West direction. On the other hand, the rocket horizontal velocity was within 2” of geomagnetic North. Thus, the wave phase velocity in the Earth-fixed reference frame equals the observed rocket-frame phase velocity to within a few percent. (A much larger correction arises due to the neutral wind, which is discussed below.) As discussed above, the effect of the rocket coning motion is not adequate to explain the change in phase velocity observed in Fig. 6. We conclude that the phase velocity in the Earth-fixed frame must change in magnitude or direction in order to explain this effect. If the waves propagate horizontahy and in the direction of I? x B as indicated by this experiment, than there exist several interpretations of the observed change in phase velocity with altitude. The most probable explanation is the existence of a shear in the zonal (East-West) component of the neutral wind. Shear in the neutral wind has been invoked to explain the variation in the phase velocity of waves associated with the “type I” echoes reported during radar aurora (Balsley et al., 1976). The neutral wind profile in the aurora1 E-region has been observed using chemical releases from sounding rockets (e.g. Pereira et al., 1980; Mikkelsen et al., 1981a,b), and these observations typically show a transition between a region of laminar flow at high altitudes and a more turbulent regime at lower altitudes. This boundary, which lies between 90 and 118 km, is associated with the turbopause, the altitude below which the atmosphere is well mixed. These observations also show that the zonal neutral wind maximizes near 130 km, where it may be several hundred meters per second westward, depending on the ambient electric field. Physically, this peak in the

Phase velocity measurements in aurora1 electrojet

zonal wind arises because the coupling of the 3 x B force to the neutrals is most efficient at this altitude. This implies that in the altitude range extending from near the turbopause up to about 130km, a shear commonly exists in the zonal neutral wind-- a shear which has the direction needed in order to explain the observations reported here. For example, suppose that the phase velocity in the neutral frame is 4OOms-’ westward and is constant with altitude. If the neutral wind is 4OOms- ’ westward at 130 km and vanishes at 110 km, as in the observations of Mikkelsen et al. (1981a), then the velocity of the waves in the Earth-fixed frame varies from 400m s- ‘ at 1lOkm to about 5OOms~’ at 1tSkm. Unfortunately, the neutral wind was not measured during the experiment reported here. Recent models show that the lower boundary of the shear in the zonal wind may be a strong function of the absolute electron density profile (M. F. Larsen, personal communication, 1985). Since our experiment took place at the same location (Alaska), at approximately the same local time (pre-midnight), and the same time of year (March) as the measurements of Mikkelsen et al. (1981a), we speculate that in our case the turbopause lay at 110 + 5 km, as in their observations. Note that the two ex~riments reported by Mikkelsen et al. (1981a) correspond to electric fields of 40 and 60 mV m-l, somewhat larger than the estimated electric field in our experiment ( - 25 mV m- ‘); however our application of their results seems plausible in the light of the barium cloud observations during the 15 March flight which indicate a larger electric field (N 50 mVm- I), comparable to that observed during the neutral wind measurements of Mikkelsen et al. (1981a). Perhaps the electric field on the night of 15 March takes on an average value of 50 mV m- * or even larger, with occasional excursions to lower values such as the 25 mV m- ’ field observed during the rocket’s passage through the electrojet. In this case, the neutral wind most certainly would respond to the long-time average field rather than the temporarily suppressed electric field present during the electrojet observations. If this is correct, there may well exist a westward zonal neutral wind characterized by a strong shear in the altitude range 1lo- 130 km, and the shear has the direction and magnitude needed to explain the observed height variation of uphase. At this point, it is instructive also to consider the stability of the neutral wind shear required to explain Fig. 6. The stability of the neutral wind to shear turbulence is determined by the Richardson criterion (Richardson, 1920; Hines, 1974): Ri > 0.25 (for stability)

1295

where Ri is the dimensionless given by

Richardson

number,

in which wsv is the Brunt-Vaisala frequency and V(Z) is the neutral wind speed as a function of altitude. In the altitude range 100-150 km, the Brunt-Vaisala period for a standard nonisothermal atmosphere is typically about 5 min (see, for example, Yeh and Liu, 1974). The shear observed in Fig. 6 is 200-300 m s- ’ over 5 km, implying that (au/&) equals approximately 0.05 s-r. Thus, obtain Ri = 0.18-unstable, though close to marginal instability. Considering the fluctuations in the phase velocity measurements (Fig. 6), which are of the order of 25%, we believe that to within the experimental accuracy, the shear in the neutral wind required to explain the observed altitudinal dependence of uphsseis probably marginally stable to shear-generated atmospheric turbulence. This is certainly the case if the observed altitudinal variation m ophaseresults from a combination of neutral wind shear and some other effect such as a vertical gradient in the electron temperature, as discussed below. Setting aside the question of the neutral wind profile, we turn to two other possible theoretical predictions of the phase velocity of the waves in the neutral reference frame. First, the waves may be travelhng at the electron drift velocity, according to t’nhase

-

@

x

B)/w(l

+ +)

(12)

with for perpendicular propagation. This dispersion relation is predicted by the linear theory of the twostream instability (Farley, 1963; Buneman, 1963), which as been proposed as a source for the shortscale waves observed in the electrojet and recognized by their distinct radar spectrum (Moorcroft and Tsunoda, 1978). Note that not only is the direction of the phase velocity consistent with l? x B as inferred from Fig. 4, but also the magnitude of l? ( - 25 mV m-r) implies a drift velocity of 5OOms-’ in the rocket frame, in approximate agreement with the observed phase velocity (Fig. 6). (Because the electric field is northward, the phase velocity westward, and the rocket velocity northward, it is valid to compare the rocket-measured phase velocity with the Earth-frame electric field in this example.) For perpendicular propagation, the parameter I++is a decreasing function of altitude. However, using tabulated values for the collision frequencies (Banks and Kockarts, 1973), one finds that at altitudes above 105 km 9 is less than 0.05, and thus the factor (1 + $) in equation (12) cannot explain the observed 25-

J. LABELLE et a[.

1296

50% change in uphase with altitude (Fig. 6). Another possibility is that a temporal or spatial change in i? occurs; however, Fig. 4a shows the electric field in the rocket frame, and although its amplitude decreases somewhat during the time interval 624-627s the decrease is far too small to explain the change in the phase velocity. In conclusion, the phase velocity measurements reported here are consistent with the I? x B drift velocity if and only if some other effect such as the shear in the neutral wind acts to create the observed altitude variation of uphase. The observed phase velocity is also consistent with another interpretation: perhaps the waves propagate at the ion acoustic speed, given by c, = JM.

(13)

The ion acoustic speed might typically be 470 m s- l (T + T, = 800K), so this interpretation is again in reasonable agreement with the observed 0phase. This interpretation is suggested by nonlinear theories of electrojet turbulence which hypothesize that the waves perturb electron orbits and cause an effective anomalous diffusion across fi, leading to an enhanced collision frequency which in turn causes the waves to be saturated at C, (Sudan, 1983). The saturation of uphase at C, is a well-recognized feature of radar Doppler spectra observations of twostream waves in the equatorial electrojet (see, for example, Fejer and Kelley, 1980). In the aurora1 zone, radar studies of the so-called “type I” spectrum of backscatter power from electrojet irregularities have also measured Doppler-inferred phase velocities of the order of the ion acoustic speed (Tsunoda, 1976; Moorcroft and Tsunoda, 1978). Nielsen and Schlegel (1983, 1985) recently have used a backscatter radar in combination with an incoherent scatter radar to show that when the E-field as determined by incoherent scatter is large (2 35 mV mm I), the phase velocities of the “Type I” irregularities determined from the backscatter radar differ from E/B and are more consistent with C,. When the E-field is small but still above the two-stream threshold, E/B and C, are comparable and the experiment could not distinguish at which velocity the waves travelled. Similarly, a previous rocket experiment using an interferometric technique obtained a phase velocity much closer to C, than to E/B (Bahnsen et al., 1978; Primdahl and Bahnsen, 1985). This experiment occurred during much more active conditions than the experiment reported here (E- 60mVm-’ in the previous experiment vs E - 25 mV mm ’ in the present experiment). Unfortunately, the present experiment is in a position similar to the radar data in the case of weak electric fields: the resolution in the observations

is not good enough to distinguish whether the phase velocity more nearly equals C, or E/B. We may test the C, interpretation by investigating the variation in upha_ with altitude. A typical experimental profile when the ambient electric field is of the order of 25 mV m-i gives T, = 303 K at 115 km and T, = 231 K at 105 km (Schlegel and St. Maurice, 1981). This implies a reduction of C, from 407 to 347 ms-i over this altitude range, or about 17%. On the other hand, the observed phase velocity, adjusted for the rocket altitude and velocity, ranges from 600 to 3OOms-‘, a reduction of 50%. Thus, the interpretation that the waves travel at the ion acoustic speed does not explain the magnitude of the change in the phase velocity which is observed. In conclusion, it seems most likely that a shear in the neutral wind explains the observations. However, if no neutral wind shear, or a very small shear, exists, the C, interpretation comes closer to explaining the observations than does the I? x B interpretation. Another possible interpretation is that the change in phase velocity is temporal. In this case, the 50% change in uphase occurs within 2s. Such a change is not unreasonable considering the rapid motions that are often visible in aurora1 forms, but Fig. 4a shows that no dramatic change in the electric field occurs in this experiment. The fact that the sounding rocket data were collected under quiet aurora1 conditions also argues against this interpretation. Perhaps the most important conclusion from this data set concerns the difficulty inherent in performing plasma physics experiments in the electrojet. This experiment includes a successful measurement of the irregularity phase velocity as a function of altitude. Nevertheless, an unambiguous interpretation of the results is not possible without even more information, such as the neutral wind velocity profile, the absolute electron density profile, etc. A successful experiment clearly must include a more full range of measurements, ground-based as well as in situ. Only then can a phase velocity measurement, such as that reported above, be interpreted reliably. AcknowLedgements~The authors wish to acknowledge R. F. Pfaff for suggesting the importance of neutral wind in this experiment and B. G. Fejer for many helpful comments concerning this work. The work has been supported by the National Aeronautics and Space Administration contract NAG5-601. REFERENCES

Bahnsen, A., Ungstrup, E., Falthammer, C. G., Fahleson, U., Glesen, J. K., Primdahl, F., Spangslev, F., and Pedersen, A. (1978) Electrostatic waves observed in an unstable polar cap ionosphere. .I. geophys. Res. 83, 5191.

Phase velocity

measure] ments in aurora1

Balsley, B. B., Fejer, B. G. and Farley, D. T. (1976) Radar measurements of neutral winds and temperatures in the equatorial E region. J. geophys. Res. 81, 1457. Banks, P. M. and Kockarts, G. (1973) Aeronomy, Parts A and B. Academic Press, New York. Bessem. J. M. and Stevens. L. J. (1984) Cross-correlation measurements in a turbulent boundary layer above a rough wall. Physics Fluids 27, 2365. Briggs, B. H., Phillips, G. J. and Shinn, D. H. (1949) The analysis of observations on spaced receivers of the fading of radio signals. Proc. R. Sot. 106. Buneman, 0. (1963) Excitation of field-aligned sound waves by electron streams. Phys. Rev. L&t. 10, 285. Farley, D. T. (1963) A plasma instability resulting in fieldaligned irregularities in the ionosphere. J. geophys. Res. 68, 6083. Fejer, B. G. and Kelley, M. C. (1980) Ionospheric irregularities. Rev. Geophys. space Phys. 18, 401. Fredricks, R. W. and Coroniti, F. V. (1976) Ambiguities in the deduction of rest frame fluctuation spectra computed in moving frames. J. geophys. Res. 81, 5591. Gresillon, D. and Doveil, F. (1975) Normal modes in the ionbeam-plasma system. Phys. Rev. L&t. 34, 77. Gresillon, D., Doveil, F. and Buzzi, J. M. (1975) Space correlation in ion-beam-plasma turbulence. Phys. Rev. Left. 34, 197. Harker, K.J. and Ilic, D. B. (1974) Measurement of plasma wave spectral density from the cross-power density spectrum. Rev. scient. Instrum. 45, 1315. Hines, C. 0. (1974) 7he Upper Atmosphere in Motion. American Geophysical Union, Washington, D. C. Holtet, J. A. (1973) Electric field microstructures in the aurora1 E-region. Geophys. norvegica 30, 1. Ilk, D. B., Harker, K. J. and Crawford, F.W. (1975) Spectral density of ion acoustic plasma turbulence. Phys. Lett. 54A, 265. Kelley, M. C. and Mozer, F. S. (1973) Electric field and plasma density fluctuations due to the high-frequency Hall current two-steam instability in the aurora1 E region. J. geophys. Res. 78, 2214. Kelley, M. C., Mozer, F. S. and Fahleson, U. V. (1970) Measurements of the electric field component of waves in the aurora1 ionosphere. Planer. Space Sci. 18, 847. Kintner, P. M., LaBelle, J., Kelley, M. C., Cahill, L. J., Moore, T. and Arnoldv. R. (1984) Interferometric phase velocity measurements. Geophys. Res. Left. 11, 19. . Mikkelsen. I. S.. Jdraensen. T. S.. Kellev. M. C.. Larsen. M. F. and Pereira, E.yl981a) Neutral winds and electric fields in the dusk aurora1 oval-l. Measurements. J. geophys. Res. 86, 1513. Mikkelsen I. S., Jdrgensen, T. S., Kelley, M. C., Larsen, M. F. and Pereira, E. (1981 b) Neutral winds and electric fields in the dusk aurora1 oval&2. Theory and model. J. geoph!, ,. Res. 86, 1525. Moorcroft, D. R. (1979) Dependence of radio aurora at

electrojet

1297

398 MHz on electron density and electric field. Can J. Phys. 57, 687. Moorcroft, D. R. and Tsunoda, R. T. (1978) Rapid scan Doppler velocity maps of the UHF diffuse radar aurora. J. geophys. Res. 83, 1482. Nielsen, E. and Schlegel, K. (1983) A first comparison of STARE and EISCAT electron drift velocity measurements. J. geophys. Res. 88, 5745. Nielsen, E. and Schlegel, K. (1985) Coherent radar Doppler measurements and their relationship to the ionospheric electron drift. J. geophys. Res. 90, 3498. Olesen, J. K., Primdahl, F., Spangsley, F., Ungstrup, E., Bahnsen, A., Fahleson, U., Falthammer, C. -G. and Pedersen, A. (1976) Rocket borne wave and plasma obersvations in unstable polar cap E region. Geophys. Res. Lett. 3, 339. Pereira, E., Kelley, M. C., Rees, D., Mikkelsen, I. S., Jdrgensen, T. S. and Fuller-Rowell, T. J. (1980) Observations of neutral wind profiles between 115- and 175-km altitude in the dayside amoral oval. J. geophys. Res. 85, 2935. Pfaff, R. F., (1985) Rocket studies of plasma turbulence in the equatorial and aurora1 electrojets. Ph. D. thesis, Cornell University. Pfaff, R. F., Fejer, B. G. and Kudeki, E. (1983) Rocket observations of the height distribution of aurora1 electrojet instabilities (abstract). Trans. Am. geophys. Un. 64, 280. Pfaff, R. F., Kelley, M. C., Fejer, B. G., Kudeki, E., Carlson, C. W., Pedersen, A. and Hausler, B. (1984) Electric field and plasma density measurements in the aurora1 electrojets. J. geophys. Res. 89, 236. Primdahl, F. and Bahnsen, A. (1985) Aurora1 E-region diagnosis by means of nonlinearly stabilized plasma waves. Ann. Geophys 3, 67. Richardson, L. F. (1920) The supply of energy to and from atmospheric eddies. Proc. R. Sot. Lond. A97, 354. Schlegel, K. and St.-Maurice, J. P. (1981) Anomalous heating of the polar E region by unstable plasma waves-l. Observations. J. geophys. Res. 86, 1447 Sudan, R. N. (1983) Unified theory of type I and type II irregularities in the equatorial electrojet. J. geophys. Res. 88. Tsunoda, R. T. (1976) Doppler velocity maps of the diffuse radar aurora. J. geophys..Res. 81, 4%. _ Tsunoda. R. T. and Presnell. R. I. (1976) On a threshold electric field associated with the 398-MHz diffuse radar aurora. J. geophys. Res. 81, 88. Wescott, E. M. Stenbaek-Nielsen, H. C., Hallinan, T., Deehr, C., Romick, J., Olson, J., Kelley, M. C., Pfaff, R. F., Torbert, R. B., Newell, P., Foppl, H., Fedder, J. and Mitchell, H. (1985) Plasma depleted holes, waves, and energized particles from high-altitude explosive plasma perturbation experiments. J. geophys. Res. 90, 4281. Yeh, K. C. and Liu, C. H. (1974) Acoustic-gravity waves in the upper atmosphere. Reu. Geophys. space Phys. 12, 193.