FLUCTUATING MAGNETIC FIELDS IN THE MAGNETOSPHERE*

Transcription

1 FLUCTUATING MAGNETIC FIELDS IN THE MAGNETOSPHERE* II. ULF Waves R. L. McPHERRON, C. T. RUSSELL, and P. J. COLEMAN, Jg. Dept. of Planetary and Space Science, and Institute of Geophysics and Planetary Physics, University of California, Los Angeles, Calif., U.S.A. (Received 21 January, 1972) Abstract. The study of ULF waves in space has been in progress for about 12 years. However, because of numerous observational difficulties the properties of the waves in this frequency band (10-3 to 1 Hz) are poorly known. These difficulties include the nature of satellite orbits, telemetry limitations on magnetometer frequency response and compromises between dynamic range and resolution. Despite the paucity of information, there is increasing recognition of the importance of these measurements in magnetospheric processes. A number of recent theoretical papers point out the roles such waves play in the dynamic behavior of radiation belt particles. At the present time the existing satellite observations of ULF waves suggest that the level of geomagnetic activity controls the types of waves which occur within the magnetosphere. Consequently, we consider separately quiet times, times of magnetospheric substorms and times of magnetic storms. Within each of these categories there are distinctly different wave modes distinguished by their polarization: either transverse or parallel to the ambient field. In addition, these wave phenomena occur in distinct frequency bands. In terms of the standard nomenclature of ground micropulsation studies ULF wave types observed in the magnetosphere include quiet time transverse - Pc 1, Pc 3, Pc 4, Pc 5 quiet time cornpressional - Pc 1 and Pi 1; substorm compressional Pi 1 and Pi 2; storm transverse - Pc 1 ; storm compressional Pc 4, 5. The satellite observations are not yet sufficient to determine whether the various bands identified in the ground data are equally appropriate in space. 1. Introduction Although low frequency waves have been studied on the surface of the earth for many years, the importance of such waves in the physical processes occurring within the magnetosphere was not generally realized until quite recently. However, in the past five years, many theories of the dynamics of the magnetospheric particle population have been formed in which these waves play a fundamental role. For example, Swift (1967) and Liu (1970) have both suggested drift wave instabilities in the ring current may be important in magnetospheric substorms. Hasegawa (1969) and Lanzerotti et al. (1969) have considered the drift mirror instability of the storm-time ring current and also its effect on precipitation. Sonnerup et al. (1969) examined several different models of wave generation in an attempt to explain modulation of energetic protons during magnetic storms. Southwood et al. (1969) studied the bounce resonant interaction between pulsations and trapped particles. Coroniti and Kennel (1970a) have examined the drift wave instability of the inner edge of the electron plasma sheet, and in addition * Publication No Institute of Geophysics and Planetary Physics, University of California, Los Angeles, Calif Space Science Reviews 13 (1972) All Rights Reserved Copyright by D. Reidel Publishing Company, Dordrecht-Holland

2 412 I~. L. MCPHERRON ET AL. how waves produced by this or other mechanisms can cause modulated precipitation of energetic electrons (Coroniti and Kennel, 1970b). Cornwall et al. (1970) have shown how ion cyclotron turbulence in the region of overlap of the ring current and plasmasphere contributes to the decay of the stormtime ring current. Dungey and Southwood (1970) find the characteristics of magnetic fluctuations near the magnetopause strong support for their theory of the Kelvin-Helmholtz instability. These theories all emphasize the importance of knowing the amplitudes, the polarizations, and the regions of occurrence of low frequency waves in the magnetosphere. Ground based studies provide some clues as to the magnetospheric population of waves, but to test the theories and determine actual character and morphology of the waves, these waves must be measured in situ, where the wave-particle interactions are taking place. Ground based observations are modified in a very complex way by both ionospheric and ground currents and may be altered or reflected in propagating from the equatorial regions through the ionosphere to the ground (Prince and Bostick, 1964; Field and Greifinger, 1967 and references therein). Furthermore, once these waves reach the ground-ionospheric wave guide, they may propagate parallel to the surface of the Earth (Tepley and Landshoff, 1966; Manchester, 1966). The only way to avoid these problems is to measure the waves on satellites deep in the magnetosphere. However, this, too, poses several problems. The first problem is that satellites move. They usually move both in radial distance, magnetic latitude, and local time simultaneously. Synchronous orbiters in circular orbits, however, restrict this movement to only a local time motion. Thus, the analysis of such data is much simpler. The synchronous orbiters can map out the diurnal variation of phenomena every day and thus supply a good statistical description of this region of space. Eccentric orbiters, although they map out a much larger volume of the magnetosphere, require a year's complete data to map out the local variation of a phenomenon and it requires many years' data to determine an accurate statistical map. Furthermore, the radial motion of an eccentric orbiter can make the detection of L-shell restricted phenomena quite difficult. Finally, we note the near impossibility of detecting ULF wave phenomena in a low altitude orbit. First, there is the difficulty of measuring the waves in a high background field (,-~ 89 G), which is compounded by the fact that the spin period of spinning satellites and the boom vibration period of stabilized spacecraft are usually in the ULF range. Second, the motion across field lines in a polar orbit, the most common low altitude orbit for scientific studies, is too rapid to identify low frequency waves. Typically, such a satellite moves 4 ~ in latitude per minute. Thus, for example, it would move from L = 6 to L---7 in less than 30 s. The second problem with satellite studies is the limitations of telemetry systems. In order to determine the frequency and polarization of a wave it must be sampled at least twice as fast as the wave frequency. Early satellites often had low sample rates. Another associated problem is the size of the digitization interval. The number of telemetry bits required for a digital sample governs the number of digital windows possible over the dynamic range of the instrument. For example if 8 bits are available for a sample and a 1 7 digital window is desired, then the dynamic range is limited to

3 FLUCTUATING MAGNETIC FIELDS IN TIlE MAGNETOSPHERE, II 4l 3 128?. However, it is desirable to have a digital window smaller than 1? and to measure waves in background fields much larger than The solution to this problem is either to increase the number of telemetry bits per word or to sacrifice the measurements of the background field. The former solution has been used on several recent spacecraft by using sets of offset fields around the magnetometer, the magnitude of which are telemetered separately. The latter solution is obtained in the use of a search coil which measures the field derivative. Because of these limitations, relatively few spacecraft have provided ideal measurements of micropulsations within the magnetosphere. In fact, all the observations of ULF waves in space have been made with only 11 of the more than 40 spacecraft which have carried magnetometers in the magnetosphere. The characteristics of these 11 magnetometers are summarized in Table I. Therefore, despite the fact that space ex- TABLE I Characteristics of various magnetometers used for the study of ULF waves in space Spacecraft Magneto- Axes Spin period Dynamic range Quantization Sample rate meter Pioneer 1, 5 Explorer 6 Explorer 12 Explorer 14 Explorer 26 Explorer 33 ATS 1 Dodge OGO 3, 5 OGO 5 Search coil s V A Search coil s ~ V A Fluxgate s =: Hz Fluxgate 3 ~5 s =: ~ 3.13 Hz Fluxgate ,/ Hz Fluxgate s =:60, =: , 1.2, Hz Fluxgate s : Hz Fluxgate 3 0 =: / Hz RB Vapor T ~ A A Fluxgate 3 0 y z Hz V- Varies with background field strength. A - Analog data whose sampling resolution can be varied in different analyses. T- Total field instrument. ploration is now in its second decade, in situ ULF wave studies are still in their infancy, and we have determined only a rough picture of the magnetospheric ULF wave population. In contrast to the study of waves in space, the study of ground micropulsations has proceeded at a rapid rate over the last decade. In a recent review, Saito (1969) shows that the current world output is of the order of 50 papers per year with more than 1000 papers published to date. Saito's paper provides one of the most recent reviews of the outstanding results of these papers. Even if ULF waves were not fundamental to the dynamics of the magnetosphere, the existence of this extensive work on ground micropulsations alone would justify the examination of these waves in space. The reader interested in ground observations of micropulsations is also referred to the recent book, Geomagnetic Micropulsations, by Jacobs (1970); to the reviews on

4 414 R.L. MCPHERRON ET AL. the use of micropulsations as diagnostics of the magnetosphere by Troitskaya and Gul'elmi, (1967) and more recently by Aubry (1970); and to the review of some theoretical aspects of micropulsations by Dungey and Southwood (1970). To date, reviews of satellite observations of ULF waves have either concentrated on one type of wave phenomena or have presented only a brief overview of the waves. Recent reviews of this type include those by Coleman (1970); Coleman and McPherron (1970); Jacob s (1970); McPherron and Coleman (1970a); Russell and H olzer (1970); McPherron (1971); and Russell (1971 a). Examining these earlier reviews, we find that while ULF waves are observed in all regions of space, their characteristics are markedly different in each region. These distinct regions include the interplanetary medium, the solar wind upstream of the bow shock, the magnetosheath, the magnetopause, the magnetosphere, and the tail. In this review we limit ourselves to discussing those waves which may have a direct bearing on ground observations, i.e.,we restrict our attention to the region enclosed by the magnetopause, the magnetosphere and the magnetotail. The organization used for ELF and VLF waves in paper 1 (Russell et al., 1972), i.e., a division into whistler phenomena, high altitude emissions and low altitude emissions obviously cannot be used for ULF waves. There is no strict ULF analogue of the whistler, and for the reasons stated above there are no low altitude satellite observations of ULF waves. However, the magnetospheric ULF wave phenomena appear to fall within certain categories based on the degree of magnetic disturbance. They can be further divided on the basis of being transverse or compressional waves, and finally, on the basis of their characteristic spectrum. We, therefore, have used the degree of magnetic disturbance and the wave polarization to organize this review. Since there is yet little direct evidence linking the satellite observations to ground micropulsations, we have avoided using the usual Pc-Pi classification to order the data. However, to facilitate a comparison with ground based work, Table II indexes the sections of this review which contain discussions of wave phenomena in the various Pc and Pi bands. In the following four sections we consider separately initial observations, magnetospheric wave phenomena occurring during quiet times, during magnetospheric substorms, and during magnetic storms. Section 6 discusses the measurement of the transfer function of a field line. Finally, Appendix I discusses the techniques used in the analysis of ULF waves. TABLE II Relation of standard micropulsation nomenclature to classification used in this paper. Table entries are the section where phenomenon is discussed Type Polarization Pc 1 Pc 2, 3 Pc 4, 5 Pi 1 Pi 2 Quiet time Transverse 3. l Compressional Substorm Transverse Compressional Storm Transverse Compressional

5 FLUCTUATING MAGNETIC FIELDS IN THE MAGNETOSPHERE~ II Initial Observations The first observations of ULF waves in space were reported by Sonett et al. (1960). Using a search coil magnetometer on Pioneer 1 they measured two components of the magnetic field perpendicular to the spin axis of the spacecraft. Power spectral analysis of the fluctuations revealed discrete lines superimposed on a 1/ffalloff towards higher frequencies. The compressional nature of these fluctuations and their association with a sharp drop in field magnitude suggested they were turbulence associated with the termination of the geomagnetic field on the dayside. The sudden decrease in magnitude at extreme distances indicates the spacecraft passed into the undisturbed solar wind and identifies the fluctuations as magnetosheath turbulence. Similar observations were reported by Coleman et al. (1960) from search coil measurements on Pioneer 5. The radial distance of the observations and the character of the fluctuations again identify these as magnetosheath turbulence. The first observations of ULF waves inside the magnetopause are those of Sonett et al. (1962). The search coil measurements of Pioneer 1 were spin demodulated, obtaining amplitude and phase of the fluctuations between 4 and 7 R e on the dayside. Spectral analysis was performed on these two quantities for intervals of s duration. This analysis revealed rms power from between 0 and 1.0 Hz. Some spectra had peaks around 0.5 and 1 Hz. An attempt was made to interpret these results in terms of wave modes, mode coupling, etc. However, the lack of the third component of the vector field made this exceedingly difficult. No clear association between these fluctuations and later satellite observations has been made. Long period waves within the magnetosphere were first reported by Judge and Coleman (1962). Search coil data from Explorer 6 were spin demodulated and expressed in terms of two orthogonal components. The field variations, which were observed at about 6 R~ in the morning sector, were compared to simultaneous variations in energetic electrons. The event chosen for detailed study was one in which regular field variations were in phase with variations in the particles. By assuming different types of wave modes present and subtracting out their contributions to the observations, the authors concluded the variations were due to a mixed transverse and compressional mode. They assigned a period of 100 s to the compressional part, and 200 s to the transverse part. The transverse wave was right hand elliptically polarized with respect to the ambient magnetic field (in the sense of electron gyration). The wave appeared to be damped with a time constant of approximately 500 s. In this case, also, the authors were hampered by the lack of the third component of the field. Despite this, however, the characteristics of the wave fall in the category of quiet time, transverse Pc 4 waves, to be discussed below. A report of a long period oscillation of period greater than 100 s was also made by Sonett (1963). Using data from Pioneer 1, he concluded that the oscillations were either a radial perturbation or the projection in the meridian plane of an elliptically polarized wave. Although the primitive apparatus precluded thorough analysis, the observation substantiated the earlier report by Judge and Coleman (1962).

6 416 R.L. MCPHERRON ET AL. The first complete vector field observations of ULF waves in the magnetosphere were reported by Patel and Cahill (1964). A three component ttuxgate on Explorer 12 recorded two long period wave events between 7 and 8 R~ around 1100 LT. These events had periods of 120 and 180 s and amplitudes of 6 to 8 7- They were transverse and right elliptically polarized with respect to the ambient field. These authors also reported the first correlation between satellite observations of waves and ground micropulsations. They observed that during both events waves of similar amplitude, period, and polarization were present on the ground near the subsatellite point. The travel time between the satellite and the ground appeared to be about 90 s. These waves are clearly identifiable as quiet time Pc 4 pulsations TRANSVERSE WAVES 3. Quiet Time Wave Phenomena A more detailed examination of quiet time transverse waves on Explorer 12 was reported by Patel (1965). He found eight examples of transverse waves between 6.8 and 10.6 R e and LT. These events were selected on the basis of having a quasisinusoidal waveform and 1-2 complete cycles. The amplitudes ranged from and periods between 100 and 180 s. All events were elliptically polarized transverse to the ambient field. Four events before 1045 LT were right hand elliptically polarized with respect to the ambient field while the four events after this time were left hand polarized (in the sense of proton gyration). This result is in agreement with ground observations. Figure 1 is an example of the waveform observed by Patel; Figure 2 illustrates their elliptical polarization. Also shown are the simultaneous ground observations near the subsatellite point. I km I Q Br 0-34 B~ I 1 I ~ I L ' I I I 1 l I I I / 2118 ::) UT Figs. la-b. Waveform of transverse, Pc 4 waves recorded during quiet times by triaxial fluxgate on Explorer 12 at noon LT. Coordinates used are geocentric spherical (Patel, 1965).

7 FLUCTUATING MAGNETIC FIELDS IN THE MAGNETOSPHERE, li I km I -2-4 Br -6-8 m 9 J -12 i -28 i B~ ! -36 I t I f I J I I I I I I I I U T Fig. lb. As pointed out by Patel, these observations were limited by the 24 y quantization error of the original data. Because the spacecraft was spinning with its axis occasionally transverse to the ambient field, it was possible to reduce the effective quantization error to about 6 7. Additional improvements in accuracy were obtained by taking 15 s averages and low pass filtering with a one minute sliding average. The final data had uncertainties of approximately 3 7 and no variation with periods shorter than 1 min. Clearly this processing limited the possible wave observations to large amplitude (> 3 7) long-period (> 60 s) waves. A study by Patel (1966a) of Explorer 14 fluxgate data gave similar results. Explorer 14 probed the magnetosphere in the LT sector, ~ below the magnetic equator from 6-10 R e. Eight events with amplitudes ranging from , periods 3-30 rain were observed. All events but one were left hand elliptically polarized. One additional event was found to correlate with ground micropulsations. Some events appeared to be coupled with compressional waves. In a short note, Patel (1966b) pointed out that the Pc 4 waves must be quite localized within the magnetosphere. He was unable to find any events at Explorer 12 and 14 which corresponded to large micropulsation events chosen from the ground magnetograms. On the other hand, the three ground events which correlated with the satellite were all within 15 ~ LT of the conjugate point of the satellite and near the same L-shell. The first observations of quiet time transverse waves with high time resolution and high sensitivity were reported by Cummings et al. (1969). These measurements were made by the biaxial, spinning fluxgate magnetometer on the synchronous satellite ATS I with a sample rate of 0.16 s -1 and approximate sensitivity of

8 418 R. L. MCPHERRON ET AL. Explorer XII Nm t Col iege, Alaska II i (o) i I T i (b) Explorer. XII Nm College, Alosko t 5 '~ 2 I 6 14 I 12 il 4 5 Fig. 2. (c) (d) Hodograms showing polarization of Pc 4 waves presented in Figure 1 and also their correlation with ground observations (Patel, 1965). An example of the waveform of a typical event is shown in Figure 3 where 15 s averages have been plotted with a resolution of about 0.5 y. Twenty-five events were observed during January Their amplitudes ranged from peak to peak with periods from 80 to 240 s. The events were frequently of several hours duration and appeared to be amplitude modulated. The waves were polarized transverse to the ambient magnetic field and nearly linear. The most probable direction of polarization was 30 ~ east of a magnetic meridian plane (in the quadrant between V and D). The diurnal occurrence and Kp dependence of the 25 events is shown in Figure 4. Note in this figure that each 10 min interval is defined as an event so that considerably more than 25 points occur. The waves appear to maximize after dawn and occur primarily in the daylight hours. No events were seen between 17 and 22 LT. The periods of the waves were grouped around 102 and 190 s. The longer periods were associated with greater magnetic disturbance. In recent work, Cummings et al. (1971) studied the statistical characteristics of these waves by visual analysis of two years of data. They find the probability of occurrence increases gradually from dawn through the day to a maximum at 1400 LT and then drops rapidly at dusk. As a function of season, the maximum occurrence (11~ of the

9 FLUCTUATING- MAGNETIC FIELDS IN THE MAGNETOSPHERE~ li 419 DAY 005 DATE O ~ --,., P,.,:'-...~-..j-.~--.,../.-.~.,~..~..f~v r...~,.~.,,f~ ~ _ i O~" _ V 0 i MINUTES Fig. 3. Waveform of transverse Pc 4 wave observed during quiet times by biaxial, spinning fluxgate magnetometer on synchronous satellite ATS 1 at 0900 LT. H is parallel to Earth's rotational axis, V radially outward in the equatorial plane and D completes right handed system (Cummings et al., 1969). 4.0 Kp 0... A 5.5 I... &O *... 9 ~ t 20 NUMBER o ~ == - ATS - I t,0 E~%,s = oo dan 1967 ~ ~ d= e,, o 9 iiiii N'~ I0 20 T (min) I9 -?. = , 9 9 9, 9 :~$i:~:i:~,%~.....,, 9 9 o co 9 ~H~:.~!E!~!~... o 9,,',, 1.0 o ~,,',~ O L.T. (HOURS) Fig. 4. Dependence of period of transverse Pc 4 waves such as shown in Figure 3 on local time and Kp (Cummings et al., 1969).

10 420 l~. L. MCPHERRON ET AL. time) is about January. The frequency of the wave events is distributed almost uniformly over the band 5-15 x 10-3 Hz with an average frequency of 10.2 Hz (100 s period). The average maximum amplitude is The authors find no evidence that the lower frequency (Pc 5) and the higher frequency (Pc 4) waves are different in any way. In a recent report, Dwarkin e t al. (1971) described shorter period Pc 3 waves recorded at the almost synchronous satellite, DODGE, at 6.3 R E in the equatorial plane. The most common period was 30_+ 10 s with peak to peak amplitudes of 2 7. The waves were linearly polarized transverse to the ambient field and oriented azimuthally. They note that Pc 3 oscillations occurred simultaneously on the ground within a sector of about 60 ~ The waves were recorded during quiet conditions. A typical waveform is shown in Figure 5. (~) ANALOGUE RECORD OF'MAGNETOMETER OUTPUT ~ LT :-- 2 el (b) TRANSFORMED DIGITAL DATA Y Fig. 5. I I I [ I Z I U.T. JULY 27, 1968 A transverse linearly polarized Pc 3 wave of 40 s period and 2 7 PP amplitude observed on the DODGE satellite (Dwarkin et al., 1971). Similar Pc 3 oscillations are observed at the synchronous satellite, ATS 1. Figure 6 is an example of previously unpublished data showing a 40 s wave of 2 7 peak to peak amplitude. The wave is nearly linearly polarized transverse to the ambient field. Such waves were not studied by Cummings et al. (1969) because of the limitations imposed by 15 s averages and resolution of the plots. In another report, Dwarkin et al. (1970) discussed a Pc 1 event observed at DODGE. The event had a peak to peak amplitude of 6 7, a period of 3 s, and it was left hand circularly polarized transverse to the ambient field. The event was seen simultaneously at two ground stations nearly conjugate to the foot of a field line passing through DODGE. A segment of the waveform of this event and a hodogram of the variation in the equatorial plane are shown in Figure 7. This hodogram provides a clear example of the effects of spectral folding, or aliasing. Although this event was left hand polarized in the analog data as expected for a Pc 1

11 FLUCTUATING MAGNETIC FIELDS IN THE MAGNETOSPHERE, II 421 ATS-I MAGNETIC FIELD HIGH-PASS FILTERED DATA OCTOBER 5, 196g i9:00 4 e I L ['IF' I ','''I... I... I... i... Bx -4 -B,,ll,l... l,,l, lllll... I... I... B 4 By 0-4 -B tlll[llllili[~l... I... I... I... I... Ill... Iiii 8 4 Bz o -4 -@ O I BO MINUTES Fig. 6. Transverse Pc 3 wave event observed at the synchronous satellite ATS l (1.28 s averages). Z axis parallel to Earth's rotation axis, Sun vector in X-Z plane, Y axis towards dusk. event, the Nyquist frequency (half the sampling frequency) of the digitized data is less than the frequency of the wave. Thus, the successive points on the hodogram appear to rotate in a right handed sense, while the major axis of this apparently very elliptical wave rapidly precesses in a left-handed sense. If the data had been digitized at a much higher rate, this hodogram would have revealed a left hand circularly polarized wave with constant amplitude COMPRESSIONAL WAVES Compressional waves have been less frequently reported in satellite observations. As mentioned previously, Judge and Coleman (1962) concluded that their Pc 4 event was a mixed transverse and compressional mode. Patel (1965) found three examples of compressional waves in the Pc 4 band. Lindsey (1968) examined Explorer 26 data

12 422 R.L. MCPHERRON ET AL. DEC. 22, 1968 (a) ANALOGUE RECORD OF MAGNETOMETER OUTPUT ~i!i~!tiii!! iii!~!'i!.iiii..!$i i iii i i i! i i i i i :::iii I!~i~!iii::i~ (b) TRANSFORMED DIGITAL DATA N~ ~ x i- > Y I- I I I I I U.T (c) ENLARGEMENT OF A SEGMENT OF (b) (dl POLARIZATION DIAGRAM OF A SEGMENT OF (c) =E x 16:00:51-16:01:07 U.T. (--10:30 S.L.T.) 1 At = 1.26 SEC Q Z Y Fig. 7.! I I U.T. 1 East 11 SENSE OF ROTATION 0 ELECTRONS Downword O PROTONS A transverse, left hand polarized Pc 1 wave of 3 s period and 6 7 PP amplitude observed on the DODGE satellite (Dwarkin et al., 1971). during both quiet and disturbed times. He found both compressional and transverse waves similar to those of Patel. Power spectral analysis suggested their energy was limited to a rather narrow frequency band. Barfield et al. (1971a) have studied a purely compressional wave of 107 s period and i0 7 peak to peak amplitude recorded on ATS 1 at 0800 LT. Coherent oscillations of energetic electrons ( MeV) in phase with the magnetic variations were recorded simultaneously on the same satellite. Figure 8 shows the waveform of the fluctuations and Figure 9 the auto spectra of particles and fields. This same event has been studied by Lanzerotti and Tartaglia (1971) and compared

13 i FLUCTUATING MAGNETIC FIELDS IN THE MAGNETOSPHERE~ II 423 ~ 5E ~5~ 5z I0{E >l.05mev ) ~ "~' ~, rr'~" -~...,~....~,... ~..~>~',,V~r : t R,~.,,,,~ ~ ~ i: '!"t ~,(ii!,'v~,~',f '/~i/'r/. '''' v,~ljl,/v'~tt d, B' ~ ',, ~ ~' '~ R ~. : i o... r,~o~- a'. <'0''... ~,3c - ~.~,r,(,@\a,%,v\,\f "<v" ~- L,E 2 17 r8 19 HOURS UI, FEBRUARY 14, 1967 Fig. 8. Compressional Pc 4 wave event observed at the synchronous satellite 0800 LT with simultaneous in phase fluctuations of energetic electrons. Two successive hours are shown. Magnetic field data have been transformed to a field aligned current system with Bp radial, B~ azimuthal and Be along the field (Barfield et al., 1971a). i I... i... I... i... I... T >_- % O'3 I0 2 -~ Specirurn 0fLN J (E = i.i MeV) So~ o o_ 9 -. o~ ooo %%0 I I o,.. _ O0 :o o ~ ~o~% oo -"- "~ o~ I1 ~ o o - 9 d~ oo o.l ~, ~o ~ ~o~ c - " ]' o ~ 'S>~ =."-..!.'...,o~ - "~" ~ :' ~ 9 ~ of LN Br * ; ~176 ~ S ~ i0-07 fc FREQUENCY, cph Fig. 9. Auto spectra of particles and fields for compressional Pc 4 wave event shown in Figure 8. Note peak of 34 cycles per hour (106 s) (Barfield et al., 1971a).

14 424 R.L. MCPHERRON ET AL ATS-L L l l I COLLEGE JbHG+ bbg+bzg io-s \ t N. ~o -4 o ',i L_ l rg 7 I ~ ~ ~ I ~, ~ p I, J I O.O FREQUENCY, cps Fig. 10. Power spectra of a Pc 4 wave event simultaneously observed at ATS 1 and near its northern conjugate point. The satellite signal was purely compressional while the ground signal was almost entirely transverse (Lanzerotti and Tartaglia, 1971). to simultaneous ground observations. Rapid run magnetograms from College, Alaska, approximately 600 miles ENE of the ATS 1 conjugate point were digitized and subjected to spectral analysis. The results shown in Figure 10 indicate the power in the ground signal was about 50 times smaller than the satellite signal although a clear peak was evident at the ground. The plane of polarization of the ground signal was tilted 12 ~ below the ground plane. The event was left hand polarized with an ellipticity (defined in appendix) of approximately 0.7. The major axis of the perturbation ellipse was oriented at 45 o to true north (NE to SW). Essentially no Z component was observed on the ground despite the fact the signal was compressional at ATS 1. A survey of the occurrence of compressional micropulsations throughout the magnetosphere has been reported by Heppner et el. (1970). The total magnetic field as measured by rubidium vapor magnetometer on OGO-3 and OGO-5 was plotted on microfilm at two minutes per frame. These plots were scanned visually for sinusoidal fluctuations of the total field. The sensitivity threshold was of order 0.3 ~ depending somewhat on the plotting scale and the wave period. To organize their results they

15 FLUCTUATING MAGNETIC FIELDS IN THE MAGNETOSPHERE, II 425 A OGO E RUBIDIUM RAW AND DIFF PLOT START TIME B V~ < E <( o Q.J ILl E MEAN RB IS E 40.0 E 30.0 i MEAN DIFF TIME IN SECONDS RB FIELD IS ~a~ DIFF FIELD IS... DIFFERENCE FIELD = RUBIDIUM-ORBIT Fig. 11. Typical microfilm plot of rubidium magnetometer data obtained by OGO 3 and 5 and used to survey occurrence of micropulsations in the magnetosphere (Heppner et al., 1969). separated the magnetosphere into volume elements of roughly 3 units of L, 3 hours of LT and 40 ~ magnetic latitude centered about the equator. All data for Kp > 5 were excluded. It should be noted that although their instrument detects only the compressional component the authors feel that most waves are not 100 K transverse enabling them to detect the occurrence of predominantly transverse waves as well. A typical example of a Pc 1 wave is shown in Figure 11. Their results show Pc 4, 5 ( s) have a maximum of occurrence on the dayside. Further, these pulsations are observed more frequently at L> 8. Pc 3 (10-45 s) also have a maximum on the dayside, but are most frequent around the auroral zone (L =

16 426 R.L. MCPHERRON ET AL. BAND LIMITED PULSATION EVENT UCLA MAGNETOMETER UT JUNE 8, 1968 PRINCIPAL + AXoSDINATES ~ A ~_ By ~ -y Bz ~'/~-/Y~'~-~/~xV~f I t I i [ i I I706 ~Jx z Fig. 12. Band pass filtered (0.05~0.05 Hz) segment of transverse waves recorded at OGO 5 during substorm recovery. Satellite was inward at 6 RE, just below magnetic equator on dawn meridian. The principal axis coordinate system has Z axis parallel to local field, Y radially inward and X towards the Sun (McPherron and Coleman, 1970). OGID-5 BLP NAVE EVENT DURING SUBSTI3RM 10 ~ B JUNE LU Z: 101 \ 10 ~ I0 ~i 1Q-a a_ """-. ~1, o_ L "'-,I IQ- I[ FREQUENCY {HERTZ) u 1 FREQUENCY (HERTZ] ~,~ ~ BZ-BX 0,,,$3,~.,,~ l~ BY-BZ 1 Flg. 13 -a' O,lO 0, FREQUENCY (HERTZ) u o.oo o,10 o:2o 0.30 FREQUENCY (HERTZ) Spectral analysis of the wave event of Fig. 12. Note peak appears on top of rapidly falling background spectrum.

17 FLUCTUATING MAGNETIC FIELDS IN THE MAGNETOSPHERE, II ). Also, Pc 3 oscillations are more frequent than Pc 4. Pc 1, 2 (T< 10 s) waves are most frequent on the dawn meridian inside the magnetopause. They seem to be closely associated with irregularities in the main field TRANSVERSE WAVES 4. Substorm Associated Wave Phenomena Quasi-sinusoidal transverse waves occurring during substorms have been reported by McPherron and Coleman (1971a). Pulsations of 20 s period and rms amplitude were observed on the OGO-5 spacecraft just below the magnetic equator as it was inbound on the dawn meridian between 7 and 5 R~. The average polarization was transverse to the local field with the major axis azimuthal in the equatorial plane. The average ellipticity was 0.3 and predominantly right handed with respect to the local field. The waves appeared to consist of bursts propagating within a cone of about 30 ~ about the local field. Spectra of the pulsations showed a large peak superimposed on a rapidly falling background spectrum. Bursts of whistler chorus at twice the wave period were observed simultaneously on the satellite, but no modulation of energetic electrons could be detected. Pc 2, 3 type pulsations were simultaneously observed during the recovery phase of a polar substorm at two stations near the subsatellite point. Figures 12 and 13 illustrate the waveform and spectra in the principal axis ATS MAGNETIC FIELD VARIATIONS AUGUST 17 [ I J, I I i I... I,, /\\ 9 //\ /\'\ // 9 BX ' ".,\/ \~\~. ~. \ 0)" i-\.,/~,-~ /\ /"\.,._; '-\/ \ /t 23see.J 9 /// 9 /\ /? L./.. i ] [ I / I I ] I I I I I UNIVERSAL TIME Fig. 14. Waveform of substorm associated transverse wave recorded at ATS 1 near the dawn meridian. The wave is nearly linearly polarized transverse to the ambient field. The Y axis is roughly azimuthal (within 30 ~ (Coleman and McPherron, 1970).

18 428 R.L. MCPHERRON ET AL. coordinate system of the perturbation. (See appendix for definition of principal axis system.) Figure 12 of Paper I shows the simultaneous dynamic spectrum of the ELF chorus and the waveform during this event. A similar wave event on ATS 1 has been reported by Coleman and McPherron (1970). This event was also observed during the recovery phase of a substorm around the dawn meridian. The wave period was 25 s and peak to peak amplitude 2 7. It was nearly linearly polarized transverse to the ambient field. The waveform of this event in a field aligned coordinate system is shown in Figure 14. A previously unpublished power spectrum for this event is shown in Figure 15. This same event has been studied by Parks and Winckler (1969) using observations of trapped energetic electrons at ATS 1, and precipitating electrons near its conjugate point. They note that both in the equatorial plane and the auroral zone, modulation with 11 s period was present. This period is roughly half the period of the waves observed at the same satellite. These results should be compared to the OGO-5 observations of McPherron and Coleman (1971a) mentioned above, that whistler chorus was modulated at roughly half the wave period, i.e., 10 s. Figures 16 and 17 show the analysis of the ATS 1 event by Parks and Winckler. Substorm associated irregular fluctuations of s period at ATS 1 have also BAND LIMITED PULSATIONS UT, AUGUST 17, 1967 UCLA FLUXGATE MAGNETOMETER ATS- I E IGENVALUES 10 '~ 10 ~ : EIGENVALUES SEC i03 ] to 2 I ~'RM~ ~: I02. ~ L ~ to 1 ~ lot to ~ ~: lo o i0-i 10-1 ~: 10 -~ oc ~ 3~ aj - ~o -3 ~ io -3_ i0 -~ i 0 - ~ _ ~ i0 -~ 01 0,0 O.l O.q 0.5 FREQUENCY ~HERTZ) FREQUENCY (HERTZ) / POLARIZATION AND ELLIPTICITY Fig. 15.,.=, _,IW,,'r'~ W ~ ~Vl~ '- 'v ~ S SPECTRAL ANALYSIS PARAMETERS NUMBER OF POINTS = 4096 i00 / SAMPLE INTBRVAL = 1.0 SEC I I 1 DEGREES OF FREEDOM 26 BX-BY BAND WIDTH = HZ o- ~V--4tr,4~'4V/-'w&Fu RANDOM BANDSE}:~RATION=.OOIg5HZ Of' ~'V'~ " "1'~' ~[v, '1 ' I 90% i O.LI 0.5 FREQUENCY (HERTZ) Eigen analysis of spectral matrix (see Appendix) for wave event of Figure 14.

19 FLUCTUATING MAGNETIC FIELDS IN THE MAGNETOSPHERE, II 429 I ' ' ' ' t ' ' ' ' I 1 v ++ L Re EQUATORIAL ELECTRONS DYNAMIC FOURIER SPECTRAL ANALYSIS OF 6,6Re EQUATORIAL ELECTRON FLUX (50~E~ 150 KeV) AUGUST I~', UT :~... ~ ~ ~ ~RELATIVE ACCUMULATED : Fig. 16. ~ UNIVERSAL TIME... +! 25.0 Dynamic spectra] analysis of fluctuations in eguatoria] electrons measured by ATS I during wave event of Figure 14 (Parks and Winckler, 1969). o3m >... <m ocz = o i [, i J i I I i i I I I i I i [ i i, i I i i BALLOON X- RAYS )YNAMIC FOURIER SPECTRAL ANALYSIS OF BALLOON X-RAYS AUGUST 17, ]658 UT RELATIVE ACCUMULATED POWER o WI~ 0.144' ul u._ ~1 ~4~;,,.~= ~!~... 4+= "~ UNIVERSAL TIME Fig. 17. Dynamic spectral analysis of modulation of precipitating electrons in auroral zone near ATS 1 conjugate point during wave event of Figure 14 (Parks and Winckler, 1969).

20 430 R. L. MCPHERRON ET AL. TUNGSTEN DYN 3.3 DB CC,5 ~.2-.I- Fig. 18. O, I / ol2o I UNIVERSAL TIME Dynamic spectrum of Pc 1 event on October 10, 1969 at conjugate point of ATS 1 (Tungsten, N.W.T., Canada). Pure white is highest power, pure black next highest, etc. ATS-I DYNAMIC PO/ER (dd/dt) 5,3 DB CONTOURS.4. 0 = 01~o UNIVERSAL TIME Fig. 19. Dynamic spectrum of Pc 1 event of Figure 18 as recorded simultaneously at ATS 1. High background noise evident in time series is spacecraft interference. This interference produces a ramp function of 5.12 s period. Fourier components of this ramp are apparent at Hz and Hz as interference lines.

21 FLUCTUATING MAGNETIC FIELDS IN THE MAGNETOSPHERE~ II 431 been correlated with simultaneous X-ray pulsations in the auroral zone by Pierson and Cummings (1969). No pronounced peaks could be found in the spectra of the pulsations at ATS 1 or the ground. McPherron and Coleman (1971b) have recently reported a substorm associated Pc 1 event observed simultaneously at ATS 1 and its conjugate point at Tungsten, N.W.T., Canada. Figure 18 shows a dynamic spectrum of the signal recorded on the ground and Figure 19 at the satellite. (For a discussion of this technique see appendix.) The ground signal was clearly more complex than the signal at the satellite. This difference was attributed to the effects of horizontal propagation of Pc 1 causing signals other than those vertically incident at the ground station to be recorded. Power spectra were calculated for the two portions of the dynamic spectra which appear to overlap. The results are summarized in Figure 20. SATELLITE- GROUND TRANSFER FUNCTION UCLA MAGNETOMETERS ATS-I AND TUNGSTEN, NWT, CANADA IPDP EVENT OCT UT UT "1- t~ i0 I i (A/T) 2 = (,62rl.217)2=8.6 I i (A/T)2= (,237/,i5 2.6 ~ ^ II I l f Fig. 20. (.9 rr" Ud ta jo-i 10.2 FO I FREQUENCY (HERTZ) I, 1 I ATS-I,,, \ FREQUENCY (HERTZ) TU~3STEN Comparison of power spectra at ATS 1 and Tungsten for two intervals when similar signals were present in the dynamic spectra of Figures 18 and 19. During the first interval the spectra corresponded best in a 0.2 Hz band centered at 0.27 Hz with the power at the satellite about 2.6 times as large as the ground. In the second interval the satellite power peaked at 0.18 Hz and was about 8.6 times as great as the ground. The interpretation suggested by the authors for this enhancement in the power ratio is motion of the satellite with respect to the field line on which the Pc 1 signal was propagating, i.e., a change in relative conjugacy COMPRESSIONAL WAVES Low frequency waves predominantly compressional in nature have been reported at ATS 1 during substorms by McPherron and Coleman (1970b). Large amplitude irregular fluctuations were found to be associated with the expansion phase of a magnetospheric substorm when the synchronous satellite was close to local midnight. Spectra

22 432 R.L. MCPHERRON ET AL. of these fluctuations are steep with no significant peaks. Near midnight the waves begin shortly after the onset of the recovery in the H component usually associated with a substorm at the synchronous orbit (Cummings et al., 1968). Near dusk the waves are observed in association with a depression in H, but after the substorm expansion has begun at midnight. Figure 21 is an example of an unusually large event. Figure 22 shows auto spectra of all three components of the field during this event. The diurnal occurrence pattern for these events begins in the late afternoon and is a maximum at local midnight. The events are rare in the early morning hours and are not seen during day time. Coleman and McPherron (1970) point out that fits MflGNET@GRflM OURING MRGNETOSPHERIC SUBST@RM MRRCH 3, UT Z F-'- LLI -9 ~. r'r- I--- V '~ EE CZ: I~l 5Z0 (/')0 Z ~" -- UJ H j Ok.~ CE ru (F) o 'o 'o ;o o TIME (MINUTES] Fig. 21. Waveform of predominantly compressional fluctations associated with substorm expansion phase at ATS 1, 01-02, LT. Same coordinate system as Figure 3 (McPherron and Coleman, 1970b). io ~ PONER $PECTRR OF MRG FIELD AT RT5 DURING ~z o Fig. 22. n_ io -~ i FREQUENCY [HERTZ] FREOUENCT ~HERTZ] Auto spectra of the three field components for the first wave event of Figure 21 (McPherron and Coleman, 1970b)..40

23 FLUCTUATING MAGNETIC FIELDS IN THE MAGNETOSPHERE, II 433 D SPIKE EVENTS AT ATS-SPRING 1967 p ~ ~ i I MAR 3 H ~ ~.-. --~ji MAR I i i,~:~in~i~.~ :F 50 GAMMA l i MAR r i i i APR r, t i ~ p i i I i i i i i J SUBSTORM TIME (MINUTES) EXPANSION Fig. 23. Association of predominantly compressional, irregular fluctuations at ATS 1 with recovery in H component and trailing edge of D spikes (shading). Note also rather sudden termination of fluctuations after interval of rain (Coleman and McPherron, 1970). when negative D spikes (sharp decreases in declination probably caused by field aligned currents) are observed, the irregular fluctuations tend to follow the trailing edge of the D spike. Further, the events tend to terminate suddenly after about one hour. Figure 23 illustrates both these points. Similar irregular fluctuations are observed in the near geomagnetic tail during substorms (Russell et al., 1970, 1971a; Russell, 1971b). An expansion of the plasma sheet on the midnight meridian is associated with the expansion phase of an auroral substorm. The region inside the expanding boundary is quite turbulent. The waveform of the fluctuations is highly irregular with no particular preference for any field component. Spectra are smooth with no significant peaks. Figures 24 and 25 illustrate the waveform and spectra of these fluctuations. In addition to these substorm associated waves which are directly observed, there have been several reports of quasiperiodic boundary motions in the tail. The existence of these boundary motions is evidence for the existence of hydromagnetic waves in the tail of the same period. Mihalov et al. (1970) show a multiple neutral sheet crossing exhibiting reversals of the field at intervals of 1 to 2 rain and lasting for 25 min at a geocentric distance of 73 R e. These data are shown in Figure 26. Note the similarity of these data to the ATS data shown in Figure 21. In studying many such multiple neutral sheet crossings Mihalov et al. find that the interval between successive crossings ranges from 30 to 1000 s with a most probable value near 100 s.

24 434 R.L.MCPHERRON ET AL. MAGN ETOTAIL FLUCTUATIONS UCLA OGO-5 FLUXGATE MAGNETOMETER AUGUST 20, UT 4O IBI 50 2O 5O B 2o o By -Io c. I...,4"" \/ w", W ~+~"~--~ ~'.. " t,.... ~.-.~i... \.,,' Bz 1o o "i~"~-~, "~'+''-'~..., ~..., "~-~"+~'~"~"~A/~"~', S.,... " UNIVERSAL Fig. 24. Irregular fluctuations inside expanding plasma sheet. Observations made by OGO 5 at position in GSM coordinates (--16.2, 1.0, 7.3 R~) during expansion phase of substorm. Approximate distance above neutral sheet is 2.3 RE (Russell et al., 1970). TIME MAGNETOTAIL FLUCTUATIONS UCLA OGO-5 FLUXGATE MAGNETOMETER AUGUST 2_0, UT I- z ~i w -r a ao L I-- IaJ o fi n I0 "z I0 -I I I0 I FRE QUENCY (HERTZ) Fig. 25. Auto spectra of magnetic field for fluctuations shown in Figure 24 (Russell, 1971).

25 FLUCTUATING MAGNETIC FIELDS IN THE MAGNETOSPHERE, II 2 I - A, B,~,y_~_ L) +!> t ~- (!> tj U #! 435 _ [ i L l I t ; l ; l l l l l + + I k t t l + l i l Z L l l L l l l l t l l i, l l l l l l l ( l l I I [ 1 1 I I I t l l l l l 6- Bz,)" I - -]- -4 L I I i i i ~ ~ i ~ t i i i ~ i, i i, t t i i I i : J : ~ i I 1 ] i I I 1 I f OOrO TIME, U T, SEPTEMBER 8-9, Fig. 26. The three solar magnetospheric vector components of the magnetic field during a crossing of the neutral sheet by Explorer 33 spacecraft 73 RE behind the Earth (Mihalov et al., 1970). IgES A similar oscillation in the boundary of the plasma sheet has been reported by Russell (1971a) at 12.5 RE behind the Earth. Figure 27 shows the successive entries into and exits from the plasma sheet which occurred during a substorm expansion of the plasma sheet. The period of this boundary oscillation was roughly two minutes, in good agreement with the observations of Mihalov et ai. at 73 R E and of ATS-1 at 6.6 RE. 5. Geomagnetic Storm Associated Wave Phenomena 5.1. TRANSVERSE WAVES Predominantly transverse waves have been reported on ATS-1 during magnetic

26 436 R.L.MCPHERRON ET AL. storms with frequencies in the Pc 1 band. The first report, by Barfield et al. (1970), described an event with 5 s period and amplitude. This event was associated with the longer period mixed mode stormtime waves described below, and may have been amplitude modulated by them (see Figure 28). Maxima of the Pc 1 wave amplitude occurred at the extrema of the long period waves. The Pc 1 waves were left hand elliptically polarized with the orientation of the major axis rather variable. tbi 20 io Bx o[ By_l ~ 20 io o Bz ioe o q O OB~8 OBI9 082O 08,2~ 0B22 30 L81 20 io ,... x 3o 20 C[ o o Bz IO[ o, Z4 OB~ OBZ6 0~7 O828 UNIVERSAL TIME AUGUST 20, 1968 Fig. 27. The three solar magnetospheric vector components of the magnetic field and the total field during a crossing of the plasma sheet boundary by the OGO-5 spacecraft. The depressions of the X component upon entry into the plasma sheet have been shaded for easy identification (Russell, 1971c). It was noted that the average flux of 600 to 1000 kev protons was unusually high, presumably due to the direct access of solar wind protons. A similar Pc 1 event was seen in association with the long period waves and solar flare protons of another storm. It was noted however that Pc 1 waves also occurred in association with the protons when no long period waves were present. Another report of transverse waves during a magnetic storm made by Russell et al. (1970) used the UCLA magnetometer on OGO-5. At the time the waves were observed the satellite was outbound at 45 ~ magnetic latitude, at a distance of 5 R~

27 FLUCTUATING MAGNETIC FIELDS IN THE MAGNETOSPHERE~ I1 437 on the noon meridian. The presence of magnetosheath electrons during the wave events indicates that the satellite was within the polar cusp (Russell et al., 1971b). The frequency of the waves was about 7 Hz or about 80% of the local proton gyro frequency. Their waveform in the principal axis coordinate system is shown in Figure 29. The peak to peak amplitude of this event at its maximum was The polarization of this segment of data was highly elliptical as shown in Figure 30. It should UCLA MAGNETOMETER EXPERIMENT ATS-I ~9 Z s w -2E ~ -- -3r -- I i [ I ] _ I _ I ~ U.T. Fig. 28. JUNE 26, [967 Waveform of storm associated transverse Pc 1 wave correlated with longer period, mixed mode waves (Barfield et al., 1970). be noted that the average direction of the ambient field was along the Y axis of the principal axis coordinate system; also, the direction of propagation of the wave should be in the direction of least variation, i.e., the Z principal axis. Thus, the direction of propagation, the ambient field, and the major axis of polarization are mutually orthogonal. This is the characteristic of the Alfv6n wave (left hand mode) propagating perpendicular to the ambient field. Power spectra of the entire wave event in the principal axis coordinate system of the previous figure are shown in Figure 31. The complex structure of the peaks in each component is consistent with the occurrence of several different bursts of waves during the interval.

28 438 R.L.MCPHERRON ET AL COMPRESSIONAL WAVES Waves with a large compressional component but having a coupled transverse variation have been discussed by Sonnerup et al. (1969). Fluxgate measurements on Explorer 26 at 5 RE, 1330 LT and 6 ~ magnetic latitude during a magnetic storm revealed fluctuations of 5 min period in magnitude, declination, and inclination. Simultaneous modulation of energetic protons was observed with minima in the field magnitude corresponding to maxima in the proton fluxes at all energies. No close Pc I MAGNETIC MICROPULSATIONS 1254 UT NOVEMBER I, 1968 I I I ~ I I I I I I 4[ UCLA FLUXGATE ~. ~4 ~. MAGNETOMETER f ~, /~ ff~ BXO O Z 0 8 x g 16.5 HZ} -27 ~ "" ~ J--2 0 Bz o "2)'~ o J--2 - I I I t [ ] I I I I I 1254 : 25.2 : 25.4 : 2:5.6 : 23.8 :24.0 Fig. 29. UNIVERSAL Waveform of high frequency Pc 1 wave event occurring during magnetic storm (Russell et al., 1970). TIME correlation between the satellite observations and ground micropulsations could be established although it was noted that the wave event was associated with a magnetospheric substorm. The polarization of the wave was determined by eigenanalysis and hodograms in the principal axis coordinate system. The wave was elliptical with a ratio of major to minor axis of / The orientation of the major axis was almost in a magnetic meridian plane, but tipped inwards towards the Earth from the ambient field by 30 ~. The normal to the polarization ellipse, i.e., the axis of wave propagation, was pointed outwards from the Earth 60 ~ above the magnetic equatorial plane and 34 ~ east of a magnetic meridian plane (towards dusk). The polarization appeared to be left handed with respect to the ambient field. Spectral analysis gave

29 FLUCTUATING MAGNETIC FIELDS IN THE MAGNETOSPHERE, II 439 < B >ErGE N (3.4, 513.2,6.5 ) NOVEMBER l, : 23.[ X 5?" EIGEN VALUES 38.4:7.1 : I -5 y 1254: ~ 57" Fig. 30. fwavr = 6.5 hz -5 fproton 6YRO = 7.8 hz fw / fp.g. =.83 FILTER CORNER FREQUENCY=2.TB hz Hodograms for Pc 1 event of Figure 29. Note average direction of main magnetic field is along //axis (Russell et al., 1970). 102 ~>~ c~ LO 10 Z --. Od 10 o i@ -I ~: 10-2 td 10-~- o_ 10-s- Fig. 31. lo -i I0 ~ I01 t02 FREQUENCY (HERTZ) Auto spectra of Pc 1 event in principal axis coordinate system of data shown in Figure 29 (Russell et al., 1970).

30 440 R.L. MGPHERRON ET AL y V ~ " t.,; ~=/80keg,.o.,IV / ~ '~ ] apr= 8z5 ~ 5.C I I I 1 6, ~ Ur Fig. 32a-b. Panel A shows the simultaneous fluctuations in the magnitude of the field and energetic protons observed in association with a substorm occurring during a magnetic storm. Explorer 26 was at 5 RE 1330 LT, and 6 ~ magnetic latitude. Pane] B shows details of the variations in components of the field (Sonnerup et al., 1969). ~,20 6.~0 6.'~0 b.~o 7.00 UT" 0 I I I I I o,,,.,,, V V V.,, v _5 ~ _ Fig. 32h.

31 FLUCTUATING MAGNETIC FIELDS IN THE MAGNETOSPHERE, n 441 a sharp peak at 315 s in all three components. The particle and field observations are shown in Figure 32. Hodograms and spectral analysis are shown in Figure 33. The same phenomenon has been reported at ATS-1 by Barfield and Coleman (1970). Quasi-sinusoidal fluctuations primarily in the magnetic meridian plane were observed with 1 to 4 h duration during four of the first six magnetic storms of Wave periods from 2-15 rain and average amplitudes of 10 7 were typical. The polarization 7o-~.B~2 (o') I! I I I 1 mo mo zoo ~3 ('r) Fig. 33a-b. /60 mo zoo ~.~ (a') Panel A shows hodogram for event of Figure 32. Orientation of principal axis explained in text. Panel B shows power spectra of same event (Sonnerup et al., 1969). I0 O." (degree)a (min) Z." x 2(degree)2(min) B." x /O0(g) 2 (rnin) DD / I 5 0 o / I " I /./B ; :r" t,k,., li ~" ' t" I '", iii \,.LJ j "~.V~ ~ " I o,i o.z. Fig. 33b. (2. 3 s cy_c/es 0.4 l_.w.=-.. m/n~

32 442 R.L. MCPHERRON ET AL. was nearly linear with both transverse and compressional components. During one event electrons were modulated in phase and protons out of phase with the waves (Parks et al., 1969; Lanzerotti et al., 1969). All events occurred around the main phase maximum and in afternoon local time. In more recent work, Barfield et al. (1971b), detailed properties of these waves were examined. Spectral analysis showed that a frequent characteristic of these waves is a harmonic structure. An example is shown in Figure 34, where the fundamental, second, and third harmonics are evident as significant peaks in one of three components. The various harmonics were found to be elliptically polarized. This is particularly ATS-I 104 WAVE EVENT DURING MAGNETIC STORM UT MAY 7, 1967 i0 ~ w o w [01 10 ~ 10 o iq o 0 o I , , FREQUENCY [HERTZ) FREQUENCY [HERTZ) 1 ~ ~... h ~ BZ-BX w 180~ % 0_ -1B0 9 0 ~ - - I g o 1 BT-BZ _ B FREQUENCY [HERTZ) (J j ~ BX-BT 0,036 0,000 0, ,036 FREQUENEY (HEFiTZI Fig. 34. Spectral analysis of storm time, mixed mode waves. Note the harmonic structure of the signal shown by upper right panel (peaks occur at , and Hz). Also, note in the lower right panel, the high coherency in the X-Y plane at the fundamental. The coordinate system is determined by the principal axis of the perturbation at the fundamental frequency (Barfield et al., 1971b).

33 FLUCTUATING MAGNETIC FIELDS IN THE MAGNETOSPHERE, II 443 evident in the example from the high coherency at the fundamental in the X-Y plane. Eigenanalysis was used at each harmonic to determine the characteristics of the polarization. The results were found to be consistent with the assumption that the major axis and direction of propagation of all three harmonics lay in a swept back magnetic meridian plane tilted approximately 45 ~ with respect to the Earth's dipole axis. Actual orientations of the principalaxes of the perturbation ellipsoids for the three harmonics in the above example are summarized in Figure 35. Ellipticities of the three harmonics were quite high, the ratio of power in the J( and Y principal axes were respectively: ~ 16, ~ 8, and ~ 4. The sense of rotation of the polarization ellipse was examined by the cumulative area technique (see appendix for description). The predominant polarization of the three harmonics were respectively right, left, and right handed with respect to the ambient magnetic field. The time behavior of the polarization of each harmonic, however, was quite complex, Figure 36. The various harmonics did not occur simultaneously, and the second and third harmonics reversed their sense of rotation at several apparently significant times. A statistical examination of the occurrence of these wave events revealed they occurred primarily in local afternoon near the maximum of the main phase. Further, ORIENTATION OF PRINCIPAL AXIS SYSTEMS, MAY 7, t967 X,,Y,,Z, ~ FUNDAMENTAL )~2,Y2,Z2 ~ 2nd HARMONIC )(3,'~3,Z3 ~ 3rd HARMONIC r \\ -t.o -~ )< ANALYSIS PERIOD 0548: :00 UT Fig. 35. Orientation of the principal axes of each harmonic of the wave event of Figure 34 in the dipole coordinate system. Note approximate alignment of X and Z axes with the expected direction of a swept back magnetic meridian plane (Barfield et al., 1971b).

34 444 MAY 7, 1967 oo TIME {~s w~'" O0 T ] ME {~ECON05) 9 10" ~')OJ O0 O0 Fig. 36. Instantaneous magnitude and cumulative area swept out by perturbation vector as it rotates in major plane of the principal axis coordinate system of the fundamental. Data shown from the bottom to top for first three harmonics (Barfield et al., 1971b).

35 FLUCTUATING MAGNETIC FIELDS IN THE MAGNETOSPHERE, II 445 nearly every wave event was found to be associated with a magnetospheric substorm at midnight. 6. The Measurement of the Transfer Function of a Field Line As mentioned in the introduction, the knowledge of the transfer function of a field line is very important in studies of micropulsation sources. At the present time there exists a wide variety of ground measurements of ULF waves which could provide detailed information on magnetospheric processes if the effect or propagation of the waves along field lines from their presumed magnetospheric sources were known. Various analytical treatments of this problem quoted in the introduction show the characteristics of ULF waves at the Earth's surface are highly dependent on the ionospheric models and approximations used. Thus, in order to have a transfer function that can be used with confidence, it must be measured OBSERVATIONS Conceptually, measuring the transfer function can be performed by simultaneously measuring the field variations at the equatorial crossing point of a field line and at its conjugate point. Several authors have attempted to do this. For example, Patel and Cahill, (1964); Patel (1965) and Patel (1966a, b) attempted to correlate quiet time transverse Pc 4, 5 waves with ground observations near the subsatellite point. In this work they found the correlation existed only when the satellite was near the same L shell and within one hour LT of the ground station. They did find for the one or two wave cycles examined, that the sense of rotation with respect to the magnetic field in the ground records was consistent with that observed at the satellite. A recent ground-satellite correlation for quiet time compressional waves has been reported by Lanzerotti and Tartaglia (1971). These authors show a purely compressional wave at ATS-1 was observed near its conjugate point as an ellipticallypolarized transverse wave. They show that although peaks were present in the spectra at both locations, the power at the ground was more than 50 times smaller. Ground-satellite correlations for substorm associated Pi 1 micropulsations have been reported by Pierson and Cummings (1969), and more recently by McPherron and Coleman (1971a). In the earlier report the authors did not find clear spectral peaks and no definite conclusions were drawn. In the work by McPherron and Coleman, two satellites, OGO-5 and ATS-1, and two ground stations, College, Alaska and Tungsten, N.W.T., Canada were used. These authors reported that the signal was seen at all locations except ATS-1, and concluded therefore that the signal was spatially localized. A more recent examination of the ATS-1 data by the authors of this review indicates that the signal was also present at ATS- 1. This result was obtained using the more sensitive techniques of eigen analysis of the spectral matrix described in Appendix I. The conclusion about spatial location still appears to be justified, however. One month of ground micropulsation data from College, Alaska (near the ATS-1 conjugate point) have been compared to ATS-1 data. Only twice during this

36 446 R.L. MCPHERRON ET AL. month did any of the frequent substorm associated Pi 1 events at the ground have associated variations at the satellite. In these two cases the ATS-1 satellite was past dawn as it was for the two other Pi 1 events discussed above. This lack of correlation between the ground and the satellite for events prior to dawn suggests that the signals are spatially localized. Another attempt to study this problem was made for the stormtime Pc 5, mixed mode waves by Sonnerup et al. (1969), and more recently by Barfield et al. (1971b). While no digital data were available at the ground for detailed spectral analysis, the analog records indicate that oscillations with similar characteristics were absent. The most recent report of a ground-satellite correlation is the work of McPherron (1971), on a substorm associated Pc 1 event. Comparison of dynamic spectra at the two points showed the ground signal had the more complex structure. For two time intervals that appeared to correlate well, the measured transfer functions were quite different. For the first of these two intervals the signal on the ground was highly polarized and left elliptical over the entire Pc 1 band. For the second interval, the polarization was low and erratic. During both events the signal was left elliptical at the satellite. The most likely interpretation of these results is that most of the signal in the Pc 1 band received at the ground station was propagating horizontally in the ionospheric wave guide. Only when the signal was systematically polarized in a left handed sense at the ground, is it reasonable to assume that the signal was vertically incident. Unfortunately it is unlikely that ATS-1 and Tungsten, N.W.T., Canada (69.96~ ~ W) were exactly conjugate at this time. Calculations of the northern conjugate points for ATS-1 by Barish and Roederer (1970) show that Tungsten is close to real conjugacy only at local midnight, while these observations were made at 1800 LT. Diurnal, seasonal and solar wind effects can move the calculated conjugate point as much as 200 km north and/or east and west of Tungsten DISCUSSION A number of questions are raised by the preceding observations. Perhaps the most significant is whether the concept of a field line transfer function is meaningful at all. It appears to be appropriate only where it is reasonable to assume that plane waves are observed at both the satellite and the ground. If waves were truly plane, conjugacy would be unimportant since measurements could be made anywhere in the planes of constant phase. However, in the real situation, it is likely that waves such as Pc 1 are collimated between closely adjacent L shells. In this case it becomes very important where the satellite is located with respect to these shells. Clearly if the wave is collimated its amplitude will be a significant function of position across these L shells. Even more serious problems arise at the ground station where ionospheric effects can convert a vertically incident wave into a wave propagating horizontally in the ionospheric cavity. In this case the wave will be significantly modified by the mode conversion and horizontal propagation. For longer period oscillations than Pc 1 it is not even obvious that the concept

37 FLUCTUATING MAGNETIC FIELDS IN THE MAGNETOSPHERE, II 447 of a propagating wave is useful. Since at low frequencies wavelengths become long compared to the length of a field line, it seems more appropriate to think in terms of oscillations of a resonant cavity. In this case a ground-satellite correlation reduces to a simultaneous pair of measurements at an unknown point on the boundary and an unknown point within the cavity. Clearly measurements at more than two points are required to obtain definite conclusions. For example, location of the conjugate point of the micropulsations source field line might be accomplished using a chain of ground observatories. An example of this technique is the work of Sampson et al. (1971), who showed for Pc micropulsations that the latitude of maximum signal amplitude and the latitude of transition from left to right handed polarization are the same. To determine the location of the satellite with respect to such a source field line is not an easy task. If the signals are of sufficient duration it may be possible to use the micropulsations themselves as field line tracers. Thus, if it is found that Pc micropulsations change their sense of polarization near local noon, as in the case for the ground signals reported by Sampson et al., they may also change their polarization sense as a function of radial distance. Since the micropulsation signals are presumed to be confined to fixed field lines it is possible for a synchronous satellite to cut through such a shell as it rotates in a distorted magnetosphere. Simultaneous observations at the satellite and the appropriate ground station determined as discussed previously, could then be used to define the transfer function. An alternative to this procedure would be the use of a second magnetometer on an eccentric satellite in conjunction with the chain of ground stations near the conjugate point of a synchronous satellite. The eccentric satellite could establish the radial properties of the micropulsations while the synchronous satellite acted as a monitor of time variations in space. It is obvious from the preceding discussion that the goal of determining the transfer function of a field line will not be easily reached. In fact, it appears likely that fluctuations in the magnetosphere and ionosphere are so closely coupled that such a simple concept as the transfer function of a field line will be of limited value. Consequently, our only method to attack this problem at present or in the near future is to determine average magnetospheric properties such as amplitude, region of occurrence and polarization, and then compare these with the average properties measured on the ground. Chance near approaches of spacecraft during wave events may give some measure of the spatial extent of these events but these near approaches are very rare events. 7. Summary As might be expected from the ground observations, a wide variety of low frequency waves occurs throughout the magnetosphere. However, at the present time it is not possible to make other than a tentative association for most of these waves with distinct phenomena observed on the ground. In fact, the limited satellite observations make it difficult to separate the magnetospheric waves into distinct phenomena.

38 448 R.L.MCPHERRON ET AL. If we attempt to do this without recourse to the ground observations, we conclude there are at least seven different types of wave phenomena observed in space. During magnetically quiet times, transverse waves are observed across a wide band of frequencies from Pc 1 to Pc 5. From the work of Heppner et al. (1970) the probability of observing a given frequency wave depends somewhat on spatial location but not sufficiently to suggest the divisions derived from ground observations. Other satellite observations are more limited and presently provide no basis for separating this broad band of quiet time transverse waves into distinct phenomena. Quiet time compressional waves have been reported in space but since the observations are limited to several events, it is not known whether they occur throughout the full spectrum of Pc 1 to Pc 5. In times of moderate magnetic disturbance (i.e., substorms) two types of transverse waves have been reported: band limited pulsations and Pc 1. Also, a distinct type of compressional wave is seen during substorms. In contrast to the transverse waves, however, its spectrum falls rapidly toward high frequencies without spectral peaks. Close to the Earth (at synchronous orbit) the disturbance is predominantly parallel to the ambient field. However, further away in the geomagnetic tail, it appears independent of direction. During magnetic storms two transverse wave events have been reported, one in the Pc 1 band and one at higher frequencies (7 Hz). Mixed mode, predominantly compressional waves have also been reported with 3 to 15 min periods. The above wave phenomena will undoubtedly be further subdivided as more satellite observations appear in the literature. However, since there are so few instruments in space capable of measuring these events, it is not likely that understanding of their origin will come in the near future. Acknowledgements We thank the many authors of original papers for permission to use their figures. We especially thank Drs Patel and Winckler for their helpful comments on the manuscript. This work was supported, in part, by the National Aeronautics and Space Administration under research grants NGL and research contract NAS , and by the National Science Foundation under research grant GA I-1. CLASSIFICATION OF WAVE PHENOMENA Appendix I. The Analysis of ULF Waves An electromagnetic wave produces fluctuations in both the magnetic and electric field. At any instant of time these fluctuations may be represented by two vectors B(t) and E(t) whose magnitude is the amplitude of the perturbing field and whose orientation is parallel to the direction of this field. A series of observations of three components of B(t) or E(t) produces what is known as a vector time series. The analysis of this signal may be carried out on the original time series (in the time domain)

39 FLUCTUATING MAGNETIC FIELDS IN THE MAGNETOSPHERE, II 449 or on the Fourier transform of the time series (in the frequency domain) or a combination of both (dynamic spectral analysis). When a wave is measured, one of the first tasks to be performed is to identify to which classification of distinct wave phenomena it belongs or to identify it as a new phenomenon. In order to do this we examine its various characteristics in the time domain and the frequency domain. The original waveform permits easy identification of the amplitude, and amplitude modulation. If only one wave is present, or there is one dominating wave train, other characteristics such as frequency and polarization may be determined from the original time series. However, often the frequency and polarization must be determined in the frequency domain especially if there is a broad band of signals present. Some signals are characterized by their change in frequency with time. In order to identify these signals, often neither the original waveform or the Fourier transform of the entire time series is sufficient. In these cases, we use dynamic spectral analysis, which Fourier transforms short segments, usually overlapping segments, of the time series so that temporal changes in the frequency of the wave can be resolved. As stated in this review, the identification of distinct ULF wave phenomena, particularly in space, is a continuing process. Once a distinct phenomenon has been identified other properties such as local time dependence, spatial location and correlations with other phenomena serve to characterize the signal. Since most observations of ULF phenomena have been made with magnetometers we shah restrict our discussion of analysis techniques to those associated with the study of magnetic time series. I-2. TIME DOMAIN ANALYSIS In the past, the classification of ground micropulsations has relied primarily on analysis of data in the time domain. This is evident from the present system of classification of these waves (Jacobs et al., 1964) which is based on the waveform and the frequency. If the waveform is regular, it is classified as a Pc (pulsations continuous). If it is irregular, it is called a Pi (pulsations irregular). It is then assigned a number 1 to 5 for Pc phenomena and 1 or 2 for Pi phenomena, according to its frequency. The use of this visual classification of time series although expedient in using analog records, is undesirable because the distinction between Pc and Pi phenomena is subjective and the measurement of periods is rather imprecise. Furthermore, there are often subsets of phenomena within each classification and some of these phenomena extend into two or more of the assigned frequency bands. One of the more fruitful auxiliary techniques of analysis in the time domain is the use of hodograms. A hodogram is a plot of one of the vector components of a wave versus another. If three components of a wave have been measured, we can construct three orthogonal hodograms. From the hodogram we can determine the sense of rotation. For plasma waves, this sense of rotation should be determined relative to the direction of the background magnetic field. Waves whose perturbation vector rotates about the magnetic field in the same sense as protons are called left handed

40 450 R.L. MCPHERRON ET AL. waves. Those which rotate about the field in the same sense as electrons are called right handed. The hodogram can also show whether a wave is circularly, elliptically or linearly polarized. If it is linearly polarized, it will appear linearly polarized on all three orthogonal hodograms. However, unless we are fortunate enough to have one of the hodogram planes lie in the wavefront we cannot easily tell an elliptical from a circular wave. However, if one of these planes (called the principal plane) does lie in the wavefront, or if by digital techniques we rotate the data into this plane, we can use the hodogram to measure quantitatively how elliptical the wave is. The most simple measure of this is the ellipticity, the ratio of the minor to major axis. We note that that the ellipticity may be more generally defined, as the ratio of the perturbation in the wavefront along the direction defined by the projection of the magnetic field in the wavefront (Russell, 1968; Russell et al., 1971) to the perturbation perpendicular to this direction. In this case, either direction may be the major or minor axis and the ellipticity ranges from 0 to oo. However, in this review we have used the simpler definition where 0 refers to a linearly polarized wave and 1 refers to a circularly polarized wave. On the other hand, it is convenient to assign a sign to the ellipticity, negative for left hand polarized waves and positive for right hand polarized waves. This can be done for either definition of ellipticity. If the vector time series is recorded on magnetic tape, we may reprocess the data at will, any number of times and with a variety of techniques. Any analogue technique has its counterpart on a digital computer and vice versa. However, since most satellite data, especially those on ULF waves, are digitized at some stage we shall discuss these operations in terms of digital techniques. The first of these operations, bandpass filtering, is a modest advance over the examination of raw data. It allows the study of waves in a particular frequency range without interference from other phenomena. This technique has been used on analog data in the past and is still quite useful in studying digital data, (cf. Figures 6, 12, 27). (For detailed information on digital filtering see the special issue on digital filters IEEE, 1968.) Upon isolating a wave by bandpass filtering, we can actually find the wavefront, or principal plane, of the oscillation if we have a plane wave. This is done by finding the eigenvalues and eigenvectors of the variance ellipsoid created by the end point of the perturbation vector as it sweeps out some volume in space. The eigenvector associated with the minimum eigenvalue is parallel to the wave normal or equivalently perpendicular to the wavefront. The eigenvector associated with the maximum eigenvalue is the direction of the major axis of the perturbation ellipse. If we have isolated a single plane wave by our bandpass operation, the ellipticity is simply the square root of the intermediate eigenvalue to the maximum eigenvalue. The third eigenvalue may be used as a measure of the noise in the analysis. This technique is entirely analogous to the method of determining the normal to the magnetopause pioneered by Sonnerup and Cahill (1967, 1968). Finally, we can transform the original data into a new coordinate system, called the principal axis system with the rotation matrix

41 FLUCTUATING MAGNETIC FIELDS IN THE MAGNETOSPHERE, II 45t formed by these three eigenvectors. In practice care must be exercised in this step not to change the handedness of the coordinate system. Once this rotation has been performed, hodograms may be constructed. Since the perturbation now, except for noise, is confined to a single plane, these hodograms provide a very convenient and useful display of the data, (cf. Figures 12, 30, 33a). An alternative approach to the analysis of bandpass filtered data may be used if we are willing to sacrifice our knowledge of the ellipticity and desire only the direction of the wave normal and the sense of rotation of the wave. In this method, cross products of successive perturbation are performed (McPherron and Coleman, 1971). To minimize errors, these cross products should use perturbation vectors spaced about 88 wave period apart. Since each perturbation vector is in the wavefront, the resulting cross product is along the wave normal. Further it is easy to show that the dot product of this cross product with the magnetic field is positive for a right hand polarized wave and negative for a left hand wave. This technique is very similar to the cumulative area technique used by Dungey and Southwood, (1970) and McPherron and Coleman, (1971). The cumulative area technique sums up the area swept out by the perturbation vector with time in some plane, for example, a plane perpendicular to the magnetic field direction or the principal plane. This area will decrease or increase depending on the polarization of the wave, and the direction of the magnetic field. The similarity of the two techniques is, of course, that the area swept out between two successive samples of the wave is equal to the cross product of the components perpendicular to the background field. These latter two techniques are most useful in studying time series consisting of many short duration wave packets from a variety of sources, (cf. Figure 36). Analyses in the time domain such as those listed above have the disadvantage that they can be used on only one frequency band at a time. It is often desirable to analyze a wide band of frequencies simultaneously. This can be done in the frequency domain. In the following section, we will outline how this is done. Analysis of the Spectral Matrix For a given time interval we calculate the full 3 x 3 spectral matrix where elements consist of all possible cross spectra between any pair of field components. We diagonalize the real part of this matrix determining its eigenvectors and eigenvalues at each frequency. These eigenvectors are then used to transform both the real and imaginary parts of the spectral matrix to the principal axis coordinate system. In this coordinate system, we take the 2 x 2 submatrix corresponding to the maximum and intermediate eigenvalues (the principal plane) and perform coherency analysis. This process separates the submatrix into two parts corresponding to the coherent and incoherent power in the principal plane. For the coherent portion of the signal we determine the ellipticity and azimuth of the polarization ellipse. The physical basis of the foregoing procedure is the following assumption. During a limited time interval the signal in a narrow frequency band is due to a single plane wave propagating in a fixed direction with respect to the ambient magnetic field.

42 452 R.L.MCPHERRON ET AL. Then from Maxwell's equation, V.B=0 and therefore k.b=0. Thus, the magnetic perturbation lies in a plane perpendicular to the direction of propagation. Consequently magnetic field measurements made in an arbitrary coordinate system show variations in all three field components only because of an inappropriate choice of coordinate axis. Diagonalization of the real part of the spectral matrix in a frequency band including the perturbation due to the wave is equivalent to diagonalization of the variance matrix and determines the plane of polarization. Since the fluctuations in this plane may be only partially polarized it is further necessary to separate coherent and incoherent power in the plane of polarization. For coherent power, one may determine the ratio of the minor to major axis of the polarization ellipse and the sense of rotation. The technique of coherency analysis of a signal measured in the plane of polarization of an electromagnetic wave has been discussed several times in recent literature. The earliest report is that of Fowler et al. (1967). Application of this technique has been made by Rankine and Kurtz (1970), and Sampson et al. (1971). Since most geophysical phenomena change rapidly with time, the foregoing procedure is best applied in a dynamic fashion. To do this we break the time series into a number of overlapping segments. For each segment we carry out the eigen and coherency analysis described above. The results are stored in two dimensional arrays with the row index corresponding to the frequency of a given spectral estimate and the column index to the time of the center of the segment. The results are displayed as contour maps of a given parameter in the frequency - time plane, i.e., as digital sonagrams. Because this dynamic analysis technique yields so many parameters we have found it convenient to apply it in a more limited fashion. For example, suppose that this procedure is applied to the entire time interval including the event. It is often found that the perturbation of interest is confined to a single plane. We then transform the original time series to the coordinate system having this plane as the X-Y plane. Application of the dynamic spectral analysis procedure then yields the following quantities as a function of frequency and time: total power, percent polarization, polarized power, ellipticity and azimuth. Since ellipticity and azimuth have no meaning unless the percent polarization is high, we do not usually display contour maps of these two quantities. If more than one wave is simultaneously present in a given frequency band, and the waves are propagating in different directions, the above procedure will be in error. Similarly if the signal cannot be represented by a plane wave, difficulties can arise. Determination of spectra over intervals longer than the duration of a typical wave also produces ambiguous results. Despite these difficulties we find the basic assumption is frequently justified and consistent results obtained. In the final analysis the merit of any technique is whether it yields new insight into the nature of the physical processes.

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