Polarization characteristics of Pi 2 pulsations and implications for their source mechanisms: Influence of the westward travelling surge

Planet. Space Sci., Vol. 31, No. 4, pp 435458, Printed in Great Britain.

0032Xl633/83/040435-24$03.00/O 0 1983 Pergamon Press Ltd

1983

POLARIZATION CHARACTERISTICS OF Pi 2 PULSATIONS AND IMPLICATIONS FOR THEIR SOURCE MECHANISMS : INFLUENCE OF THE WESTWARD TRAVELLING SURGE J. C. SAMSON and G. ROSTOKER Department of Physics and Institute of Earth and Planetary Physics, University of Alberta, Edmonton, Alberta, Canada T6G 251 (Received 5 October 1982) Abstract-This paper expands the earlier results of Rostoker and Samson (1981), who noted that there are two latitudinal areas of Pi 2 localization near the high latitude, substorm enhanced electrojets. The detailed study presented here outlines the morphology of the polarizations of the Pi 2’s in and near the westward travelling surge.TherearetwolatitudinalareasofPi2localization.ApolewardPi2predominateswithinthesurgeandto the East, whereas an equatorward Pi 2 predominates equatorward and West of the surge. These Pi 2 localizations appear to correlate with the substorm enhanced westward and eastward electrojets respectively. However, the maximum in the Pi 2 power does not always coincide with the center of the electrojet. The poleward Pi 2 has largest amplitudes to the East of the head of the westward travelling surge. This Pi 2 shows a latitudinal polarization reversal from clockwise on the equatorside (viewed down on H-D plane) to counterclockwise on the poleside of a latitudinal demarcation line, which occurs just poleward of the initial breakup. This demarcation line is usually equatorward of the most poleward expansion of the surge. To the West of the surge front, where the equatorward Pi 2 predominates, there is again a latitudinal polarization reversal but in this case the polarization is counterclockwise equatorward and clockwise poleward of the demarcation line. This demarcation is equatorward of that for the poleward Pi 2, and appears to lie at the latitude of the initial breakup. Consequently, the westward travelling surge appears to mark the longitudinal transition from equatorward to poleward Pi 2. The elliptical polarization of the Pi 2’s is most likely caused by azimuthal (longitudinal) expansion of the field-aligned currents in the surge, in association with reflection of the field-aligned current pulses from northern and southern high latitude ionospheres.

In the present study, we shall present a detailed extension of our earlier study (described above) in which we shall deal with features of Pi 2’s in and near the region ofthe westward travelling surge(WTS). We have placed particular emphasis on choosing simple, isolated onsets and on a careful correlation of the Pi 2’s morphology with the behaviour of the ionospheric currents and FAC in the surge. Review material pertinent to our study can be found in the references of Rostoker and Samson (1981) and Samson (1983a). We would, however, like to draw attention to the recent work of Pashin et al. (1982) in which some of the polarization features of Pi 2’s near the aurora1 breakup region and head of the WTS have been outlined. They found that the maximum in Pi 2 intensity was near the head of the WTS where the most intense luminosity of the aurora is located. Insofar as polarization characteristics are concerned, they found a four quadrant pattern for the Pi 2’s with the center of the pattern being coincident with the head of the WTS. In particular, they report that the polarization is clockwise to the North-West and South-East and counterclockwise to the North-East and South-West. This pattern is in substantial agreement with that

INTRODUCTION

In an earlier paper (Rostoker and Samson, 1981) we outlined the morphology of the Pi 2 pulsations near the substorm enhanced aurora1 electrojets in terms of the polarization characteristics of the Pi 2’s. In that paper, we showed that high latitude Pi 2’s are closely associated with the substorm enhanced eastward and westward electrojets. In particular, we demonstrated that the Pi 2’s exhibited, in addition to an intensity maximum near the equatorward border of the substorm enhanced westward electrojet, an increase in intensity near the equatorward border of the substorm enhanced eastward electrojet. All events studied in that paper featured a polarization reversal across the region of upward field-aligned current (FAC) marking the location of the equatorward border of the westward electrojet in the morning sector and the region of the Harang discontinuity in the evening sector. This polarization reversal featured a change from clockwise polarization poleward of the FAC to counterclockwise polarization South of it. Accordingly the polarization reversal tended to be located to the South of the center of the substorm enhanced westward electrojet. 435

436

J. C.

SAMSON

obtained for the Southern Hemisphere by Kuwashima (1978). Pashin et al. also suggested that much of the magnetic field perturbation of the Pi 2 observed on the ground was due to oscillating FAC near the head of the WTS. Although our results agree with those of Pashin et al. in some details, we find however that the spatial character of the polarization pattern deviates from the four quadrant picture suggested by both Pashin et al. and Kuwashima and, in addition, the intensity maximum of the Pi 2 is not necessarily at the head ofthe WTS.

A CANONICAL

MODEL OF THE WESTWARD

TRAVELLING

SURGE

Before continuing in a discussion of the Pi 2’s it is essential to delineate themajor features ofa WTS which allow us to identify these surges by ground based magnetometer and riometer observations. Since we wish to correlate the Pi 2 morphology with FAC and ionosphericelectrojets, themagneticsignaturesofthese currents must be clearly understood. Field-aligned and ionospheric currents The substorm onset begins with intense electron precipitation, and the brightening of an aurora1 arc (Fig. 1) (Akasofu, 1968). In the aurora1 zone poleward of the arc, the ionospheric electric field is predominantly

Geomagnetic

and G. ROSTOKER

toward the Equator, and to the South of the arc the electric field can range from weakly equatorward to strongly poleward (Horwitz et al., 1978; Inhester et al., 1981) depending on the ambient convection electric fields, and the brightened arc’s position relative to the Harang discontinuity. The net upward field-aligned current over the arc closes through the ionosphere as enhanced Pederson and Hall current in the precipitation region (Fig. 1). At the edge of the region of enhanced conductivity and precipitation, a downward, field-aligned return current completes the circuit. Since Hall conductivities can be very much larger than Pederson conductivities near the arc (Z&/C, N 3-5; Brekke et al., 1974) ground based magnetometers see an effective westward electrojet to the North and East of the brightened arc, and a somewhat weaker eastward electrojet to the South and West (Fig. 1). Directly after the brightening of the arc, the electron precipitation region can expand poleward and the WTS forms (Akasofu, 1968). Figure 2 gives a summary of the ionospheric currents and FAC currents associated with the WTS. A list of references for the various features is given in Table 1. In general, a sometimes weak eastward electrojet occupies the region to the South-West and South of the WTS. Intense FAC flow upward at the head or westward edge ofthe WTS. The ionospheric electric field tends to point

-

I

1 f -i, i

FIG. l.A

i.

11

MODEL FOR THE FIELD-ALIGNED AND IONOSPHERIC CURRENTS ASSOCIATED WITH THE ONSET OF THE SUBSTORM.

In the figure, crHand cp are Hall and Pederson conductivities (arrows indicate direction of Hall and Pederson currents), E is the ionospheric electric field,ji andj/ are the ionospheric and field-aligned currents, respectively.

Pi 2’s and the westward

travelling

431

surge

I%.2. THECONFIGURATION OF THECURRENTSASSO(‘IATEI)W~TH THESLIKGE. Solid lines and arrows are ionospheric currents. Dots indicate upward FAC, and crosses are downward FAC. The dashed line indicates the region of substorm-enhanced conductivity. The letters indicate the regions covered by the references in Table 1.

toward the region of intense upward FAC, and consequently these upward currents are fed by an ionospheric electrojet which curls around the leading westward edge of the WTS. This ionospheric current becomes a predominantly westward electrojet to the East of the WTS front, and the current tends to be localized in the poleward portion of the WTS. Where this westward electrojet reaches the edge of the enhanced conductivity zone, a region of downward FAC flows. The intense upward FAC at the surge front, and the net downward FAC to the East, lead to the magnetic signatures typical of a substorm current wedge at mid latitudes (McPherron et ul., 1973). The mean features in Fig. 2 are compatible with the current

system shown in Fig. 16 of the study by Kamide and Rostoker (1977). At positions to the East of the WTS front (East of line Bin Fig. 2), thepolewardedge ofthe westward electrojet will often appear to expand suddenly poleward, sometimes over a very short interval (l-3 min; see the example to be given later in the paper, or Pytte et al., 1976). For a single onset, this poleward expansion seems continuous, but for multiple onsets, the expansion can appear in discrete steps (Kisabeth and Rostoker, 1974; Wiens and Rostoker, 1975). In order to interpret the WTS characteristics in the ground based magnetometer data, we have used the simple model of currents shown in Fig. 3. The relative

TABLE 1. REFERENCESFOK FIG. 2 Region in Fig. 2

Feature

Reference -_____

A

D

Field aligned currents Ionospheric electrojet Field-aligned currents Electric fields Electric fields and electrojets Electrojets Electrojets Field-aligned currents Electric fields and Field-aligned currents Field-aligned currents Electrojets Field-aligned currents and electrojets Electric fields Electric fields Electric fields and electrojets

Armstrong et nl. (1975) Fig. 7. Wallis et al. (1976) Figs. 1, 4. Kamide and Rostoker (1977) Fig. 6. Horwitz er al. (1978) Fig. 17a. Inhester et ul. (1981) Fig. 3. Kisabeth and Rostoker (1973) Figs. 2a, 2b. Wallis et nl. (1976) Figs. 1, 4. Kamide and Rostoker (1977) Fig. 11. Inhester et al. (1981) Figs 3, 5e. Kamide el al. (1976) Wallis et ul. (1976) Figs. 2, 5. Kamide and Rostoker (1977) Fig. 11. Inhester et ul. (19X 1) Fig. 3. Horwitr et al. (1978) Fig. 17a. Inhester et al. (1981) Fig. 3.

438

J. C.

FIG. 3.

SAMSON

and G. ROSTOKER

THE IONOSPHERIC CURRENT AND FAC MODEL OF THE WTS WHICH MAGNETICFIELDSASSOCIATFiD WITHTHEWTS.

ARE USED FOR

COMPUTING

THE

are ionospheric currents. The open circles and dark circles are downward and upward FAC respectively. The current has the same value in each circuit.

The solid lines and arrows

strengths of the currents in the eastward and westward electrojets are highly variable. We have chosen a net westward electrojet current which is three times that in the eastward electrojet, as a representative value (see e.g. Kisabeth and Rostoker, 1973). To calculate the magnetic fields associated with the model in Fig. 3, we have integrated over great-circle paths in the ionosphere, and along field lines in the magnetosphere. We have used a simple dipole model, and stopped the integration where the field line reaches

the equatorial plane. Details on the type of programs used for these calculations can be found in Kisabeth (1979). The equivalent ionospheric currents for the model in Fig. 3 are given in Fig. 4. These results show that one of the most reliable methods for finding the WTS boundary in the magnetic data is to look for the transition from positive Z (vertical component, positive downward) (outside WTS) to negative Z (inside). All regions with negative Z areencircled by the ionospheric

t

FIG. 4. EQUIVALENTCURRENTSASSOCIATED WITHTHEMODELIN FIG.~. The equivalent currents were obtained by rotating the SD field by 90” clockwise. Dark circles represent negative Z-components, and crosses are positive Z. To simulate earth induction effects, a perfect conductor was placed at a depth of 200 km.

439

Pi 2’s and the westward travelling surge PROFILE

RT

LONGITUDE=26

PROFILE

RT

LONGITUDE=16

PROFILE

RT

LRTITUOE=69

PROFILE

AT

LRTITUOE=66

,

t64

58

LHT

16Th

66

69

Fro. 5. REPRESENTATIVELATITUDE AND LONGITUDEPROFILESOFTHEMODEL IN Flc.4. (a) Latitude profiles, (b) longitude profiles. H is magnetic North (dipole), D is magnetic East, Z is vertical (positive down).

electrojets feeding the intense FAC near the westward head of the WTS. Some representative latitude and longitude profiles of the magnetic field for the model are given in Fig. 5a, b. These profiles will be used later in determining the position of the WTS in specific events. Riometer signatures The brightening of the aurora1 arc at the substorm onset is associated with intense precipitation of electrons in the 10-50 keV energy range. During the initial brightening of the quiet arc (Fig. l), the absorption is confined to a narrow strip along the arc (Akasofu, 1968, Fig. 64). When the WTS develops, the

intense absorption region to the East of the head of the WTS jumps suddenly northward, following the poleward border ofthe aurora(Nielsen and Greenwald, 1978) giving the “spike” absorption events often seen in riometer data at substorm onset (Hargreaves et al., 1979; Nielsen, 1980). Under the arc with the initial brightening, an isolated “spike” with rapid recovery to almost no absorption can be seen (A in Fig. 6). As the WTS evolves, the absorption region jumps rapidly poleward, and a “spike” appears at higher latitudes (position B). The absorption in region B often starts simultaneously with that in A, but the peak absorption in B is seconds to minutes after that in A. Also, at position B,

440

J. C. SAMSONand G. ROSTOKER

FIG. 6. TYPICALRIOMETER-ABSORPTION EVENTS ASSOCIATED WITHVARIOUS REGIONS

which is near the high latitude border of the WTS, the absorption is still appreciable after the “spike”. After the expansive phase, the poleward border of the WTS drifts equatorward, and absorption at position B slowly decreases (over tens of minutes), and absorption at A slowly increases again. In contrast to the sharp “spikes” at A and B, a station at position C, to the West of the initial WTS development, will see a relatively slow (tens of minutes) increase in absorption as the WTS moves over this station. We must emphasize at this point that the events we have discussed in (a) and (b) are single onsets. Multiple onsets will show a much more complicated development of the WTS, associated absorption, and electrojet, see e.g. Wiens and Rostoker (1975), Pytte et al. (1976). EXPERIMENTAL DETAILS This study is based, for the most part, on digital magnetometer data from the University of Alberta, and the Department of Energy, Mines and Resources (EMR) (Canada). This suite of data has been complemented by magnetograms from observatories at Newport, Meanook, Yellowknife and Cambridge Bay (see Table 1 in Rostoker and Samson (1981)), by riometer data from the University of Alberta, and by DMSP aurora1 photographs. The ionospheric beam-widths of the Alberta riometer are shown in Fig. 1 of Tighe and Rostoker (1981). All the data presented here are plotted in local

IN THESURGE

magnetic coordinates, H (positive northward), D (positive eastward), and 2 (positive downward). In some of the analyses, we have used substorm centered coordinates. These coordinates are defined in the following way. The substorm centered latitude, B,, is given by 0, = 0-- 0d(n,) where B is the centered dipole latitude, and II&,) is the latitude of the onset of the breakup, at the longitude, A,, of the center of the substorm current wedge. The substorm centered longitude is & = 1- /2,. The longitudinal center, i,, of the substorm current wedge (see McPherron et al., 1973 for a description of this wedge) has been determined by using data from the Canadian and American mid latitude standard observatories at Victoria, Newport, Tucson, Whiteshell, Ottawa and Fredericksburg, as well as data from the seven magnetometer stations of the Air Force Geophysics Laboratory (AFGL). A value for 1, is determined by a linear interpolation to find the longitude at which AD = 0, where AD is the maximum magnetic excursion within - l-2 min of the substorm onset. To estimate OS we have used the perturbation field AZ due to the substorm onset, at stations near the substorm enhanced westward electrojet, and as close as possible to 1,. The breakup latitude was determined by a linear interpolation to find AZ = 0, where AZ is the maximum substorm perturbation with 1 min of the onset. Thus Bs should be the approximate position of the center of the substorm enhanced westward electrojet. Three representative events have been chosen for

441

Pi 2’s and the westward travelling surge TABLE ~.COORDINATE~OFTHESUBSTORMONSETS 0, (centered

Event

04: 00 U.T. Day 363,1977 II:02 U.T. 04: 56 U.T. 07 : 50 U.T. 05 : 08 U.T. 08 : 09 U.T.

Day Day Day Day Day

281, 1978 325, 1978 265,1978 325, 1978 59, 1979

detailed analysis, 08 : 08 : 45 U.T. (onset) 28 February (Day 59), 1979 ;07 : 49 : 30 U.T. 22 September (Day 265), 1978; and 05:07:45 U.T. 21 November (Day 325), 1978. All substorm onset times were determined from the initial pulse of the associated Pi 2 at our station at LEDU. These events were classified as single onsets by using two criteria. First, the riometer data at one or more stations showed a single, well-defined absorption “spike”, with no subsequent absorption “spikes” for at least 10 min after this initial “spike”. Second, the Pi 2 recorded at LEDU showed a well defined onset, with no further Pi 2 bursts for at least 10 min after the initial onset. The centered dipole coordinates of the substorm onsets (BB,a,) are given in Table 2. Also included in this table are the coordinates of the events discussed by Rostoker and Samson (1981). These events will be included in a composite diagram to be given later. The positions of the Alberta stations with respect to the WTS were determined by matching the magnetometer and riometer data with the results from the models in Figs. 3 and 6 respectively (see the latitude and longitude profiles, and the equivalent current vectors to be presented later). The approximate border of the WTS was determined by using the AZ = 0 demarcation line, where AZ is the substorm perturbation field. This method gave values which agreed with those determined by using the riometer data and the DMSP photograph for Day 59. Figure 7 gives a summary of the

A DAY 59 0 DAY 265 a DAY 325

A FIG.7. THEPOSITIONSOFTHEALBERTASTATIONSWITHRESPECT TOACANONICALSURGE, FORTHETHREEEVENTSINTHISSTUDY.

dipole)

66”+ 1”N 66” IO.5 65” *OS 63”&0.5 67” +0.5 65” 50.5

0,,1.,

1, 340”kY’E < 290 340” + 5” 308” 2 2 324” k 2” 301”+2”

position of the Alberta stations for the three events, with respect to a canonical WTS. Further details on the estimation of the position of the WTS will be given in the discussion of the data. To determine the configuration of the substorm enhanced FAC and electrojets, three representations of the magnetometer data were used. The data were represented as standard magnetograms (H, D, Z coordinates), latitude and longitude profiles of substorm perturbation fields, and equivalent current vectors of perturbation fields. The latitude profiles presented here used data from the Alberta stations, and standard observatories at Newport, Meanook, Yellowknife, and Cambridge Bay (see Rostoker and Samson, 1981). The equivalent current vectors were determined by removing a pre-substorm baseline from the data and then rotating the horizontal magnetic vector by an angle of 90” clockwise. In analysing the Pi 2 data, a number of different representations of the magnetic field data were used. Since all computations were done using the spectral representation of the data (see the Appendix), the data were first detrended by filtering with a 3 mHz high pass filter. The data were then transformed to the frequency domain where the pure states or polarized waves were extracted (see the Appendix). From the frequency dependent state vector of the polarized states we have calculated : (a) total power (H + D + Z) spectra of pure states,(b) power spectra in directions W, D and Z, (c) the parameters of the polarization ellipse in the horizontal (H-D) plane (see Appendix) including ellipticity and angle of polarization. In addition, the spectra of the pure states have been inverse Fourier transformed to give filtered magnetograms of the pure states or polarized waves (see the Appendix). Although these methods of analysis may appear somewhat complicated, they are often essential for determining objective estimates of the parameters of the Pi 2’s. This is particularly true near the WTS, where the Pi 2 spectral band becomes filled with electrojet noise (Samson, 1983a).

442

J. C.

SAMSON and G. ROSTOKER

MRGNETDMETER DAY

59

i973,

200 FEB.

28

8 TIME

97 IHRSI

NT

I

FTCH MCMU LEDU URRN SMIT HAYR PROV

7

8

37 UNIVERSRL

8

3

FIG. 8. MACNET~CRAMSOF THE28 FEBRUARY(DAY 59) 1979 SUBSTORM.

THE DATA

Day 59,1979

The magnetograms for this event (Fig. 8) show a clearly isolated substorm onset at -08:08:45 U.T. The large, negative H-component perturbation indicates that most of the stations are in the vicinity of the enhanced substorm westward electrojet. Consequently the head of the WTS is most likely far to the West of the stations. A positive H-component excursion at MCMU and LEDU indicates the presence of a weak eastward electrojet to the South of the westward electrojet. Inspection of the Z-component shows that the westward electrojet was centered (AZ = 0)just South of FTCH at onset (note positive Z spike at onset at FTCH), and then jumped rapidly northward to be centered at URAN. The center of the electrojet first reached FTCH, and then PROV, HAYR and SMIT, in that order, indicating that the electrojet was tilted with respect to magnetic East-West. This tilt gives a negative AD. Latitude profiles at 08 : 10: 30 U.T. and 08: 12: 30 U.T. emphasize this apparent northward motion (Fig. 9). At 08: 10: 30 U.T. the electrojet was centered (AZ = 0) at 66-67”N, whereas at 08 : 12: 30 U.T. the electrojet was centered at 68-69”N. The D-component shows some correlation with the H-component because of the tilt of the electrojet. Note, however, that there is no latitudinal level shift in the D-component (i.e. D-components at 55”N and 77”N are the same),

indicating no net FAC. This feature suggests that the stations are situated to the East of the head of the WTS. The longitude profiles (Fig. 10) emphasize the northward expansion over the stations. At 08 : 10 : 30 U.T., all stations had positive AZ, whereas at 08 : 12 : 30 all stations had negative AZ. Riometer data from three Alberta stations are given in Fig. 11. All three stations show strong absorption spikes, with the southernmost station, MCMU, showing almost complete recovery to no absorption after the spike. A closer inspection of the traces indicates that absorption peaked at PROV approx. 2 min after the peak at MCMU. These riometer data suggest that the stations were at positions A (MCMU) and B (SMIT, PROV) in Fig. 6. A comparison of the latitude profile at 08 : 12 : 30 (Fig. 9, top) with the latitude profile in Fig. Sa, top, suggests that at this time the stations were far to the East of the head of the WTS. A comparison of the longitude profile at 08 : 12 : 30 (Fig. 10, top) with the longitude profiles in Fig. 5b supports this conjecture. Consequently we have placed the stations as shown in Fig. 7. Note, however, that at 08 : 10: 30, the stations were more poleward with respect to the WTS border, and also closer to the head of the WTS (compare Fig. 10 08 : 10: 30, with Fig. 5b, top). Finally we turn to the DMSP photographs ofauroral features at times near this event. The first photograph, Fig. 12, scanned over the interval 06360646 U.T., shows several quiet arcs including a faint arc at - 65”N.

443

Pi 2’s and the westward travelling surge DRY 59/79

8t2

30 UT

DAY

+~-----------+

59/79

BRSE

DRY 59/79

TIME

812:30

UT

730UT

810 30 UT

“l-7 P-

2-

2

a

2

0

2

R

D *-

5 H H

2.. 7 B ', 290

H / 293

/ 296 LONSI

F1c.9. LATITZJDEPROFILESFROMTHEALBBRTAARRAY,FORTHE DAY 59 EVENT, AT 08: lo:30 U.T. (BOTTOM) AND 08:12:X0 (T0P).

To compute the values for these latitude profiles, and those that follow, we have used the Alberta stations LEDIJ, MCMU, FTCH, and URAN, as well as standard observatories at Newport, Meanook, Yellowknife, and Cambridge Bay (see Table 1 in Rostoker and Samson, 1981). Basehneswereset at07: 3O:~U.T.,DayS9,1979. Amplitudes are in nT. All latitudes and longitudes are centered dipole coordinates.

Since the magnetic records showed no significant activity between 06:46 U.T. and 08:OY U.T. in the Alberta sector, this faint arc was possibly in the region of enhanced precipitation at onset. The second photograph (Fig. 13) (08 : 18-08 : 27 U.T.) shows a pronounced WTS with the head far to the West of the

299

302

305

TUCE

FIG. 10.LQNGITUIE YKOFILESOFTHE DAY PREVENT.

The stations used for the plot are PROV, HAYR, SMIT, and URAN; 8: 10: 3O(bottom); 8: 12: 30(top). Amplitudes are in nT. Alberta stations. Inspection of the magnetograms in Fig. 8 indicates that the westward electrojet tilted at an angle to magnetic East--West (Aif K 0), and was centered near HAYR (AZ = 0) at 8 : 23 : 00 U.T., with PROV to the South and URAN to the North of the center of the electrojet. All these features are compatible with the canonical mode1 of the WTS given in Figs. 2 and 3, and also indicate that the positions ofthe stations in Fig. 7 are essentially correct. The filtered pure states for the Pi 2’s are plotted in Fig. 14. The box at LEDU indicates the Pi 2 we are studying. A second Pi 2 occurred at 08 : 21 U.T. (see

444

J. C. SAMSON and RI

OXUER

i 1 za

iiHY 59

pcr?ti

157s,

FEB.

!

78.

_

I \L”-r””

*w

*[ SMrT -.*7

1

9 71

YE

CHRS I

Pm. 11.RIOMETERDATA FOR DAY 59, 1979. Quiet day baselines have been removed from this data. LEDU and MCMU). However, this onset was - 13 min after the first Pi 2, allowing us to classify this as an isolated event. The Pi 2 at LEDU had a frequency of - 8 mHz, and was also seen at this frequency at the AFGL mid latitude stations.

G. ROSTOKER

Pure state power spectra of the magnetic pulsation data are given in Fig. 15. The 8 mHz peak shows at all stations except HAYR and SMIT. The lack of a peak at HAYRandSMITisdueto thenorthwardmotionofthe westward electrojet, which crossed over these two stations in the interval of the Pi 2. This motion distorts the Pi 2 fields, making them look unpolarized. We shall classify the 8 mHz pulsations as the Pi 2’s for this event. We consider the other spectral peaks to be due to pulsations from other sources. Hence it is clear that the Pi 2 frequency is latitudinally invariant, at least within the spectral resolution (resolution of E 2 mHz) of the data here. Another interesting feature in these spectra is that three peaks (4,8 and 16 mHz) predominated at most of the stations, particularly at PROV. The 16 mHz pulsations are clearest at HAYR (Fig. 14). Since these 16 mHz pulsations had peak intensities at much higher latitudes than the Pi 2’s, they were most likely not harmonics of the 8 mHz Pi 2, and we infer that they had a distinctly different source. The latitudinal polarization characteristics of the 8 mHz Pi 2 are depicted in Fig. 16. There is a clear latitudinal change in the sense of polarization from counterclockwise (+) at LEDU, to clockwise (-) at the other three stations. This polarization change was caused by a near 180”latitudinal phase changein the H-

c

.

I FIG. 12. DOT-DIAGRAM OFA DMSP

PHOTOGRAPHOF THEAURORAOVERTHETIMEINTERVAL06 : 30-06 : 46 U.T., DAY 59, 1979.

Coordinates

are centered

dipole.

445

I y”N ‘.

yO”

3oo”

I

!

;lO”E

-

I’ -

.A_..

. F~13.

PHOKGRAPHOFTHEAURORAOVEKTHETIMEINTEKVAL 08:18-08:27U.T., DAY 59,1979. The scan at the latitude of 67”N geomagnetic occurs at -08 : 23-08 : 25 U.T.

DOT-DIAGRAMOFA

DMSP

vRGNETCt?fTER DRY

59

‘23 1973.

FCt?.

?F!

NT

I

FIG. 14. FILTERED PIJRE STATESOF THE MAGNETOMETER DATA FOR DAY 59 (SEEAPPENDIX). These data were first detrended with a 3 mHz high pass filter before filtering for pure states. The Pi 2 associated with the event is outlined by the box on the LEDU data.

446

J. C. SAM~N and

FREQUENCY

G. ROSTOKER

(mHz 1

FIG. 15. PURE STATEPOWERSPECTRAOF THEDATA OVERTHEINTERVAL08 : 0848

The spectra shown are the functions

: 20 U.T., DAY 59.

fP(f) where f is frequency, and P is the pure state power (W + D + Z), at the frequency f (see Appendix).

component. A local intensity minimum occurred at or near the latitude of the polarization reversal (at least in the H-component). The polarization reversal also occurred South of MCMU, and consequently was South of the substorm enhanced electrojet. As we shall discuss later, we consider this polarization reversal and H-component minimum to indicate two distinct regions (poleward and equatorward) of Pi 2 localization (see also Rostoker and Samson, 1981, Fig. 19). We note at this point that the absolute maximum in the power occurred at FTCH, just South ofthecenter of the westward electrojet in its most poleward position. This observation is compatible with the results of Rostoker and Samson (1981). To emphasize the dynamiccharacter and complexity of the Pi 2 polarizations near the onset, we have plotted a hodogram (H-D plane) ofthe Pi 2 perturbation vector at PROV (Fig. 17). The initial cycle of the Pi 2 had (+) polarization, and then the polarization switched to (-). The time of the switch corresponds to the time when the center of the precipitation region passed over PROV. Since the data presented in Fig. 16 are an average over a 12 min interval, this initial (+) polarization is not seen.

The magnetic and riometer-absorption data indicate that PROV was initially North of the center of the precipitation, and the enhanced westward electrojet. Consequently there were, in fact, two latitudinal polarization reversals. This high latitude reversal, which is evident in Fig. 17, correlated with the northern border of the WTS and a region of net FAC. This high latitude reversal also shows in the data for Day 265. Day 265, 1978 This breakup event occurred at a relatively low latitude (see Fig. 18a, b, c) and consequently many of the Alberta stations remained north of the poleward border of the WTS, even after the poleward expansion. Inspection of the magnetograms in Fig. 18 shows that the westward electrojet intensified at - 07 : 49 : 30 U.T., just South of MCMU, and then jumped rapidly northward (note the positive 2 spike at MCMU). The northernmost position of the center of the electrojet was between FTCH and MCMU. The Pi 2 for this event is very large (- 100 nT), and can be clearly seen at MCMUin the H-component (Fig. 1Sa).

Pi 2’s and the westward 1.0

travelling 9

H

II.

447

surge (1. 0.

-29.0

PROV

0. 11.0.

I

I

0.0

29.0

D

64 GEOMAGNETIC

66

68

70

72

LATITUDE

FIG. 16. LATITUDE PROFILESOF THE POLARIZATION PARAMETERS (H-D PLANE) OF THE 8mHz Pi2, IN THE INTERVAL 08 : OS-08 : 20 U.T., DAY 59. The powers (pure state power in direction H, etc) have been normalized by dividing by the maximum observed power in any ofthe three components. The solid line and circles indicate

the ellipticity.

The riometer data are shown in Fig. 19. Only MCMU had a strong absorption spike at the onset time, and absorption continued after the initial spike. These absorption features, and the magnetograms, suggest that the Alberta array was slightly to the East of the head of the WTS. Also, both the magnetic and absorption data indicate that the onset was South of MCMU. Latitude and longitude profiles ofthis event are given in Fig. 20, and equivalent current vectors (including standard observatories, and the EMR stations) are given in Fig. 21. The latitude profiles have a large Dlevel shift, indicating the presence of a latitudinally localized, net upward FAC near 65-66”N. A comparison of the latitude profile with Fig. Sa(bottom), the longitude profile with Fig. 5b (top), and the equivalent currents (Fig. 21) with those in Fig. 4, indicates that the Alberta array should be situated as shown in Fig. 7. The high-pass filtered Pi 2 data are given in Fig. 22. These Pi 2 data and the riometer data indicate that this was an isolated event, with the next onset at -08 : 04 U.T., at least 14 min after the original onset. The filtered data also suggest that the Pi 2 was localized at MCMU, just South of the northernmost excursion of the center of the westward electrojet.

FIG. 17. POLARIZATION HODOGRAM OF THE 8 mHz Pi 2 AT PROV, OVER THE INTERVAL 08 : 08 : O&O8 : 12 : 00 U.T., DAY 59. The data were band pass filtered (7-9 mHz) before plotting the hodogram.

The latitudinal polarization data are depicted in Fig. 23. The powers in the H-component emphasize the extreme latitudinal localization of the Pi 2. A latitudinal polarization reversal occurred between MCMU and FTCH, coinciding with the region of net upward FAC, and the D level shift in the latitude profile (Fig. 20). This polarization reversal is consistent with that inferred from the PROV data from Day 59, with (+) polarization to the North of the surge-border, and (-) polarization within the region of the WTS. The summary plot of the polarization at the Alberta and EMR arrays (Fig. 24) shows that the high latitude polarization reversal extended over a large longitudinal range. A comparison of Figs. 24 and 21 suggests that this latitudinal reversal was near the northern edge of the WTS. At the EMR stations the vectors are predominantly northward, indicating polarization which is dominated by ionospheric current flowing East-West. At the Alberta array there was some tilt to the North-East, possibly due to the influence of net oscillating FAC. Day 325, 1978

This event, which occurred at 05:07:45 U.T., followed an earlier event studied by Rostoker and Samson (198 1). The magnetograms can be found in Fig. lOa, b,c of that reference. The equivalent current vectors for this event are shown in Fig. 25. At 05 : 10 : 00, the Alberta stations clearly covered the head of the WTS, as the AZ = 0 transition (dotted line) indicates. The riometer data (Fig. 26) shows that this was a simple onset, and that SMIT was slightly to the North of the

448

J. C. SAMSON and G. ROSTOKEIR

Pi 2’s and the westward

travelling

449

surge

5511 287

301

329%

315

LONGITUDE

FIG. 21. EQUIVALENT CURRENT VECTORSAT 07 : 55 265.

8’

I~

IJ II : “i E i?‘3 i

L

5

T :lic

; “KL

’

FIG. 19. RI~METEK DATA FOR DAY 265.

onset. The riometer at MCMU showed only minimal absorpion, and PROV showed absorption characteristics of the head of a WTS (see pulse C in Fig. 6, and Tighe and Rostoker, 1981). The filtered pure states at LEDU (Fig. 27) indicate that the activity over the interval from 04 : 00 to 05 : 10 U.T. had many substorm onsets. However, after the 05 : 07 onset, there were no further Pi 2’s, allowing us to classify this as an isolated event. Pure state power spectra at LEDU indicate that the Pi 2 had a frequency of 8 mHz. DRY265/78

755

: 00, DAY

Quiet day baselines from Day 262 have been subtracted from the data. These data are from the Alberta array, the EMR array, and the standard observatories at Meanook and Yellowknife. Dark circles are negative AZ.

The polarizations of the 8 mHz Pi 2 in the H-D plane are summarized in Fig. 28. The northern and western border of the WTS correlate with a polarization change in the Pi 2’s, with (-) polarization South and (+) polarization North of the border. We do not, however, have sufficient stations to determine whether the border and reversal are coincident. These northern polarizations agree with those on Day 265. Note also that there is a lower latitude polarization reversal, with LEDU and MCMU having (+) polarization. An inspection of Fig. 7 indicates that both Day 325 and Day 59 had the Alberta stations situated at about the same latitude with respect to the WTS, and ORY265/76

0 UT

755

0 UT

:7$-

&-l--

293

296

LONGITUDE-BASE

FIG. 20. LATITUDE AND LONGITUDE PROFILESFOK07 : 55

Quiet day baselines

: 00 U.T.,

from Day 262, 1978, have been subtracted

299 DFIY

DAY 265

from the data.

262

302

c

305.00

J. C.

SAMSON

and G. ROSTOKER

MRGNETOMETER

H

DRY 265

_.-_I.

1978.

c

SEPT

22lJRY

265

1978.

SEPT

22

I

100 Nl

l_-.-..

FTCH

MCMU

URRN

PF?OV

7 UNIVERSRL

9

8 TIME

7

UNIVERSRL

ftlRS1

8

TIME

9

LtiRSI

Fro. 22. HIGH PASS (3 rnHzw~o~f)PxLrE~~ DATAFROMTHE ~AN~~c(~A~~N~N~,~AY 265. Thesedata were not filtered for pure states, because the Pi 2 is quite large and clearly visible in the high-passed

data. consequently this southern polarization reversal on Day 325 matches the data from Day 59. Thus there are actually two latitudinal polarization reversals in regions slightly to the East of the head of the WTS. A model to explain both these reversals will be given in the discussion of this paper. Finally, we turn to contour plots of the pure state power in the 8 mHz Pi 2 (Fig. 29). These data emphasize that the peak intensity of the Pi 2 is not always coincident with the WTS, but is further to the East, possibly at the position of the initial breakup. This interpretation seems reasonable, since 2, for this event is at 32412”. These results for the intensities appear to disagree with those of Pashin et al. (1982), who found that the intensitymaximaofthePi~scoinc~d~with theheadof the WTS. This disagreement might arise from three factors. First, if the WTS shows little westward motion

after the initial breakup, the surge and intensity maximum might appear to coincide. The WTS on Day 325 showed considerable westward motion. Second, if the azimuthal wave number of the Pi 2 is very large, the contribution of ionospheric currents to the magnetic field can be much less than the contribution from fieldaligned currents near the edge of the Pi 2 localization (see Samson, 1983a). Third, the data in our study are based on pure state powers, whereas Pashin et al. analysed all the power centered near the frequency of the Pi 2. Random ~uctuations from the large FAG near the head of the WTS can add considerable power to the Pi 2 band. RISCTJSSION

A composite plot of the polarjzation data from this study, and that of Rostoker and Samson (1981) is given

451

Pi 2’s and the westward travelling surge

551 287

301

315

329%

LONGITUDE FIG. 25. EQUIVALENTCURRENTVECTORSAT 05 :10: 00 DAY 325, 1978. A quiet day baseline has been removed. The dotted

indicates

-‘.:-2goo GEOMAGNETIC

LATITUDE

FIG. 23. LATITUUEPROFILES OFTHEPOLARIZATION PARAMETERS PLANE)OF THE9 mHz PULSATIONS, OVERTHEINTERVAL 07 : 47 : O&O7: 51: 00 U.T., DAY 265 (SEE CAPTION TO FIG. 16 (H-D

AND APPENDIX).

in Fig. 30. In order to simplify the interpretation, local substorm coordinates (@,,A,) have been used. Inspection of this plot shows that the sense of polarization shows quite distinct patterns, whereas the orientations (polarization angles) show considerable scatter. This scatter in the orientations might possibly be caused by earth-induction effects which are quite prevalent in this frequency band. Consequently the orientations should be interpreted with care.

the estimated

position

The region to the West of the wedge-center (A.,= 0) shows what looks like, at first appearance, four quadrants of the sense of polarization, similar to the results of Kuwashima (1978) and Pashin et al. (1982). The pattern is, however, much more complicated than this. If we place a longitudinal demarcation line at I, = - 20”, then in the interval - 40” < I, < - 20”, there is a latitudinal reversal in the sense of polarization at 8, N O”, whereas in the interval - 20 < A, < 20”, there are latitudinal reversals at 0, = 4” and at 0, N -3”. Clearly the longitudinal and latitudinal demarcation lines do not intersect at a common origin, and the four quadrant pattern of Pashin et al. does not explain the data in Fig. 30. The longitudinal demarcation at 1, % - 20” appears

3RY 325

il DB

1978.

NOV.

21.

LONGITUDE 24. SUMMARY OF H-D

POLARIZATIONS OF THE

Pi 2,

07:47:00-07:51:OOU.T.,D~~265. indicate the orientation of the major axis of the polarization ellipse. Black arrows indicate (-) polarization.

line

of the WTS boundary.

?ICYETER

FIG.

U.T.,

The arrows

FIG. 26. RIOMETER DATA

FOR

DAY 325.

I

452

J. C. SAMSONand G. ROSTOKER MOGNETOMETER

LEDU DAY t

325 ___

1978,

NOV.

T10

21

NT

1

'-_I

I-

F ’

61

I

267

/

301

315

9%

LONGITUDE

5

4 UNIVERSAL

TIME

FIG. 29. CONTOURS OF THEPURESTATEINTENSITIES OR POWER (nT*/Hz) (H + D +Z) FORTHE8 mHz Pi 2’s IN THEINTERVAL 05 : 08 : 005 : 13 : 00 U.T., DAY 325. The circles indicate the stations, and the dotted line is the border of the surge.

6 ItlRSl

FIG. 27. FILTEREDPURESTATESOF THEMAGNETOMETER DATA FROMLEDU FORDAY 325.

to lie near the head of the WTS. To the East of this demarcation,

the high latitude

(0, N 4”) lies near, but slightly poleward

polarization

reversal

equatorward

of the

border

of the WTS. To the West of the demarcation line, the latitudinal reversal is near the latitude of the substorm onset (0, N 0”). Both of these latitudinal reversals coincide with regions of net FAC associated with substorm enhanced current systems. In both cases, the ambient substorm FAC is flowing upward. Examples of this feature are found in the latitude profile for Day 265 (Fig. 20), where the D-level shift indicates net upward current near the polarization reversal (Fig. 23), and in Fig. 12 of Rostoker and

730v

55-----k267

301

329’E

LONGITUDE

FJG.28.SUMMARY OFTHEH-D POLARIZATIONSOF THE8 mHz Pi 2’s OVERTHEINTERVAL 05 : 08 : 00-05 : 13 :00 U.T., DAY 325. The absolute values of the ellipticities are given beside the arrows. A dark arrow indicates negative ellipticity. The dotted line indicates the boundary of the surge.

Samson(l981)(Day325,04: 50U.T.; thisevent is to the West ofthe surge). These field-aligned currents will play an important role in the model of the Pi 2’s to be discussed later. A clue to the reason for the low latitude (0, N - 3”) polarization reversal in the interval -20” < 1, ,< 20 can be found by inspecting the latitudinal powers in Fig. 16. The latitudinal reversal coincides with a minimum in the H-component. We interpret this minimum as being due to the transition from the poleward Pi 2 associated with the westward electrojet, to the equatorward Pi 2 associated with the eastward electrojet (Rostoker and Samson, 1981, Fig. 18). A study of the powers in the region -40” < i, < -20” indicates that most of the power in the Pi 2 is localized near, or South of our lowest latitude station, LEDU (see e.g. Rostoker and Samson, 1981, Fig. 13). Conversely, Figs. 23 and 29 indicate that East of i, N - 20” the poleward Pi 2 shows the greatest intensities. The polarizations that are seen in the Pi 2’s near the electrojet are most likely due to phase differences between the local net Hall current (integrated over latitude) and the local net field-aligned current (Samson, 1983a), as well as latitudinal motion of the field-aligned current region (see e.g. Day 59). Obviously the polarization problem is a complicated one, and a detailed picture will require numerical models. We can, however, drive some of the essential details of the polarizations by considering a very simple model with azimuthal propagation of the FAC. Since the onset of the Pi 2 and the onset of the substorm currents coincide (see e.g. MCMU in Fig. 18), the substorm currents and the Pi 2 currents must share a common morphology at the substorm onset. Thus the Pi 2 must evolve from the current system given in Fig. 1.

453

Pi 2’s and the westward travelling surge

FIG. ~O.ASUMMARYOFTHEPOLARIZATIONS(H--DPLANE)OFTHEEVENTSGIVENBYROSTOKERANDSAMSON(~~~~) ANDTHEEVENTSINTHISSTUDY.

Local substorm coordinates (8,, I,) are used. Dark arrows indicate clockwise polarization.

The westward electrojet is associated with the poleward Pi 2 and the eastward electrojet is associated with the equatorward Pi 2. In Fig. 31 we have assumed that the initial upward current (arc brightening) occurs simultaneously over the region -x0 < x < x,,, at the latitude y,. This FAC pulse is partially reflected from the ionosphere (Maltsev

et al., 1974; Mallinckrodt and Carlson, 1978 ; Nishida, 1979), and multiple reflections from both hemispheres (or from the distant magnetotail) give oscillating currents. Just after the onset time, t,, the initial upward current expands in the y-direction (azimuthally), at a velocity II, to the West, and v, to the East. Note that v, need not be the WTS velocity, since the WTS can be considered a latitudinal expansion of an established FAC. Suppose v, = v, = v, and that the FAC at latitude y, expands in a self-similar form, then the current is j, (~3Yz>t) = 1(x/R(t))

0

(onset 1

where R(t) = x,, + vt, 1(x/R(t)) = 0 if 1x1> R(t), and the onset is at t = 0 (R(0) = x0). ff, in addition, we assume that reflection begins at the time, t,, when the FAC reaches a specific longitude x (t, = (x-x,,\ v-r), then the FAC can be approximated by the function

X’

if@, y,, t) = 1(x/R(t)) [l -a(t-

FIG.

31. A

MODEL FOR THE TIME DEPENDENT ASSOCIATEDWITHTHE Pi 2 (TOP).

(1)

CURRENTS

The polarization diagrams (middle and bottom) are explained in the text. The symbol (+) denotes counterclockwise polarization (H-D plane) and (-) denotes clockwise. D, indicates a reversal due to field-aligned currents and D, denotes a reversal due to ionosphericcurrents. Thedashed line (top) is the boundary of the enhanced conductivity. Open arrows show the electric field.

t,) sin w(t- t,)]

(2)

where w = 27cTg ‘, and Tsis the “travel” time from the ionosphere to the reflection point and back. The time dependent function a(t - t,) will depend in a complicated way on the time-dependent reflection coefficients in the ionosphere (Ial K 1.0) and T,.Figure 32 illustrates the FAC function (2) for a specific case. We shall also assume that, in general, the azimuthal scale sizes, 1,, of the Pi 2, are much greater than the latitudinal scale sizes, 1, (I, >> Q. Then the quasistatic condition V x E N 0 gives E,jl, = E,/1,, and E, = 0. To a first order, the electric field points either North or South (depending on the position and the time in the Pi 2 cycle). Consequently the picture for the ionospheric closure currents ji is greatly simplified, and these currents flow at an angle 0 = tan -I (X&‘) Fig. 31, or Samson, 1983a, Fig. 9). The net field-

454

J. C.

aligned current associated Mx) = js (x7 Yz) -j,

with the poleward

SAMSON

and G. ROSTOKER

Pi 2 is

(x, Y3) = j, (x, YZ) -j,(x-(Y3

-Y,)GG

integrated

Hall

‘>Y,).

(3)

\ The latitudinally poleward Pi 2 is j,(x)

Y3 ji(x, Y) *n dY 1 YZ x = cos 0 s (x-(Y, -YzPHZP

current

in the

=

j/(x’, ~2) dx’

(4)

l)

where n is a unit vector pointing eastward, and j, is positive downward. Equation (4) indicates that in the region of the poleward Pi 2, j,(x, t) will lag jt(x, t). This lag is caused by the westward expansion, since much ofjH(x, t) is due to FAC in the westward expansion. Similarly, the Hall current in the region of the equatorward Pi 2 (this Hall current is antiparallel to the Hall current in the poleward Pi 2), will lag the net FAC due to the eastward expansion of the FAC region. To illustrate this point, we have computed j,(x = 0, t) and j,(x = 0, t) for the model in Fig. 32. The time series in Fig. 33 shows j,(t) (solid line) and j,,(t) (dashed line) for the poleward Pi 2. The FAC and Hall current

180

sec.

10

*

100 80

3S /\

1:

A0

-1000/\fO

A

h.

FIG. 32. THE FAC j, (x, y,, t) I;OR EQUATION (2) WITH a(t- t,) = 0.7(INDEPENDENT OF TIME), u = 3 km s-l, AND TB = 100 s. The FAC are plotted as a function of longitude x, at the given times. In this case, a positive amplitude indicates upward FAC.

I

0

I

100

I

200

TIME(sec.) FIG. 33. THE TIME SERIES j,(x = 0, t) (SOLID LINE) AND j,,(x = 0, t) Pi 2, BASEDON THE MODELIN FIG. 32. ZH/XP = 3.0, and y, -y, = 100 km. Units are arbitrary and the two plots are not to scale. (DASHED LINE) FOR THE POLEWARD

are initially in phase, and then as the FAC expands westward, j, begins to lag j,. Since the FAC contributes largely to the Dcomponent of the magnetic held, and the Hall electrojets contribute to the H-component, the polarization pattern shown in Fig. 31 (middle) should occur. The demarcation at the line D, is caused by the FAC, with a 180” latitudinal phase shift in the Dcomponent. Line Di marks the transition from regions dominated by the magnetic fields of the equatorward Pi 2 to regions dominated by the poleward Pi 2. Consequently, line Di should show a 180” latitudinal phase shift in the H-component. The formation of the WTS complicates the pattern. Since the WTS is associated with a poleward excursion of the substorm currents, the polarization pattern of the Pi 2’s in thesurge might be found bydistortingline D, to follow the northern border of the WTS. If this is done, the pattern in Fig. 31 (bottom) results. Acomparison ofFig. 3 1 (bottom) with Figs. 28 and 30 indicates that this pattern is quite compatible with the experimental results. Thus we see that the head of the WTS marks the longitudinal transition from regions which are dominated by the equatorward Pi 2 (to the West) to regions which are dominated by the poleward Pi 2 (to the East). The model in Fig. 31 can also be used to explain the intensity data in Fig. 29. The Hall conductivity in the aurora1 region can be 3-5 times the Pederson

Pi 2’s and the westward travelling surge conductivity (Brekke et al., 1974), and consequently a large East-West electrojet will form in the region associated with the poleward Pi 2, but to the East of the initial onset. In analogy with the substorm enhanced westward electrojet, the Hall current associated with the poleward Pi 2 will give maximum field intensities to the East of the onset, and the polarization will be predominantly in the H-direction. These polarization directions are compatible with the results in interval 0 < dj < 20” (Fig. 30). If, however, /, is relatively small (but still greater than ‘J, the net Hall current will be small (i.e. j&,, see Samson, 1983a),and magnetic fields associated with the Pi 2-Hall electrojet would be very small. In a sense, the electrojet component would seem to disappear, and only the held-aligned component would remain. The results of Pashin et al. (1982) were possibly for an event with small azimuthal scales. Then the intensity maximum would be expected to be near the head of the WTS, where the FAC is largest. One last point must be considered, even though it complicates the picture. We have shown that near the onset, the net Hall current generally lags the net FAC (Fig. 33). However, in regions far to the East, or West of the onset (i.e. x >> (y3 - y,)C& ’ for thepoleward Pi 2) the net Hall current j, will lead the net FAC, j, (see Samson, 1983a). The reason for this is that j, now involves an integral over FAC which occurred before those at position x (i.e. we are in the eastward expansion region of the FAC, where the poleward Pi 2 dominates). Most of the data presented here are not in this region, but are close enough to the onset for the polarizations in Fig. 31 to be valid. We emphasize, at this point, that even though the Pi 2 currents, and the substorm enhanced currents have a similar morphology, the regions of the substorm enhanced currents and the Pi 2 currents are not always coincident during the evolution of the substorm. Often the latitudinal localization of the Pi 2 is equatorward of the center of the corresponding substorm electrojet (see e.g. Rostoker and Samson, 1981, Figs. 3 and 4) apparently reflecting the configuration of the substorm during early stages of its development.

CONCLUSIONS

In summary we would like to list the following features of Pi 2’s near the surge : (a) In analogy with the substorm enhanced eastward and westward electrojets, the Pi 2’s have poleward and equatorward localizations. Further results from mid latitude stations are needed to delineate the region of localization of the equatorward Pi 2. Most of our data

455

have shown only that the magnitude of the equatorward Pi 2 magnetic field is increasing toward the South, and no local maximum has been observed. (b) The poleward Pi 2 shows the largest amplitudes, but these amplitudes are maximum to the East of the head of the WTS. The maximum of this Pi 2 is probably associated with large, ionospheric Hall currents. If, however, the azimuthal scale size is small, the magnetic field from this electrojet will be severely attenuated at the ground (see the discussion). (c) The elliptical polarizations of the Pi 2’s (as observed on the ground) are caused by azimuthal expansion of the latitudinally localized FAC associated with the arcs. This expansion ofthe region of FAC gives latitudinally integrated Hall currents which are phase shifted with respect to the net FAC at the same longitude. These apparent propagations in the East and West directions might also be used to explain the polarization of mid latitude Pi 2’s (Samson, 1983a). (d) The westward front of the surge marks a longitudinal demarcation of the Pi 2’s, with equatorward Pi 2’s predominating to the West, and poleward Pi 2’s predominating to the East. The actual mechanism for the formation of the Pi 2 is still far from resolved. However we would like to present the following picture to summarize our observations, and to point out some future directions for study. Many observations support the possibility that the substorm current system is, at least in part, due to a redirection of the cross-tail current from the plasma sheet, along field lines to the ionosphere (see e.g. McPherron et al., 1973, and references therein). The westward edge of the FAC current system (net upward current) apparently maps to the equatorward end of the Harang discontinuity (see e.g. Baumjohann et al. (198 I), and references therein). Directly after the onset of the FAC, a WTS forms and travels along the Harang discontinuity. The formation of the WTS is accompanied by a poleward jump of the westward electrojet and the precipitation region (see the results in this paper, and Fig. 2). We believe that the Pi 2 forms from the reflection of the initial FAC pulse at the ionosphere, and that some of this energy is trapped on field lines which collapse to dipolar, just after onset. This dipolarization is seen in the ionosphere as the sudden northward expansion of the WTS. Consequently we expect the largest amplitudes of the Pi 2 to be near the equatorward border of the Harang discontinuity, and possibly equatorward of the substorm enhanced electrojet. As the FAC expands westward, in conjunction with the WTS. there may be a further dipolarization of these

456

J. C. SAMSON and G. ROSTOKER

field lines to the West of the initial onset and also the development of the “trapped” Pi 2 in this region. It is this longitudinal expansion of the FAC, and the large Hall conductivities in the region of the WTS which lead to the elliptical polarizations of the Pi 2’s. This expansion velocity is probably a direct (along the field lines) mapping of the expansion of the perturbation region in the magnctotail. Thus the polarizations of the Pi 2’s might contain considerable information

on

mechanisms

associated

the

evolution with

and substorm

morphology

of

onsets.

AcknowledgementsWe are grateful to Transport Canada (Telecommunications Branch), Dept. of Environment and Fisheries (Atmospheric Environmental Service- Western Regional Headquarters) and to Mr and Mrs Ted Malewski of Fort Providence, N.W.T. for their help in operating the magnetometer array whose data were used in this study. Data from the Churchill array and the standard magnetic observatories in Canada were provided by the Dept. of Energy, Mines and Resources (Earth Physics Branch). in Ottawa, Canada, and by the World Data Center A (Solar Terrestrial Physics) in Boulder, Colorado. The Air Force Geophysics Laboratory in Bedford kindly supphcd mid latitude magnetometer data which we used to identify the center of the substorm current wedge. We also wish to thank Dr H. N. Kroehl of WDC-A in Boulder. Colorado for providing us with the DMSP amoral data. This research was supported in part by the Department of Energy, Mines and Resources (Earth Physics Branch, Geomagnetism Division) under Contract OSU79-00025, and in part by the Natural Sciences and Engineering Council (NSERC, Canada). This research is part of the International Magnetospheric Study. One author (J. C. Samson) currently holds an NSERC University Research Fellowship. REFERENCES Akasofu, S. I. (1968) Polar and Magnetospheric Suhstorms. Springer, New York. Armstrong, J. C., Akasofu, S.-I. and Rostoker, G. (1975) A comparison of satellite observations of Birkeland currents with ground observations of visible aurora and ionospheric currents. J. yeophys. Res. 80, 575. Baumjohann, W., Pellinen, R. J., Opgenoorth, H. J. and Nielsen, E. (1981) Joint two-dimensional observations of ground magnetic and ionospheric electric fields associated with aurora1 zone currents: Current systems associated with local aurora1 breakups. Planet. Space Sci. 29,431. Brekke, A., Doupnik, J. R. and Banks, P. M. (1974) Incoherent scatter measurements of E region conductivities and currents in the aurora1 zone. J. yeophys. Res. 79,3773. Brillinger, D. R. (1975) Time Series, Data Analysis and Theory. Holt, Rinehart and Winston, New York. Hargreaves, J. K., Chivers, H. J. A. and Nielsen, E. (1979) Properties of spike events in aurora1 ratio absorption. J. geophys. Rex 84,4245. Horwitz, J. L., Doupnik, J. R. and Banks, P. M. (1978) Chatinika radar observations of the latitudinal distributions of aurora1 zone electric fields, conductivities, and currents. J. geophys. Res. 83, 1463. Inhester, B., Baumjohann, W., Greenwald, R. A. and Nielsen,

E. (1981) Joint two dimensional observations ofground and ionospheric electric fields associated with aurora1 zone currents. J. Geophys. 49, 155. Kamide, Y., Akasofu, S.-I. and Rostoker, G. (1976) Fieldaligned currents and the aurora1 electrojet in the morning sector. J. yeophys. Res. 81, 6141. Kamide,Y.andRostoker,G.(1977)Thespatialrelationshipof field-aligned currents and aurora1 electrojets to the distribution of nightside auroras. J. yeophys. Res. 82, 5589. Kisabeth, J. L. and Rostoker, G. (1973) Current flow in aurora1 loops and surges inferred from ground-based magnetic observations. J. geophys. Res. 78,5573. Kisabeth, J. L. and Rostoker, G. (1974) Theexpansion phase of magnetospheric substorms, 1. Development of the aurora1 electrojet and aurora1 arc configuration during a substorm. J. geophys. Res. 79, 972. Kisabeth, J. L. (1979) On calculating magnetic and vector potential fields due to large scale magnetospheric current systems and induced currents in an infinitely conducting earth, in Quantitative Modeling of Magnetospheric Processes (Edited by Olson, W. P.), pp. 473-498. Geophysical Monograph 21, Amer. Geophys. Union. Kuwashima, M. (1978) Wave characteristics of magnetic Pi 2 pulsations in the aurora1 region-spectral and polarization studies. Mem. Nat. Inst. Polar Rex Japan, Series A, 15, l-79. Mallinckrodt, A. J. and Carlson, C. W. (1978) Relations between transverse electric fields and field-aligned currents. J. geophys. Rex 83, 1426. Maltsev,Yu. P., Leontyev, S. V. and Lyatsky, W. B.(1974) Pi2 pulsations as a result of evolution of an Alfven impulse originating in the ionosphere during a brightening of aurora. Planet. Space Sci. 22, 15 19. McPherron, R. L., Russell, C. T. and Aubry, M. P. (1973) Satellite studies ofmagnetospheric substorms on August 15, 1968,9.Phenomenologicalmodelforsubstorms. J.geophys. Res. 78, 3131. Nielsen, E. and Greenwald, R. A. (1978) Variations in ionospheric currents and electric fields in association with absorption spikes during the substorm expansion phase. J. qeophys. Res. 83, 5646. Nielsen, E. (1980) Dynamics and spatial scale of aurora1 absorption spikes associated with the substorm expansion phase. J. geophys. Res. 85, 2092. Nishida, A. (1979) Possible origin of transient dusk-to-dawn electric field in the nightside magnetosphere. J. yeophys. Res. 84, 3409. Pashin, A. B., Glassmeier, K. H., Baumjohann, W., Raspopov, 0. M., Yahnin, A. G., Opgenoorth, H. J. and Pellinen, R. J. (1982) Pi 2 magnetic pulsations, aurora1 break-ups, and the substorm current wedge: a case study. J. Geophys. 51.223. Pytte, T., McPherron, R. L. and Kokubun, S. (1976) The ground signatures of the expansion phase during multiple onset substorms. Planet. Space Sci. 24, 1115. Rostoker, G. and Samson, J. C. (1981) Polarization characteristics of Pi 2 pulsations and implications for their source mechanisms ; location of source regions with respect to the amoral electrojets. Planet. Space Sci. 29, 225. Samson, J. C. (1972) Three-dimensional polarization characteristics of high latitude PC 5 geomagnetic micropulsations. J. geophys. Rex 77, 6145. Samson, J. C. (1983a) Pi 2 pulsations : high latitude results. Planet. Space Sci. (in press). Samson, J. C. (1983b) Pure states, polarized waves, and principal components in the spectra of multiple, geophysical time-series. Geophys. J.R. astr. Sot. (in press). Samson, J. C. and Olson, J. V. (1980) Some comments on the

Pi 2’s and the westward descriptions of the polarization states of waves. Geophys. J.R. astr. Sot. 61, 115. Tighe, W. G. and Rostoker, G. (1981) Characteristics of westward travelling surges during magnetospheric substorms. J. Geophys. 50, 51. Wallis, D. D., Anger, C. D. and Rostoker, G. (1976)The spatial relationship of aurora1 electrojets and visible aurora in the evening sector. J. geophys. Res. 81, 2857. Wiens, R. G. and Rostoker. G. (1975) Characteristics of the development of the westward electrojet during the expansive phase of magnetic substorms. J. yeophys. Res. 80, 2109.

APPENDIX Estimation of the parameters oj‘pure states und polarized waves The time series representation of the data from the three component magnetometer is xT = [f{(t). D(r), Z(t)] = Ix,(t), xl(t)> x,(t)] where t = 0, N - 1 and N is the length of the individual series. The spectral representation of (A-l) is N-L C x(t) e--i”r, 1=0

~((0) = (2x)-’ An estimator 1975)

for the spectral

s(k) = (2mf where t denotes

(A-l)

the Hermitean

(A-3)

(A-4) if (A-5)

where p(t) gives the temporal evolution direction of polarization. In analogy polarized in the spectral representation

of the pulse, and r is its with (A-5) a wave is if

z(w) = a(w)u

(A-6)

s(k) = (2m+l)-’

‘r &Jllll+. ,=t-m

(z and u Thus for have the spectrum,

have our form then

(A-7)

The matrix S(k) has only one non-zero eigenvalue, and the degree of polarization is equal to one (Samson and Olson, 1980). We shall call a process of this forni a pure state or linearly polarized wave (in a unitary space). In general our observations will have the form (assuming a pure state is present) z(j) = a(j)u + Ej where cj is a random use the model

noise vector. In a statistical z = au+&

and 5 denotes the expectation. The problem now is to determine estimators for a(j) and u, denoted d(j) and ti respectively. Since the d(j) and i are generally nonunique, some optimality criterion must be used. of the If ci(i) = b’z(j) (i.e. the a(j) are linear combinations components of z(j)) then a suitable optimality criterion is (Samson, 1982b) the mean square error ([z-E-b+zB)+E-‘(z-c-b’zii)]

(A- 10)

where the variances have been standardized using the metric E-‘. By minimizing (A-10) with respect to b and ti we obtain the estimators (Samson, 1983b) cio’) = i+(k)(E-

l(k)-s-‘(k))z(j)(ii+E-‘i)-’

(A-11)

(A-12)

where fi(k) is the eigenvector corresponding to the maximum eigenvalue of E- “Z(k)$k)E-“Z(k). For each position, k, of the spectral window, we can compute a new set of 6(j). However, we shall choose the center estimate b(k) and thus the pure state spectral representation is ci(k)ti(k), where b(k) and B(k) are defined in (A-l 1) and (A-12). The power spectrum of the pure states is power(k)

x(t) = &)r

where z and u are vectors in a unitary space complex components), and a is complex. representation (A-4), we look for waves that z(j) = a(j)u. If the waves are polarized over the

ii{E} = 0, cias +) =E

and

and where

polarized

~{uE) = 0 (signal and noise are uncorrelated)

C(k) = E”‘(k)@(k)

N-l z(j) = C x(t) e-2nUrN-1, f=O In a real space, a wave is linearly

({au} = 5{a}u,

(A-2)

Ir+?#l c z(j)z’(i) ,=tmm adjoint,

451

surge

where

time

density matrix S(k) is (Brillinger,

l)-’

travelling

(A-8) sense, we shall

(A-9)

= d2(k)ut(k)u(k).

(A-13)

Note that this power is the sum of the pure state power in all three spatial directions H, D and Z. Since the power spectra tend to fall off rapidly with frequency, the plots given in this paper are k (power(k)). The H component powers (plotted in the latitudinal data) are power,,(k)

= ti’(k)tif

(A-14)

and the others are defined accordingly. The parameters ofthe polarization ellipse in the H-D plane are determined in the following fashion. From (A-11) and (A-12) we take the two components (A-15) Since (e-‘Bci(k))(e’8iwD(k)) = d(k)ti,,(k)

(A-16)

we can choose 0 such that e%,,(k)

= rl +ir,

where ryrZ = 0 and r I and rZ are real vectors in the H-D plane (Samson and Olson, 1980). Then ifr: > r:, rl is in the direction of the major axis of the polarization ellipse, and rZ is in the direction of the minor axis. The sense of polarization can be found by the vector product of r, and rZ (Samson and Olson, 1980). In our analysis we have used the parameters denoted by the ellipticity, and orientation, theta, of the polarization ellipse. The ellipticity is the ratio of the minor to major axis of the

458

J. C. SAMSON

polarization ellipse (i.e. )r#r, I) and theta is the angle between the major axis and the H-direction. Positive ellipticity indicates counterclockwise polarization viewed down on H-D plane. Positive theta indicates orientation to the North-East, and negative theta is orientation to the North-West (-90” G 8 $ 90”) (see Samson, 1972, Fig. 2). The adaptive filter to filter pure states (see e.g. Fig. 14) is based on the inverse transform N-l

p(t)

=

N-’

c

i(

eznikrrm’

(A-17)

li=0 whereti(k)and

u(k)aregiven

in (A-l 1 and A-12). In filtering the

amd G. ROSTOKER data we used a sliding time domain window, 15 min long, stepped by 5 min. In processing the data, all the recordings have been detrended with a 3 mHz high pass filter before transforming to the frequency domain. A spectral window with m = 3 (14 degrees of freedom) was used. The noise matrix E(k) was estimated by using the estimator f?,(k) = I(k where i?(k)is the minimum eigenvalue of i?(k) (Samson, 1982b). The isotropic noise model we have used will not always be the best choice. However, for simplicity and standardization in the analysis, we have used this noise model. It will be important, in further studies, to find better procedures for estimating E(k) from the data.