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Interplanetary magnetic field, solar wind and geomagnetic micropulsation Nourry, Gérard Robert 1976

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INTERPLANETARY KAG NET IC F I E L D , SCLAR WIND AND GEOMAGNETIC MICROPULSATION by G e r a r d R o b e r t N o u r r y B . S c , U n i v e r s i t e da M o n t r e a l , 1971 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY I n t h e D e p a r t n e n t o f G e o p h y s i c s and A s t r o n o m y We a c c e p t t h i s t h e s i s as c o n f o r m i n g t o t h a r equ i r ed s t a n d a r d The U n i v e r s i t y C f B r i t i s h C o l u m b i a M a r c h , 1976 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of Geophysics and Astronomy The University of British Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 Date March 31, 1976 i ABSTRACT M i c r o p u l s a t i o n s i g n a l s recorded at the m i d - l a t i t u d e s t a t i o n , S a l s t c n , A l b e r t a , are compared with simultaneous Explorer 34 o b s e r v a t i o n s of the i n t e r p l a n e t a r y f i e l d and plasma. The a n a l y s i s i s d i v i d e d i n t o two p a r t s . F i r s t , a study of the i n t e r p l a n e t a r y parameters c o n t r o l l i n g Pc3-4 a c t i v i t y i s made, and second, s p e c t r a cf upstream waves and continuous micrc-p u l s a t i o n s are compared. A case by case study r e v e a l s that Pc3 and PcU occurrence i s determined by the i n t e r p l a n e t a r y f i e l d d i r e c t i o n . Pc4 r e q u i r e s a f i e l d d i r e c t i o n w i t h i n 30° of the Earth-Sun l i n e , while Pc3 takes place f o r a wider range cf f i e l d l a t i t u d e s and azimuths. Cn a time s c a l e of the order cf hours, the amplitude of Pc3-4 continuous p u l s a t i o n s c o r r e l a t e s with the s o l a r wind v e l o c i t y . Large amplitude events a s s o c i a t e with high speed s o l a r wind, while s m a l l amplitude events c o r r e l a t e with low speed s o l a r wind. Three dimensional d i s t r i b u t i o n s of Pc3 and Pc4 versus the i n t e r p l a n e t a r y f i e l d d i r e c t i o n are c a l c u l a t e d . Ihe d i s t r i b u t i o n s are then c o r r e c t e d f o r the amplitude of the s i g r a l and f u r t h e r normalised by the IMF d i s t r i b u t i o n . The r e s u l t i n g d i s t r i b u t i o n s show that the f i e l d d i r e c t i c n - c o n t r c l cf Pc3-4 a c t i v i t y i s net a r e s u l t cf the IMF d i s t r i b u t i o n , and f u r t h e r , the f i e l d d i r e c t i o n i s a l s o an a m p l i t u d e - c o n t r o l cf these continuous p u l s a t i o n s . They show t h a t Pc4 i s e q u a l l y l i k e l y f c r toward and away s e c t o r s , while Pc3 e x h i b i t s a s i g n i f i c a n t preference f o r tcward s e c t o r s . i i F i r a l l y power s p e c t r a cf upstream waves are compared with s p e c t r a cf continuous p u l s a t i o n s . I t i s found that the s p e c t r a of Pc2-4 continuous p u l s a t i o n s are determined by the s p e c t r a l content cf upstream waves. Cn a time s c a l e of the order cf h a l f an hour, the n d c r c p u l s a t i c n spectrum c o r r e l a t e s with the t r a n s v e r s e components spectra of the upstream waves. On a s h o r t e r time s c a l e , the i s i c r o p u l s a t i c n spectrum i s determined by the peaks, t r a n s v e r s e cr compressicnal, that c a r r y the roost power i n space. F i n a l l y , t h e spectra of upstream waves and m i c r o p u l s a t i o n s are c o n s i s t e n t with the e x i s t e n c e of fundamental waves i n space. l i B L E OF CONTENTS CHAPTER I: ..1 A) Review of Sun-Earth Relationships ............1 B) Geomagnetic Hicropulsations .........................12 B-1) Pc2-3 Pulsations ........15 B-2) Pc4 Pulsations 16 C) Thesis Outline ....17 CHAPTER I I : 19 A) Present State of the Art ...............19 B) Restrictions on the Present Research ..26 C) Source of Data 23 C-1) Ground Station 28 C-2) Explorer 33 Magnetic F i e l d Experiment 28 C-3) Explorer 34 Fields and Plasmas Experiments .....33 CHAPTER I I I : INTERPLANETARY MAGNETIC FIELD, SOLAR WIND AND PC3-4 HICROP1USATIONS 37 A) Introduction 37 B) Case by Case Study .......38 B-1) I.M.F. Direction-Control of Pc4 A c t i v i t y .......38 B-2) I.M.F. Direction-Control of Pc3 A c t i v i t y 47 B-3) Solar Wind and Micropulsations .........55 B-3-1) Transient Pulsations 55 B-3-2) Continuous Pulsations .....................64 B-4) Summary ........65 C) S t a t i s t i c a l Study 66 C-1) S t a t i s t i c a l Distributions of Microplusations ...66 C-2) Summary of S t a t i s t i c a l Results .......98 CHAPTER IV: UPSTREAM WAVES VERSUS MICRCPULSATIONS 100 A) Introduction 100 B) Spectral Analysis via Conventional Methods .......... 102 B-1) Meaning of the Various Quantities 102 B-2) Results . 106 C) Power Spectral Analysis via Autoregressive Models ...131 C-1) Method 131 C-2) Besults 137 D) Some Discrepancies 159 E) Summary 160 CHAPTER V: DISCUSSION OF THE RESULTS AND CONCLUSIONS 161 A) On the IMF Direction-Control 161 B) On the Results of Spectral Analysis ................. 167 C) Theoretical Implications 171 D) Conclusions ..172 BIBLIOGRAPHY ...174 V LIST OF TABLES Table I Hicropulsations C l a s s i f i c a t i o n 13 Table II P r i n c i p a l Continuous Pc4 Events .39 Table III Simultaneous Magnetosheath and Pc4 Events 45 Table IV Events Showing More E f f i c i e n t I.M.F. Direction-Control For Pc4 Than For Pc3 54 Table V F i r s t and Second Moments of Pc3-4 Histograms 81 Table VI F i r s t and Second Moments of Pc3-4 Normalised Histograms .............................................92 LIST OF FIGURES Figure 1.1 Regions of the Magnetosphere Shown in the Noon-Midnight Meridian Plane 5 Figure 1.2 An Open Magnetosphere Model ........9 Figure 2.1 Dependence of Pulsation Period on Interplanetary Parameters ......25 Figure 2.2 Explorer 33 Trajectory 30 Figure 2.3 Explorer 34 Apogee 32 Figure 3.1 Pc4 Occurrence Versus IMF Direction ...........40 Figure 3.2 Pc4 A c t i v i t y Versus Enhanced Fluctuations i n the Magnetosheath ......44 Figure 3.3a Correlated Upstream Waves and Pc3 A c t i v i t y ...48 Figure 3.3b Correlated Upstream Waves and Pc3 A c t i v i t y (coat d) 50 Figure 3.4 Transient Pulsation Associated With HM Shock Wave ...........57 Figure 3.5 Transient Pulsation Associated tfith D i r e c t i o n a l Disco n t i n u i t i e s 59 Figure 3.6 Succession of Transient Pulsations and Dynamic Pressure Changes ...........61 Figure 3.7 Pc3 Raw Distribution Versus IMF Direction 68 Figure 3.8 Pc3 Corrected Distribution Versus IMF Direction 70 Figure 3.9 Pc4 Raw Distribution Versus IMF Direction 72 Figure 3.10 Pc4 Corrected Distribution Versus IMF Direction .........74 figure 3.11 Pc3 and 4 Distributions Versus IMF Latitude ..76 Figure 3.12 Pc3 and 4 Distributions Versus IMF Azimuth ...73 Figure 3.13 Comparison of Pc3 and 4 Raw and Normalised Azimuth Histograms .........34 Figure 3.14 Comparison of Pc3 and 4 Corrected and Normalised Azimuth Histograms 86 Figure 3.15 Comparison of Pc3 and 4 Raw and Normalised Latitude Histograms .88 Figure 3.16 Comparison of Pc3 and 4 Corrected and Normalised Latitude Histograms ...............90 Figure 3.17 Pc4 Eguiprobability Contours for Toward Sectors 94 Figure 3.18 Pc3 Eguiprobability Contours for Toward Sectors ....96 Figure 4.1 Comparison of Upstream waves and Micropulsations Spectra on Oct 16, 67 ....108 Figure 4.2 Comparison of Upstream Waves and Micropulsations Spectra on Nov 6, 67 110 Figure 4.3 Comparison of Upstream Waves and Micropulsations Spectra on Nov 6, 67 ......112 Figure 4.4 Comparison of Upstream Waves and Micropulsations Spectra on Nov 6, 67 .............114 Figure 4.5 Comparison of Upstream Waves and Micropulsations Spectra on Oct 26, 67 ..................116 Figure 4.6 Comparison of Upstream Waves and Micropulsations Spectra on Oct 23, 67 1 18 Figure 4.7 Comparison of Upstream Waves and Micropulsations Spectra on Aug 18, 67 .........120 Figure 4.8 Special Event i n the Interplanetary Medium: T=11.6 sec Wave 127 Figure 4.9 Special Event i n the Interplanetary Medium: T-7.7 sec Wave ......12 9 Figure 4.10 Comparison of Upstream Waves and Micropulsation Spectra on Sept. 11, 67 139 Figure 4.11 Comparison of Upstream Waves and Micropulsation Spectra on Oct. 25, 67 14 1 Figure 4.12 Comparison of Upstream Waves and Micropulsation Spectra on Oct. 16, 67 ,143 Figure 4.13 Comparison of Upstream Waves and Micropulsation Spectra on Sept. 5, 67 ...145 v i i i Figure 4.14 Comparison of Upstream Haves and Micropulsation Spectra on Oct. 25, 67 ... 147 Figure 4.15 Comparison of Upstream Waves and Micropulsation Spectra on Sept. 16, 67 149 Figure 4.16 Comparison of Upstream Waves and Micropulsation Spectra on Nov. 6, 67 ........151 Figure 4.17 Comparison of Upstream Waves and Micropulsation Spectra on Oct. 26, 67 ...153 Figure 5.1 Field-Aligned Coordinate System 169 ix iCKNCWLECGEflENlS I wish to express my sincere thanks tc Prof. 1. watanabe for his guidance and for many stimulating discussions during the course cf t h i s research. I am deeply indebted to him for his patient supervision and much encouragement. I am also greatly indebted to Prof. R . D. Russell for his interest and encouragement, and for prevision cf an atmosphere conducive tc research. During a stay i n Japan, I had stimulating discussions with Prof. 1. Saitc and Dr. T. Sakurai. In the preparation of the manuscript, I received tremendous help from my colleagues. In particu l a r , Mr. R. W. Clayton spent long hours helping with various aspects of the manuscript. Without their help and encouragement, this thesis would have never beer completed. This research was supported ty a National Research Council of Canada post-graduate scholarship, and by an INCO graduate research fellowship (1572-73). F i n a l l y , the s a t e l l i t e data were kindly provided by the World Data Center A, Rockets and S a t e l l i t e s . 1 CHAPTER I A) Review of Sun-Earth R s l a t i o n s h i r j s p r i o r t o t h e d i s c o v e r y of tne i n t e r p l a n e t a r y plasma, the i n t e r p l a n e t a r y medium was regarded more or l e s s as a vacuum which might have been i n v a d e d by the s o l a r g e n e r a l magnetic f i e l d o r the g a l a c t i c magnetic f i e l d , depending on which would be s t r o n g e r . H i s t o r i c a l l y , the s t u d y of a u r o r a , geomagnetic storm and comet t a i l o r i e n t a t i o n p r o v i d e d evidence f o r a s o l a r c o r p u s c u l a r r a d i a t i o n . The s t r e a m i n g of p a r t i c l e s from the sun i s now a w e l l e s t a b l i s h e d f a c t and i s r e s p o n s i b l e f o r a number of g e o p h y s i c a l and a s t r o p h y s i c a l e f f e c t s . In the e a r l y s i x t i e s , d i r e c t measurements c f the plasma f l o w were made from l u n a r and i n t e r p l a n e t a r y probes. The r e s u l t s were i n agreement w i t h P a r k e r ' s (1958) p r e d i c t i o n c f a s u p e r s o n i c a l l y expanding s o l a r corona which he termed " s o l a r wind". Forbush ( f o r a r e v i e w , see Forbush,1954) showed t h a t the i n t e n s i t y o f g a l a c t i c cosmic r a y s c o r r e l a t e s w i t h the sunspot c y c l e . I t tends to be h i g h e r when s o l a r a c t i v i t y i s low. Forbush f u r t h e r p o i n t e d out the tendency f o r the g a l a c t i c c o s m i c - r a y i n t e n s i t y t o decrease d u r i n g a geomagnetic storm. 2 Both of these effects might be explained by solar plasma moving past the earth, provided that the plasma carried a magnetic f i e l d . For a low energy solar wind, the sun's magnetic f i e l d would be t i g h t l y wound into a s p i r a l . Actually, t h i s winding does not occur because the average energy density of the r a d i a l , continuous solar wind i s very much larger than the magnetic energy density of the f i e l d and because the solar wind has a very high e l e c t r i c a l conductivity, i t therefore controls the f i e l d . The c r i t i c a l parameter here i s the r a t i o of the gas energy density to the magnetic energy density or, eguivalently, the square of the gas velocity to the Alfven v e l o c i t y . If t h i s r a t i o i s much greater than one,the plasma controls the f i e l d ; i f i t i s only s l i g h t l y greater than one, then we wculd observe the tight winding. If t h i s r a t i o was much smaller than one even beyond the solar corona, there could be no solar wind. The sun's magnetic f i e l d would simply be distorted by the hydrostatic pressure of the plasma. F i n a l l y , in the absence of a plasma, we would merely observe the sun's general magnetic f i e l d . The solar wind i s composed mainly of electrons, protons (N (e)/N (p)sSl) and alpha p a r t i c l e s (N (<*)/N (p)~0.046) . Observed electron and proton densities are egual within experimental errors and range from about 0.4 to 80/cm3 with an average near 5 / c m 3 . Bulk v e l o c i t i e s ranqe from 200-900 Kra/sec with an overall of 400-500 Km/sac, this flow being mainly r a d i a l from the sun. Once again, within experimental errors, the streaming v e l o c i t i e s of protons and electrons are equal. 3 Extreme values of the proton temperature are a maximum of 10 6 'K and a minimum of 5X103 *K, a t y p i c a l value being 4X10**K. The electron temperature averages about a factor of 3-4 times the proton temperature. If p a r a l l e l and perpendicular r e f e r to the d i r e c t i o n with respect to the magnetic f i e l d , the average proton temperature anisotropy i s Tu/Tj*2 . The tendency for the d i r e c t i o n of maximum proton temperature i s to point away from the sun, regardless of whether the orientation of the vector magnetic f i e l d i s toward or away from the sun. These two observations indicate that the protons carry thermal energy away from the sun, along the l i n e s of force (Hundhausen et a l , 1967). The combination of the solar rotation and the approximately r a d i a l solar wind forces the frozen-in interplanetary magnetic f i e l d i n t o the form of an Archimedean s p i r a l . As a r e s u l t of t h i s configuration a f i e l d of 1 Gauss at the surface of the sun leads to about 3X105 Gauss near the earth. Furthermore, i n the e c l i p t i c plane, the tendency i s for the f i e l d to make an angle of approximately 45° with the Sun-Earth l i n e at the o r b i t of the earth. Observed values for the interplanetary magnetic f i e l d f a l l between a low of 0.25^ (1y=10s Gauss) and a high of 40y with an average value of 6. T y p i c a l l y , most of the f i e l d i s contained i n the e c l i p t i c plane but there exists a small component perpendicular to the e c l i p t i c plane. The l a t t e r i s of considerable importance f o r geomagnetic phenomena and the topology of the magnetic f i e l d in the v i c i n i t y of the earth. The main s t r u c t u r a l feature of the interplanetary magnetic f i e l d i s the presence of sectors in which the f i e l d i s ii predominantly directed toward or away from the sun. So f a r , patterns consisting of either 2 or 4 sectors have been observed by s a t e l l i t e experiments. The f i e l d l i n e s are rooted i n the sun and frozen i n the interplanetary plasma. Therefore the sector structure corotates with the sun. Space in the neighbourhood of the earth can be divided into three regions (see figure 1.1) : 1) the interplanetary, medium undisturbed or only s l i g h t l y affected by the presence of the earth and i t s magnetic f i e l d ; 2) the majgngtosheath which i s b a s i c a l l y a t r a n s i t i o n region where solar p a r t i c l e s and f i e l d s i n t e r a c t with the geomagnetic f i e l d ; 3) the macjnetosjxhere, the cavity containing the geomagnetic f i e l d . Separating these regions are two physical surfaces: 1) the bow shock separating the interplanetary medium and the magnetosheath; 2) the jnajjnetojDause, i , e. the outer boundary of the magneto-sphere. The solar wind interaction with the magnetic f i e l d can be broken down into three main features: 1) the bow shock; 2) the confinement of the geomagnetic f i e l d i n the magnetospheric cavity; 3) the geomagnetic t a i l . Pig.*. 1 * 1 Regions of the Hacjnetosjjhere Shown i n the Noon-Midnight-Meridian Plane. The thin l i n e s i n the solar wind are a schematic representation of plasma flow l i n e s . The thi n l i n e s within the magnetosphere represent magnetic f i e l d l i n e s (after Vette, 1971). 6 7 The presence of a magnetic f i e l d in the solar wind makes i t behave as a f l u i d . He are therefore i n the s i t u a t i o n where a supersonic (Ms*5) , super alfvenic (Ma=s8) aerodynamic f l u i d encounters a large blunt object, namely, the dayside magneto-sphere. By analogy with f l u i d mechanics, one would then expect a standing shock wave. In the solar wind, the mean free path i s of the order of 1 A.U. (Astronomical Unit) and the bow shock wave i s therefore of the c o l l i s i o n l e s s type, so the thickness of the shock cannot be related to c o l l i s i o n a l mean free paths. This i s the major d i s t i n c t i o n from f l u i d mechanics where shocks usually occur i n collision-dominated gases. As i t crosses the shock, the solar wind becomes more dense, the bulk velocity decreases to subsonic l e v e l and the plasma i s thermalized. As the interplanetary magnetic f i e l d i s convected through the shock, i t s strength i s increased and i t s d i r e c t i o n i s changed. In the magnetosheath, the magnetic f i e l d always shows fluctuations which, at times, have amplitudes comparable to the background f i e l d i t s e l f . There, the solar wind i s deflected on both sides of the magnetosphere cavity and the magnetic f i e l d l i n e s , being frozen i n t h i s plasma, are draped around the magnetosphere. The magnetosphere cavity can be discussed either i n terms of an 'open' or 'closed* model. In the l a t t e r , the net magnetic flux crossing any substantial portion of the magnetopause i s too small to generate any magnetospheric dynamo ef f e c t of conseguence. In the former, there i s reconnection between geomagnetic f i e l d l i n e s and interplanetary f i e l d l i n e s and the net crossing flux i s s u f f i c i e n t to account d i r e c t l y for such 8 dynamo e f f e c t s . In view of the growing evidence in favour of an open magnetosphere model, the following discussion i s based on such a model. The magnetosphere interface with the magnetosheath i s c a l l e d the magnetopause. This boundary i s well defined on the dayside of the earth and i t s distance from the center of the earth to the subsolar point i s t y p i c a l l y 10 Re (earth radius) while the bow shock i s at 13-14 Re. On the nightside, the magnetopause i s rather d i f f u s e and very often hard to observe. Above the surface of the earth, the magnetosphere can be said to begin at approximately 2000 Km., where c o l l i s i o n s are no longer important. Op to 5-6 Re from the earth, the magnetic f i e l d i s very l i t t l e affected by the impact of the solar wind on the cavity and the l i n e s of force are close to dipole l i n e s of force. On the dayside, as we move closer to the magnetopause, the l i n e s of force d i f f e r s u b s t a n t i a l l y from what one would expect for a dipole f i e l d , t h i s being the r e s u l t of the compression of this part of the cavity by the magnetosheath flow. On the nightside, l i n e s of force are stretched out to form a long t a i l . In the northern half of the t a i l , t h e 1 f i e l d i s directed toward the sun while i n the southern ha l f , i t i s pointing away from the sun. These two flux tubes are separated by the neutral sheet (see figure 1.1). The existence of the long geomagnetic t a i l implies that the wind must catch up to the l i n e s of force and blow them out behind the earth. This process i s i l l u s t r a t e d in figure 1.2 for a southward interplanetary magnetic f i e l d , i n the noon-midnight 9 l i f l i la.2 fin Ojjen Ja^ne to sphere Model. The numbers indicate the successive positions of geomagnetic f i e l d l i n e s , with reconnection occurring at points 1 and 6 (after Axford, 1969) . IQ 11 meridian (after Axford, 1969). The numbers indicate the successive positions of the geomagnetic l i n e s of force. Reconnection occuring at points 1 and 6. As one f i e l d l i n e reconnects (1) and i s pulled back from the eguatorial plane (2-5) another (10) moves out to take i t s place. The newly reconnected f i e l d l i n e s (6) contract rapidly and move toward and around the Earth (7-10). In the magnetosphere, the magnetic energy density i s much larger than the gas pressure and, therefore, t h i s motion of l i n e s of force produces a flow of plasma around the earth and inward from the t a i l . This inward flow produces a variable e l e c t r o s t a t i c p o t e n t i a l between the dawn and dusk side of the magnetosphere and i s maximum on the dawnside magnetopause. The plasma near the earth rotates with i t and we have two d i s t i n c t regions i n the magnetosphere: one region where the plasma i s mainly of solar wind o r i g i n and i s frozen i n the solar plasma i . e . the orientation of this region i s fixed with respect to the sun (e.g. the magnetotail); the other region where the plasma i s of ionospheric o r i g i n i s c a l l e d the plasmasphere and corotates with the earth. The boundary between these two regions i s the plasmapause and i s t y p i c a l l y situated at 4 Re i n the eguatorial plane. This interface i s f i e l d - a l i g n e d and as we cross i t , there i s a sharp decrease i n plasma density from 100/cm3 in the plasmasphere to 1/cra3 outside i t . The above br i e f outline of the basic features of Sun-Earth interactions provides the background necessary for t h i s thesis. It should be kept i n mind that many physical phenomema are taking place in the di f f e r e n t regions described above ( c f . 12 Egeland et a l , 1973), many of them s t i l l unresolved. B) Geomagnetic Mcrojoulsations Ever since means of measuring the Earth's magnetic f i e l d were available, changing features of the f i e l d have been observed. As the instruments gained i n precision and s e n s i t i v i t y , more and more variations of the main f i e l d have been i d e n t i f i e d . Here, according to t h e i r c h a r a c t e r i s t i c times, we divide the variations of the magnetic f i e l d of the earth into two classes: a) slow variations . Their c h a r a c t e r i s t i c times are cf the order of a few decades or more. B) rapid variations . Their c h a r a c t e r i s t i c times are of the order of a few months, a l l the way down to frac t i o n s of seconds. The main representatives of class A are the secular variations and geomagnetic f i e l d reversals, while i n class B, we have the Sq and i variations, geomagnetic storms, magnetospheric substorms, bays and micropulsations. Mechanisms causing variations in c l a s s A have t h e i r o r i g i n s within the earth, while those responsible f o r the fluctuations belonging to c l a s s B are of e x t r a t e r r e s t r i a l o r i g i n and, most often d i r e c t l y or i n d i r e c t l y caused by the sun (except f o r the L=Lunar va r i a t i o n ) . Micropulsations are short period ( 0.2-600 sec), small amplitude ( t y p i c a l l y less than one part i n 10* of the main fi e l d ) fluctuations of the earth's f i e l d . They l a s t from a few minutes to a few hours and leave no permanent ef f e c t on the 13 geomagnetic f i e l d (Jacobs, 1970). Part of the inte r e s t in micropulsations i s the fact that they are the longest electromagnetic waves known. I t seems that the f i r s t report on pulsations of the Earth's electromagnetic f i e l d was by Stewart (1861) (Kato and watanabe,1957). Elementary waves, geomagnetic o s c i l l a t i o n s , f l u c t u a t i o n s , micro-pulsations, pulsations and u l t r a low frequency (UL?) waves a l l refer to the same type of variation of the geomagnetic f i e l d . Intensive research on this subject started i n 1957 ( Saito,1969), the IGY year, and from them on, as new variations were discovered, new names were invented. The s i t u a t i o n was getting out of hand when, i n 1963, at the IAGA Berkeley Meeting, an i n t e r n a t i o n a l c l a s s i f i c a t i o n was agreed upon (Jacobs et al,1964). The c l a s s i f i c a t i o n scheme then proposed appears i n Table I. TA.B.LE_I Micropulsations C l a s s i f i c a t i o n I 1 T 1 1 1 J Class | Type | Period (sec) j Frequency(mHz) J 1 _,— 4 1 1 | | Pel J 0.2 - 5 | 200 - 5000 | I I + -\ -I j Continuous | Pc2 | 5 - 10 | 100 - 200 | I j + H 4 | Pulsations | Pc3 | 10 - 45 J 22 - 100 I | | Pc4 \ 45 - 150 |~ 6.7 - 22 | I 1 ^ + 1 | | Pc5 | 150 - 600 | 1.7 - 6.7 J 1 -I + -I -I I I I I I I Irregular J Pi1 J 1 - 4 0 | 25 - 1000 | | Pulsations | Pi2 | 40 - 150 | 6.7 - 25 J % j l i . : j In Table I, micropulsations are divided into two broad 14 c l a s s e s — t h o s e characterized by f a i r l y regular, guasisinusoidal waveforms and of a continuous character belong to the Pc class (Continuous Pulsations) and those with more i r r e g u l a r waveforms belong to the Pi class (Irregular Pulsations). Two points should be kept in mind when using the c l a s s i f i c a t i o n of Table I . F i r s t l y , t h i s c l a s s i f i c a t i o n i s based s o l e l y on the morphological c h a r a c t e r i s t i c s of geomagnetic micropulsations e.g. t h e i r periods, amplitudes, time of occurrence, waveforms, etc... and secondly, the c l a s s i f i c a t i o n i s based mainly on analysis of data gathered during the sunspot maximum years. The research reported below deals mainly with Pc3 and Pc4 pulsations and to a lesser extent with Pc2. Better magnetometers and more advanced technigues of analysis of data made i t possible to find genetically d i f f e r e n t signals within some subclasses (e.g. Pc1,Pi1) of pulsations and the c l a s s i f i c a t i o n had to te refined (Saito,1969;Saito,1974). In the range of i n t e r e s t , namely Pc2-4, the c l a s s i f i c a t i o n has remained unchanged and we w i l l follow the c l a s s i f i c a t i o n of Table I whenever we refer to these pulsations. Pc3-4 are probably the oldest, most common and yet least known of a l l pulsations. Shile s i g n i f i c a n t advances have been made i n the physical understanding of Pel and P i , the si t u a t i o n i s d i f f e r e n t for Pc2-4 where some of the morphological c h a r a c t e r i s t i c s s t i l l have to be agreed upon by the various researchers. Below, we l i s t the main c h a r a c t e r i s t i c s of the Pc2-4 band of pulsations. Pc2-3 are reviewed together and Pc4 by i t s e l f . The l i s t of references i s by no mean complete, the 15 reader i s referred to Saito (1969) and Jacobs (1970) from which we borrow heavily. B-1) Pc2-3 Pulsations This group i s characterized by th e i r long-lasting guasi-sinusoidal waveforms, t y p i c a l periods from about 5 to 30 sec and amplitudes of the order of 0.1JJ i n low l a t i t u d e s (Saito, 1969). Pc3 amplitude increases with l a t i t u d e to reach a value of at mid-latitude , i t s maximum amplitude i s at approximately 60° geomagnetic l a t i t u d e , a t noon (Jacobs and Sinno, 1960). - The amplitude of Pc2-3 correlates p o s i t i v e l y with Kp and further shows a 27-day recurrence tendency (Saito, 1964). Diurnal variations of the amplitude of Pc3 show that i t i s a dayside phenomenon while Pc2 i s a nightside phenomenon (Saito,1969); Jacobs (1970) claims that both are dayside phenomena maximizing around noon. Everybody agrees though, that they are most c l e a r l y recorded on the dayside of the earth and that the waveforms are more i r r e g u l a r and the duration shorter at night. The dynamic spectrum (frequency versus time) of Pc3 i s freguently an assembly of two or three horizontal structures that l a s t for hours (Hirasawa and Nagata,1966). The structure i s not similar at conjugate stations, although the period i s . Pc3 tends to be l i n e a r l y polarized i n the North-South meridian at low lat i t u d e s (Saito, 1969) ; during the daytime maximum occurrence, they are generally left-handed in the northern hemisphere and display e l l i p t i c a l p olarization patterns at mid-and high-latitudes. F i n a l l y , i n the waveforms, polarization rule,dynamic spectra, Pc2-3 do not show any d e f i n i t e conjugate r e l a t i o s h i p s 16 as i s the case for P d , Pc4-5 and Pi's (Campbell, 1959). For geomagnetic pulsations i n the period range 5-40 sec, strong cor r e l a t i o n s with pulsating aurora were reported by Campbell (1960a, b); furthermore, a decrease i n the magnetotail f i e l d seems to take place at the onset of a Pc3 event (Perkins et al,1972). B-2) Pc4 Pulsations Pc4 signals usually l a s t from 10 minutes to several hours, the waveform i s rather sinusoidal and the i r amplitudes are c h a r a c t e r i s t i c a l l y of the order of a few gammas. Like Pc3, Pc4 amplitudes increase with l a t i t u d e , although not in a monotonic fashion . In fa c t , two peaks have been reported—one near the subauroral zone (latitude 50°) and another one near the auroral zone (Kato and Saito, 1962). Contrary to Pc3, no spec i a l r e l a t i o n s h i p s with Kp or the 27 day solar rotation period have been found for the amplitude of Pc4. The diurnal variation of the ampliude of these pulsations has only one broad maximum i n the daytime (Saito, 1964); they are thus s t r i c t l y a dayside phenomenon. Dynamic spectra of Pc4 events are s i m i l a r at conjugate stations (Saito, 1967) . Their polarization i s divided i n the northern middle l a t i t u d e s , into clockwise i n the dayside (06:00-18:00 LT) and counterclockwise i n the nightside (18:00-06:00 LT) . This polarization i s reversed i n the southern middle l a t i t u d e s (Mather et a l , 1964 ;Troitskaya, 1967) F i n a l l y , l e t us note that Pc4 occur mostly on geomagnetically quiet days (0<Kp<2.5), Pc3 on less quiet days (1<Kp<3.5). The number of cases where Pc3 a c t i v i t y i s observed 17 f a l l s sharply for Kp>5, F i n a l l y , Pc2 tends to occur on very disturbed days . In f a c t , many researchers (e.g. Troitskaya and Gul•el*mi;1967} consider Pc2-4 to be one type (genetically) of micropulsations with Pc4 transferring to Pc3 and down to Pc2 with increasing Kp; other researchers (e.g. Nagata and Fukunishi,1968) think that they belong to genetically d i f f e r e n t groups of pulsations. C) Thesis Outline In view of the fact that they are the longest electromagnetic wave known, the interest i n micropulsation has been related to communication problems. For example, they could be used for underwater telecommunications. Their wavelengths i n the Pc4-5 range i s of the order of the radius of the earth. I t has therefore been thought to use them as probe for the inner regions of the earth. Any of these applications ask for a better understanding of the natural phenomenon. For reasons given below, in t h i s research, we look for interplanetary control of Pc3-4 a c t i v i t y . In chapter I I , the state of the art in Pc2-4 micropulsation research i s reviewed and the sources of data are discussed. In chapter I I I , which i s the f i r s t part of t h i s research, the parameters that control Pc3-4 occurrence and amplitudes are determined; their effectiveness and some of th e i r properties are discussed using s t a t i s t i c a l d i s t r i b u t i o n s . In chapter IV, i t i s shown that the micropulsation spectrum i s determined by the spectrum of upstream wave and therefore, Pc2-4 continuous micropulsations are simply upstream waves that have propagated through the magnetosphere, to the earth. As a by-product of the spectral 18 a n l y s i s , some properties of upstream and micropulsation spectra are discussed. F i n a l l y , i n chapter V, the r e s u l t s are evaluated and the t h e o r e t i c a l implications of the findings are discussed. 19 CHAPTER I I A) Present State of the Art In essence (see chapter I) the key morphological c h a r a c t e r i s t i c s of Pc2-4 are: 1) they are dayside phenomena (except, possibly, for Pc2); 2) t h e i r .27-day recurrence tendencies; 3) the Kp dependence of t h e i r periods, amplitudes and probability of occurrence. Items 1) and 2) suggest that the sun, d i r e c t l y or i n d i r e c t l y , plays a key role in the generation of these pulsations. On the other hand, even though the physical meaning of the Kp index i s obscure, i t has been shewn to correlate with the solar wind velocity (Snyder et a l . , 1963; Hilcox et a l . , 1967) and with the strength of the interplanetary magnetic f i e l d (Hilcox et a l . , op. c i t . ; Schatter and Wilcox, 1967). On the basis of the Kp-wind velocity and the Kp-pulsation amplitude relationships, Saito (1964) showed that a c t i v i t i e s of Pc3 and Pc4 micropulsations correlate, on a long time scale (of the order of a day), with the solar wind ve l o c i t y . Therefore, i t seems l o g i c a l to look for an explanation of Pc2-4 a c t i v i t y i n the magnetosphere or, even i n the interplanetary medium. 20 The location of the magnetopause i s determined by the dynamic balance of the solar wind pressure, on the one hand, and the magnetic pressure of the Earth's f i e l d , on the other; hence, the s i z e of the magnetosphere cavity, on the dayside, should vary with the magnetic a c t i v i t y l e v e l , on earth. Higher magnetic a c t i v i t y l e v e l , corresponding generally, to a more intense solar wind should, i n turn, be associated with a smaller cavity, and vice versa, lower magnetic a c t i v i t y with a larger cavity. On the basis of the inverse dependence of the period of Pc2-4 micropulsations on the magnetic a c t i v i t y l e v e l , as indicated by Kp, Bolshakova (1965) t r i e d to relate the period of micropulsations to the distance from the center of the earth to the subsolar point, on the magnetopause. More s p e c i f i c a l l y , she looked for a relationship of the type: where T i s the micropulsation period, in seconds, and Bm i s the radius of the magnetosphere, in earth r a d i i . Her r e s u l t , based on the analysis of 5 events, gave ns5. Patel and Hastings (1969) found nss13. A more extensive analysis has been performed by Patel (1974). He noted that the value of n changes very appreciably (from--1.5 to 8.8) for d i f f e r e n t ranges of periods between 20 and 120 seconds. For the range 20<T<60 seconds, he finds n«4.7 which agrees with Bolshkova's value. I t seems that the function T (Rm) i s e x p l i c i t and reproducible, only i n t h i s range (Patel, 1974) , or for K40 seconds (Troitskaya et a l . , 1971). It should be kept i n mind that Patel's correlation (2.1) 21 c o e f f i c i e n t between T and Rm, based on a s t a t i s t i c a l l y valid number of events i n the range 20-60 seconds, i s extremely low (0.13). In the late f i f t i e s and i n the s i x t i e s , the consensus on Pc2-4 pulsations was that they were caused by the continuous flow of solar wind impinging on the magnetosphere cavity and exciting surface waves, on the magnetopause, by a Kelvin-Helmholtz i n s t a b i l i t y mechanism. On the other hand, i t was known that there are days when Pc2-4 pulsation a c t i v i t y i s absent, or days of worldwide micropulsation event(s), that i s , events where the onset and the end are approximately simultaneous throughout the world. These facts could not be reconciled with the idea of these Pc's are being excited by a continuous solar wind, at the magnetopause. Bolshakova and Troitskaya (1968) noted the dilemma and looked for some other parameters c o n t r o l l i n g Pc a c t i v i t y . The parameter they considered, i s the di r e c t i o n ot the interplanetary magnetic f i e l d i n the plane of the e c l i p t i c . We quote from them the r e s u l t : "the most common Pc3 type of stable o s c i l l a t i o n s (T=10-45 sec.) corresponds to the main f i e l d d i r e c t i o n coincident with that of the Parker s p i r a l , while o s c i l l a t i o n s of type Pc4 (T=50-150 seconds) or Pc3 to 4 are co r r e l a t i v e with a nearly r a d i a l d i r e c t i o n . Quite s p e c i f i c i s the case of f i e l d d i r e c t i o n perpendicular to the Sun-Earth l i n e , when stable o s c i l l a t i o n s are not excited and are absent from t e r r e s t r i a l scales." An important point i s that the data analysed were from the period December 1-14, 1963, for which the degree of magnetic a c t i v i t y was f a i r l y high (Kp-3-5) from December 1-9 and then very low 22 (KpsO-1) from December 10-15. a further attempt to relate pulsations of the Earth*s f i e l d with solar wind parameter, was made by Gringauz et a l . (1971). In the f i r s t part, they t r i e d to correlate the int e n s i t y of micropulsations and short-period disturbances of the Earth*s electromagnetic f i e l d with the solar wind fl u x . For the period January 21 to Harch 21,1969, a clear dependance of the general i n t e n s i t y of these signals on the solar wind flux was observed. However, for the period June-July,1967, there were times when increase of the ion density would not accompany any appreciable r i s e i n the pulsation i n t e n s i t y and vice-versa, times when increase in the int e n s i t y of pulsations were observed without s i g n i f i c a n t changes in the ion density. In the second part, they found a cor r e l a t i o n between the period of continuous micro-pulsations and the solar wind ion flu x . For T<40 seconds, the pulsation period decreases, and for T>40 seconds increases, with increasing ion f l u x . They further attributed t h i s dependence of the period on the f l u x , to the ion density and not to the bulk ve l o c i t y of the solar wind. As mentioned e a r l i e r , changes i n the solar wind dynamic pressure are associated with changes i n the size of the magnetospheric cavity. On the other hand, changes in dynamic pressure usually p a r a l l e l changes i n the solar wind mass flux and i n turn, solar wind flux increases (decreases) are usually associated (at least on a long time scale) with increases (decreases) i n the strength of the interplanetary f i e l d . Therefore, since the micropulsation period has been postulated to relate with the size of the geomagnetic cavity and to the 23 solar wind ion f l u x , there should also be some sort of rel a t i o n s h i p between the period of the micropulsation, on the one hand, and the strength of the interplanetary f i e l d , on the other. Troitskaya et a l . (1971) investigated that p o s s i b i l i t y and found that, except for a group of points at large T (T>60 sec) and B (B > 6y ) , the Pc 3-4 pulsation period decreases with increasing strength of the interplanetary magnetic f i e l d . There i s also a tendency f o r the pulsation period to be modulated by changes in the orientation of the f i e l d i n the e c l i p t i c plane. The modulation curve for a northward and a southward interplanetary f i e l d are almost mirror images of each other. F i n a l l y , for the dependence of the pulse amplitude on the interplanetary f i e l d parameters, no d e f i n i t e conclusion could be drawn. They could only conclude that the most intense pulses are observed more frequently when the f i e l d i s aligned with the Sun-Earth l i n e ( i . e . when # =0 or 180° ) than when the f i e l d i s approximately perpendicular to i t (i . e . ^ =90 or 270° ). The l i s t of cor r e l a t i o n s above i s what seems to be the general trend i n studies and the present state of the art in micropulastion research, up to 1972, when t h i s research was begun. The lea s t we can say i s that the picture i s s t i l l very much obscure. Pc 3-4 micropulsation periods and a c t i v i t y have been related to, in some way or other, almost a l l the parameters of interplanetary f i e l d s and plasmas. These parameters are, on the other hand, a l l i n t e r r e l a t e d . However, these i n t e r r e l a t i o n s h i p s among the various parameters, are c r i t i c a l l y dependent on the time scale chosen. For example, on a time scale of the order of one solar rotation, the di f f e r e n t 24 quantities a l l vary i n a systematic way ( c f . Belcher and Davies, 1971), while on a time scale of the order of a day, the same state of the interplanetary f i e l d can be associated with d i f f e r e n t solar wind states and vice versa. This we believe, i s one of the factors obscuring the picture outlined above. Which one, among those parameters, i s the most c l o s e l y associated to the pulsation period of t h e i r a c t i v i t y ? What i s the respective role of each parameter? Here, we anticipate one of the r e s u l t s in the next chapter. I t seems that only the f i r s t guestion can be answered with some confidence; the Pc 3-4 pulsation period i s most c l e a r l y related to the magnitude of the interplanetary f i e l d ( c f . Gul'yel'mi et a l . ,1973), and the pulsation amplitude, to i t s orientation (Nourry and Watanabe, 1973a, b; Gul'yel'mi et a l . , op. c i t . ) . Figure 2.1 summarizes the d i f f e r e n t relationships discussed above (from Gul'yel ,mi, 1974) . B) Restrictions on the Present Research In the f i r s t part of t h i s research, (Chapter I I I ) , we do not take into account the micropulsation periods, instead we try to f i n d out the respective roles of plasmas and f i e l d s i n the occurrence of pulsations or i n the modulation of their a c t i v i t y . As a s t a r t i n g point, we use the r e s u l t of Bolshakova and Troitskaya (1968), that the occurrence of Pc3-4 pulsations i s related to the d i r e c t i o n of the f i e l d i n the e c l i p t i c plane. Waves, whether they are generated i n the interplanetary medium or i n the magnetosphere, have to propagate in the magnetospheric cavity, i f they are to be observed on Earth. P r a c t i c a l l y nothing i s known of the way, or how much, the waves 25 f i f l i Zs.1 Dependence of Pulsation Period on Interelanetary lS£ai§i§£§« Prom top to bottom, dependence versus the radius of the magnetosphere <R), solar wind velocity (V), concentration of the plasma <H), doubled pressure cf protons (P), and the value of the magnetic f i e l d i n front of the bow shock (B) <Gul*el»mi, 1974). 400 50 30 20 i5 i0 I 1 1 1 1 1 I 1 1 i i i i i i I HO . 2 0 3 0 A O 5 0 6 0 7 0 S O 90 100 PeziocC, sec 27 are affected as they t r a v e l i n t h i s region. The Alfven velocity i s not a mono-tonic function of the distance from the Earth and, we know of some physical boundaries { e.g. plasmapause, magnetopause ). Hence, there i s a d e f i n i t e p o s s i b i l i t y that the magnetosphere behaves as an active element or, as a hydromagnetic waveguide, in the propagation of the waves. For these reasons, i n t h i s research, we consider the magnetospheric cavity as a black box and further, to reduce i t s e f f e c t s {if any), we r e s t r i c t the analysis to f a i r l y quiet days ( Kp < 3 . 5 ) and a l l disturbed days are eliminated. In the Pc 3-4 range of micropulsation, we distinguish between two d i f f e r e n t kinds of signals: i) transient signals which resemble wave packets and are attenuated. They are also usually dispersed. i i ) continuous signals which are more stable and have a more "permanent" character. Unless otherwise mentioned here, we deal with the l a t t e r , namely, the continuous signals. For this study, we need simultaneous observations on earth and i n space. This r e s t r i c t s us to the period August-November, 1967, where good guality ground micropulsation records are a v a i l a b l e and the s a t e l l i t e Explorer-34 spent most of i t s time i n the interplanetary region, on the dayside of the earth. At times, we also use results from the magnetic f i e l d experiment onboard Explorer - 3 3 . Below, we describe the relevant parts of the data gathering process on earth and onboard the two spacecrafts. 28 C) Source of Data C-1) Ground Station The ground station i s situated at Ralston, Alberta, seven hours west of Greenwich. I t s geographic la t i t u d e and longitude are '51° 12• and 111° 17', while the geomagnetic l a t i t u d e and longitude are 58° 8» and 305° 5' respectively. The magnetic i n c l i n a t i o n at t h i s l a t i t u d e i s 72.0° and the average t o t a l f i e l d i s ( H , D, Z ) = ( 17,045^; 19° 45'; 52,466y). The micropulsation signal was detected along three orthogonal axis: the North-South component X, the East-West component Y, and the v e r t i c a l component Z. Here, we use only the two components i n the horizontal plane namely, X and Y. The X and Y sensors are mumetal-core solenoids; the freguency response of the system extends from 0.01 Hz to approximately 4 Hz, with a broad peak s e n s i t i v i t y centered at around 0.12 Hz. Since the magnetometers are of the induction type, the time derivative of the magnetic signal i s actually recorded. C-2) Explorer 33 Magnetic Fi e l d Experiment Alternate names for t h i s spacecraft are IMP-D, AIHP-1. I t was launched on July 1, 1966 and f a i l e d to achieve the intended lunar o r b i t , but attained an earth o r b i t with apogee 440,000 km and perigee 50,000 km. The s a t e l l i t e i s spin s t a b i l i z e d with the spin axis p a r a l l e l to the e c l i p t i c plane. Over a three year period, the perigee varied between 32,200 km (5.1 He) and 274,000 km ( 43.0 Re), the apogee varied between 436,000 km 29 ( 68.4 fie) and 859,000 km ( 134.8 Re) and the i n c l i n a t i o n with respect to the earth's equatorial plane varied between 7 and 60 degrees. The i n i t i a l spin period of 2.28 sec increased to 3.6 sec. During the period from Sept 9, 1967 to Nov 18, 1967, the spin period changed from 0.442 Hz to 0.362 Hz ( O.Saka, private communication). Figure 2.2 depicts the solar e c l i p t i c plane projection of a few o r b i t s of Explorer 33 (Jan 1 i s day 0). A strong lunar perturbation of the spacecraft o r b i t i s evident. The magnetic f i e l d experiment of Explorer 33 consisted of a boom mounted t r i a x i a l fluxgate magnetometer. Each of the three sensors had a range of ±64 and a d i g i t i z a t i o n error of ±0.25y. The three sensors were mounted together as single physical unit; the boom was e f f e c t i v e in reducing the spacecraft body magnetic contamination to l e s s than the d i g i t i z a t i o n uncertainty, at the sensor l o c a t i o n . The bandpass of the magnetometer was 0-5 Hz, with a 20 db per decade f a l l o f f for higher freguencies. Vector measurements were obtained every 5.12 seconds. A more detailed description of t h i s experiment can be found i n Scearce et al (1969). C-3) Explorer 34 Fields and Plasmas Experiments Alternate names for t h i s spacecraft are IHP-F and IMP-4. It was launched on May 24, 1967, and placed into a highly eccentric, polar o r b i t with apogee near the e c l i p t i c plane. I n i t i a l perigee of the s a t e l l i t e was 278 km, apogee 211,024 km (31.4 Re ), i n c l i n a t i o n 67.4° and a period of 4 days, 7 hours and 45 minutes. This spacecraft i s also s p i n - s t a b i l i z e d , and had i n i t i a l spin period of 2.593 sec that monotonically increased to 2.670 sec at reentry time (J3ay 3, 1969). The spin 30 Ix£l2ier 33 Trajectory,. Projection of Explorer 33 trajectory i n the e c l i p t i c plane (Behannon et a l . , 1970) . 21 -80 32 HAS*. 2-.3 Explorer 34 Agcgee. Projection of Explorer 34 Apogee i n the e c l i p t i c plane (top) and perpendicular to the Sun-Earth l i n e (bottom) (Behannon et a l . , 1 9 7 0 ) . 33 MAGNETOPAUSE SEPT 27 vector was approximately perpendicular to the e c l i p t i c plane. The o r b i t i s shown i n figure 2.3. Figure 2.3 (top) i s a projection of the o r b i t i n the xy solar e c l i p t i c plane. The apogee at launch was near 1900 LT and the motion of the earth around the sun caused i t to sweep across the dayside hemisphere. Figure 2.3 (bottom) i s the projection of the o r b i t onto the yz plane. The magnetic f i e l d experiment on Explorer 34 consisted of three orthogonal fluxgate magnetometers with sensor ranges of ±32 and ±128 gamma. The range selection i s controlled by ground command. When the spacecraft i s beyond approximately 15 Re, the most s e n s i t i v e range i s selected, while when the s a t e l l i t e i s within that distance, the magnetometers are commanded to the high range. To reduce magnetic contamination, the sensors are mounted on two six foot boom-supports. The f i r s t sensor i s mounted on a boom p a r a l l e l to the spin axis, while the other two sensors, orthogonal to each other and to the spin axis, share the boom diametrically opposite the f i r s t . The analog sensor outputs were d i g i t i z e d on board the spacecraft, with d i g i t i z a t i o n errors of ±0.16 and ±0.64^ i n the low and high ranges, respectively. The bandpass of the magnetometers was 0 to 10 Hz in the low range, with a f a l l o f f of 20 db/decade in amplitude response beyond 10 Hz. Zero l e v e l s of the sensors are determined to an accuracy estimated as ±0.1^, except for the sensor p a r a l l e l to the spin axis for which i t i s estimated at ±0.3^. The sensors are sampled sequentially every 80 milliseconds and vector measurements of the f i e l d are made every 2.556 seconds. The output of an onboard autocorrelation 35 computer using 80 millisecond samples i s used to determine whether the 2.5 second vector samples are aliased. A more extensive description of the experiment as well as the ele c t r o n i c c i r c u i t r y can be found in Seek and Ness (1971). The plasma detector i s a mass-energy spectrometer which observes the f l u x , energy spectrum and the d i r e c t i o n of flow of the hydrogen and helium ions, independently. A complete description of t h i s b a s i c a l l y e l e c t r o s t a t i c analyser i s given by Ogilvie et a l . (1968). The detector rotates i n a plane nearly p a r a l l e l to the e c l i p t i c plane and views i n the azimuthal d i r e c t i o n close to t h i s plane. During one spacecraft revolution, the instrument measures the counts C/ (E:) (i=1,16) a at the energy E^ i n each of 16 contiguous 22.5° sectors in the azimuthal plane. Due to telemetry r e s t r i c t i o n s , the following information i s calculated for each rotation by an onboard computer and i s transmitted to the earth every 20 seconds: a) Tcf(E;)# *-he t o t a l number of counts which f a l l within i * an energy per charge i n t e r v a l around E j . ^ ,a. b) X c i (E») * which i s a measure of the dispersion of the d i r e c t i o n a l d i s t r i b u t i o n . c) L ( E p , a number from 0 to 15 which s p e c i f i e s i n which of the 16 sectors, the maximum of Clt occurs. Spectral information i s obtained by changing the energy per unit charge and the charge per unit mass during successive rotations. A histogram of the proton or alpha spectrum i s obtained as a re s u l t of 15 rotations ( i . e . 15 energies up to 5.1 keV f o r protons and 10.2 keV f o r alphas). I t takes one minute to acguire a complete spectrum for one species. A spectrum for one 36 species i s generally available every three minutes. Our main in t e r e s t l i e s i n the hydrodynamic plasma parameters such as density, velocity and temperature. Each measured spectrum i s f i t t e d empirically with segments of Maxwellian d i s t r i b u t i o n s , and the f l u i d guantities are determined i n terms of the moments of the resulting curve. From the guantities telemetered to the ground, the process to obtain the plasma parameters i s not t r i v i a l and has been described i n d e t a i l by Ogilvie et a l . (1967). 37 CHAPTER I I I INTERPLANETARI MiGNETIC fIELJDx SOLAR WIND AND PCJhii MICROPROSATIONS A) Introduction The Pc3 and 4 pulsation periods have been related to the radius of the magnetosphere, the solar wind ion f l u x , the ion density and to the strength of the interplanetary magnetic f i e l d . To the guestion, what are the respective roles of i n t e r -planetary f i e l d s and plasmas in the occurrence of micro-pulsations, no answer has been given. In t h i s chapter, we attempt to answer that guestion. To attain t h i s goal, the period August 13 to November 6, 1967, i s selected. For t h i s i n t e r v a l , good micropulsation records are available from Ralston, Alberta, and the spacecraft Explorer-34 which swept the 08:00-14:00 l o c a l time sector, spending most of i t s time i n the interplanetary region sunward of the shock. At f i r s t , we perform a case by case study. The method followed presents no s u b t l e t i e s : i n a f i r s t step, we consider only well defined Pc3 or 4 events characterized by a sudden onset or a c l e a r end, and check f o r any s i g n i f i c a n t changes i n the interplanetary medium parameters. Once these events are understood, we go on to consider a l l Pc3 and Pc4 events occuring on magnetically guiet days, i n the time i n t e r v a l 38 under consideration. actually, the method used i s one of t r i a l and error. There are simply too many parameters involved to look at the records and try to f i n d r e l a t i o n s h i p s . Instead a guess as to what would be a reasonable mechanism was made, and then we t r i e d to either prove or disprove i t . at t h i s point, we re-emphasize that the present analysis i s r e s t r i c t e d to magnetically quiet days (Kp < 3.5) and, unless otherwise mentioned, w€ are dealing with continuous micro-pulsation signals as opposed to signals with transient character. Below, mention i s often made of the angles © and 56 , they are the solar e c l i p t i c l a t i t u d e and longitude cf the interplanetary magnetic f i e l d , respectively (Heppner et a l , 1963). F i n a l l y , i n section B, the res u l t s of the case by case study are presented, while section C deals with the s t a t i s t i c a l r e s u l t s . fi) Case bj Case Study, B-1) 1.1.1^, girecticn-Control of Pc4 Activity. From a c o l l e c t i o n of well over 40 events such that the concurrent IMP-P i s outside the fcow shock, i t i s obvious that Pc4 a c t i v i t y i s controlled by the interplanetary magnetic f i e l d d i r e c t i o n i n the e c l i p t i c plane as well as perpendicular to t h i s plane. The p r i n c i p a l Pc4 events considered appear i n Table I I . In order that Pc4 a c t i v i t y should take place, the following conditions have to be s a t i s f i e d : 1) the interplanetary f i e l d l a t i t u d e © has to be within 30° of the e c l i p t i c plane 39 TflBLE_II P r i n c i p a l Continuous Pc4 Events DD-MM-YY* |Time Interval(UT) 'TT | DD-MM-Y Y* Time Interval (UT) 1 22-08-67 05-09-67 11-09-67 16-09-67 17-09-67 24-09-67 13-10-67 16-10-67 I 18-10-67 23-10-67 20:15 - 22:00 18:00 21:34 18:50 01:00i 18:20 - 22:25 13:30 -13:00 -18:20 14:402 00:30 15:40 01: 20 17:05 •If 17:50 - 19:50 16:25 - 02:30i 10:40 - 13:083 18:03 19:43 19:43 20:23 24-10-67 18:25 20:05 19:08 20:40 25-10-67 14:28 15:37 16:00 20:48 15:11 16:00 19:40 23:00 26-10-67 10:32 - 13:22 30-10-67 09:50 13:35 17:47 13:30 17:47 18:32 06-11-67 10:30 12:04 13:05 18:32 11:10 13:05 15:56 19:38 „ i. j-. * Day-Month-Year 1 the following day 2 end of record at 16:38 UT 3 end of record 2) the interplanetary f i e l d azimuth o> must be within 30° of the Sun-Earth l i n e . Figure 3.1 shows a Pc4 event with a clear end at 17:48 UT. On t h i s figure, the upper three traces are the X, Y and Z in t e r -planetary f i e l d components; i n the middle section, the micro-pulsation signal, to which analog f i l t e r i n g has been applied, i s plotted. For the pulsation s i g n a l , the s e n s i t i v i t i e s for the di f f e r e n t freguency ranges are chosen in order to compensate for the freguency response curve of the ground station (Ng, 1969). 40 l i s - . I i i Pc4 Occurrence Versus IMF Directions. Example of l a t i t u d e - c o n t r o l of Pc4 a c t i v i t y (see text for the description of the f i g u r e ) . INTERPLRNETRRT MAGNETIC FIELD IMP F DATs DAT = 302. TERR 67 ' SE COORDINATES IMP F DATA R A L S T O N X S E — T E S 0 C t 0 b e r 3 Q . 6 7 1+7 42 The dotted l i n e i s the solar wind dynamic pressure and the l a t i t u d e and azimuth of the f i e l d are shown i n the lower part of the f i g u r e . The s a t e l l i t e position i s indicated i n brackets (X,Y,Z) , in SE coordinates and i n units of earth radius. F i n a l l y , 20 .5-sec average values for the f i e l d components and d i r e c t i o n were used. This figure serves to i l l u s t r a t e three points. F i r s t l y , i t shows an example of l a t i t u d e - c o n t r o l of Pc4 a c t i v i t y . From early on that day, the magnetic f i e l d component perpendicular to the e c l i p t i c i s approximately zero; the f i e l d i s directed toward the earth and nearly coincides with the Sun-Earth l i n e . Therefore, the f i e l d s a t i s f i e s the conditions mentioned above and, conseguently, we have a Pc4 event. At 17:42, the f i e l d l a t i t u d e suddenly increases beyond +30° and t h i s i s followed by the end of the Pc4 pulsation event, even though the f i e l d azimuth has not changed. Secondly, the purpose of t h i s event i s also to separate the e f f e c t of f i e l d d i r e c t i o n and solar wind pressure changes. The end of the continuous micropulsation event i s not associated with any noticeable change in solar wind dynamic pressure; i n f a c t , the wind f l u x , velocity and proton density dc not shew changes either. Hence, the termination of the pulsation signal can only be attributed to the f i e l d l a t i t u d e change. F i n a l l y , p a r a l e l l i n g Pc4 a c t i v i t y , a weak Pc3 event i s also taking place. Note however, that the l a t t e r i s not affected by the end of the Pc4 event. The time lag between the change i n f i e l d l a t i t u d e and the end of the continuous pulsation event i s 6 + 1 minutes. The 43 events l i s t e d i n Table II are the p r i n c i p a l continuous Pc4 events for the period under consideration and they a l l f a i t h f u l l y follow the r e s t r i c t i o n on the f i e l d l a t i t u d e and azimuth. They occur only when the interplanetary magnetic f i e l d vector l i e s in a cone whose axis coincides with the Sun-Earth l i n e and whose half vertex angle i s approximately 30° degrees. The reason for omitting to l i s t some Pc4 events, i s that they t y p i c a l l y lasted only a few tens of minutes or were often i s o l a t e d in the sense that they were the only event taking place on a given day. Nevertheless, they did s a t i s f y the f i e l d d i rection-control as scrupulously as any other events. Another inte r e s t i n g piece of evidence i s the set of micro-pulsation events for which Explorer-34 i s inside the magneto-sheath. Eecause of i t s o r b i t (see figure 2.3), Explorer-34, i n the time i n t e r v a l under consideration, spent very l i t t l e time i n that region and also, because we are concerned with a dayside phenomenon, such events are bound to be very rare. Nevertheless, we have collected 3 such events; they appear i n Table I I I , along with the s a t e l l i t e position. TABIE_III Simultaneous Magnetosheath and Pc4 Events i 1 1 1 | DD-MM-YY*|Time Interval (UT) »| Explorer-34 Location 2! | 18-08-67 | 18:50 - j (12.5,4.7,5.5,14.4)3 | | 05-09-67 | 17:50 - 18:50 | (10.4,1.7,-7.0,12.7)3| i -i -i H | 18-10-67 | 10:00 - I (10.0,-7.8,6.2,14.7)3j L L — i : j * Day-Month-Year 1 for the magnetosheath event 2 in SE Coordinates 3 the format i s (X,Y,Z,B), i n units of earth radius 44 i i 2 Pc4 A c t i v i t y Versus Enhanced. Fluctuations In The Magnetosheath. Example of enhanced fluctuations correlated with Pc4 a c t i v i t y . 46 Figure 3.2 shows a change i n the magnetosphere f i e l d associated with a continuous pulsation event on earth. The format of t h i s f i g u r e i s the same as that of the previous one, except that here, the t o t a l force F i s plotted instead of i t s three components. In the time i n t e r v a l 17:50-18:50, the magnetosphere f i e l d exhibits enhanced fluctuations ( p a r t i c u l a r l y obvious on the angles) corresponding to <f> moving closer to 180°. At Ralston, with a time lag of 10 + 1 minute, a Pc4 event takes place. The onset and the end of the pulsation signal are c l e a r l y related to the f i e l d i n the e c l i p t i c plane, moving close to the Sun-Earth l i n e at 17:50 and then, away at 18:50 UT, respectively. The average values of the f i e l d l a t i t u d e and azimuth are approximately -45 and 200 degrees, respectively. Notice that, the ©-value of the f i e l d i s not i n disagreement with the condition outlined above, since the f i e l d i n the magnetosheath tends to drape around the magnetosphere cavity (Fairfield,1967). The other two events also show enhanced fluctuations. Actually, for the August 18 event, the enhanced fluctuations are due mainly to the f i e l d l a titude vanishing. During t h i s event, we can c l e a r l y see the bow shock sweeping by the s a t e l l i t e s i x times, i . e . , on three d i s t i n c t occasions, the spacecraft finds i t s e l f i n the interplanetary medium, ahead of the shock. Interestingly enough, the shock motions are approximately eguispaced i n time with a period of 7 minutes. In the l a s t event, namely, Oct 18, the enhanced fluctuations are associated with a f i e l d azimuth change. The onset of the Pc4 event does not correlate with the beginning of 47 the enhanced fluctuations because Ralston was i n the early morning hours (02:30 LT). The Pc4 event takes place l a t e r on while there s t i l l i s increased magnetic a c t i v i t y in the magneto-sheath. For t h i s p a r t i c u l a r event, Explorer-33 was sunward of the shock and i t confirmed that there, the interplanetary f i e l d d i r e c t i o n was in the range favourable to Pc4 occurrence. B-2) I AM AF A Direction-Control of Pc3 A c t i v i t y The number of Pc3 micropulsation events, i n the i n t e r v a l under consideration, i s too large to be l i s t e d here. However, the reader can refer to Table II since most of the events there were also associated with Pc3 a c t i v i t y . The st a r t i n g and ending times of the two types of pulsation may be d i f f e r e n t though. The interplanetary magnetic f i e l d d i r e c t i o n also controls Pc3 a c t i v i t y . Figure 3.3a and b show an example of l a t i t u d e -control of Pc3. The format of these figures i s b a s i c a l l y the same as before. Here, the East-West (EW) component at Ralston i s plotted and the f i e l d data are from Explorer-33. The solar wind dynamic pressure i s calculated from Explorer-34 data. F i n a l l y , the 5.12-sec values of the f i e l d components are plotted while, for the angles, we used the 82-sec average values. This i s the reason why fluctuations of the f i e l d components do not show up i n the f i e l d d i r e c t i o n . In figure 3.3a, u n t i l 18:38 UT, the magnetic f i e l d i s very nearly perpendicular to the Sun-Earth l i n e , i n the e c l i p t i c plane, and as a r e s u l t the micropulsation record i s extremely guiet i n the Pc3-4 range. Then, the f i e l d d i r e c t i o n slowly changes u n t i l & and ^ reach stable values at approximately +10 48 Ha.± l A 3 a Correlated Upstream Waves And Pc3 A c t i v i t y . Gradual onset of wave a c t i v i t y in space correlated with Pc3 continuous pulsations. IMP D DATA DAT : 2 3 7 . SE COORDINATES T P CO "8' 10 —I 10 o ro O 8 c —i ro o "8 CD j->l "l OJ CT) f o r o N — ro Fo co o o R A L S T O N ? O c t o b e r 15, 6 7 i cn I I +o ro cn eg In o ° TO 1 INTERPIRNETAST f . S 3 N E T I C F I E L D W 0 DATA Cflt = 2 8 7 . TERR 67 SE COORDINATES O ' O : CD O r in ro: o s cn c n ^ o O 0 : 0 O —I 2 • A 5 O A -ti 1/1 "3f & - f t ^} f l : 1 i 1 -o o o N 50 Ii3.s. i ..3b C o r r e l a t e d Up stream Waves and Pc3 A c t i v i t y J c c n t ' d l . Example o f l a t i t u d e - c o n t r o l o f Pc3 a c t i v i t y and o f c o r r e l a t e d upstream wave and Pc3 p u l s a t i o n . —10 .-+10 •0 Y(r) --10 -+10 -0 Ztw -+10 100 MV/oiv T<45s RALSTON ? October 15 , 67 (18.6,-11.9,12.9) (19.8.-10.7,13.2) 100 M % i v _60s<T< 150s 50"MVW J50s<T 20 S v / D i v 45s<T<90s 100 M^oiv -5.0 2i:00 UT I 21:30 UT 22:00 UT I • 22:30 UT 23.00 UT I 180° 2330 UT i 52 and 324 degree, respectively. This value of the azimuth i s outside the range favourable to Pc4 a c t i v i t y and, consequently, no continuous pulsation a c t i v i t y i s seen i n that band. On the other hand, a gradual onset of Pc3 a c t i v i t y can be seen at Ralston p a r a l e l l i n g , with a time lag of about 10 minutes, the change i n f i e l d d i r e c t i o n and the detection of a wave event whose Doppler s h i f t e d freguency i s i n the hydromagnetic regime (HM), i n the interplanetary medium. From 20:15 UT, the dominant wave period for the MHD wave event i s 35 seconds, corresponding to the Pc3 observed on earth, and the peak to peak amplitude reaches a maximum of 8y. This event i s continued on figure 3.3b. There, the two black spots from 21:16-21:19 UT, on the u n f i l t e r e d and T < 45 sec traces, are the c a l i b r a t i o n s i g n a l and should be ignored. From 21:20-21:46 UT, the f i e l d l a t i t u d e becomes greater than +30 and the azimuth d e f l e c t s only s l i g h t l y (<~100) . The Pc3 event disappears at Ralston u n t i l the f i e l d d i rection becomes favourable again to Pc3. F i n a l l y , the micropulsation event terminates at 23:40 due to e deflecting beyond -30°. The f i e l d changes at 18:45 and 21:20 are probably associated with solar wind pressure change, while for the f i e l d re-orientations at 21:46 and 23:31, the solar wind has probably no role to play. The co r r e l a t i o n times for the four vector f i e l d changes and micropulsation a c t i v i t y changes, are about 10, 8, 1 and 5 minutes, respectively. Dual s a t e l l i t e observation i s possible f o r t h i s event. Explorer-34 was sunward of the shock at (25.4,-17.0,-5.2), R=31.0 Re, at the beginning of the event. Me observed time 53 differences of 7, 2.5, 3.5 and 2.5 minutes, respectively, for the four f i e l d re-orientations, at the two s a t e l l i t e locations. The problem i s : Explorer-33 being closer to the earth observed a l l four changes f i r s t . This i s not to be expected from the picture of an interplanetary f i e l d frozen i n the solar plasma and being convected away from the sun at a speed of 520 km/sec, for t h i s p a r t i c u l a r event. The time differences should be le s s than one minute and should also be observed at the Explorer-34 lo c a t i o n f i r s t . F i n a l l y , we note that Explorer-34 did not detect any wave a c t i v i t y at a l l , even though i t was situated only 9 Re upstream from Explorer-33 i n the e c l i p t i c plane. Given the f i e l d d i r e c t i o n , both s a t e l l i t e s should have observed the upstream wave events (see Chapter IV). The main difference here i s that Explorer-33 was seeing the region of the shock from about 12-15 Re above the e c l i p t i c plane, while Explorer-34 saw a region a few earth r a d i i (3-6) below t h i s plane. Hhy only one s a t e l l i t e observed the wave, remains unexplained. This might be evidence that the upstream wave phenomenon can at times have a l o c a l character. In the previous section, we have presented Pc4 micro-pulsation events that were associated with enhanced fluctuations in the magnetosheath f i e l d . The same events (Table III) are used to gain i n s i g h t into Pc3 a c t i v i t y . For example, on figure 3.2, we see that Pc3 was active prior to the beginning of increased magnetic a c t i v i t y i n the magnetosheath. Hhen the enhanced fluctuations s t a r t , Pc3 a c t i v i t y i s increased (obvious on the Y component) and, l a t e r on, i t disappears, along with 54 Pc4, due to the end of the magnetosheath event. In figure 3.3a,b, we have seen superb worldwide Pc3 a c t i v i t y , even though the f i e l d azimuth was s l i g h t l y outside the 30° domain defined f o r Pc4, In figure 3.2, we have also seen that Pc3 existed prior to Pc4 a c t i v i t y . At t h i s point, we would l i k e to note that Pc3 i s controlled l e s s s t r i c t l y than Pc4 by the interplanetary magnetic f i e l d d i r e c t i o n . More s p e c i f i c a l l y , Pc3 tends to take place for a wider range of f i e l d azimuth and la t i t u d e . More tolerance for Pc3 than f o r Pc4, i s evidenced by the fact that, Pc3 can remain active while Pc4 ends because G and/or ^ become unfavourable to Pc4, or by events such that Pc3 a c t i v i t y i s taking place when a Pc4 event st a r t s due to 0 and $ becoming favourable to thi s l a t t e r type of micro-pulsation. Table IV gives a l i s t of such events. TABLE_IV Events showing more e f f i c i e n t I.M.P. Direction-Control for Pc4 than f o r Pc3 T T I DD-MM-YY* | Time(UT) || DD-MM-YY* r + -H-| 05-09-67 j 01:10 z || 16-10-67 r ^ y. | 16-09-67 J 10:50 3 j | 24-10-67 I I I! I \ 17:40 2 j | I I I r J 17:57 i |j 25-10-67 | 17-09-67 j 14:38 2 || 30-10-67 f ^ , | 24-09-67 J 15:40 1 | | I i II I L I 19:25 2 | | -I LJL. Time (UT) 16:30 1 19:30 2 20:05 1 19:40 2 17:50 2 * Day-Month-Year 1 Pc4 star t s 2 Pc4 ends 3 Pc3 s t a r t s . Pc4 onset i s not c l e a r , but i s posterior to Pc3»s 55 Further evidence i s the fact that many Pc3 events take place when there i s no continuous Pc4 a c t i v i t y (e.g. figure 3.3), while we have not observed the reverse. On the ground, Pc3 i s known to be more common than Pc4 and t h i s agrees with a looser vector f i e l d control of Pc3 a c t i v i t y . This looser control has been observed mainly for the azimuth-control. This s i t u a t i o n i s c l a r i f i e d l a t e r on. B-3) Solar Wind and Micropulsations B-3-1) Transient Pulsations The p a r t i c l e density, the bulk v e l o c i t y , the flux and the dynamic pressure are a l l parameters that y i e l d information on the state of the solar wind. Among these, the pressure i s a function of the p a r t i c l e density and the sguare of the v e l o c i t y . To simplify the analysis, we at f i r s t compared the solar wind dynamic pressure with pulsation a c t i v i t y . Besides, i f one considers interaction of the wind with one of the physical boundaries (e.g. the magnetopause) i n the neighbourhood of the earth, the important parameter i s the solar wind dynamic pressure. Since the bulk v e l o c i t y varies l i t t l e compared to the p a r t i c l e density, which can vary by more than an order of magnitude, changes i n dynamic pressure are determined generally, primarily by changes in the density. In the following, when we use terms l i k e 'sudden1 or •abrupt' changes, i t should be kept i n mind that the solar wind measurements for a given species, are available only every three 56 minutes and, these words apply on t h i s time scale. F i n a l l y , even though we focused the attention on the proton pressure, every time we calculated and plotted i t , the proton density, the bulk v e l o c i t y and the proton flux were plotted as well. They are, therefore, not ignored. we found that an abrupt change i n solar wind dynamic pressure gives r i s e to a transient pulsation whose •period 1 f a l l s usually i n the Pc4 range, but also, at times, i n the Pc3 range. Figure 3.4 shows a transient pulsation with period i n the Pc4 range. The f i e l d magnitude and the dynamic pressure, both exhibit a sudden increase at 17:32 UT, which i s followed by the transient pulsation at 17:39. Actually, the interplanetary event i s a hydromagnetic shock wave which triggered a geomagnetic storm on earth. Figure 3.5 i s an example of two transient pulsation events triggered by d i r e c t i o n a l d i s c o n t i n u i t i e s which are coupled with two large decreases i n solar wind dynamic pressure. Figure 3.6 i l l u s t r a t e s what happens when a succession of abrupt changes takes place i n the interplanetary plasma. Here, plasma data have been shifted by 10 minutes to correlate with the transient pulsations. Associated with the plasma changes, we observe groups of transient pulsation a c t i v i t y and, i t appears as i f the solar wind i s modulating the micropulsation a c t i v i t y . Up to 17:30 UT, the f i e l d azimuth was between 45 to 90 degrees away from the Sun-Earth l i n e , and the transients attenuate rapidly. Notice the event at 17:42 UT where the excited transient has a period in the Pc3 range. The sudden jump at 17:32 l e f t the f i e l d coincident with the Sun-Earth l i n e 57 T r a n s i e n t P u l s a t i o n A s s o c i a t e d With M Shock Haves. T r a n s i e n t p u l s a t i o n f o l l o w i n g a s s c on August 29, 1967. RALSTON t August 29, 67 INTERPLRNETRRY MAGNETIC FIELD IMP F DRTfl DRY = 240 . . YERR 67 SE COORDINATES o o 9 a o e o o 4 e CD 6 o co >™ £ ro I IN) b O < m =. X ) is m N I I 'I I ° o 5 ° 5 h ° I I ± ± O O -< o X ro bo N i. w r o i o F i c j i 3 A 5 Transient Pulsation Associated With Directional D i s c o n t i n u i t i e s . ,Pc<Jl transient pulsation following two decreases i n dynamic pressure and associated f i e l d changes. R A L S T O N £ September 7 , 6 7 INTERPLANETARY MAGNETIC FIELD IMP F DATA OAY = 249. YEAR 67 SE COORDINATES (7) 6 ' o <z —I CD OJ O O ^ P 1 cn o "0 O i CO o -< zz. CT 2 o o T I OJ CD I I 1 I I ± _L o ± _L o + o o o o o N -< "2 X 3^6 Succession of T r a n s i e n t P u l s a t i o n s and Dynamic Pressure Changes. Example showing the importance of the r e p e t i t i o n r a t e of pressure changes on the appearance of the e x c i t e d t r a n s i e n t s . S o l a r wind data have been advanced 10 minutes to o b t a i n t h i s c o r r e l a t i o n . 17:10 BROAD-BAND 1 | 1 rr—i 1 1 1 1 1 1 1 1 r 17:20 17:30 -i 1 1 r—i r r 17:40 O I— CO Q Q 45<T<150 SEC CC PRESSURE Q -0 - 2 . 0 X ) 0 * 8 D Y N E / C M 2 C E I— C E Q O FLUX . , h - 0 - 4 . 0 X 1 0 t 8 / C M 2 / S E C O CC Q_ Q VELOCITY -5 0 - 4 0 0 KM/SEC CC CE _J o CO DENSITY , 0 - 1 0 IONS/CM 3 1 H 1 1 1 X 1 1 1 1 1 w 1 1 1 * 1 1 1 * 1 1 I * 1 1 1 * 1 1 | 1 * 1 1 * 1 1 1 * 1 1 | 1 1 1 * 1 1 * A A A A A A A A A A A A A X X X X X X X X X —X X X 1 i i i i z 1 1 1 1 1 z 1 1 1 X , 1 , X 1 1 1 X 1 1 1 X 1 1 1 L X 1 1 X 1 1 1 Z 1 1 1 Z 1 1 1 Z 1 1 17:20 rv 17:30 63 u n t i l 17:40. Consequently, the transient i s followed by a short continuous Pc3 event that lasted u n t i l the f i e l d azimuth d r i f t e d away from t h i s favourable d i r e c t i o n . Figure 3.6 i l l u s t r a t e s two points. F i r s t l y , depending on the r e p e t i t i o n rate of the solar wind sudden changes, i t can become very d i f f i c u l t , i f not impossible, to distinguish between a continuous micropulsation event and a succession of transient sig n a l s . Fortunately, i n t h i s f i g u r e , the r e p e t i t i o n rate i s slow enough that we can s t i l l c l a s s i f y the 'Pc4 event' as a ser i e s of transients. During magnetically disturbed days or else, for a disturbed interplanetary medium, we believe that often 'continuous' Pc3-4 micropulsation events,, actually are a sequence of transient pulsation events. In the next chapter, we discuss the p o s s i b i l i t y of making the d i s t i n c t i o n using spectral analysis. Secondly, changes in dynamic pressure are usually coupled with changes i n the direction and/or magnitude of.the interplanetary f i e l d . The excited transient signal depends strongly on the d i r e c t i o n of the f i e l d after the discontinuity. The picture seems to be the following: for a Pc4 transient, i f the f i n a l values of © and <p are outside the range favourable to Pc4 a c t i v i t y , then the transient attenuates rapidly and usually l a s t s only 4-5 o s c i l l a t i o n s . On the other hand, i f the f i n a l values of ©• and <f> f a l l i n s i d e the range, then the transient i s usually followed by a continuous Pc4 event. In the l a t t e r case, the transient i t s e l f i s strongly attenuated. The same applies to Pc3. This i s to be expected since, most of the time, the way in which the f i e l d d e f l e c t s inside or outside the range favourable to Pc3-4 pulsation a c t i v i t y , often has the 64 c h a r a c t e r i s t i c s of a d i r e c t i o n a l discontinuity. In t h i s respect, a gradual onset as in figure 3.3, i s unusual. Not a l l transient pulsation events were checked for changes i n the interplanetary parameters. Besides, some events could not be associated with changes in the solar wind parameters and t h e i r connection with changes i n the f i e l d or i t s d i r e c t i o n , was doubtful or at l e a s t , the cause and e f f e c t r e l a t i o n s h i p could not be ascertained f o r sure, Therefore, the p o s s i b i l i t y of the magnetospheric o r i g i n of some transient pulsations, cannot be ruled out. B-3-2) Continuous Pulsations I f we divide the pulsation events (Pc3 or 4) that occurred in the three month i n t e r v a l under consideration, into large amplitude, medium amplitude and small amplitude events, there i s a very clear association of the average amplitude of the sig n a l with the solar wind v e l o c i t y . A l l the largest pulsation events, namely. Sept 16-17, Oct 13-15-16-17-30, 1967, were associated with wind velocity not lower than 470 km/sec and generally larger than 500 km/sec. The association with the ion density i s less clear, even though, in general, they associated with low density solar wind ( t y p i c a l l y 1.5-2.0 /cm3, up to 3 /cm 3). Small amplitude events associated c l e a r l y with solar wind v e l o c i t i e s less than 400 km/sec and generally denser plasma (2-4 cm 3). The r e l a t i o n s h i p , i f any, with the ion temperature i s not c l e a r . Medium amplitude events associated with medium vel o c i t y (40 0-47 0 km/sec), but t h i s group has many exceptions such as 65 medium amplitude associated with low solar wind velocity. The notorious exceptions here are Sept 11, 1967 and Oct 26, 1967. The former i s a strong Pc3 day, even though the wind ve l o c i t y was only 340 km/sec and the density varied from 2-4 cm3 and the plasma was hot (1.2x10 s K). Spectral analysis has revealed the upstream wave spectra to be unusually r i c h i n compressional power. The l a t t e r was a medium Pc3-4 day. The wind ve l o c i t y was extremely low (270 km/sec), the plasma generally very dense (2-20 /cm3) and very hot (2-3x105 K). This day was also very r i c h i n compressional waves. many discrepancies between simultaneous spectra occurred on t h i s most unusual day and i t i s discussed in the next chapter. Apart from these exceptions, the association of large amplitude micropulsation events with high speed solar wind, small amplitude events with low speed solar wind and medium events generally with medium velocity solar wind, i s quite c l e a r . B-4) Summary In conclusion, the case by case study has permitted us to r e s t r i c t the occurrence of Pc4 continuous pulsations to a very narrow range of f i e l d direction around the Sun-Earth l i n e . For Pc4, i t i s also evident that larger amplitude signals correspond to f i e l d directions closer to the Sun-Earth l i n e , so that t h i s angle-control i s also an amplitude control. Likewise, for Pc3, we have observed the ^ - c o n t r o l of Bolshakova and Troitskaya and also added a ©-control of Pc3 occurrence on the interplanetary f i e l d d i r e c t i o n . This 66 d i r e c t i o n control i s looser for Pc3, i n that t h i s type occurs for a wider range of directions of the f i e l d , and also, i n that large amplitude signals (e.g. f i g 3.3) can happen for f i e l d d i r e c t i o n s u b s t a n t i a l l y away from the Sun-Earth l i n e . Therefore, for Pc3, the angle control i s c e r t a i n l y not as e f f i c i e n t an amplitude-control, as i t i s for Pc4. F i n a l l y , on a longer time scale, the continuous micro-pulsation amplitudes associate very c l e a r l y with solar wind v e l o c i t y . This time scale i s of the order of hours. C) S t a t i s t i c a l Study, C-1) S t a t i s t i c a l D i s t r i b u t i o n s of Micrecusations The case by case study has revealed the important parameters that control Pc3-4 occurrences and their amplitudes. Here, to investigate the possible coupling between these parameters and also to make the statements more quantitative, we r e l y on s t a t i s t i c a l d i s t r i b u t i o n s . Once again, i n the construction of the following d i s t r i b u t i o n s , we considered only continuous micropulsation signals. Three g u a l i t i e s are affixed to the d i s t r i b u t i o n s : raw, corrected and normalised. The f i r s t one i s s e l f explanatory. Corrected refers to weighting events by t h e i r amplitudes, while normalised refers to d i s t r i b u t i o n s normalised by the interplanetary magnetic f i e l d d i s t r i b u t i o n . The raw s t a t i s t i c a l d i s t r i b u t i o n to be presented, are constructed i n the following way: 1) F i r s t , only one type of micropulsation signal i s 67 considered 2) Second, for the duration of the pulsation event, the interplanetary magnetic f i e l d d i r e c t i o n i s divided i n c e l l s Ae XA^> degrees ( Ae =10°) . 3) F i n a l l y , we count the number of minutes of pulsation a c t i v i t y for which the f i e l d vector l i e s i n one given c e l l and repeat the process u n t i l a l l pulsation events of one type have been accounted f o r . Figures 3.7 and 3.9 show the raw d i s t r i b u t i o n s f o r Pc3 and Pc4. A t o t a l of 10,752 minutes of Pc3 a c t i v i t y , and 8,519 minutes of Pc4 a c t i v i t y , subject to the constraints of the present analysis, were used i n the i r constructions. The size of t h i s sample i s appreciable. The f i r s t modification to these d i s t r i b u t i o n s i s to weigh the pulsation signal by i t s amplitude, i . e . , more importance i s attached to a si g n a l with larger amplitude. To do so, an extra step i s added to the process above: each pulsation event i s subdivided into i n t e r v a l s of constant peak to peak amplitude and, the duration of each i n t e r v a l i s multiplied by i t s amplitude. The corrected d i s t r i b u t i o n for Pc3 and Pc4 are presented in figures 3.8 and 3.10, respectively. F i n a l l y , to ease v i z u a l i s a t i o n , these 3-dimensional d i s t r i b u t i o n s are integrated over the f i e l d l a t i t u d e to yi e l d histograms of Pc occurrence versus azimuth, and vice versa, integration over the azimuth gives histograms of Pc occurrence versus l a t i t u d e . The histograms for the l a t i t u d e and azimuth are shown in figures 3.11 and 3.12, respectively. The f i r s t and 68 f i S l i 1 A7 Pc3 Raw D i s t r i b u t i o n Versus IMF Direction. A t o t a l of 10,752 minutes of Pc3 a c t i v i t y was used in the compilation of t h i s fugure. 69 CT CC QQ CC f— CO CD cn q in d OJ o CO d in d co d CD d CO d d CM d rv d CO d i n d in d m co' GO CM in rv d CM d CM d CM d r~-d in d co d CD d in d CO d d CM d CM d d d d q d d d CM d in d d co o cn o CM o co o CM CM i n o" rv d rv d rv CD CD d cn CM' CO d CM d CM o O CM CO co m CD in m in P J CD CM o -< d CO d CO CM co' co' in co' in CM' q co d co d CM* co in rv rv. CD d co d c co. d co" CD CO d c c CO d CM d CM d co d d c c c CM d c '-r' LU CO -e-o 00 o • o o o CM O CN O O •0 O 00 LU CO CD 70 1..8 Pc3 Corrected E i s t r i b u t i o n Versus IMF Direction. Pc3 d i s t r i b u t i o n where the sign a l is weighted by i t s amplitude. 71 C D (_J cn cn m i — i cn \— c o i — i o Q_ d d CNJ d d d m d co d d d CM d CM CO d o° CM d CO CO d CM d CM d co d d d co d CO d in d CO d CO d d d it d d d d o d o d d d in d d d d co d CD d •<r CO d io o LO d <-. CD d 00 co" o oi cn d CM d CM O o O co in CO CO in m . CM o co o -d d CO co o co" co co" CM o> d d ro d CO CD co •-. co CD in d d co d CM' CO d d CO d d d d d c < c co d c o co o o -e-o o CN o CN o o •o o CO LU CO C D 72 3.9 Pc4 Raw D i s t r i b u t i o n Versus IMF Direction. A t o t a l of 8,519 minutes of Pc4 a c t i v i t y was used i n the compilation of t h i s figure. 73 C E CC QQ i — i cc h— CO a C L CM d d CO d CO d CD o' CO d CM d d CM d CO d d CM co" co <* CO CO d d CM d CO d cn co co CM d . cn d in d CM d d IO d d CO q d cq d CO d co d d co d co CM" CM d d to d d d CM d d d cn d CO d co CM* q CM co d tv CM' tv. q o CM O o CM co CM CO CD o CO CO co CO CO o o CO O CM o CO CM CO o CO CM tv. o CO CO d tv CM* co d CM d CN d d CO d in d CM d co d < c o oo o o o o CN LU CO -e-o o •o o co LlJ CO C D 74 l i S i 3.10 Fc4 Corrected D i s t r i b u t i o n Versus IMF Direction. Pc4 d i s t r i b u t i o n when the s i g n a l i s weighted by i t s amplitude. Pc4 ^-DISTRIBUTION(CORRECTED) 8 0 6 0 4 0 20 8 S E °' -20 -40 - 6 0 -80-2 7 0 0.3 0.3 0.3 0.2 0.4 0.5 3 0 0 0.4 2.9 1.5 0.3 1.0 0.8 0.1 0.1 0.3 2.1 5.8 4.6 2.1 0.7 1.1 0.2 0.2 1.9 2.5 10.0 8.0 6.2 0.8 0.5 0.1 3 3 0 0.3 0.4 0.9 1.9 1.3 1.6 0.2 0.2 1.2 0.3 1.3 0.5 0.1 0.1 0.2 0.3 0.1 0.2 3 0 6 0 0.4 0.3 0.1 0.2 0.4 0.7 9 0 120 0.2 0.6 0.4 0.6 1.4 0.0 0.4 0.2 0.6 1.4 1.9 2.4 0.4 0.4 0.2 0.1 0.4 1.8 0.7 4.5 6.0 2.1 0.4 0.2 0.2 0.9 0.3 0.0 0.8 0.5 0.3 150 1 8 0 0.1 0.7 210 SE 2 7 0 l i a * 1 i l l £c3 and Pc4 Distributions Versus IMP Latitude. This example shows the tigh t e r l a t i t u d e - c o n t r o l of Pc4 occurrence and amplitude (right) compared to Pc3 ( l e f t ) . 30 2 Pc3 vs 8 5 E RRV-DISTRIBUTION 30 60 [30 / , Pc3 vs B SE C0RRECTE0-D1SIRIBUT1 ON 30 60 90 I30Z Pc4 vs B S E RflU-DI5TRIBUT I ON •90 -60 -30 30 60 90 1.30 % Pc4 vs 8 5 E ; CORRECTEO-DISTRIBUTION -90 -60 30 60 90 lia* IJLIZ £C3 and P c 4 Distributions Versus IMP A2imu.th. Same as previous fig u r e but now for the azimuth-control. Notice how P c 3 observations f o r away sectors have been reduced upon correction by the amplitude. [20 V. P c 3 vs 4>5E RAW-DISTRIBUTION 120 P c 3 vs c|>5E CORRECTEO-OISTRIBUTION -f=)= 20 Z Lo P c 4 vs 4>5E R R V - D I S T R I B U T I O N 2"o~' 300 330 ^ 0 30 60 9 0 120 150 180 210 240 TfO D - O -.20 P c 4 vs 6 S E C0RRECTE.0-015TRIBUT ION t m 270 300 330 0 30 6 0 9 0 t20 150 160 210 240 270 80 second moments of the histograms are l i s t e d i n Table V. TAELE_V F i r s t and Second Moments of Pc3-4 Histograms - - 1 T T ! , , Pulsation|Distribution j Mean \Variance|Standard lPercent of Type j Type Angle| | jDeviation|Observation r - H — I -) -j -I = H Pc3 Pc3 Pc4 Pc4 Eaw <p I 353.0 | 359.6 j 19.0 | Corr. Q | -2.6 | 300.1 | 17.3 Haw Corr. e | -2.5 | 311.4 | H 4 +-17.6 j 100.00 79. 48 <£ 2 I 178.4 | 334.4 j 18.3 | - | 4 -| -T-20.52 100.00 * 1 354.2 j 352.8 | 18.8 ±4 4-<J>2 i 179.9 j 413.5 | 20.3 84.98 e |__" 1 , 0 1 3 1 7 , 4 1 17.7 I 15.02 <J>i | 357.5 | 350.5 | H +. I 18.7 | 100.00 63.39 fa* | 169.6 | 392.4 | 19.8 - 1 — T -I e I -0.6 | 244.7 J 15.6 i 36.61 | 356.0 J 261.8 | 16.2 | H H -I + | 100.00 T 1 66. S7 A 2 | 173.9 | 286.6 | 16.9 | 4 I t 33.03 Means and Standard Deviations i n degrees » 270 < $ < 90 2 90 < (p < 270 In figures 3.7-3.12, some of the observations at the periphery of the nuclei of the d i s t r i b u t i o n s , and some observations completely detached from those n u c l e i , might be due to transient pulsations. At times, f o r the reason mentioned previously, i t i s d i f f i c u l t to distinguish between a seguence of transient pulsations and a continuous micropulsation. In such cases, they were assumed continuous and included i n the compilation of the d i s t r i b u t i o n . Anyhow, they represent only a small percentage of the t o t a l of the observations. 81 From figure 3.7 to 3.12, i t i s apparent that, both the la t i t u d e and azimuth controls are ti g h t e r for Pc4 than for Pc3. Comparison of figures 3.8 and 3.10 shows that, for Pc4 pulsations, weighting the signal by i t s amplitude has rendered the d i s t r i b u t i o n more anisotropic. This point i s p a r t i c u l a r l y obvious i n the r i g h t halves of figures 3.11 and 3.12. On Table V, t h i s appears as a systematic reduction i n variance for the corrected d i s t r i b u t i o n , as compared to the raw d i s t r i b u t i o n . C l e arly then, the dire c t i o n - c o n t r o l for Pet occurrence, i s also an amplitude-control of PcU a c t i v i t y . For Pc3, the amplitude correction has reduced the sig n i f i c a n c e of events taking place for large 6 and^. In the la t i t u d e range { -30°,+30° } and in the azimuth range { 320°,30° } events generally have larger amplitude. But within that region, there does not seem to be any systematic variation in amplitude. In figures 3.11 and 3.12 ( l e f t halves), t h i s i s represented by more f l a t - t o p d i s t r i b u t i o n s , especially for the f i e l d azimuth. For a f i e l d directed away from the sun, amplitude correction has systematically reduced the significance of these observations, therefore indicating that they generally had smaller amplitudes. In Table V, we see that amplitude correction has l e f t the lati t u d e and the f i r s t azimuth variances p r a c t i c a l l y unchanged, whereas the azimuth variance f o r away f i e l d s has been increased subs t a n t i a l l y . Therefore, for Pc3 a c t i v i t y , the angle control i s only a weak amplitude-control, over the range of f i e l d directions for which t h i s type of a c t i v i t y takes place. On Table V, i t w i l l be noticed that the r a t i o of 82 observations for f i e l d s toward and away from the sun, for both Pc3 and Pc4, has been s l i g h t l y increased i n favour cf toward f i e l d s , upon amplitude correction. This i s a re s u l t of the association of the amplitude of pulsation events with solar wind ve l o c i t y . In the i n t e r v a l considered, there was b a s i c a l l y only one high speed solar wind event that occurred for a f i e l d directed away from the sun, and for which the f i e l d d i r e c t i o n was favourable to micropulsation a c t i v i t y . Most pulsation events taking place for f i e l d directions away from the sun are associated with medium or slow solar wind streams. This i s s u f f i c i e n t to explain the amplitude correction s h i f t i n favor of toward f i e l d s . There s t i l l remains to check whether cr not the fact that a l l d i s t r i b u t i o n s have mean values at negative f i e l d l a t i t u d e s and o f f the Sun-Earth l i n e in the e c l i p t i c plane, i s r e a l . The di s t r i b u t i o n of observations for f i e l d s toward and away from the sun should also be compared to the f i e l d d i s t r i b u t i o n to provide a consistency check. f i n a l l y , normalisation by the f i e l d d i s t r i b u t i o n i s necessary tc verify that the pulsation d i s t r i b u t i o n s retain t h e i r anisotropics. Two 3-dimensional f i e l d d i r e c t i o n d i s t r i b u t i o n s were compiled. The f i e l d d i s t r i b u t i o n s are calculated from the sum of the i n d i v i d u a l d i s t r i b u t i o n for each o r b i t , from o r b i t 19 to 39, i . e . , from August 10 to November 8, 1967. 20 .5-sec average values of the l a t i t u d e and azimuth were used. The f i r s t d i s t r i b u t i o n includes a l l days in the i n t e r v a l just mentioned. The second d i s t r i b u t i o n uses only Kp < 3 .5 days and also, a l l disturbed interplanetary f i e l d s are discarded. There i s very 83 l i t t l e difference between the two d i s t r i b u t i o n s , indicating the s t a t i s t i c a l v a l i d i t y of the sample. Here, to be consistent with the r e s t r i c t i o n s of t h i s analysis, we use the second d i s t r i b u t i o n . The d i s t r i b u t i o n s l i g h t l y favours positive f i e l d l a t i t u d e s (51.73%) and the time i n t e r v a l i s situated i n a predominantly toward sector (69.11%). The f i e l d directions are clustered around the garden hose angle. However, the most probable value of the f i e l d d i r e c t i o n i s shifted toward the Sun-Earth l i n e , by approximately 10 and 20 degrees for toward and away f i e l d s , respectively. Both d i s t r i b u t i o n s exhibit t h i s s h i f t . The time i n t e r v a l i s close to sunspot maximum and on the average, one would expect a fas t e r solar wind and, therefore, a f i e l d d i r e c t i o n closer to the Sun-Earth l i n e . However, the discrepancy for toward and away sectors, even though s i g n i f i c a n t , i s not re a d i l y explanable. The r e s u l t s of this normalisation are shown in figures 3.13 to 3.16. For the raw azimuth histograms ( f i g 3.13), the tendency i s to make a l l f i e l d directions favourable to Pc3 and Pc4, eguivalent. The situ a t i o n i s di f f e r e n t in figure 3.14, where now the f i e l d d i rection amplitude-control i s included in the d i s t r i b u t i o n s and they retain t h e i r anisotropics. On these two f i g u r e s , the s i t u a t i o n for Pc3 for away f i e l d s , i s more d i f f i c u l t to in t e r p r e t . The l a t i t u d e histograms (fig 3.15,3.16) ret a i n t h e i r anisotropies as well. Table VI summarizes the main s t a t i s t i c a l changes brought upon by the f i e l d d i r e c t i o n normal-i s a t i o n . The variances of a l l histograms have increased. The l i f l i li.ll Comparison of Pc3 and 4 Raw and Normalised Azimuth Histograms. This figure shows that for the raw d i s t r i b u t i o n s , normalisation by the f i e l d d i s t r i b u t i o n tends to make a l l angles favourable to Pc3-4 a c t i v i t y , equivalent. 85 + 1 8 ; 270 300 -t—+ +12 330 30 Pc3 vs 4>SE RflV NORMALISED r m r H I I I i i 60 90 r T ~ r i i 120 150 180 1—i—i—r 210 240 270 +18 7 +12 r -i • i • i l i i— I — r 270 300 330 30 — i — r 60 -f= +6 SO "^ 120 Pc4 vs tj> S E RflV NORMALISED r -\ A i • t i r t I ' i I 150 I—i—r 180 210 240 ""270 Fig... 3^14 Comparison of Pc3 and 4 Corrected and Normalised Azimuth Histograms. This figure shows that Pc3 and 4 d i s t r i b u t i o n s do re t a i n their anisotropy, even though i t has been weakened by the normalisation. 87 +18 J +12 2 7 0 3 0 0 3 3 0 I—" T 1 i—i— Pc3 Y3 c^se CORRECTED NORMALISED r n r T i 30 60 9 0 - 4=U h i — i — i — i — i — i 1 2 0 1 5 0 1 8 0 2 1 0 2 4 0 2 7 0 i i i F~"F 2 7 0 3 0 0 + 1 2 6 0 ' -f=4 1 8 7 +6 Pc4 vs (}>SE CORRECTED NORMRLISED r n i r -i t I > I • t i - t i 3 3 0 30 9 0 1 2 0 1 5 0 1 8 0 2 1 0 — i — i — i — i 2 4 0 2 7 0 l i i l i 3..1 5 Comparison of Pc3 and 4 Raw and Normalised Latitude Histograms. Upon normalisation the Pc3-4 raw l a t i t u d e histograms have the i r values reduced for f i e l d d i r ections close to the e c l i p t i c plane. .89 +30 ; Pc3 vs 8s£ RflV NORHRLISED +20 +10 -90 + = N -60 -30 30 60 "so +30 X PC4 VS Bc-j; RflV NORHRLISED +20 +10 -90 4 = | 1--60 -30 30 60 "90 f I 3 i 3..1.6 Comparison of Pc3 and 4 Corrected and Normalised l a t i t u d e M§tograms. Combined with figure 3,15, t h i s figure demonstrates that the la t i t u d e - c o n t r o l of Pc3 and 4 occurrence i s not merely a r e s u l t of the f i e l d d i s t r i b u t i o n . 91 Pc3 V3 Ssi +30 ; CORRECTED NORMALISED -10 • i -i -90 -60 -30 30 60 "90 - 3 0 ; Pc4 vs 6SE CORRECTED NORMALISED +20 +10 -90 -60 -30 -T-0 ~30~ 60 SO TABLE_VI F i r s t and Second Moments of Pc3-4 Normalised Histograms PuIsation Type Pc3 Pc3 Pc4 p e a Distribution! Type Angle " i 1 Raw i e Corr. Raw Corr, <t>; e 4 > 2 4 > ' 4 > f— e <t>3 Mean + 1.0 1.9 185.6 + 2. 8 1.6 186. 3 -0.5 8. 3 174.8 -1.0 3. 9 Variance 515.2 530.6 363.8 517.0 418.1 389.0 612. 1 571.5 536. 1 469.0 480.3 181.4 J 472.0 j Standard Deviation 22.7 23.0 19.1 22.7 20.4 19.7 24.7 23.9 23.2 21.7 21.9 Percent of Observation 100.00 59. 22 40.78 100.00 63.45 36.55 100.00 46.06 53. 94 100.00 48. 21 -J 21.7 51.79 Means and Standard Deviations i n degrees » 270 < <p < 90 2 90 < 0 < 270 exception here i s again Pc3 for f i e l d s away from the sun, where the change i s hardly s i g n i f i c a n t . The means of the azimuth histograms have been displaced by an average of 8 degrees and t h i s i s a direct e f f e c t of the f i e l d d i r e c t i o n . However, whereas the means of.the la t i t u d e histograms were a l l negative before the normalisation, now Pc3 has positive mean while Pc4 has remained negative. The si t u a t i o n i s p a r t i c u l a r l y c l e a r with the corrected d i s t r i b u t i o n s ; for Pc3, the mean has become po s i t i v e , while for Pc4, i t has become more negative. However, we are dealing with small changes and i t i s d i f f i c u l t to say i f they are s i g n i f i c a n t . On Table VI, the percentage of observation shows that Pc4 93 i s equally l i k e l y to occur for toward or away sectors. On the other hand, the f i e l d normalisation has f a i l e d to completely correct the Pc3 d i s t r i b u t i o n s . The s i t u a t i o n being worse for the corrected Pc3 d i s t r i b u t i o n , i t merely r e f l e c t s the f a c t that t h e i r amplitudes are not determined as e f f i c i e n t l y as Pc4's by the f i e l d d i r e c t i o n . This analysis has survived many self-consistency checks, and besides, i t gives a very consistent picture for Pc4, and also for Pc3*s occuring in toward sectors. Therefore, t h i s substantial difference between toward and away sectors for Pc3, i s believed to be r e a l . F i n a l l y , to see mere c l e a r l y the e f f e c t s of each operation performed on the various d i s t r i b u t i o n s , and also to study possible coupling of the angles involved in the d i r e c t i o n -c o n t r o l , we present in figures 3.17 and 3.18 contour plots of the d i s t r i b u t i o n s for f i e l d s directed toward the sun. To produce the eguiprobability contours, i t was necessary to interpolate l i n e a r l y between the data points. The v e r t i c a l (latitude) and horizontal (azimuth) scales simply represent the c e l l number i n figures 3.7 to 3.10. For example, c e l l (1,1) corresponds to an azimuth i n the range {270°,280°} and a l a t i t u d e in the range (-900,-80°} ; up to c e l l (36,18) which corresponds to {260°,270°} and {80°,90°), respectively. If the d i s t r i b u t i o n s were Normal, the contours would be concentric c i r c l e s , i n dicating independent la t i t u d e and azimuth control. If the l a t i t u d e (azimuth) was more important than the azimuth (la t i t u d e ) , the pattern would be an e l l i p s e with i t s major axis aligned along the azimuth (latitude) axis. F i ^ i 3.17 Pc4 Eguiprobabilit^ Contours for Toward Sectors. Clockwise from the top l e f t corner, we have the raw, corrected, corrected-normalised and raw-normalised d i s t r i b u t i o n s f o r Pc4. The numbers on the figure are percentages of the t o t a l of the observations. The horizontal and v e r t i c a l axes are the f i e l d l a t i t u d e and azimuth, respectively (see text f o r d e t a i l s ) . The most interesting feature i s the contours f o r the corrected d i s t r i b u t i o n . Close to the Earth-Sun l i n e , they are a f a i r approximation of concentric c i r c l e s , indicating the nearly egual importance of the la t i t u d e and azimuth for Pc4. This feature i s s t i l l apparent upon normalisation. 95 Fig... 3^18 £c3 u i ^ r o b a b i l i t y Contours for Toward Sectors. Same as Fig 3.17, but now for Pc3. The most s t r i k i n g feature i s the fa c t that Pc3 favours certain combinations of f i e l d l a t i t u d e and azimuth, even upon normalisation by the f i e l d d i s t r i b u t i o n . 98 Figure 3.17 (top,right) indicates that, the corrected Pc4 d i s t r i b u t i o n i s a f a i r approximation of a Normal d i s t r i b u t i o n . The coupling between l a t i t u d e and azimuth i s weak. For Pc3, figure 3.18 (top) shows that the raw and corrected d i s t r i b u t i o n s exhibit strong anisotropy and therefore, favour c e r t a i n combinations of f i e l d l a t i t u d e s and azimuths. For the corrected d i s t r i b u t i o n s , the pattern exhibited by the Pc3-4 d i s t r i b u t i o n s remains after normalisation by the f i e l d d i s t r i b u t i o n . F i n a l l y , i n away sectors, the Pc4 d i s t r i b u t i o n s exhibit features s i m i l a r to the one observed for toward sectors, while for Pc3, the contours seem to be random and no information can be extracted. C-2) Summary of S t a t i s t i c a l Results The s t a t i s t i c a l analysis has reinforced the results of the case by case study. For the corrected d i s t r i b u t i o n s , 91.34% and 94.34% of a l l observations f a l l within a 30° l a t i t u d e range from the Sun-Earth l i n e , for Pc3 and Pc4 respectively. also for the corrected d i s t r i b u t i o n s , 88.16% and 94.16% of a l l observations f a l l within a 30° azimuth range about the Sun-Earth l i n e , for Pc3 and Pc4 respectively. The d i s t r i b u t i o n s are characterized by small standard deviations. While Pc4 was found eguiprobable for f i e l d sectors toward and away from the sun, Pc3 showed a s i g n i f i c a n t bias, favouring toward sectors. The angle control of Pc4 occurrence i s also a very e f f i c i e n t amplitude-control, whereas for Pc3, i t i s less e f f i c i e n t in c o n t r o l l i n g t h e i r amplitudes. F i n a l l y , while Pc4 showed only weak coupling of the 99 l a t i t u d e and azimuth, Fc3 exhibited very strong coupling of the angles. Evidence for the s t a t i s t i c a l v a l i d i t y of the results i s the fact that, the picture obtained f o r Pc3-4 i n toward sectors i s very consistent. For away sectors, the Pc4 picture i s s t i l l very c l e a r , while Pc3 f a i l s to y i e l d a consistent behaviour. 100 CHAPTER IV UPSTREAM HAVES VERSUS HICBOP0LSATIONS A) Introduction In figure 3.3, we have seen an example of a magnetohydro-dynamic wave event ahead of the bow shock. The existence of these long period waves was shown to be an upstream phenomenon by Greenstadt et a l . (1968). The large s p a t i a l volume occupied by these waves, as well as many of their c h a r a c t e r i s t i c s (e.g. attenuation, p o l a r i s a t i o n , etc. ) was demonstrated by F a i r f i e l d (1969). In t h i s f i r s t detailed analysis, he showed that these waves are observed only when the projection of the interplanetary magnetic f i e l d , intersects the shock. Out of a t o t a l of 134 days of interplanetary data, the waves were observed 18.5% of the time, but more than 90% of the time when the f i e l d had the proper orientation with respect to the shock. On t h i s basis, he therefore concluded that they are a permanent feature of the solar wind-earth i n t e r a c t i o n . Since during the time i n t e r v a l considered, Explorer 34 was always within a few degrees of the e c l i p t i c plane, i t i s obvious that the best orientation of the f i e l d to observe upstream waves i s when the f i e l d i s in the neighbourhood of the Sun-Earth l i n e . As a matter of f a c t , a l l Pc4 events l i s t e d i n table 3.1 were associated, for most of t h e i r duration, with upstream wave 101 a c t i v i t y . Some Pc3-4 events are "apparently" not associated with space waves. This i s no surprise since the conditions for occurrence of pulsation a c t i v i t y on earth and for observation of the space waves are d i f f e r e n t . In the l a t t e r case, a f i e l d l i n e must connect the s a t e l l i t e and the shock. Hence, depending on the azimuthal position of the s a t e l l i t e and i t s distance from the shock and the d i r e c t i o n of the interplanetary f i e l d , we may or may not observe the space wave event. In figure 3.1, the wave a c t i v i t y i s d i f f i c u l t to see for two reasons: f i r s t l y , we used the 20.5 second average values of the f i e l d and secondly, the wave, i n t h i s p a r t i c u l a r case, has small amplitude. The wave a c t i v i t y lasted u n t i l 17:10 UT. Given t h i s close association, i t i s natural to consider the p o s s i b i l i t y that these waves propagate to the Earth's surface and contribute tc the spectrum of micropulsation. Of prime importance here, i s the fact that both the bow shock and the magnetopause are "th i n surfaces". They are both less than a hundred kilometers thick. On physical grounds, one then expects the waves, convected through or propagating through these boundaries, to retain their i d e n t i t y . Furthermore, from the wave point of view, the sub-solar magnetosheath in the v i c i n i t y of the nose of the magnetosphere, i s at most a few wavelengths thick. If the solar wind i s strong enough to confine the dipole f i e l d of the earth, then, the waves carrying t y p i c a l l y 1% cf the solar wind energy, being probably amplified across the shock (as evidenced by the enhanced fluctuations of figure 3.2) can either propagate through the magnetopause, or el s e , perturb the solar wind-dipole f i e l d eguilibrium and thereby force the 102 magnetosphere to o s c i l l a t e . For these reasons, we adopt the working hypothesis that upstream waves do propagate to the earth and can contribute to the micropulsation spectrum. In t h i s chapter, we demonstrate that t h i s i s the case. The waves do, in f a c t , contribute s i g n i f i c a n t l y to the power spectrum of micropulsations. Actually, i t i s shown that the power spectrum of continuous pulsations in the Pc2-4 range, i s determined by the power spectrum of upstream waves. In part A, some results obtained using conventional methods of spectral analysis are presented; while in part B, an autoregressive model (Maximum Entropy Method) i s f i t t e d to the time series. B) Spectral Analysis via Conventional Methods B-1) Meaning, of the Various Quantities Conventional methods of spectral analysis have been extensively treated i n many textbooks. Here we stress the physical meaning of the various spectra. For d e t a i l s of the method i t s e l f , the reader i s referred to Jenkins and Hatts (1968). The periodogram, rather than the Blackman-Tukey technigue, i s used for two reasons: f i r s t l y , computer wise i t i s much less expensive and secondly, for cross-spectral analysis, i t i s much easier to automate the process using the former. Each data segment i s tapered, at each end, with a cosine b e l l 10% the length of the time s e r i e s ; t h i s tapering i s to reduce side lobe leakage. The periodogram i s then calculated using the Fast Fourier Transform (FFT) algorithim. The raw spectrum i s convolved with a spectral window to give the end 103 r e s u l t , the smoothed poser spectrum. Suppose we have two t i m e s e r i e s x (t) and y ( t ) , w i t h F o u r i e r t r a n s f o r m s X ( f ) and Y ( f ) . Then t h e v a r i o u s s p e c t r a a r e d e f i n e d by t h e f o l l o w i n g r e l a t i o n s . <<*.2) (4.3) where * i n d i c a t e s complex c o n j u g a t e g u a n t i t i e s and the bar {-) denotes smoothed e s t i m a t e s of t h e s p e c t r a . (f) , (f) , Cji(^(f)# Qj(£<f)# Vx^(f) a n a " ©x<ji(f) a r e the smoothed autopower spectrum, cross-power spectrum, c o - s p e c t r u m , g u a d r a t u r e -spectrum, coherence spectrum and phase spectrum, r e s p e c t i v e l y . The autopower spectrum g i v e s the d i s t r i b u t i o n of power v e r s u s f r e g u e n c y . The co-spectrum and t h e q u a d r a t u r e spectrum a r e t h e spectrum of the i n phase and out of fihase components of x ( t ) and y ( t ) , r e s p e c t i v e l y . In o t h e r words, t h e c o - and 104 quadrature spectrum measure the covariance of the in phase and out of phase components of x(t) and y ( t ) , separately. To understand the physical meaning of the coherence spectrum, l e t us consider the following l i n e a r system with transfer function H (f) ( c f . Bendat and P i e r s o l , 1971) . XLt.) -Kit) H if) The output y(t) generally consists of the t h e o r e t i c a l output, which i s the convolution of h (t) with the input x ( t ) , plus noise n(t). From the theory of l i n e a r systems, we can express the coherency function as: H(f) i s simply the f o u r i e r transform of the impulse response function h ( t ) . From (4.5), i t i s r e a d i l y seen that, the noise has the effect of reducing the coherency. In f a c t , 2 (f) can be thought of as a measure of the signal to noise r a t i o . This i s apparent i f we rewrite (4.5) as SlJ) - iHtf)!* Pxx(l) = )Txy (I) {li 6 ) where s stands for s i g n a l . The important point to remember here, i s that the coherence function i s b a s i c a l l y defined for a l i n e a r , stationary system. I f the system i s nonlinear, the products of the nonlinearity are treated as system noise and 105 reduce the value of the coherence. From (4.5), i t i s evident that "^y, (f) t e l l s us how much energy comes from the input. For example, a value of (f)=0.36 indicates that, at t h i s freguency, 36% of the output energy comes from the input s i g n a l . It would be wrong to interpret the coherence spectrum as a c o r r e l a t i o n c o e f f i c i e n t at each frequency. l e considered three methods of studying wave po l a r i z a t i o n . The hodogram technigue i s well known and need not be discussed here. Secondly, one could plot the function S(t) defined by t S It; ta) =-i j[x(r.'; fa1) - xitf> pt'j] {4-7) t. where the dots indicate time derivatives, S(t) i s simply the area swept by the vector whose components are x(t) and y ( t ) . It i s a monotonically increasing (decreasing) function of time for an anti-clockwise (clockwise) sense of rotation. The actual pol a r i z a t i o n pattern i s determined by the slope of t h i s curve. Both of these methods are weak when one i s dealing with a spectrum of waves. For t h i s reason, we use the phase spectrum. This spectrum t e l l s us, at each frequency, i f x (t) i s leading or lagging y(t) and, f o r each case, the value of the phase difference. This i s a l l the information required. The values of the coherence and of the phase at frequency f, are read only i f the autospectra and the coherence spectrum, a l l exhibit a peak at t h i s frequency, and i f the value of the phase i s stable. The value of the phase i s r e l i a b l e only i f i t i s stationary or varies slowly i n the neighbourhood of the 106 freguency f. For t h i s analysis, i n t e r v a l s 32 minutes long were selected and spectra with 23 degrees of freedom, produced. The number of frequency estimates i s 1024 and 512 corresponding approximately to sampling frequencies of 1 and 0.3906 Hz at Ralston and Explorer-34 respectively. Furthermore, i t should be remembered that induction-type and fluxgate magnetometers are used on the ground and i n space, respectively. The doppler-shifted frequencies of the upstream waves f a l l i n the magnetohydrodynamic regime, and i t i s l i k e l y that they are magnetohydrodynamic waves ( c f . F a i r f i e l d , 1969). Some f i e l d guidance of the waves i s therefore expected; hence, upstream spectra are produced in a f i e l d - a l i g n e d frame of reference. Following F a i r f i e l d (1969), we define the Zp-A component to be i n the average f i e l d d i r e c t i o n , the X F A component i s i n the plane containing Z p A and the Earth-Sun l i n e , and i s perpendicular to Z F A ; the Y F A component completes the orthogonal system. B-2) Results A set of s a t e l l i t e spectra, here consists of 4 autopower spectra, for the vector components and the magnitude of the f i e l d , and an additional autopower spectrum i n the plane perpendicular to the t o t a l f i e l d . I t also consists of three coherence spectra and 3 phase spectra. A set of ground spectra consists of three autopower spectra f o r the NS and EW components, and also for t h e i r sum, i t further includes one coherence and one phase spectrum. Using conventional methods of spectral analysis, we have 107 produced well over 200 sets of s a t e l l i t e spectra from 21 d i f f e r e n t days, and well over 400 sets of ground spectra from also, 21 different days. Obviously, only a small (infinitesimal) sample of the whole i s presented. The spectra in figures 4.1-4.5 are a l l i n the same format. The v e r t i c a l scale i s i n decibels (0- -50) r e l a t i v e to the peak value, space and ground spectra are normalised independently. The horizontal scale i s the period from 200 down to 2 seconds. In the middle section of each graph, to the l e f t , i s the 95% confidence l e v e l ; i n the lower l e f t corners i s the bandwidth plotted at d i f f e r e n t freguencies. For s a t e l l i t e spectra, the v e r t i c a l l i n e i n the middle i s drawn at the ion gyrofreguency, which i s printed as PERI0D= i n the lower l e f t corner. In the upper r i g h t corner of each graph, we have the day , the s a t e l l i t e , the time i n t e r v a l , the component plotted and the number of degrees of freedom. F i n a l l y , the numbers plotted on each spectrum, are s t r i c t l y to ease the comparison between spectra. F a i r f i e l d (1969), i n his analysis of upstream waves, compared the power i n the transverse components (Xp^# ^ ) to the power i n the compressional components ( Z F A ) . He noted a s i g n i f i c a n t power enhancement, i n the 20-100 second band, in the transverse components as compared to the compressional components. He also pointed out that some of t h i s power enhancement remains at periods smaller than 20 seconds. When one examines figures 4.1-4.3, the f i r s t thing that one notices, i s the very obvious decline i n power for periods less than approximately 17 seconds, at Ralston. This i s t y p i c a l of 108 Fig.. 4 ..J. Comparison of Upstream Waves and Micropulsation Spectra on October J6 j , 67 . This figure exhibits good agreement down to T=11 sec. At Ralston, higher frequencies should be ignored because the signal exceeded the dynamic range of the tape recorder. 109 ^ < ' P E R I 0 W , >^ t^, b b ' '< • !, 2 110 Fig... 4..2 Comparison of Upstream Waves and Micro gul sat ion Spectra on November 6 X 67. fis for the previous spectra, the agreement extends down to the l i m i t of Pc3 pulsation. Enhanced power i n the Pel region i s evident. ^ T = 3 0 , T= 1 0 P E R I 0 D = 1 8 . 4 3 ^o.bb - V - fc • b Nov fe, £,? IMPF 14:40-15:12 VB = 23 2 F A I6D P E R I O  ( S E C ) 112 Fig.-, jis.3 Comparison of Upstream Hayes and Micropulsation Spectra on November 6^  67. This example shows agreement even i n the Pc2 region. The signature of the enhanced power in the Pel region i s t y p i c a l . 113 Nov fc,C7 114 l i f l i i i i i i Comparison of Upstream Waves and M i c r o t i s a tion. Spectra on November 6^  67. Spectra exhibiting agreement i n the high freguency Pc3 and Pc2 band ( T<20 sec ) . 115 N0V6,t? RALSTON lt :2i-lC :S8 V-ZJ X 3.02. 2.5 ? e •> 4 7.6. { b-k , V s J 'J • k 116 Fig... 4^5 Comparison of Upstream laves and Micropulsation Spectra on October 26 x 67. For t h i s example, the spectra are from the anomalous day, October 26, 67. There i s disagreement at low freguency |Pc4), but good agreement i n the Pc2 region. T-79 T-60 ^ T=30 , T= ID P E R I 0 D = 1 5 . 2 2 118 Fig... i i i 6 Comparison of Upstream Waves and Micropulsation Spectra on October 23 x 67. This upstream wave event took place a few earth r a d i i from the shock. There i s evidence that Pc2 i s also determined by the spectral content of upstream waves. OCT23,fc7 ihpr . _ T=ll9 . , T-79 1 _i_ T = 60 ^ T=30 PER 100=13.47 u i . V f c - i - f c - ! , • i • s • p t B I ^ I 5 t c - K / . i - l - i - k - i • !. • S O C T 2 3 , f c ? 30 PALSTON 16.51-i7-.2fc V,= 23 X T- i ?n 120 P i g i 4j,7 Comparison of Upstream Waves and Micropulsation Spectra on August _18x 67, This event was detected within half an hour of the inbound shock crossing. Visual inspection of the record indicates that the upstream wave i s r i c h in high freguencies ( T<13 sec ). This example i s further evidence of association of the spectra i n t h i s high freguency band. T=119 T = 79 _ ^ T=GO 1-30 , 1=10 P£RI0D=8.37 ic'.-t-l-S-t • k • '« • i 2.53 . .M.M.-„\,II-122 continuous micropulsation spectra. In space, even though i t i s not as clear, the power also decreases at approximately 19 seconds. On figures 4.4-4.6, we see that the breakpoint has been pushed toward higher freguencies. This corresponds t c upstream events where there i s appreciable power and usually well defined peaks i n the range beyond 0.05 Hz, up to, at most, 0.08 Hz. We have never observed a cutoff at Ralston beyond 0.09 Hz, that i s , the main decrease in power always takes place before t h i s upper l i m i t . The second most s t r i k i n g observation, i s the good agreement i n the 20-100 second band, between space observations and stable micropulsations. In f a c t , a look at the spectra of both transverse components i n space, accounts for a l l micropulsation peaks i n that band; This i s also t y p i c a l of pulsation spectra, that i s , they agree well with the spectra of the transverse components i n space, i n the region from 20-100 seconds. Here we take the spectra one by one and discuss the apparent discrepancies. In figure 4.1, the 69 second peak i s missing at Ralston, t h i s component i s observed even though weak, on the analog f i l t e r output. Its disappearance i s due to the fact that i t has l i t t l e power and therefore, the smoothing window absorbs i t i n the neighbouring large peak. Also the power at T=20 seconds, on the Yp A component, i s absorbed in the shoulder of the 27 second peak at Ralston. On figure 4.2, the compressional component i s displayed, the reason being that t h i s figure i s used for some other purpose l a t e r . In fact, at low freguency, the agreement of the ground 123 spectrum with the transverse components i s better. The main difference i s that, on the transverse components, the 101 second peak does not show up and, instead there i s a very clear 71 second peak, completing the i d e n t i f i c a t i o n of the two spectra. Figure 4.4 i s also used for other purposes. The agreement down to T=15 seconds, i s f a r better with the other transverse component. For t h i s p a r t i c u l a r event, the f i e l d - a l i g n e d transformation was not very successful. On fig u r e 4 . 5 , we d e f i n i t e l y have disagreement at low frequencies. The Pc4 peaks are extremely weak and the 50 second peak has been gobbled up by the 37 second component. On t h i s day, the interplanetary f i e l d l a t i t u d e and/or azimuth were often close to t h e i r 30° l i m i t from the Sun-Earth l i n e . This day was also characterized by an extremely slow solar wind (214<V<270 km/sec) and a very dense plasma. This day was p a r t i c u l a r l y r i c h in compressional wave power. Most of the spectra taken on that day show t h i s kind of disagreement at low frequencies. The spectrum on fiqure 4.6 (top) was taken from an i n t e r v a l where p r a c t i c a l l y no upstream wave a c t i v i t y was taking place, except for some high freguency a c t i v i t y . The low frequency peaks carry l i t t l e power, except for a 33 second peak on the other transverse component. F i n a l l y , figure 4.7 i s taken from a shock precursor; the s a t e l l i t e crossed the shock only half an hour a f t e r t h i s spectra was calculated. To understand t h i s spectrum i n the 20-100 second band, one has to go back to the vector f i e l d plot. There i t can be seen that, the power from 26-33 second comes from a subevent, i n the middle of the i n t e r v a l , that lasted 6 minutes and whose amplitude i s three 124 times larger { 6^, ) than the main event. The solar wind v e l o c i t y , d i r e c t i o n and density do not change s i g n i f i c a n t l y but, the s a t e l l i t e detected the beginning of a region of colder plasma a few minutes before the onset of t h i s subevent. At Halston, the X spectrum does show the ef f e c t of th i s subevent. The 44 second peak i s c l e a r l y seen on YrA and there i s also a weak T=64 second component. The analysis of a l l spectra shows that the 20-100 second band, presents no d i f f i c u l t y . The spectrum of stable, continuous micropulsations, in that band, i s determined by the spectrum of the upstream waves. It i s then natural to t r y to extend t h i s r e s u l t to higher freguencies. The spectra presented here, have been chosen primarily to exhibit the relationships at higher freguencies. The f i r s t two figures (4.1 and 4.2) show agreement i n the lower Pc3 band, namely the 10-20 second band. On figure 4.1, the micropulsations with period smaller than 11 sec. , are unreliable. This day was one of the two strongest micropulsation days, and the waveform maxima and minima were associated with noise bursts. This i s interpreted as the signal exceeding the dynamic range of the tape recorder. The rest of the spectra (figures 4.3-4.7) show some agreement even down to the Pc2 range. It i s of interest tc note, that the best agreement i n the high freguency region, say for freguencies greater than 0.06 Hz, i s obtained for spectra taken close to the shock wave (e.g. figures 4.5, 4.6, 4,7). Figures 4.1 to 4.3 are more t y p i c a l of the kind of agreement exhibited at high frequencies; the others have obviously been 125 chosen among the best. In f a c t , of a l l spectra of t h i s type, about 30-50% indicate a clear relationship at high freguency. This i s not surprising because, i n t h i s frequency range, waves carry much less energy than in the 20-100 second range. For t y p i c a l values of the interplanetary f i e l d and plasma, th e i r doppler-shifted wavelengths range from about 200-800 kilometers; they are therefore more prone to be affected by the microstructure of the interplanetary medium. A c a r e f u l study of phase spectra indicated that a record length of 32 minutes i s probably longer than t h e i r l i f e t i m e . In the next section, we reduce the record length i n order to get better insight into the high freguency region. The next point to be discussed, i s the power enhancement i n the Pel region, of the micropulsation spectra. Figures 4.2-4.5 show di f f e r e n t signatures of t h i s phenomenon. By f a r , the band(s) excited i s (are) i n the Pel region; that i s also the region (Pc1-2) of maximum s e n s i t i v i t y of the pulsation detecting system, at Ralston. The enhancement has never been observed beyond (i.e. at lower freguency) the region of sharp decrease i n power at T=17 seconds. I f the band(s) excited i s (are) in the Pel region, then the most conspicuous peaks, superimposed on the enhanced power, tends to be harmonics of Pc2 peaks (e.g. f i g . 4.3-4.5). S i m i l a r l y , i f the enhancement i s i n the Pc2 region, then they tend to be harmonics of lower Pc3 (T<20 sec) peaks. What causes t h i s power enhancement? What determines which bands are excited? A l l we can say i s , the tendency seems to be that when the micropulsation a c t i v i t y i s very low, they 126 generally seem to be associated with d i r e c t i o n a l d i s c o n t i n u i t i e s in the interplanetary medium. When the pulsation a c t i v i t y i s high, t h i s connection i s not clear at a l l ; in fact, i t seems as i f they are simply associated with the upstream wave a c t i v i t y . In figures 4.8 and 4.9, we show two events associated with enhanced power at Ralston. Figure 4.8 shows an 11.6 second wave, i n space, that corresponded to an abnormally high coherence (0.95) at t h i s p a r t i c u l a r frequency, at Ralston. Figure 4.9 shows a broad ,wave packet, centered at 7.7 sec. , that probably corresponds with a broad region of enhanced power, centered at 4.1 seconds, at Ralston. In any case, t h i s power enhancement does not constitute the main thrust of t h i s thesis and we just mention i t as a most inter e s t i n g research d i r e c t i o n . F i n a l l y , a l a s t piece of information to be extracted from micropulsation spectra, has to do with the region of sharp decrease in power. The peaks at the low frequency ( f < 0.06 Hz ) show greater v a r i a b i l i t y . That i s , they appear only i f there i s a Pc3 or Pc4 event and, i n turn, the peaks excited depend intimatley on the freguency content of the upstream waves. In t h i s respect, t h i s region i s unstable, that i s , from event to event, the power spectra may exhibit d i f f e r e n t spectral peaks. The region at higher frequency ( f > 0.06 Hz ) i s composed of extremely stable peaks. With a record length of 32 l i f i u t e s , t h i s region of the spectra i s nearly always composed of the same spectral peaks. The most conspicuous are 15.1, 13.3, 10, 8.7, 7.6, 6.6, 3, and 2.5 seconds; less conspicuous are 11.5, 5.8, 5.0, and 2.13 seconds. This separation of the micropulsation spectrum into two 127 Fig... 4_. 8 Special Event i n the Inter planetary Medium: TffVT.6 sec wave. Example of wave associated with anomalous power i n a certain band at Ralston. In t h i s p a r t i c u l a r case, the band i s around T=11.6 sec. 4 2 XSE^T ) o -2 -4 4 2 Y S E( T) 0 -2 -4 4 2 -2 -4 129 Fig... 4 A9 Special Event i n the I n t e r p l a n e t a r y Medium. : T=7.7 sec Have. This type of event i s believed to be responsible for some power enhancements i n the Pel region at Balston. NOV 6,67 (17.8,-26.5.-4.0) 131 regions, has been noted before by Davidson (1964). He divided the spectrum into 17-70 second periods and periods l e s s than 13 seconds. In the l a t t e r region, he i d e n t i f i e d the 10, 5 and 2.5 second "extremely stable" spectral peaks. The region 17-70 seconds, he characterized as the only feature of the spectra strongly dependent on l o c a l time. That i s , both the freguency and occurrence of sp e c t r a l peaks are variable. A very c a r e f u l analysis of the phase spectra indicated that the autospectra could be further resolved. For example, the 20-35 second band seemed to consist of peaks at 33,27, 23 and 20 seconds; i t also indicated that higher freguency peaks are merely harmonics of peaks in that band. The Maximum Entropy Method of spectral analysis has been shown to be exceptional in resolving freguency components; in the next section, we apply t h i s method i n order to get a deeper insight into the spectra. C) Power Spectral Analysis via Autoregressive Models C-1) Method Conventional methods of spectral analysis make un j u s t i f i e d assumptions about the data outside the record length. For example, the periodogram technigue assumes periodic extension of the data. If the record length i s long enough, (of the order of 5-10 periods of the smallest freguency to be studied) the spectrum i s guite independent of these assumptions. However, we want to reduce the record length and therefore, a method i s needed that i s maximally non-committal about the unavailable data. 132 The Maximum Entropy Method (MEM) i s es p e c i a l l y designed for short record lengths. Since this method i s f a i r l y recent and less well-known than the previous, a b r i e f , h e u r i s t i c outline of the method i s presented. The reader i s referred to Smylie et a l . (1973) f o r th e o r e t i c a l considerations i n i t s development and to Dlrych and Bishop (1975) f o r a review, as well as some recent advances. Van den Bos (1971) has shown the eguivalence of the prediction error f i l t e r approach to MEM with the least sguares f i t t i n g of an autoregressive model to the process. Therefore, we use the autoregressive (AB) formulation. Let us assume that we have an n sample time series x t, which we assume to be stationary, r e a l and with zero mean. This time series i s modelled with an order m (n>m) AB process. X t « Z X t - j + (4.8) where the seguence n t i s ca l l e d the innovation of the process; n^ has zero mean and E{ n£ n/} ~ 0 f o i : "t#l. Taking the Fourier Transform of (4.8) X<*> • ± _ tx^l"ivrjO \ =N(t) (4.9) hence, the power spectrum i s l x c *U J J l i i ) ] ! (4.io) 133 I f we set cj;=\N(f)\ the variance of the innovation, the one-sided power spectrum i s ^ ^ ^  \o±4*f„ (4.11) The problem i s now to determine the c o e f f i c i e n t s o i j of the Afi model, assuming the order m known. Multiplying (4.8) by xt-£ a n ^ taking expected values, we get J K * ) = ^ y i f t-J) ^ (4.12) P(o) ^ X * j f^P * = ° ( i |. 1 3 ) where >^(1) = E{ xtxi.^} and we used E{ n^n^} = 0, for l * p . I f the expected values are taken over the n point seguence, the system of eguations (4.12) - (4.13) i s known as the Yule-Walker eguations or as the normal eguations. Cleary, i f the m+1 autocovariances p(k), k=0...m are known, then (4.12) can be solved for the <*^'s» From the point of view of spectral analysis, the estimator i s p a r t i c u l a r l y well suited since i t s mean square error i s generally smaller than that of other estimators. Formally, the estimates obtained via (4.14) can be substituted back into 134 (4.12) and the AR c o e f f i c i e n t s evaluated. The formal solution to (4.12) involves inverting the autocovariance matrix. In practice, t h i s i s very i n e f f i c i e n t i f the order m i s large. The Levinson-Durbin recursive formulae afford a way of computing the c o e f f i c i e n t s of an AR process of order m from a knowledge of the c o e f f i c i e n t s of the process of order m-1. The recursive formulae are written as A - - ^ ^ t ! (4.16 f c o - 2 ; P l i ) The carets indicate an estimate of the »^*s obtained since we started f i r s t of a l l with an estimate of the autocovariances. The seguence <X*\ * j = 1...m i s known as the Yule-Halker estimates of the c o e f f i c i e n t s of the autoregressive process of order m. In th i s method the autocovariance matrix i s Toeplitz ( i . e . eguidiagonal) and semi-positive d e f i n i t e . On the other hand, the fact that the autocovariances are estimated here via (4.14), i s not quite i n the s p i r i t of maximum entropy of being maximally noncommittal about the unknown data. In f a c t , the estimator (4.14) assumes zero extension of the data. Other estimators have dif f e r e n t drawbacks. Furthermore, the Yule-Halker estimates are p a r t i c u l a r l y sensitive to round off errors when the process i s close to the l i m i t of s t a t i o n a r i t y . I t i s therefore desirable to have some other way to estimate the 135 c o e f f i c i e n t s of the AR process. The new method should not r e l y on a prior estimation cf the autocovariances. Let us define the prediction error as the variance of the innovation i n the range of prediction, that i s (4.17) I t i s easy to show that the normal eguations and therefore, the Yule-Walker estimates, actually minimize t h i s guantity with respect to the AR c o e f f i c i e n t s at that p a r t i c u l a r order. Now, i f x t i s stationary, the same Yule-Salker estimates minimize the "reverse" prediction error. (4. 18) Burg ( c f . Burg (1975)) suggested that the errors i n the forward and reverse directions be mimimized together. That i s , the new prediction error i s defined as the sum of the variances of the innovation of both the "forward" and "reverse" auto-regressive model. The solution to the mimimization of e 2 with respect tc the AR c o e f f i c i e n t s uses the recursive formula (4.15) and equation (4.16) i s now modified to 136 (4. 20) where (4.21) This method has the advantage that only the variance of the s i g n a l i s needed and t h i s can be determined from the available data only. The other autocovariances may be determined recursively. As f o r the Yule-Walker estimates, the autocovariance matrix i s Toeplitz and the eigenvalues and the determinant are non-negative d e f i n i t e . There i s a t h i r d method, known as least-sguares estimation, for determining the AS c o e f f i c i e n t s . The method i s e n t i r e l y s i m i l i a r to the way the Yule-walker estimates were obtained, except that the expected values are taken over a d i f f e r e n t range. As i n the previous method, i t minimizes (4.19). However, i n t h i s research, t h i s method i s not used (see Ulrych and Clayton, 1976). In the derivation of the AR c o e f f i c i e n t s , i t was assumed that the order m of the AR model was known. Based on the autoregressive model, a c r i t e r i o n (due to Akaike) has been proposed ( c f . Ulrych and Bishop, op. c i t . ). The Akaike c r i t e r i o n works well for non-harmonic processes. However, our time series do approximate a harmonic process. Therefore, we do not use the Akaike c r i t e r i o n . Instead, we choose a prediction error f i l t e r one sixth the record length, f o r the spectra to be shown here. Too short a f i l t e r r e s u l t s i n highly smoothed 137 spectral estimates, whereas too long a f i l t e r introduces spurious d e t a i l . Extensive tests were conducted to make sure that we are not overresolving the spectra. I t turns out t h i s length of prediction error f i l t e r i s a conservative choice. In practice, an upper l i m i t i s set at half the data length (Ulrych and Bishop, op. c i t . ) . A drawback with HEM i s the lack of a variance estimate. MEM i s known to be asymptotically unbiased and the variance of the MEM estimator tends asymptotically to the estimates of the windowed-periodogram. Here, because of the record length chosen, the method i s not pushed to i t s resolution l i m i t and these considerations are ir r e l e v a n t . The spectral peaks obtained are very stable. In t h i s t h e s i s , the Burg estimates of the AR c o e f f i c i e n t s are used. I t should be remembered that in using t h i s method, we are actually c a l c u l a t i n g the power spectrum of the auto-regressive model f i t t e d to the time s e r i e s , and not the spectrum of the data i t s e l f . C-2) Results The spectra to be presented are calculated from a 256 point time series with the order of the AR process set to 40. The spectra consists of 256 spectral estimates. MEM spectral estimates are actually spectral density estimates and the spectra are therefore integrated with a 5 point boxcar. A l l spectra are i n the same format. The four space components are plotted f i r s t , s h i fted 0, -20, -40, and -50 db to prevent overlap. The two ground components are shifted by 0 and -24 db, respectively. The value of the f i e l d , as well as i t s 138 d i r e c t i o n , i s indicated. Generally, we try to have a time lag of about 8 minutes, between space and ground spectra. As before, the numbers plotted ease the comparison between spectra. The micropulsation signal has been decimated to make i t s sampling rate egual to that of the s a t e l l i t e data. Increased spacing between the compressional and transverse components, indicates the enhanced power i n the l a t t e r . The t o t a l f i e l d spectrum (F) i s plotted to indicate, by comparing i t to Z F A, how successful the f i e l d - a l i g n e d transformation i s . With t h i s higher resolution, shorter length spectra, i t becomes obvious that the spectra depend on the micro structure of the interplanetary medium. Therefore, for each spectra, the interplanetary f i e l d and plasma are checked f o r th e i r constancy or v a r i a b i l i t y ; t h i s i s absolutely necessary i n order to understand them. The f i r s t two examples (figures 4.10, 4.11) are taken from i n t e r v a l s for which the background f i e l d was extremely guiet, even though the density was fluctuating. This i s probably simply due to the presence of upstream waves. For both events, the upstream waves exhibit good waveforms, are strongly l e f t -c i r c u l a r l y polarised and have amplitudes of about 3 ^ f> . In figure 4.10, the T=55 sec peak has most power i n the compressional component and that i s where i t s counterpart cn earth, i s coming from. In figure 4.11, the compressional power i s depressed and agreement i s good with the transverse components. On X , the low freguency peaks seem to be harmonically related, with th e i r fundamental at 120 sec, or else at T=240 sec and then the peaks are interpreted as the even 139 £iSi, i i * . ! 0 . Comparison of Opstream Javes and Micropulsation Spectra on September J 1 x 67. Example of a Pc3 event at Ralston. The ground spectra has picked up power from the compressional component ( T=55 sec ). i 1 1 ~~r 1 1 1 1 1 RALSTON LRG=7 HZ 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 SEC DC 51 26 17 13 10 8.5 7.3 6.4 5.7 5.12 141 F i c j i 4..1.1 Comparison of Upstream Waves and Micropulsation Spectra on October 25 x 67. This figure shows that the compressional power i s low and the micropulsation spectra show agreement with the transverse component. Ik2 CO a LU 3 : O CL LU a LU CO CE o 0 - 1 0 - 2 0 - 3 0 - 4 0 - 5 0 - 6 0 - 7 0 0 •12 - 2 4 -36 -48 -60 -72 n r I 1 1 1 r O C T O B E R 2 5 , 6 7 2 1 : 1 0 . 1 - 2 1 : 2 1 . 0 I M P - F R = 3 1 . " 7 ( 2 2 . 6 , - 2 2 . 1 , 2 . 0 ) 8 = - l l 4>=169 F = 5 . 0 R A L S T O N L f l G = 1 0 HZ 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 S E C DC 51 2 6 17 1 3 10 8.5 7 3 6.4 5.7 5.12 143 £i2i i i i l 2 Comparison of Upstream Saves and Micropulsation Spectra on October 16^ 67. a T=34 sec wave in space and the corresponding Pc3 event on earth. Spectra have very l i t t l e power i n the Pc2 region. 1 1 1 H 1 1 H 1 1 1 1 HZ 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 S E C DC 51 2 6 17 1 3 10 8.5 7.3 6.4 5:7 5.12 145 Z i2 i f i i l J Comparison of Upstream Waves and Microgulsatipn Spectra on September 5 X 67. Example of a wave event near the shock. Note how r i c h in high freguencies (Pc2) the transverse component i s . This i s also obvious by visu a l inspection of the record. For T < 50, the role of the compressional component i s apparent. ike H Z 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 S E C DC 5 1 2 6 17 1 3 10 8.5 7.3 6 4 5.7 5.12 147 Fig.. 4 ..1.4 Comparison of Upstream Waves and Micropulsation Spectra on October 25 x 67. Example showing the eff e c t of compressional power on the micropulsation spectra. The T=132 and 69 sec at Ralston are interpreted as coming from T=146 sec on the compressional component. 148 H Z 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 S E C DC 51 2 6 17 1 3 10 8.5 7 3 6.4 5.7 5.12 149 Fig... 4 Comparison of Upstream Waves and Micropulsation Spectra on Sept J 6 X J 9 6 7 . Example showing the effects of a small jump i n plasma density, coupled with a f i e l d exhibiting compressional "wave a c t i v i t y . The Zp./* shows the f i r s t three harmonics of the T=187 sec wave. The ground spectra has not yet been s i g n i f i c a n t l y affected by the space event. 150 T i i ; i i i i i i I H Z 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 S E C DC 51 2 6 1 7 13 10 8.5 7.3 6.4 5.7 5.12 151 Comparison of Upstream Waves and Micropulsation Spectra on Nov 6^  67. The opposite s i t u a t i o n to Fig. 4.15 i s observed here. The density increase occurred before the time i n t e r v a l considered. Notice how the compressional power associates with the ¥ component, while the transverse power determines the * content of the X component. l 1 1 ;—i 1 1 1 1 r L R G = 8 I 1 1 1 1 1 1 1 1 1 1 HZ 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 S E C DC 51 2 6 17 13 10 8.5 7.3 6.4 5.7 5.12 153 l i f l i H-.ll Comparison of Upstream Haves and Micropulsation Spectra on Oct 26 x 67. This figure exhibits disagreement. This event i s taken from an anomalous day characterized by very low solar wind velocity and high plasma density (see text for d e t a i l s on th i s anomalous day) . T 1 1 p 1 1 1 1 r H Z 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 S E C DC 51 2 6 17 13 10 8.5 7.3 6 4 5.7 5.12 1 5 5 harmonics of th i s fundamental. Also notice, i n both figures, at low freguencies, how the Xp^ component associates best with the East-West component and the Y^A component, with the North-South component at Balston. This i s often the case, that i s , where spectral peaks in space d i f f e r e n t i a t e between the ground components. Overall, bcth figures show good agreement. The next figure (4.12) i s from an i n t e r v a l when the plasma density and v e l o c i t y showed no fluctuations and the background f i e l d was guiet. The waveform i s excellent, c i r c u l a r l y polarised and the amplitude i s from 2-4 *, peak to peak. This f i g u r e shows a Pc3 event. The power i n the compressional component i s extremely low and the power i n the Pc2 region, both in space and on the ground, i s also very low. The spectra on earth indicate that, there was a c t i v i t y i n the Pc4 range, i n space, even though i t was not detected. On t h i s assumption, t h i s example shows the effect of the angle control and the f a c t that i t i s tighter for Pc4 than for Pc3. The low frequency (Pc4 range) on earth, i s very much attenuated compared to the middle frequency Pc3 event. The spectra i n figure 4.13 were calculated less than four hours a f t e r the outbound shock crossing. The magnetic f i e l d plot shows high wave a c t i v i t y in the low freguency range as well as at higher freguencies. I t i s also clear that there i s substantial power i n the compressional component, at low frequencies. C l e a r l y , in figure 4.13, the power in the Pc4 range comes from the Z F A component, while the remainder of the spectra agrees best with the transverse components. The next three examples are from an i n t e r v a l when the solar 156 wind density and the f i e l d were fl u c t u a t i n g . In such case, the compressional components usually have well defined spectral peaks with more power, and therefore play a more important r o l e . For example, in figure 4.14, we interpret the T-132 and 69 sec peaks at Ralston, to be mainly due to the 146 sec compressional wave. Figure 4.15 shows the ef f e c t of a small jump i n density, coupled with a f i e l d exhibiting compressional wave a c t i v i t y . In that f i g u r e , the density increase occurred i n the second half of the i n t e r v a l , and therefore, the space spectra picked up only a l i t t l e of i t s e f f e c t . This e f f e c t i s evident i n the compressional components which exhibits c l e a r l y the f i r s t three even harmonics of a 187 second fundamental. The earth spectra agree well with the transverse components; i t i s apparent, as a shoulder to the l e f t of T=60 sec, that the compressional power i s just s t a r t i n g to be f e l t . The opposite s i t u a t i o n can be seen i n figure 4.16. There, a density increase (3.0 to 5.0/cm3 ) took place at about 13:20 UT. The compressional component has more power due to the remnants of t h i s jump. Notice how the compressional power associates with the Y component, while the tranverse power determines the content of the X component. This i s often the case for such events. F i n a l l y , for t h i s example, there i s very l i t t l e power in the Pc2 freguencies i n space. In fact, except for the 9 sec peak, the compressional power component c a r r i e s more power than the transverse, at high freguency. The l a s t example (figure 4.17) shows disagreement. This event i s again from t h i s anomalous day, October 26, 1967. In the previous section we have mentioned the unusual 157 c h a r a c t e r i s t i c s of that day. Most of the day, compressional wave a c t i v i t y took place as indicated by a varying density, ve l o c i t y and f i e l d strength. Except for a period i n the early morning, where the f i e l d d i r e c t i o n was favourable and the ether parameters less variable, the spectra on t h i s day generally disagree at low freguency ( T > 40 sec). The example shown here, exhibits the poorest o v e r a l l agreement. Even though the high freguency portion of the spectra agrees poorly i n figure 4.17, the other spectra do not seem to be affected by the unusual c h a r a c t e r i s t i c s of t h i s day, i n t h i s freguency range. When due account has been made of the state of the solar plasma and f i e l d , the spectra just discussed, exhibit agreement over the Pc2-4 range. This i s the general picture. I t should be remembered that the propagation c h a r a c t e r i s t i c s of upstream waves have never been studied in d e t a i l . It i s our b e l i e f that some occasionally missing spectral peaks could be understood i f more was known about these waves. Some of the spectral features brought to l i g h t by maximum entropy, could not be r e a l i z e d with conventional methods because of the smoothing window that smears out the d e t a i l s , and also because of the long record length which i s actually eguivalent to producing an average picture. Maximum entropy has confirmed that, at high freguency, some of the sprectal peaks are short-lived. On the basis of some Pc2 peaks always being present on the micropulsation spectra, we believe that t h i s s i t u a t i o n in space, i s more a propagation c h a r a c t e r i s t i c than the peaks actually being s h o r t - l i v e d . From an analysis of nearly 100 MEM spectra of upstream waves, certain features become evident. There seems to be four 158 fundamental waves i n space that can explain a l l the upstream spectra as well as the micropulsation spectra. The f i r s t one i s near 328 seconds. For example, evidence for t h i s peak i s the 164 sec. peak on figu r e 4.17, the 109 sec. peak on figures 4.12, 4.13 and the 82 sec. peaks on figure 4.16. The next fundamental would be below 300 sec. , at approximately 264 seconds. It i s shown c l e a r l y on figure 4.17, some of i t s harmonics on figures 4.14, 4.11(on earth) and also on figure 4.10. Next would be a fundamental between 220-240 sec. »e mentioned previously that i n figure 4.11, the peaks on or X are harmonics of 120 or even harmonics of a 240 second fundamental, & great many spectra show peaks at 73 and 56 seconds, which i s further evidence for that peak. For example, on figure 4.13, the peaks on Y F f t could be interpreted as harmonics of a 232 second peak. These f i r s t three fundamentals have been observed both as transverse and as compressional waves. The l a s t fundamental i s at T-187 seconds. For example, the compressional component in figure 4.15 exhibits i t s f i r s t three even harmonics. The main piece of evidence f o r t h i s peak i s the 94 second peak that often shows on earth, associated with transients and also shows i n space. This mode i s the only one that can be characterized as compressional. I t has nearly always been observed i n conjunction with d i s c o n t i n u i t i e s i n the f i e l d and a density jump in the plasma. On earth, i t seems s t r i c t l y associated with transients. It should be noticed that these fundamentals are deduced only from the low freguency (T>60 sec. ) part of the spectra. 159 Their harmonics are too close to be able to d i f f e r e n t i a t e between the fundamentals at higher freguency. Furthermore, i t seems that spectra always show two of these fundamentals, at any times. This further complicates the picture where, as a r e s u l t of integrating the spectra, some harmonics of the two fundamentals can combine to form a new peak. Patel(1965) in a study of low freguency waves i n the magnetosphere reported the presence of compressional magnetosonic waves with periods in the range 150-200 seconds. Judge and Coleman{1962), i n one of the early s a t e l l i t e experiments, reported a transverse mode with a period of about 200 sec. and a compressional mode with a period near 100 sec. ; however, this analysis was based on only three magnetospheric wave events. F i n a l l y , Burlaga (1968) has reported T=270 and T=180 second waves associated with d i s c o n t i n u i t i e s in the interplanteary medium. These observations support the idea of fundamental modes i n the interplanetary region. D) Some Discrepancies It i s evident that the spectrum of upstream waves cannot explain why certain high freguency peaks on earth, carry so much power. For example, the 15 and 10 second spectral peaks at Balston are very strong and t h i s can d e f i n i t e l y not be explained by t h e i r counterparts i n space. There i s a d e f i n i t e p o s s i b i l i t y that our spectra at T<15 sec. may contain power from Pi1 pulsation event (e.g. HcPherron et a l , 1968). Besides, the magnetosheath, from the f i r s t s a t e l l i t e experiments, was recognized as being extremely r i c h in high frequency (T<15 sec. ) waves. These are two 160 possible explanations for the abnormal power, especially at T=10 sec. , but they w i l l have to wait for further studies to be checked. E) Summary The power spectrum of micropulsation, i n the Pc2-4 range, i s determined by the spectrum of the upstream waves. On a time scale of the order of half an hour, the micropulsation spectrum divides into two regions. The region from 17-100 sec. , i s characterized by v a r i a b i l i t y i n the occurrence and the freguency of i t s spectral peaks. The high freguency region i s composed of extremely stable spectral peaks that can be explained completely by harmonics of fundamentals situated from 20-35 seconds. On a shorter time scale, i t i s found that the micropulsation spectrum i s determined by the peaks, transverse or compressional, that carry most power i n space. In p a r t i c u l a r , some transient pulsations on the ground are seen to associate with spectral peaks i n the compressional components. F i n a l l y , the spectra can be explained by four fundamental waves with periods of approximately 328, 262j 232 and 187 seconds. Of these four modes, only the l a s t one can be c l a s s i f i e d as compressional; the others are at times observed as compressional and as transverse waves. At any given time, the spectra are consistent with the presence of two of these fundamentals. 161 CHAPTER I DISCUSSION OF THE RESULTS AND CONCLUSIONS A) Qn the IMF Direction-Control Because of the close association of upstream saves and micropulsations, we are faced with the question: Are the f i e l d d i r e ctions favourable to Pc3-4 continuous micropulsation a c t i v i t y d i r e c t l y associated with the generation of the space waves, and, i n turn, with the generation of Pc3-4 continuous micropulsations? The answer to t h i s guestion i s simple and r e l i e s on the fact that the condition for observing upstream waves and the conditions on the f i e l d d i r e c t i o n for the occurrence of micropulsation a c t i v i t y , are d i f f e r e n t . When the spacecraft i s far enough from the Sun-Earth l i n e , toward dawn or dusk, i t i s easy to f i n d events where upstream waves are detected because a f i e l d l i n e connects the spacecraft to the shock, and no concurrent micropulsation a c t i v i t y takes place because the f i e l d d i r e c t i o n i s outside the range favourable to their occurrence. Further support i s the f a c t that upstream waves are found to be a nearly permanent feature i n the interplanetary medium ( F a i r f i e l d , 1969}, while there are days with l i t t l e or no micropulsation a c t i v i t y . Because of i t s bowed geometry, the shock wave i s bound to have a l o c a l character; t h i s has been 162 demonstrated experimentally by Greenstadt (1972). Formisano et a l . (1973b) showed that, close to and sunward of the shock, absence of upstream waves corresponds to an IMF and the shock normal making an angle greater than 45 degrees. Upstream waves favour small (<45°) angles between the f i e l d and the shock normal. Hence, taking into account the interplanetary magnetic f i e l d d i s t r i b u t i o n , there should most of the time be some "knowing" region, that i s , a region of space exhibiting some upstream waves (Formisano et a l , 1973c). F i e l d directions nearly tangent to the shock front near the subsolar point, are c l e a r l y net favourable to upstream wave a c t i v i t y . This i s i n l i n e with the fact that upstream waves are more common than micropulsations, and therefore, the f i e l d d irections favourable to Pc3-4 pulsation a c t i v i t y are not d i r e c t l y associated with the generation mechanism i t s e l f . If the waves are nearly always present i n some region of the interplanetary medium, what i s the role of the interplanetary magnetic f i e l d d i r e c t i o n i n determining the occurrence of continuous micropulsations? We believe the d i r e c t i o n of the f i e l d plays two ro l e s . F i r s t l y , the f i e l d d i r e c t i o n determines which region of the magnetosheath i s excited and, i n turn, which region of the subsolar magnetopause i s excited, and how e f f i c i e n t l y . We c l a r i f y these statements below. The bow shock structure and the changes in solar wind density, velocity and temperature across i t , depend strongly on whether or not upstream waves are present (Greenstadt et a l . , 1970a,b,c; Formisano et a l . , 1973a,b,c). Formisano et 163 a l . (1973 op. c i t . ) noted that the maximum amplitude of magnetosheath f i e l d fluctuations observed within one hour of the shock crossing was, on the average, 7 . 7 y when upstream waves were present and only 3 . 9 y when they were absent. Therefore, enhanced fluctuations i n the magnetosheath i s an indicator of upstream wave a c t i v i t y . Extensive measurements of magnetic f i e l d fluctuations i n the sunward hemisphere of the magnetosheath have been performed by F a i r f i e l d and Ness (1970) , They found that wave amplitudes are quite variable on a time scale of hours and days; the amplitudes of the transverse waves are enhanced near the magnetopause and shock front. Mariani et a l . (1970) found that the magnetic energy associated with fluctuations (f<0.05 Hz) on the dawn side of the nightside magnetosheath decreases exponentially with increasing distance transverse to the Sun-Earth l i n e . I f t h i s behaviour i s t y p i c a l of the whole magnetosheath, then c l e a r l y an interplanetary magnetic f i e l d d i r e c t i o n aligned with the Sun-Earth l i n e would provide optimum exc i t a t i o n of the magnetopause. For a f i e l d d i r e c t i o n within 30° of the Sun-Earth l i n e , the whole dayside magnetopause would be subject to the e f f e c t s of the enhanced fluctuations i n the magnetosheath. Secondly, the d i r e c t i o n of the f i e l d plays a key role i n the propagation of upstream waves through the shock. The interaction of hydromagnetic waves with hydromagnetic shocks has been studied by McKenzie and Sestphal ( 1 9 6 8 , 1 9 6 9 , 1 9 7 0 ) , Sestphal and McKenzie ( 1 9 6 9 ) , Mckenzie ( 1 9 7 0 ) , Asseo and Berthomieu (1970). From a hydromagnetic point of 164 view, the bow shock i s a fast shock. This means that the f l u i d v e l o c i t y upstream i s super fast magnetoacoustic, but the vel o c i t y downstream i s sub fast magnetoacoustic and super Alfvenic. For such a shock, there can be no reflected waves and an incident wave gives r i s e to six r e f l e c t e d waves: two Alfven waves (forward and backward), two slow magnetoacoustic waves (forward and backward), one fast magnetoacoustic wave (forward) and one entropy wave (non-propagating). Here, forward (backward) refers to propagation i n the (opposite) d i r e c t i o n of the f l u i d flow. For the special case where the wave vectors l i e i n the shock plane (defined as the plane containing the flow velocity and the magnetic f i e l d ) , the Alfven and magnetosonic waves decouple. In t h i s case, an incident Alfven wave gives r i s e to two refracted Alfven waves. McKenzie and Westphal (1969) found that the magnetic f i e l d amplitude of the transmitted Alfven wave i s about three times larger than the incident amplitude and, i n addition, the generated Alfven wave has a magnetic f i e l d amplitude roughly egual to the incident one. Hence, the magnetic energy density of Alfven waves behind the shock i s approximately ten times greater than i n front. They also pointed out that, f o r strong shocks, the order of amplification i s rather i n s e n s i t i v e to the shock angle (the angle between the upstream flow velocity and the plane of the shock). Therefore, the same order amplification should occur over most of the surface of the bow shock, except on the flanks where the shock i s weak. It i s also shown that for a f l u i d v e locity nearly perpendicular to the plane of the shock, the transmission 165 c o e f f i c i e n t i s larger for small angles between the flow velocity and the f i e l d d i r e c t i o n , but t h i s variation i s not c r i t i c a l . Also, i n t h i s s p e c i a l case, the transmission of Alfven waves through the bow shock i s considerably enhanced i f the Alfven Mach number (MA=Viw/Vft) i s lowered. This i s accomplished by a decrease i n the solar wind ve l o c i t y or an increase i n the Alfven speed. For reasons mentioned before (see Chapter I I ) , the v a r i a t i o n of the Alfven Mach number i s primarily determined by the variation in the density of the solar wind. Fast (slow) streams are associated with smaller (larger) p a r t i c l e density. This i s consistent with the association of larger (smaller) micropulsation amplitudes with larger (smaller) solar wind v e l o c i t i e s . The more general case of an arbitrary orientation of the incident wave vectors has been treated by McKenzie and Mestphal (1970) and, Asseo and Berthomieu (1970). Hhen the incident wave vector i s not in the plane of the upstream velocity and f i e l d (shock plane), the waves couple, i . e . , we cannot separate the e f f e c t s of Alfven waves and magnetoacoustic waves. An incident Alfven wave gives r i s e to a l l s i x types of refracted waves mentioned previously. In t h i s case, the coupling i s determined by the angle between the shock plane and the incident wave vector, and the results are extremely se n s i t i v e to the coupling between the waves (Asseo and Berthomieu, op. c i t . ) . The general case shows that the amplification of the incident energy fluxes and the generation of high energy fluxes i s very d i r e c t i v e . I t also shows (Asseo and Berthomieu, op. c i t . ) that, in general, amplification i s 166 enhanced when the sonic Bach number (M=VSW/VS) grows. This also supports the association of micropulsation amplitudes with solar wind veloci t y . The problem here i s that the di r e c t i o n of the wave vector(s) for upstream waves has been determined. Given the strong dependency of the r e s u l t s of amplification of waves through the shock on the direction of the wave vector (s), i t i s therefore useless to discuss the problem further. It seems that the differences between Pc3 and Pc4, for ' example, the d i r e c t i o n control, the amplitude control and the dir e c t i o n of anisotropy for the angle control, could be explained by a study of their transmission across the shock. The indications are that some aspects of Pc3 (e.g. the weak f i e l d d i r e c t i o n control) are consistent with a wave vector i n the shock plane, while Pc4 would be more consistent with the case in which coupling i s important. This i s supported by a finding of F a i r f i e l d and Ness (1970) that, in the magnetosheath, compressional fluctuations tend to be larger than transverse fluctuations at low frequencies, but transverse amplitudes dominate at higher freguencies. A study of the transmission of waves across the shock has to wait f o r better knowledge of the propagation c h a r a c t e r i s t i c s of upstream waves. This i s a goal for future research. 1 6 7 B) On the Results of Spectral Analysis He mentioned previously that the sp e c t r a l peaks of the upstream waves seem to be harmonics of a few fundamental lew frequencies. The question i s : does t h i s hold i n the rest frame of the plasma? In t h i s frame, the frequency w i s related to the wave vector k and the Alfven v e l o c i t y VA by The measurements are made in a frame of reference p r a c t i c a l l y at rest with respect to the earth. In t h i s s a t e l l i t e frame, the observed frequency i s to* = \ ' { X?" *~ ~* ^ (5.2) where V s w i s the so l a r wind v e l o c i t y . The Dpppler s h i f t in frequency i s given by (5.3) Actually, we are interested i n the r a t i o of the Doppler shi f t e d freguency to the frequency i n the plasma frame, that i s ^ ! = ± + 4 • V * v o (5.4) U3 ~ I f we choose a .field-aligned coordinate system (see figure 168 5 . 1 ) , t h i s eguation can be written as b>l s ± -+• VsvO . CoS (5.5) This eguation i s independent of fi since perpendicular to the flow velocity there i s no floppier s h i f t . Now, i f the spectral peaks are to be harmonically related i n the plasma rest frame, then the LHS of (5 .5) must not be a function of freguency. For a given solar wind state, the constancy of t h i s r a t i o depends O B O ( . I f the angles between the background f i e l d and the projections of the wave vectors onto the xz plane were the same for a l l spectral components, then c l e a r l y , there would also be a harmonic re l a t i o n s h i p i n the rest plasma frame. However, i n practice, we are s t i l l faced with unknown orientations of the wave vectors. The next guestion to be discussed i s : Do the magnetosheath and the magnetosphere behave l i n e a r l y i n the propagation of the upstream waves through these regions? No conclusive answer can be given. The observed low coherencies can be interpreted as additive noise during t h e i r journey through these regions, or else, as meaning that the propagation path i s not li n e a r . This problem i s complicated by the fact that means of detecting the waves i n space and on the ground were d i f f e r e n t . F i n a l l y , we have observed a tendency for the period of pulsations to associate with the strength of the interplanetary magnetic f i e l d . Higher frequencies correspond to larger f i e l d strengths and, vice versa, lower frequencies to weaker f i e l d s . This i s in l i n e with results of Russian researchers (see 169 Fig.. 5JS,1 f i e l d - a l i g n e d Coordinate System. The angle fi i s the elevation of the wave vector with respect to the BV plane. The solar wind velocity l i e s i n the X,Z plane. 170 171 Chapter II) that the micropulsation period varies with the f i e l d strength. This i s not the main theme and, consequently, t h i s tendency was observed only for the dominant freguency component of the spectrum. The same tendency was observed for upstream waves ( F a i r f i e l d 1969; and also i n t h i s research). C) Theoretical Implications Many attempts have been made to explain Pc3-5 magnetic pulsations using the cold plasma MHD equations, in order tc determine the eigenmodes of the magnetosphere (e.g. Watanabe, 1961;8adoski, 1967). fihen the azimuthal eigenmode number m ( for e i w ^ dependency) i s f i n i t e , the t o r o i d a l and poloidal modes are coupled and no eigen o s c i l l a t i o n s of a f i e l d l i n e are possible. The problem arises because adjacent f i e l d l i n e s have di f f e r e n t resonant freguencies and so, a resonating f i e l d l i n e tends to "pump" i t s neighbours (Southwood 1974). A more sophisticated model has been presented by Hasegawa and Chen (1974). There, the continuous pulsations are explained by a resonant Alfven wave excitation of a l o c a l f i e l d l i n e with a monochromatic wave generated at the magnetopause. They remarked that to excite a l o c a l f i e l d l i n e i t i s necessary to have a monochromatic Alfven wave as an excitor. For the possible excitor, a l l theories r e l y on a wave excited at the magnetopause by a MHD Kelvin-Helmholtz i n s t a b i l i t y (e.g. Sen, 1963; Boiler and Stolov, 1970). In view of the present r e s u l t s , t h i s i s c l e a r l y not the case. The input to the magnetosphere i s a spectrui o f waves originating i n the interplanetary medium. 172 0) Conclusions The physical picture for Pc3-4 continuous pulsations i s cl e a r . Their occurrence i s determined by the d i r e c t i o n of the interplanetary magnetic f i e l d and t h e i r amplitudes are controlled by the f i e l d d i r e c t i o n and the solar wind ve l o c i t y . Furthermore, the present analysis indicates that, at least for the dominant freguency component, the freguency varies with the f i e l d strength. F i n a l l y , the spectrum of Pc2-4 micropulsations i s determined by the spectrum of the upstream waves. Therefore, under the r e s t r i c t i o n of t h i s analysis, Pc2-4 continuous pulsations ultimately come from the interplanetary medium. In chapter IV, i t was mentioned that, often there i s an intimate relationship between the i n d i v i d u a l components i n space and on earth. Hore s p e c i f i c a l l y , a p a r t i c u l a r component i n space i s found to associate with a p a r t i c u l a r component on the ground. This c e r t a i n l y constitutes one of the outstanding unresolved problems. It c l e a r l y indicates, at least for those events, a very peculiar propagation of the waves i n the magneto-sheath and in the magnetosphere. This problem can only be solved by a study of wave propagation i n these two regions. Another unresolved problem i s determining the direction(s) of the wave normals for upstream waves. Without this information, the usefulness of theories of t h e i r propagation through the shock i s greatly reduced and progress i n the understanding of the phenomenon at hand has to wait for experimental r e s u l t s . F i n a l l y , i t i s indeed remarkable that a phenomenon i n appearance as t r i v i a l as micropulsation, can y i e l d so much 173 information on the interplanetary medium and some of the dynamical processes occuring therein. 174 BIBLIOGRAPHY Asseo, E., and G, Berthomieu, Amplification of hydromagnetic waves through the earth's bow shock, Planet. Space S c i . , 18, 1143, 1970 Axford, fl.I., Magnetospheric Convection, Rev. of Geophjsics, 7, 421, 1969 Behannon, K. W. , Mapping of the earth's bow shock and magnetic t a i l by Explorer 33, J. Geophys. Res., 73, 907,1968 Behannon, K. W., K. H. Schatten, D. H. F a i r f i e l d , and N. F. Ness, Trajectories of Explorers 33, 34, and 35. July 1966 A p r i l 1969, NASA Tech. Rept., X - 692 - 70 - 64, 1970 Belcher, J. 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