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World-wide changes in the geomagnetic field Nishida, Atsuhiro 1962

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WORLD-WIDE CHANGES IN THE GEOMAGNETIC FIELD by ATSUHIRO Nl SHIDA B.Sc , University of Tokyo, 1958 M.Sc, University of Tokyo, 1960 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in the Department of PHYSICS We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA September, 1962 In presenting this thesis in p a r t i a l fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make i t 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 i s understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department The University of British Columbia, Vancouver 8, Canada. Date PUBLICATIONS 1. Nishida, A. and N. Fukushima. Three dimensional consideration for current-system of geomagnetic variations (II) Sq-field, Report of Ionosphere and Space Research in Japan L3, 273-282, 1959. 2. Nishida, A. On the earth storm II. Stability of solar corpuscular stream. Report of Ionosphere and Space Research in Japan 14, 250-258, 1960. 3. Nishida, A. and J.A. Jacobs. World-wide changes in the geomagnetic f i e l d . Journal of Geophysical Research _67, 525-540, 1962. 4. Nishida, A. and J.A. Jacobs. World-wide changes in the geomagnetic fi e l d . Journal of the Physical Society of Japan _17, A l l , 55-63, 1962. 5. Nishida, A. and J.A. Jacobs. Equatorial enhancement of world-wide changes. Journal of Geophysical Research 6]_, 1962 (in press). The University of British Columbia FACULTY OF GRADUATE STUDIES PROGRAMME OF THE FINAL ORAL EXAMINATION FOR THE DEGREE OF DOCTOR OF PHILOSOPHY of ATSUHIRO NISHIDA B.Sc, University of Tokyo, 1958 M.Sc, University of Tokyo, 1960 TUESDAY, SEPTEMBER 25, 1962, at 10:30 A. IN ROOM 301, PHYSICS BUILDING COMMITTEE IN CHARGE Chairman: F.H. SOWARD A.J. BARNARD F.K. BOWERS R.E. BURGESS K.L. ERDMAN CHARLOTTE FROESE J.A. JACOBS J.C. SAVAGE P.R. SMY External Examiner: CO. HINES Defence Research Board, Ottawa WORLD-WIDE CHANGES IN THE GEOMAGNETIC FIELD ABSTRACT The geomagnetic field is found to change quite frequently on a world-wide scale. In the three months' period near sunspot maximum, such changes are found on 90 per cent of a l l days. Most of these changes are not registered either as sudden commencements or as sudden impulses, and are tentatively called in this thesis 'world-wide changes'. The frequent occurrence of world-wide changes seems to be consistent with the idea that world-wide features of the geomagnetic field are always influenced by a permanently flowing corpuscular stream from the sun. The physical state of the corpuscular stream may be as variable as that of the solar atmosphere, and sudden changes in it will give rise to sudden, world-wide changes in the geomagnetic field. The morphology of world-wide changes is studied, and the form of the change, the distribution of magnitude and the mode of spreading over the earth are clarified. It is found that world-wide changes can be classified into two groups according to the sign of the main part of the change which appears all over the world. Those with an increase in the total force are called positive changes and those with a decrease are called negative changes. Except for the sign of the change, negative changes are morphologically indentical to positive changes, Since the morphology of sudden commencements and sudden impulses is the same as that of world-wide changes, they must be produced by a common mechanism, and an explanation of negative changes is a new,"fundamental requirement imposed upon any theory of these changes. The observed change in the geomagnetic field may originate at the magnetospheric boundary where the solar corpuscular stream interacts with the geomagnetic field. The change may be modulated by the screening effect of the ionosphere before it is observed at ground level. Although this effect has been shown to be negligible for changes with a time scale of the order of world-wide changes, incorrect assumptions have been made in existing theories. More accurate calculations show that this effect is actually significant for a certain mode of the incident field. . From these results, a physical picture is obtained of events taking place at the magneto-spheric boundary at the time of world-wide changes, and the cause of such events is considered. It seems that positive and negative changes correspond to a sudden increase and a sudden decrease respectively in the intensity of the solar corpus-cular stream. The main part of the change which is observed a l l over the world may result from the sudden change in the impact pressure of the stream on the magnetosphere, and the reverse change which precedes the main part of the change on the after-noon side of the Earth may be due to a sudden change in the shear stress exerted on the matnetosphere as the stream passes by. Field of Study: Geomagnetism and aeronomy Electromagnetic Theory Elementary Quantum Mechanics Theory of Relativity Geomagnetism Related Studies: GRADUATE STUDIES G„M„ Volkoff W. Opechowski P. Rastall J„As Jacobs Applied Digital Electronics Computers M.P. Beddoes H. Dempster i i ABSTRACT The geomagnetic f i e l d i s found to change quite frequently on a world-wide scale. In the three months' period near sunspot maximum, such changes are found on 90 "per cent of a l l days. Most of these changes are not registered either as sudden commencements or as sudden impulses, and are tentatively called in this thesis 'world-wide changes'. The frequent occurrence of world-wide changes seems to be consistent with the idea that world-wide features of the geomagnetic f i e l d are always influenced by a permanently flowing corpuscular stream from the sun. The physical state of the corpuscular stream may be as variable as that of the solar atmosphere, and sudden changes In i t w i l l give rise to sudden, world-wide changes in the geomag-netic f i e l d . The morphology of world-wide changes i s studied, and the form of the change, the distribution of magnitude and the mode of spreading over the earth are c l a r i f i e d . It i s found that world-wide changes can be classified into two groups according to the sign of the main part of the change which appears a l l over the world. Those with an increase in the total force are called positive changes and those with a decrease are oalled negative changes. Except for the sign of the change, negative changes are morphologically identical i i i to positive changes. Since the morphology of sudden commencements and sudden impulses is the same as that of world-wide changes, they must be produced by a common mechanism, and an explanation of negative changes i s a new, fundamental requirement imposed upon any theory of these changes. The observed change in the geomagnetic f i e l d may originate at the magnetospheric boundary where the solar corpuscular stream interacts with the geomagnetic f i e l d . The change may be modulated by the screening effeot of the ionosphere before i t i s observed at ground level. Although this effeot has been shown to be negligible for changes with a time scale of the order of world-wide changes, incorrect assumptions have been made in existing theories. More accurate calculations show that this effect i s actually significant for a certain mode of the incident f i e l d . From these results, a physical picture i s obtained of events taking place at the magnetospheric boundary at the time of world-wide changes, and the cause of such events i s considered. It seems that positive and negative changes correspond to a sudden increase and a sudden decrease of the Intensity of the solar corpuscular stream respectively. The main part of the change which i s observed a l l over the world seems to result from the sudden change in the impact pressure of the stream on the magnetosphere, and the i v reverse change which precedes the main part of the change on the afternoon side of the Earth may be due to a sudden change in the shear stress exerted on the matnetosphere as the stream passes by. v i i i ACKNOWLEDGMENTS I wish to express my gratitude to Profo Jo ko Jacobs for his kind encouragement and advice throughout this work, and for making i t possible for me to work here,, I should like to thank Dr« To Watanabe and Dr. K 0 Yanagihara for the Instructive discussionso I wish to appreciate the kind help given by Dr„ Veldkamp and the IGY Data Center A in obtaining the data* This work i s financially supported by the Office of Naval Research under contract Norr 3116 (00). V TABLE OF CONTENTS Page I INTRODUCTION 1 II MORPHOLOGY OF WORLD-WIDE CHANGES 13 1. Data 13 2. Form of the change 23 3. Distribution of the time of onset 31 4. Distribution of the magnitude of the change .. 40 5. Related phenomena 49 6. Summary 54 III IONOSPHERIC SCREENING EFFECT 65 1. Electromagnetic f i e l d in the neutral atmosphere 65 2. Field lh the ionosphere 75 . 3. Field i n the magnetosphere 85 Appendix A 96 Appendix B 98 IV THEORY OF WORLD-WIDE CHANGES 104 V CONCLUSION 121 APPENDIX I CLASSIFICATION OF SUDDEN IMPULSES IN THE GEOMAGNETIC FIELD 125 .APPENDIX II THE OBMIC LAW IN THE UPPER ATMOSPHERE .. . 134 1. Introduction 134 2. Fundamental equations 136 3. The Ohmic law 142 BIBLIOGRAPHY 162 v i LIST OF FIGURES Page 1. Examples of world-wide changes in the geomagnetic 2. Locations of geomagnetic stations 20 3. Comparison of magnetograms covering world-wide 4. Examples of following reverse change ............ 25 5. Region where following reverse change i s found .. 27 6. Examples of preoeding reverse change .» 28 7. Region where preceding reverse change i s found 50 8. Schematic i l l u s t r a t i o n of the three parts of OllEliQ^Q a « « « « « * * * o o « o o « s o « * o o o e « * « o « o * » » * « * o o o « « 0 u 32 9. Method used in obtaining the local time dependence curve of time of onset in low latitudes ......... 34 10. Local time dependence of the time of onset in low jL.£l t 1 fcUCl© S o o » o « o » » o » * » 9 o o o e a o 6 « o o o o o » » * » 0 o o » 0 * o * o 35 11. Difference in time of onset at middle-high latitude stations from that at low-latitude S tjQ. t .1^ 0X13 • o e o o o o o 0 o e o e o « « o o e 0 e » * « * « o * « 0 * o e * o o e o o o 37 12. Isochronlc curve of the time of onset 38 13. Distribution of magnitude of world-wide changes . 41a 41b 14. Latitude dependence of the magnitude 43 15. Equatorial enhancement of a sudden commencement . 45 16. Equatorial enhancement of a positive change 47 17. Equatorial enhancement of a negative change ..... 48 18. Variation of various characteristic Indices in Ap r i l , 1958 53 19. Distribution of the horizontal component of a world-wide change for three stages of the change 57-59 20. Equivalent overhead current system corresponding to figure 19 „ 61-63 21. Vectors of the observed and incident fields (mode 1) I l l 22. Vectors of the observed and incident fields (mode 2) 115 23. Configuration of lines of force 123 24. Examples of sudden impulses 129 25. Distribution of the conductivity with height .... 156 v i i LIST OF TABLES Page 1 . List of time.s of world-wide changes 1 4 - 1 8 2 « Ratio of the magnitude of the change at Koror t O t i l Sit £ t t 0*1X3111 o e * e o « « e g o « * « » « o * 0 * o o o « O 9 * * « * « » « 46 3 . Ionospheric stations 5 0 4 o Observatories recording ionospheric absorption . 5 2 5 . Observatories recording night airglow . 5 2 7 . E l e c t r i c a l conductivity in the ionosphere . 1 5 5 8 . Check of the uniformity of the magnetosphere ... 1 6 1 CHAPTER I INTRODUCTION It i s known that there are sudden changes in the geomagnetic f i e l d which appear almost simultaneously a l l over the world with certain features in common. When such a change marks the beginning of an interval of increased activity, i t i s called a sudden commencement, which i s classified as ssc or ssc* depending on i t s detailed features. (The present o f f i c i a l classification of sudden commencements seems to present certain d i f f i c u l t i e s . These are discussed in Appendix I ) . Chapman and Eerraro (1931) related a sudden commencement to the approach of a solar corpuscular stream towards the earth. The existence of a solar corpuscular stream was presented by them as a hypothesis, but later observations have testified the correctness of this hypothesis. These observations are: (1) The existence of a solar corpuscular stream at about 1 A.U. was inferred by Biermann (1957) from observations of comet t a i l s . He showed that the form and the degree of ionization of a comet t a i l could not be explained solely by electromagnetic radiation from the sun and that at 1 A.U. there might exist corpuscular radiation from the sun with a 2 -3 -i density of 10 cm and a velocity of 500 km sec - J- when the 4 -3 sun i s quiet, and with a density of 10 cm and a velocity of 1500 km sec" when the sun i s active. (2) Those sudden commencements which are preceded by an increase in - 2 -the absorption of radio waves over the polar cap can be correlated with solar flares accompanied by type IV radio bursts (Sinno and Hakura, 1958), and (3) Direct observa-tion of a corpuscular stream has been obtained by space vehicles, and an increase In i t s intensity has been observed at the time of a sudden commencement (IG-Y Bulletin, 1962)o The main feature of a sudden commencement i s an increase in the horizontal component of the geomagnetic f i e l d . This occurs with a time scale of the order of a few minutes and appears a l l over the world. Chapman and Ferraro originally demonstrated that this can be produced when a highly ionized corpuscular stream i s propagated from the sun across the empty space between the sun and earth. The additional magnetic f i e l d due to the Induction current produced on the surface of the stream by the intrusion of the highly conductive corpuscular stream into the geomagnetic f i e l d can be represented approximately, outside the stream, by an image of the geomagnetic f i e l d with respect to the surface of the stream, thus resulting in an increase in the horizontal component of the magnetic f i e l d as observed at the surface of the eartho This theory has been modified since i t has now been shown that the space inside the geomagnetic f i e l d i s f i l l e d with sufficient plasma to be a good ele c t r i c a l conductor (Storey, 1953: Pope, 1961). It i s now considered that the geomagnetic f i e l d Is always - 3 -confined to a region of f i n i t e dimensions by the impact pressure of a continuously flowing corpuscular stream. The space occupied by the geomagnetic f i e l d is compressed when the impact pressure of the corpuscular stream is increased. The resulting increase in the geomagnetic f i e l d i s trans-mitted to the surface of the earth as a magnetohydrodynamlc wave (Dungey, 1954; Hoyle, 1956; Parker, 1958; Obayashi, 1958; Dessler and Parker, 1959; Francis, Green and Dossier, 1959; Plddington, I960; Dessler, Francis and Parker, 1960; and Beard, 1960, 1962). The overall Increase of the horizontal component (which w i l l be called the main change) i s accompanied, in particular regions of the earth determined by latitude and local time, by two kinds of decreases In the horizontal component (Nagata, 1952; Oguti, 1956; Obayashi and Jacobs, 1957; Abe, 1959; and Matsushita, I960). The f i r s t type (which w i l l be called a preceding reverse change) precedes the main change and occurs mostly on the afternoon side of the earth. The second type (which w i l l be called a following reverse change) follows the main change In high latitude regions in the morning hours. These have been attributed largely to electric currents flowing in the ion-osphere, and an atmospheric dynamo action (Obayashi and Jacobs, 1957) or the separate injection of positive and negative particles into the ionosphere at high latitudes (Vestine and Kern, 1962) have been suggested as possible - 4 -causes. Singer (1957), on the other hand, considered as a possible cause of the f i r s t type of decrease an extension of the auroral zone magnetic tubes of force by the intrusion of the corpuscular stream into the geomagnetic f i e l d , Wilson and Sugiura (1961) studied the sense of rotation of the horizontal magnetic vector instead of noting the change in the horizontal component, and attributed the resulting regularity in the sense of rotation to the incidence of a transverse magnetohydrodynamic wave due to the deformation of the magnetosphere by the solar corpuscular stream. So far, no general agreement has been reached concerning the mechanism responsible for these reverse changes. When a sudden change appears almost simultaneously a l l over the world, but not followed by an interval of increased activity, i t is called a sudden impulse. Exoept for the lack of association with an Interval of increased activity, sudden impulses have the same characteristics as sudden commencements (Jackson, 1952; Ferraro, Parkinson and Unthank, 1951; Matsushita, 1962), and are attributed also to a solar corpuscular stream. The difference between sudden commencements and sudden impulses may result from the difference in the energy spectrum of the corpuscular stream. « # # # # Thus, two kinds of sudden, world-wide changes in - 5 -the geomagnetic f i e l d (sudden commencements and sudden impulses) have been known and studied. In the geophysical and solar data of the Journal of Geophysical Research several sudden commencements and sudden impulses are liste d each month from reports obtained from stations distributed a l l over the world. From the viewpoint of theories of these changes summarized above, the reported number of occurrences seems to be rather too small. Through the medium of the continuously flowing solar corpuscular stream, world-wide features of the geomagnetic f i e l d are always related, with some time lag, to the physical state of the sun. Since the physical state of the solar atmosphere i s known to be quite variable, i t seems reasonable to expect world-wide changes in the geomagnetic f i e l d to occur quite frequently. Hence magnetograms have been examined to find hitherto unnoticed changes recorded almost simultaneously a l l over the world. Data were obtained over a three-month period during the IGT from an extensive network of stations. Results are presented in Chapter I I . It was found, as was expected, that world-wide changes in the geomagnetic f i e l d take place almost every day, at least around sunspot maximum. Sometimes i t was found that magnetograms from a l l over the world showed similar traces for several hours. These changes are morphologically identical to sudden commencements (regardless of the activity in the following interval) and sudden impulses. However, many of these - 6 -changes are not listed as sudden commencements or sudden Impulses by a single station,, These have been l e f t unnoticed, possibly because their intensities are small (mostly less than a few tens of gammas in middle and low latitudes)* and because they do not give a strong impression of an impulse since they occur so frequently that they seldom appear isolated. Partly to distinguish these newly-found changes from the already known and confusingly defined sudden Impulses and partly to stress their morphological, Instead of their configurational, characteristics, these changes w i l l be called in this thesis 'world-wide * change s. * * * # * The frequent occurrence of world-wide changes supports the idea that sudden changes in the geomagnetic f i e l d appear on a world-wide scale as a result of a sudden and sharp change in the physical state of the solar corpus-cular stream. Moreover, the present study of world-wide changes has revealed another fact that imposes a new requirement on any theory of a l l types of world-wide changes. This fact i s that not only a sudden increase in the horizon-t a l component, but also a sudden decrease in i t , is found to occur on a world-wide scale. Changes w i l l be called 'positive' or 'negative' according to the sign of the main - 7 -change. Except for the sign of the overall change, negative changes are morphologically identical to positive changes. In regions where reverse changes appear as a decrease in the horizontal component in association with positive changes, an increase in i t i s found in the case of negative changes. This indicates that positive and negative changes are produced by a mechanism which can work equally well for both senses of the change. Since sudden commencements, sudden impulses and world-wide changes show identical features (regardless of the activity in the following interval),these must originate from the same mechanism. Thus any theory of sudden commencements and sudden impulses must also be able to explain world-wide changes, both positive and negative. Suggested theories of sudden commencements are now examined from this point of view. Two regions have been considered as possible places where the change in the elec-tromagnetic f i e l d originates. These are the magnetospheric boundary and the ionosphere. In cases where the former i s assumed, the ehange in the electromagnetic f i e l d i s considered to result directly from the interaction between the solar corpuscular stream and the magnetosphere. This idea Is adopted in a l l theories of the main change but only by Wilson and Sugiura (1961) for the preceding reverse change. Mechanisms described by them may be applied to negative changes merely by replacing an increase by a - 8 -decrease in the intensity of the solar corpuscular stream} but in theories where the ionosphere i s considered as the position of the source of the ehange in the electromagnetic f i e l d , an extension to negative changes involves a problem. An ionospheric source i s assumed in most theories of the preceding reverse change and the following reverse change, and according to them an essential role Is played by the intrusion of an aggregate of charged particles into the ionosphere at high latitudes. This aggregate of charged particles i s assigned certain properties which vary depend-ing on the author. Thus i t is polarized in a certain way (Yestine and Kern, 1962), or i t is able to create a s u f f i -cient increase in the ionospheric conductivity (Obayashi and Jacobs, 1957), or i t i s intense enough to distort the configuration of the auroral zone lines of force (Singer, 1957). With these properties, this aggregate of charged particles has been shown to produee the ionospheric current system which gives rise to the observed change In the geomagnetic f i e l d . Hence to explain a negative change by an extension of this type of theory, one of the following mechanisms must be proved to be possible. These are: (1) An outflow, instead of an inflow, of particles from the ionosphere to the outside; (2) The creation of a polarization opposite to that required for sudden commencements; and (3) The permanent presence of the intrusion of charged particles whose intensity experiences a sudden decrease, as - 9 -well as a sudden increase. Of these mechanisms, the f i r s t may be impossible since such an acceleration of charged particles in the ionosphere i s hard to understand. The second and third may be possible, but they imply the presence of a complicated mechanism which has not so far been detected by any observations«, Hence the magnetospherio boundary, rather than the Ionosphere, seems to be more promising as the position of the source of the observed changes in the electromagnetic f i e l d . # # # # # The observed changes in the geomagnetic f i e l d are assumed to originate at the magnetospherio boundary. In this case, the f i e l d may be modulated during i t s propaga-tion through the space between the source and the ground. To investigate the nature of i t s origin, therefore, i t Is necessary to eliminate the Influenoe of the intermediate medium. It i s particularly important to eliminate any modu-lation by the ionosphere - the lowest part of the upper atmosphere. For phenomena with a time scale of the order of world-wide changes (1 to 10 see), the medium of the ionosphere behaves as a metallic conductor with high ani-sotropic conductivity, while the upper part of the atmosphere is the medium for magnetohydro&ynamlc wave propagation, as shown in Appendix I I . Hence, by eliminating modulation by - 10 -the ionosphere, that i s , the effect of ionospheric screening, direct information about the origin of the observed changes in the geo-electromagnetic f i e l d can be obtained. A general discussion of ionospheric screening i s presented in Chapter III. The screening effect of the ionosphere has been discussed by various authors (Ashour and Price, 1948; Sugiura, 1949 and 1950; Watanabe, 1957; Francis and Karplus, 1960). They concluded that the screen-ing effect is negligible for changes with a time scale longer than about 1 sec, and thus for most of the phenomena of interest in geomagnetism, ionospheric screening need not be taken into account. Hence the observed f i e l d has been regarded as equivalent to that incident on the ionosphere. However, these results are based on questionable approximations. In their estimation of the ionospheric screening effect, the observed f i e l d was represented either by (1) an electromagnetic wave (e.g. by Francis and Karplus) or (2) a magnetostatic f i e l d (e.g. by Sugiura). Neither i s an exact representation of the observed f i e l d , since (1) the observed f i e l d varies horizontally with a characteristic 8 scale of the order of 10 cm, which i s far smaller than the wavelength of an electromagnetic wave with a period longer than 1 sec, and (2) as far as the observed f i e l d is time dependent, the displacement current i s not exactly zero, and the f i e l d in the neutral atmosphere is not exactly - 11 -magnetostatie. Therefore certain errors must be intro-duced by adopting these approximate representations. However, the above authors did not estimate these errors and verify the applicability of the approximations. Hence an attempt i s made to relate the observed f i e l d with the f i e l d incident on the ionosphere avoiding the above approximations. The general solution of Maxwell's equations near the highly conductive earth i s used to represent the observed f i e l d . It is found that the degree of ionospheric screening depends not only on the scale in,, time, but also on the scale in space and on the mode of the incident f i e l d . In the case when the time scale i s about 2 10- 10 sec and the scale of the horizontal distribution on the ground i s about 10 cm, as they are for world-wide changes, the results show that (1) for a certain mode screening may not be effective and the observed f i e l d is well approximated by the magnetostatic f i e l d , but (2) for another mode screening may have a significant effect. For this case a magnetostatic f i e l d i s a poor approximation for the observed f i e l d although i t may be impossible to detect the difference with the present accuracy of observations. * * * * * Using this result, the incident f i e l d corresponding to the main and preceding reverse changes i s derived and a - 12 -model ©f these changes is constructed In Chapter I V o It Is found that for the main change ionospheric screening Is not effective, and this part of the change may be explained by the compression (for a positive change) or by the expansion (for a negative change) of the magnetosphere due to a sudden change in the impact pressure of the solar corpuscular stream,, But for the preceding reverse change, screening i s significant and the incident f i e l d differs in direction by 90° from the observed f i e l d . This part of the change can be interpreted as a result of the deformation of the magnetosphere produced by the blowing of the lines of force towards the night side by the shear stress exerted by the solar corpuscular stream,, - 13 -CHAPTER I I MORPHOLOGY OP WORLD-WIDE CHANGES 1. Data Magnetograms were compared from several widely-separated stations: Hartland (54.6°N, 79o0°) (geomagnetic coordinates are used throughout), Fredericksburg (49.6°N, 349 09°), T b i l i s i (36.8°N, 122.0°), .Honolulu (21.0°N, 266.4°), and Hermanus (33.3°S, 80.3°)• Changes that were recorded almost simultaneously at a l l of them were selected. During the 3-month interval from April to June 1958, which Is around sunspot maximum, at least 20 per cent of a l l 1-hour periods and at least 90 per cent of a l l days contain at least one such change. These are lis t e d In Table 1. For a study of the morphology of these changes, 24 of the larger ones were randomly selected. They are shown in Figure 1 by arrows on magnetograms from Honolulu. Magnetograms from 20 stations, most of which are uniformly distributed in middle- and low-latitude zones in the northern hemisphere as shown in Figure 2, were obtained from the IGY World Data Center. Although data were collected also from high-latitude stations, they could not be used in this analysis, because the phenomena studied were almost always obscured by local disturbances. The data confirm that - 14 -Table 1. List of times of world-wide changes In the  geomagnetic f i e l d from Ap r i l to June 1958. When more than one change was found during any one hour period, the largest has been tabulated. Negative changes are shown by writing the time in parenthesis. Date Ap r i l 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 Time of Occurrence (GMT). 0230, 0540, 0750, (0820), 0910, (1010), (1250), 1320, (1430), 1510, 1650> 1740, 1810, (1930), 2030. 0330, (1820). (1420), 2050, 2150. (2140), 2220, 2310. 0000, 0520, 0820, 1100, (2320). 0540. 1530, (1710),(2010), 2200, 2320. 0710, (0930). 0050, (0130), 0230, (0410), (0900), (1640), (1730), 1950, 2030, 2130. (0400), (1010), 1440, 1720, 2040, (2300). (0140), (0540), (0720), 1410, 1720, 1820. 0910, 1010, 1130, 1220, (1330), 1500, 1650, (1800), (2040), (2220), (233 0). (1120), (1400). 1910, 2210, (2330) 0500, 1540. - 15 -Table 1. (cont'd) Date Apri l 20 21 22 23 24 2 5 26 27 28 29 30 2 3 4 5 6 7 8 Time of Occurrence (GMT) May 10 11 12 1900, (2300). 1120, 1830, 2300. 0120, (0220), (0540), (1310), 2050. 1250, 1350, (1440), 1530, (1610), 1710, 1820, 1910, 2110, 2230, 2340. 1230, 1350, 1530. 0030, (0740). 0100 (1050), 1520, 1620. 1730, 1840. 0130, 0250. (0120), (0740), 1050. 0140, (0120), 0220, 0500, 1250, 1350, 1800, (1930), 2240. 0100, 0520, 0650, (0740), (0820), 1110, (1200), (1330), (1540). 1340, 1650, 200, 2140. 0100, 0200, 1510. (0140), 0430, (1520), 1700, (1750), 1810, 2010. - 16 -Table 1. (cont'd) Date Time of Occurrence (GMT) May 13 0500, 8140, 2230, (2310), 14 (0020), 1720, 2130, (2220), 2300. 15 0220, (0930), 1010, 1320, 2050. 16 1300. 17 18 1010. 19 20 0030, 1100, 2310. 21 0100, 0320, (0410), 0500, 1730, 1850, (1930), 2200. 22 23 0220. 24 25 0310, (0650), 1040, (1530), 1620, (1730), (1830), 2000, 2300.• 26 (0240), 0310, (0720), 1050, 1610, 2320. 27 0030, 1100, 1240, 1330, 1350, 1500, 1920, (2000), (2110). 28 29 0420, (0810), (1040), (1350), 1520, 1720, (2330). 30 0110, 0820. 31 (1350), 1650. June 2 0410, (0830), 1020, 1210, 1450, (1810). 3 0250. 4 - 17 -Table 1. (cont'd) Date Time of Occurrence (GMT) June 5 0040, 0430, (0910), 2100. 6 0920, 1100, 1840, 1930, (2010). 7 0040, 1820, 2100. 8 1040, (1320), 1600, 1730, (1850), 1920, (2010), 2150, (2250), 2320. 9 0000, 0440, 0630, (1450), 1530, 1620, 1750, (1940), 2340. 10 0020, 1200, (1350), (2110). 11 0120, (1010), 1520, 1850. 12 0010, 1140, (1920), 2220. 13 0240, 1650. 14 1830, 2110. 15 0230, 0510, 0630, 0710, (0930), 1210, (1410),1540. 16 0600, (1320). 17 2020, 2220. 18 0040, (0950), 1150, 1240, (1440), (1940), (2000), (2200), (2300), 2350. 19 0340, (0800), 0950, 1050, 1500, (1610), (1940), 2230. 20 (0240), (1130), (1320), 1820, 1900. 21 0210, (1130), (1200). 22 1010, 2020. 23 1040, 1630, 2300. 24 1050. 25 (1400), 1510, 2150. - 18 -Table 1. (cont'd) Date Time of Occurrence (GMT) June 26 2130. 27 (2050). 28 0710, (0940), (1250), 1740, 1800, (1900), 2120. 29 - 19 -Figure 1. Examples of world-wide changes in the geomagnetic f i e l d (indicated by arrows) shown by the horizontal intensity magnetogram from Honolulu. Figure 2. Locations of"geomagne tilGestations,1 data"from which are used for analysis. From stations shown by closed dots, normal-run magnetograms are available; from those shown by open dots, normal- and rapid-run magnetograms are available. - 21 -these changes are of world-wide character, as can be seen by the examples in Figure 3. Among these changes are included those with a decrease as well as those with an increase in the horizontal intensity. The world-wide changes with a decrease in horizontal intensity are not the immediate recovery from an increase in i t , like the recovery following a sudden impulse; although they mostly appear after an increase in the horizontal intensity, some tens of minutes usually pass between the two changes, and their magnitude frequently exceeds that of the preceding increase. Thus i t seems proper to regard changes having a deorease in the horizontal component as independent phenomena. Changes having an increase in the horizontal intensity w i l l be referred to as 'positive changes' and those with a decrease as 'negative changes'. Since the change in vertical intensity i s far smaller than that in the horizontal intensity, these changes correspond to increases and decreases in the total force. Among the examples selected, 14 were positive and 10 were negative changes. According to the Geomagnetic and Solar Data published in the Journal of Geophysical Research in 1958 and 1959, none of the selected cases were registered as a sudden commencement (abbreviated as sc) or a sudden impulse (abbreviated as si) by more than 5 stations, and, in fact, none of them preceded an interval of increased activity as an sc does, and only a few of them were impulse-shaped April 2.1956 June 8. 1958 Figure 3. Comparison of magnetograms covering world-wide changes (indicated by arrows). - 23 -like an s i . Only 3 of them occurred during the period of a magnetic storm that was reported by more than 3 stations. The average magnitude at 50°N of the change in the hori-zontal intensity of the selected cases i s 16 ^ . This i s far smaller than ehanges appearing during a magnetic storm, and accordingly such an occurrence i s seldom reflected in geomagnetic K indices. For the sake of comparison, magnetograms were also obtained from the same stations at the time of 4 widely recognized sudden commencements during the same time interval; 1247 April 28, 1652 May 31, 0046 June 7, and 0713 June 28. Magnetograms were also obtained of 2 s i ' s : 0408 June 2, and 1600 June 19 (only 3 si's were reported from more than 5 stations during this 3-month interval). Most of the data are normal-run magnetograms, but, from the 7 sta-tions indicated by open dots instead of closed dots in Figure 2, rapid-run magnetograms were also available. 2« Form of the change. As can be seen in Figure 3, the traces of world-wide changes on the magnetograms of the horizontal Intensity are similar in most parts of the world. At stations with geomagnetic latitude higher than about 40° at around 0800 IMT however (represented by Fredericksburg and Sitka in the record of Ap r i l 2 and by Sitka in that of June 8), the form of the change differs from that at other stations. - 24 -Examination of rapid-run magnetograms shows that in this particular region the change i s composed of two parts, as can he seen in Figure 4 0 F i r s t there appears a change having the same sign as that at a l l the stations, but immediately after this there i s a change with opposite sign. Thus, i n spite of the complexity in the trace of normal-run magnetograms in this part of the world, i t i s found that the horizontal intensity experiences a change in the same sense almost simultaneously once in any part of the world, later, however, while this change continues in most parts of the world, another change, whose sign i s opposite to that of the f i r s t , appears in a particular region. The fact that the horizontal intensity changes once with the same sign on a world-wide seal© distinguishes this phenomenon from other geomagnetic disturbances such as bays and solarflare effects, which are known to show changes of the same sign only in limited parts of the world. In the following description, the part of the change in which the horizontal intensity changes with the same sign, a l l over the world w i l l be called the "main change'. The change that immediately follows the main change in some part of the world with i t s sign opposite to that of the main change w i l l be called a 'following reverse change'. Th© over-all change i s called 'positive' or 'negative 9 according to the sign of the main change. The regions where these following reverse changes are observed are found to be the same for both - 25 -0 7 0 0 L T 0 8 0 0 M 0 S K 0 W G U A M June 2.195*1 L . T . 1 4 0 0 1 5 0 0 0 9 0 5 0 9 1 0 0 9 1 5 I L.T Fredericksburg F R E D E R I C K S B . 0 0 0 5 A p r i l 1 6 . 1 9 5 8 0 0 ! 0 0 0 1 5 G U A M L.T. Guam 0 7 0 0 _ 0 8 0 0 L . T . H A R T L A N D v r ^ t u I— i G U A M K M a y 9 . 1 9 5 8 v. L . T . 1 7 0 0 1 8 0 0 Figure 4 . Examples of following reverse change (abbrevi-ated to f r c ) recorded following main change (abbreviated to mc). Simultaneous records of Guam, where f r c i s never found, are attached as reference. Upper h a l f , p o s i t i v e change; lower h a l f , negative change. - 26 -positive and negative changes. They are a function of both local time and latitude as i s shown in Figure 5. The duration of a main change when followed by a following reverse change ranges from a few to several minutes. This type of reversal i s known to occur in asso-ciation with sc's (Oguti, 1956; Obayashi and Jacobs, 1957; and Matsushita, I960). The region where this reverse change was recorded in 4 sample storms, which i s also shown in Figure 5, is in good agreement with the results obtained by the authors mentioned above. For s i ' s , Jackson (1952) gave some examples of this type of reverse change recorded in the same region, and the complexity of the form of the change, due to the existence of this reverse change, might explain the apparent minimum in the occurrence frequency of si's around 0800 LMT in middle and high latitudes, as observed by Ferraro, Parkinson, and Unthank (1951). A f o l -lowing reverse change i s found in the same region also for 2 sample si's studied here. Figure 5 shows that the region of occurrence of the following reverse change for sc's Is In good agreement with that for world-wide change analyzed here. A reverse change of a different type, i s found to precede the main change on the afternoon side of the earth. As can be seen by the examples in Figure 6, this i s a decrease in the horizontal intensity for a positive change and an increase in i t for a negative change. It w i l l be called here a 'preceding reverse change'. The preceding - 27 -Following reverse change i • 1 8 12 16 World wide changes Y///////A Sudden commencements 20 24 Figure 5. Region where following reverse change i s found for world-wide changes and for sc's. - 28 -0235 0240 o u L.T. E Sitka onse \ ^ ^ SITKA GUAM May 9. 1958 L.T. Guam 2135 2140 1440 1445 03 w o L.T. Tucson o o °-rucsoN GUAM June 8. 1958 L.T. Guam 0740 0745 1225 1230 TUCSON April 2. 1958 GUAM L.T Guam 0525 0530 L.T. Paramaribo PARAMARIBO April 2. 1958 GUAM L.T. Guam 0320 0325 Figure 6. Examples of preceding reverse change (abbreviated to pre) recorded preceding main change (abbreviated to mc). Simultaneous records from Guam, where pre i s not observed at this time, are attached as reference. Upper half,positive change; lower half, negative change. - 29 -reverse change can be distinguished from other variations recorded before the onset of the main change, f i r s t , by the closeness of the time of i t s onset to the time when the main change appeared at stations where no preceding reverse change was observed, and second, by the regularity of the region in which i t appears,, This reverse change usually lasts for about 1 minute, and can usually be detected only on rapid-run magnetograms. This type of reversal i s known to exist also in sudden commencements of magnetic storms, and i s called a preceding reverse kick, the whole phenomenon being desig-nated ssc*. It Is found to occur also for si's In the same region. Figure 7 shows for both world-wide changes and sc's the regions where this preceding reverse change takes place. The region of appearance of ssc*'s obtained from tjie records of 4 sudden commencements Is In good agreement with the results of studies by Nagata (1952) and Abe (1959). Although Matsushita (1960) obtained a different result, a note added to his paper states that the results may be changed i f rapid-run magnetograms are used in the analysis. The ambiguity in the extent of the region i s mainly due to the limitation in the number of rapid-run records that were available. It can be seen that the regions of occur-rence of preceding reverse changes for sudden commencements and for world-wide changes correspond closely. The forms of the changes in the horizontal compon-ent of the geomagnetic f i e l d described above are illustrated - 30 -Geomagnetic Latitude Preceding reverse change 60° 50° 40° 20° 5° 0 ° LT. V/////////7Z77/ '////////////// 77/////,\ v;;;/;/;;;;;/ ////////////777/ v////////////, \ 8 12 16 World wide changes W/MWA Sudden commencements l l Uncertain 20 24 Figure 7. Region where preceding reverse change i s found for world-wide changes and for sc's* - 31 -schematically in Figure 8. The only difference between a negative change and a positive change i s in the sign of the whole change. A l l sc's, si' s , and world-wide changes analyzed here correspond to one of the forms shown in this figure, the type depending on the latitude and local time. The difference between sc's, si' s , and world-wide changes l i e s in their behaviour after the peak of the change i s attained. For an sc, an interval of increased activity follows; for s i , the change i s supposed to be impulse-shaped. The world-wide changes analyzed here do not precede an interval of increased activity and are not necessarily impulse-shaped. An association with micropulsatlons cannot be inferred because of the low sensitivity of the rapid-run magnetograms used in the analysis. 3. Distribution of the time of onset The way in which the changes spread successively a l l over the earth i s of interest in a consideration of the physical mechanism of the changes. The time of onset i s read on rapid-run magnetograms of the horizontal intensity because the change in this component i s usually more conspi-cuous than that in other components. The error in reading is less than a few seconds. When a preoeding reverse change is recorded, the time of onset of this part of the change i s regarded as the time of onset of the phenomenon, because this time i s closer than that of the onset of the main change to the time of onset of the phenomenon at other stations - 33 -Positive change Negative change Schematic illustration of the Structure of changes. Figure 8. Schematic i l l u s t r a t i o n of the three parts of change: (a) main change (mc), (b) following reverse change (frc), and (c) preceding reverse change (pre). - 33 -where a preceding reverse change i s not observed. This has been noted for sc's "by Gerard (1959) and by Williams (1960). A more systematic distribution of plots can be acquired by this method than by taking the time of onset of the main change everywhere. This strongly suggests that the preceding reverse change i s an essential part of the phenomenon. Local time dependence in low latitudes i s studied by data from Guam (5«,9°N, 212.8°), Honolulu (21.0°N, 266.4°), Tucson (40e4°N, 312.1°), and Paramaribo (17o0°N, 14*5°). As these stations cover only a 9-hour range in time, the local time dependence for a whole day i s obtained by superimposing the local time dependence curves obtained for events that occurred at different GMT* This method i s explained by the example shown in Figure 9, and Figure 10 i s drawn by superimposing a l l the par t i a l local time dependence curves obtained by means of this method. The effect of difference in the latitude of the stations can be eliminated s t a t i s t i c a l l y . Figure 10 shows that positive changes (including two cases of s i ) , negative changes, and sc fs spread in a similar manner from the noon side to the night side of the earth in low latitudes. Latitude dependence i s studied by a comparison of rapid-run magnetograms from two stations on approximately the same meridian, one in a low and the other in a middle-high latitude. Two pairs were chosen for this purpose: - 3 4 -I 5 s e c . 1 2 1 8 ( a ) 1 4 1 5 A p r i l 2 . 2 4 L T . 0 s e c . 6 - i — 1 2 i — 1 8 ( c ) 1 1 3 5 M a y 9 . 2 4 L I Figure 9 . Illustration of the method used in obtaining the local'time dependence curve of the time of onset in low latitudes. From curves (a), (b), and (c), each of which covers only a 9-hour range, curve (d) i s derived, which shows the local time dependence for a whole day. - 3 5 -Figure 1 0 . Local time dependence of the time of onset in low latitudes for (a) positive change, (b) negative change, and (c) sudden commencement. - 36 -Honolulu and Sitka (60.0°N, 275*4°) and Paramaribo and Fredericksburg (49.6°N, 549.9°). The amount of us.able data i s limited 9 because reliable reading of the time of onset becomes d i f f i c u l t in higher latitudes since the record i s frequently obscured by local disturbances. Figure 11 shows the difference in time of onset between higher- and lower-latitude stations. It can be seen that the latitude dependence of the time of onset also seems to be similar for positive changes (including two cases of s i ' s ) , negative changes, and sc's. The changes begin f i r s t in high latitudes at almost a l l local times. Thus the distribution of the time of onset i s the same for sc's and si's and world-wide changes both positive and negative. The overall similarity in the dis-tribution of the time of onset between positive and negative changes supports the idea that a negative change should be regarded as an independent phenomenon, because, i f a negative change i s nothing more than a recovery following a positive change, i t must f i r s t appear in the region shown in Figure 5 where the main change Is interrupted by a following reverse change, while the main change s t i l l continues at other stations. From Figures 10 and 11 the world-wide distribution of the time of onset common to a l l these phenomena i s obtained (see Figure 12). This is similar to the result obtained by Gerard (1959) and Williams (1960). Thus i t seems that in a l l world-wide changes, sc's,and si's^ - 37 -Figure 11. Difference in time of onset at middle-nigh latitude stations (Sitka or Fredericksburg) from that at low-latitude stations (Honolulu or Paramaribo): (a) positive change, (b) negative change, and (c) sudden commencement. - 38 -Figure "12. Isochronic curve of the time of onset of world-wide changessi's, and sc's. Average value of the relative time of onset i s given in seconds. - 39 -the preceding reverse change appears f i r s t in high latitudes on the afternoon side of the earth and then spreads toward the afternoon side in lower latitudes. Then, more than 20 seconds after the f i r s t appearance of the preceding reverse change, the main change appears outside the region where the preceding reverse change i s recorded, and spreads from the noon to the midnight side. In the region where the preceding reverse change appears, the main change occurs about 1 minute after the onset. In contrast to the present result, Troitskaya (1961) has reported from an examination of data from the USSR that the time of onset of sc i s simultaneous everywhere. Since the USSR records sent to the IGY World Data Center have a slower speed of run (5..0 cm/hr) than those shown in her paper and those sent from other stations (20.0 cm/hr), i t i s impossible to check her result. Different methods of observ-ing the phenomena are suggested as a possible cause of the discrepancy. Rapid-run tellurigrams are used by Troitskaya while rapid-run magnetograms are used here,and the frequency response of these two methods are not the same. But a com-parison of the time of onset at Kanoya (tellurigram) and Guam (magnetogram) shows that the difference i s small: -7+ 12 sec for world-wide changes and 2 + 3 sec for sc's. As these stations are nearly in the same meridian and d i f f e r in l a t i -tude by about 20°, this amount of difference in the time of onset i s to be expected from the distribution shown in - 40 -Figure 12, and the difference in apparatus does not seem to affect the result significantly. Since tellurlgram records shown in Troitskaya*s paper are rich in high fre-quency oscillations, the determination of the time of onset may be more d i f f i c u l t than in the present analysis, and i t is suspected that the time of onset taken by her might be erroneous. 4. Distribution of the magnitude of the change The dependence of the magnitude of the change on latitude and local time i s also studied. Since only normal-run magnetograms can be used for this analysis, i t i s d i f f i c u l t to read a l l three parts of the change. When a following reverse change appears, the magnitude of this part is read, because i t i s usually larger and lasts longer than the remaining parts of the change. In other cases, the magnitude of the main change i s read. The magnitude of the change i s measured from the level preceding the onset of the change, as shown in Figure 8. To combine the data from different cases, readings of the magnitude are normalized by the sum of the readings at 5 stations with latitude approxi-mately 50°N: Hartland (54.6°N, 79.0°), Moscow (50.8°N, 120.5°) Yakutsk (51.0°N, 193.8°), Victoria (54.1°N, 293.0°) and Fredericksburg (49.6°N, 349.9°). The local time dependence of both the northward and the eastward components of the change at 60°N, 50°N, 40°N, 20°N, 5°N, and 0° obtained in this manner are shown in Figure 13, for positive changes, _ 41a -4 0 ° X * 4 0 ° Y . 10 y for selected samples Positive change Negative change Sudden commencement Sudden impulse Figure 13. - 41b 6 0 ° X 6 0 ° Y Figure 13. Distribution of magnitude of world-wide changes in the geomagnetic f i e l d as compared with that of si's and sc's: 2, northward component; Y, eastward component. Scale corresponds to average of selected world-wide changes. Data are from Leningrad, Sitka (60°); Hartland, Moscow, Yakutsk, Victoria, Fredericksburg (50°); T i b i l i s i , Sakhalinsk, Tucson (40°); Kanoya, Honolulu, Paramaribo (20°); Bangui, Guam (5°); Koror and Huancayo (0°). - 42 negative changes (with sign reversed), sc's, and s i ' s . The change in the vertical component i s less than one-third that in the horizontal component, and, since the sensitiv-i t y of this component i s usually less than that of the other components, reliable readings are d i f f i c u l t and the plots f a i r l y scattered. Therefore the distribution of the vertical component i s not reproduced here. Near the equa-tor, the change in declination becomes very small and the distribution of the eastward component at 5°N and 0° cannot be obtained. The distribution shown in Figure 15 does not necessarily show simultaneous values of the change, but the figure probably represents the distribution of magnitude to a f a i r approximation. When the considerable dispersion of the plots, due possibly to the smallness of the values to be read from the records, i s taken into account, Figure 15 can be regarded as showing close similarity between the world-wide changes analyzed here, sc's, and si's in the dependence of magnitude on latitude and local time. Latitude dependence of the average value•of the change in a day can be obtained from Figure 15; i t i s shown in Figure 14. It can be seen that the amplitude of the change increases for both positive and negative changes near the equator. The daytime enhancement, at the equator, in the magnitude of the change has been noticed by a number of authors (Vestine, 1955; Suglura, 1955; Maeda and Yamamoto, - 43 -P o s i t i v e c h a n g e N e g a t i v e c h a n g e 1 1 1 1 1 1 1 1 1— 90° 80° 70° 60° 50° 40° 30° 20° 10° 0° G e o m a g n e t i c L a t i t u d e Figure 14. Latitude dependence of the magnitude of the horizontal component of world-wide changes in the geomagnetic f i e l d . - 4 4 -1960) for the main change of sc. But this type of enhance-ment i s also found in the preceding reverse change. An example i s shown in Figure 15 in records from Guam and ' Koror. These stations differ only by about one hour in local time, but have a difference in dip angle of about 12°, Koror being closer to the dip equator. It can be seen that the magnitude of the overall change at Koror i s two or three times larger than that at Guam. The ratio of the magnitude of the change in the horizontal component at Koror to that at Guam i s calculated for several cases recorded during the IGT when a preceding reverse change was present at both stations. This, and the ratio of the amplitude of Sq on a quiet day near the day of the sc are tabulated in Table 2. A close similarity is found between the ratios for the main change of sc and for Sq, in accordance with the earlier results of Forbush and Yestine (1955). The ratio for a preceding reverse change of sc i s of the same order, but a few times larger than that for the main change or Sq. Equatorial enhancement i s found to occur in a similar manner for world-wide changes. Examples are given In Figure 16 (for a positive change) and Figure 17 (for a negative change). Magnetograms from several widely separated stations are presented to show the world-wide occurrence of the phenomenon* The magnitude of the overall change at Koror i s a few times larger than that at Guam. (A preceding reverse change i s distinguished from other small changes by - 45 -FIGURE I FREDERICKSBURG Figure 15. Equatorial enhancement of so shown i n a record from Koror. - 46 -Table 2. Ratio of the magnitude of the change In the horizontal component at Koror to that at Guam, Date  sc 21 June 1958 17 August 1958 22 August 1958 27 August 1958 IMT(Guam) 1200 1600 1300 1300 Preceding Main Reverse Change Change 3.3 2.0 6.7 2.5 1.9 2.0 2.4 1.8 Sq, 1.4 1.7 1.6 1.9 world-wide positive change 21 May 1958 0900 02 June 1958 1400 3.0 3.9 1.8 2.1 1.6 2.0 world-wide negative change 25 December 1957 1300 6.0 3.4 2.2 - 4 7 -I3|I5 LT. m MV m a t e r i a l e — e f o f - ^ ^ 0 ^ fea'SSr^^ SSS Sfworia-wide occurred ot the change. - 48 -FIGURE 3 Figure 17. Equatorial enhancement of world-wide negative change shown in a record from Koror. Records from other stations are presented to show the world-wide occurrence of the change. - 49 -being confined to certain regions of the Earth and by the closeness of i t s time of onset to the time when the change is recorded in other parts of the world). Ratios of the magnitudes of changes are estimated in the same way as for sc's, and are given i n Table 2. It can be seen that the ratios for the main change,, preceding reverse change and Sq are related in a similar way to those for sc's,and moreover, the figures in the corresponding columns for sc and world-wide change are quite similar. 5. Related phenomena Phenomena associated with the occurrence of world-wide changes in the geomagnetic f i e l d were looked for in the following records. (1) Orbit of the sate l l i t e 1958 «'(Explorer III). The speed of orbiting of the a r t i f i c i a l s a t e l l i t e i s reported to vary during a magnetic storm (Jacchla, 1959), and explained by ,an increase in the atmospheric density. However, the orbit shown in the publication by NASA (technical report P-356) i s a result of theoretical calcu-lations on the basis of observations made every 48 hours. This time interval i s too long to detect the effect of such small and frequent phenomena as world-wide changes, and no conclusions can be drawn. (2) Vertical incidence ionograms. Data were obtained from the stations tabulated in Table 3. Nothing particular can be found which may be - 50 -Table 3. Ionospheric stations. Station Geographic Latitude Akita 39.7°N Baker Lake 64.3°N Churchill 58o8°N Fort Monmouth 40.3°N Kokubunji 35.7°N Meanook 54.6°N Ottawa 45.4°N Resolute Bay 74.7°N St. Johns 47.6°N Talara 64.6°S Yictoria 48.4°K Wakkanal 45.4°N Yamagawa 31.2°N Geographic Longitude 140.1°E ,96.0°W 94.2°W 74.1°W 139.5°E 113.3°W 75.9°W 94.9°W 52.7°W 81.3°W 123.4°W 141.7°E 130.6°E - 51 -associated with the occurrence of world-wide changes. However, the time interval of 15 min between which these ionograms are taken may be too long to find out any effect related with world-wide changes which last only a few minutes. (3) Ionospheric absorption. Data were obtained from the stations tabulated in Table 4. No association is found with world-wide changes. Although an increase in absorption is reported to occur at the time of some sc's, more than half of the sc's studied do not show this feature (Ortner et a l , 1962; Matsushita, 1961). Hence this does not seem to be an essential part of the phenomenon. (4) Night airglow. Data from two stations tabulated in Table 5 were used, but no relationship can be found. The hourly values used here may be quite unsuitable for the present purpose because of smallness of the duration of world-wide changes. (5) Overall features of the geomagnetic f i e l d . The daily number of occurrences of world-wide changes i s compared with the index and reproduced in Figure 18. It can be seen that the number of occurrences of world-wide changes i s not related with K at a l l , and hence i s independent of the degree of disturbance of the overall features of the geomagnetic f i e l d . - 52 -Table 4. Observatories recording ionospheric absorption. Station Geomagnetic latitude Geomagnetic longitude Barrow Churchill Colombo Ft. Yukon Thule University Park 71.5°N 58ft8°N 06.6°N 66.5°N 76.5°N 40.8°N 156.4°W 94.2°W 80.0°E 145.3UW 68.8°W 77.9°W Table 5. Observatories recording night alrglow. Station Geomagnetic latitude Geomagnetic longitude Haute Provence 43.9°N 5.7°E l'Irsao a Lwiro 2.2°S 28.8°E - 53 -p a. Figure 18. Variation in (a) the number of occurrences of world-wide changes (WWC) (multiplied by two), (b) the geomagnetic kp index, (c) the number of solar flares and (d) the sunspot number during April 1958. - 54 -(6) Solar phenomena. The daily number of occurrences of solar flares (IG-Y solar activity report series No. 12, 1960) and the sunspot number are compared with the daily number of occurrences of world-wide, changes. As can be seen from Figure 18, no correlation appears to exist between them. Bursts in solar radio noise (Solar-geophysical data, NBS, 1958) are also not related with world-wide changes. Since world-wide changes are small in magnitude and frequent in occurrence, i t i s not preferable to try and associate them with the limited number of particular events picked out in the published data. The original, continuously monitored record w i l l have to be studied. Thus so far, no phenomena can be detected which are related with world-wide changes in the geomagnetic f i e l d . But since most of the data used here is not suit-able for the present purpose, a definite conclusion can not be drawn, and a detailed study w i l l have to be made in the future. 6. Summary World-wide changes are found to exist in the geo-magnetic f i e l d . They are changes of magnitude less than about 20 $ in low and middle latitudes and are not registered as sc's or si's by most stations. However, they are quite similar to sc's or si's in most features such as form, manner of spreading over the earth, and distribution - 55 -of magnitude. This conclusion is based on the analysis of randomly selected samples, but the other examples of changes selected at the beginning of this study but not subjected to detailed analysis are found to show the same characteristics,, This fact, together with the broadness of the area covered by the 5 stations used to determine them, seems to Justify the conclusion that a l l belong to the same class of phenomena. It follows that world-wide changes of the geomagnetic f i e l d are observed quite fre-quently; at least SO per cent of every 1-hour period and at least 90 per cent of a l l days contained at least one of them during the 3-month period near sunspot maximum. The frequent occurrence of changes in the geomagnetic f i e l d on a world-wide scale Is In accordance with the idea that world-wide features of the geomagnetic f i e l d are always related with the highly variable physical state of the solar atmosphere, although the relationship between individual events has not yet been found. An sc i s distinguished from a world-wide change by i t s association with an interval of increased activity. An s i actually differs but l i t t l e from a world-wide change. Si's are supposed to be impulse-shaped, but, as can be seen by the example of 1600 June 19 in Figure 1, some of those reported are not impulse-shaped, and, moreover, many of those that are really impulse-shaped are missed in the reports from the majority of stations. Thus si's seem to - 56 -be nothing more than the world-wide changes that are widely recognized because of their large s i z e 0 The distribution of the horizontal component of the change in the geomagnetic f i e l d at the time of a world-wide (positive) change, sc, and s i , i s drawn schematically in Figure 19, maMng use of available rapid-run magnetograms and the results obtained in the previous sections of this paper. For a negative change, the direction of a l l the vectors i s reversed- As only the distribution below 60° geomagnetic latitude i s studied, the difference between geo-magnetic and geographic latitude i s ignored. Figure 19a shows the f i r s t stage of the change, in which only a preceding reverse change appeared In a limited region of the earth. Figure 19b, corresponding to the stage more than 1 minute after the stage shown in Figure 19a, represents the distribution of the main change. This stage continues from a few to several minutes, and then a following reverse change appears as shown in Figure 19c. In the region kept blank in Figure 19c, the f i e l d vectors are but l i t t l e altered from those shown in Figure 19b. The preceding reverse change and the following reverse change of sc are regarded by Oguti (1956) as similar phenomena differing only in the local time of the region of appearance. He proposed that the reverse change d r i f t s westward from the afternoon side of the earth (where i t appears as pre) to the morning side (where i t appears as - 57 -(a) Figure 19a. Distribution of the horizontal component of a positive world-wide change In the geomagnetic f i e l d shown for three stages of the change. (For negative change, the direction of the vectors must be reversed). The scale given corresponds to the average of selected samples, (a) F i r s t stage, in which only preceding reverse change i s observed In a limited region. - 58 -Figure 19b. (b) Second stage, in which main change i s observed a l l over the world. Figure 19c. (c) Third stage, in which following reverse change appears in the region shown. - 60 -f r c ) . But the present result shows that pre and frc are quite different in the broadness of the region where they are observed, frc being more restricted to high latitudes. Hence i t seems preferable to regard preceding reverse change and following reverse change as independent pheno-mena. An 'equivalent' overhead current system i s frequently employed as a convenient way to represent the distribution of changes in the geomagnetic f i e l d . This i s an ionospheric current system drawn on the assumption that the observed magnetic f i e l d i s entirely due to a closed electric current system flowing in the ionosphere. The equivalent current system constructed from the distribution of the magnetic f i e l d shown in Figure 19 i s drawn in Figure 20. However, i t should be noted that the'distribution of a magnetic f i e l d that can be equivalently represented by a closed electric current system in the ionosphere i s limited. Phenomena due to ionospheric currents which are divergent or convergent, or due to current systems which include flow along lines of force as an essential part, or due to hydro-magnetic wave of some kind, can not be represented by an 'equivalent' current system. ,The equivalent current system is frequently employed nevertheless, because with the limited amount of data now available, the distribution can be approximated by that due to an ionospheric closed current flow. Thus there is no guarantee of the r e a l i t y of an - 61 -Figure 20a. Equivalent overhead current system (assumed height 100 km) of a positive world-wide change in the geomagnetic f i e l d . The amount of electric current indicated in the figures flows between successive lines for the average of selected examples, (a) Fi r s t stage. Figure 20b. (b) Second stage. Figure 20c. (c) Third stage. - 64 -equivalent current system, which could also represent the distorted distribution of the magnetic f i e l d . The equivalent current systems of preceding reverse change like the one shown in Figure 20a have been given by several authors. These show that the electric current flows northward around noon. If this i s true, westward deflection of the magnetic f i e l d must be observed in middle and low latitudes around noon at the same time as pre in the afternoon side. Nevertheless, i n no examples ever published (works already referred to and Sato, 1961, Sano, 1962), and in no cases studied by the author could such a change be found. Since the amount of rapid-run magnetograms i s s t i l l limited, this finding can not be decisive but i t seems to cast strong doubt to the validity of the equivalent current system for the representation of the observed magnetic f i e l d . - 65 -CHAPTER III IONOSPHERIC SCREENING EFFECT 1. Electromagnetic f i e l d in the neutral atmosphere From Maxwell's equations in free space: C\MI E - -TTI , 1^) UAAJL § = T W , (2) o l ; B = o . (4) the electromagnetic f i e l d E and B in a neutral atmosphere can be written as E — Z_i ^ 6/ (5) 1 = P e j (6) where jLl -f 4vt J +- VI* ==• - 66 -The x, y and z axes are directed toward the south, east and vertically upwards respectively, and the ground i s represented by z = 0. The horizontal components of £ i'*'t''vt'^  and j^ 5-'**'*'^ a r e r e]_ ated by the equations The solid earth behaves almost as a perfect conduc-tor for a change with a time scale of world-wide changes (Appendix A). Hence at z = 0, the horizontal component denoted by suffix k of the electric f i e l d i s approximately zero, i.e., = Z •+- 1* ) t ' = 0 Hence <CJU +- = o . do) From equations (8), (9) and (10) i t follows that: fit = £ t . (11) - 67 -Using equations (10) and (11), equations (5) and (6) may-be simplified, (12) =-Z 21», i t 1 ' " ' " e- U 8 x +n-^ ft, to,i*> (13) where £k = = " I"*-y and £t = = I< A summation over n i s omitted since n i s uniquely determined when ]2 ,m and UJ are given, £t''*,^ ^ 3 approxi-mated by I £ A%T: since |n4,£| « | in a l l cases to be discussed later. - 68 -The time scale of world-wide changes ranges from 10 to 10 sec, depending on the part of the change. Obser-vation shows that their characteristic length of variation, measured along the surface of the earth, given by where F denotes the f i e l d strength and i s the hori-zontal gradient, i s of the order of 10 cm in middle and low latitudes. Hence, in middle and low latitude regions, the electromagnetic f i e l d of world-wide changes may be represented by harmonics specified by From the observed value of f ^ can be derived using equations(8) and (9). The electromagnetic f i e l d E(d) and B(d) at the upper boundary of the neutral atmosphere z « d, i.e., at the lower boundary of the iono-sphere, i s obtained by substituting z = d into equations (12) and (13). In the above representation of the electromagnetic f i e l d in the neutral atmosphere, the nature of the f i e l d is not specified; the solution of Maxwell's equations in the free space close to a perfect conductor i s used in i t s general expression. This i s in contrast to the discussions given by Ashour and Price (1948), Sugiura (1950) and Francis and Karplus (1960) on the ionospheric screening effect. These authors assumed, without any verification, that the observed f i e l d can be expressed either by an electromagnetic wave (Francis and Karplus) or by a mag-netostatic f i e l d (Ashour and Price, Sugiura), Of these representations the former, the electromagnetic wave, seems inadequate. Observation shows.that the characteristic 8 length of variation in space i s about 10 cm or loss. Such a sharp variation can hardly be expected for an electro-magnetic wave with a peribd. longer than 10 sec, since the 11 corresponding wavelength i s longer than 3 x 10 cm. This significant deviation of the observed f i e l d from an electro-magnetic wave is physically reasonable, because the vert i c a l 7 s c a l e of the neutral atmosphere i s only 10 cm - less than about 10'^' of a wavelength. The source is too close for the changing electromagnetic .field to have the properties of an electromagnetic wave.. Hence an. electromagnetic wave can not be regarded as^-a, suitable' approximation, With these given scale values in space and time, i t follows from e q u a t i o n (7) that 4'1 — " L — W A - 1 — (14) Since the horizontal distribution of the f i e l d may be repre-sented by a Fourier series from observations on the ground, I and lit are taken as real. It follows then from equation (14) that ty, is purely imaginary-. The latter type of approximate representation, i.e., by a magnetostatic f i e l d , is c h a r a c t e r i z e d by the entire neglect of the - 70 -displacement current. This neglect can not be taken for granted, as shown below. The degree of the effect of ionospheric screening may be measured by the magnitude of E (d): since E i s ~"h "Ta almost constant in the ionosphere as shown in the next section, E (d) i s proportional to the magnitude of the ionospheric current which screens the incoming magnetic f i e l d . From equations (1) and (2), for dominant harmonic t and' ', which compose E and B, the following relationships hold: I UMi i | k L i - / <15) where L and ^ denote orders of magnitudes of £_ and _^ and L i s the reciprocal of the characteristic length of variation of the f i e l d in space. Numerical factors k and k f satisfy * ' £ i . (wi (here every figure represents an order of magnitude). This means that the order of magnitude of curl E and curl B i s - 71 -obtained by multiplying the magnitude of the terms compos-ing them by a factor which i s smaller than unity. From equations (15) and (16) i t follows that: f k L C and where for wj£ lO" 1 sec" 1 and L~10 -8 -1 cm (18) From equations (17) and (19) we have (20) It can be seen from equations(19) and (20) that except for certain special cases, both k and k* are smaller than unity. If the distribution only of the magnetic f i e l d or only of the electric f i e l d i s under consideration, this w i l l allow us to approximate the f i e l d by a magneto-static or electrostatic f i e l d . However, in the case where - 72 -relationships between the magnetic and electric fields are involved, this approximation by a static f i e l d i s not permissible: since i s quite sensitive to the values of k or k' as can be seen from equation (18), k and k' must hot be approximated by zero, small their values may be. A pair of k and k* values l i e s between two extreme cases. The f i r s t i s when ~ 1 / (21) k'~ (rr/ « 1 The ratio of £ to f i s then given by This means that the electromagnetic f i e l d i s , in the f i r s t approximation, a magnetostatic f i e l d with the non-static electric f i e l d of magnitude far smaller than that of the magnetic f i e l d . In the following, this case w i l l be called a Tmagnetostatic f i e l d * . It i s the case adopted by Ashour and Price (1948) and by Sugiura (1950). (They represented the magnetic f i e l d in the neutral atmosphere by a potential f i e l d , i.e., k ? i s equated to zero. However, as k' cannot be set exactly to zero,as can be seen by equation (19), their assumption can be interpreted as assigning to k' i t s smallest possible value: [~Cc J T t L e opposite extreme - 73 -case i s when In this case £ L C « 1 7 (23) >, ? X IP 3 (24) This shows that the electromagnetic f i e l d can be described, to a f i r s t approximation, by an electrostatic f i e l d , with the magnetic f i e l d non-static and far smaller than the electric f i e l d . In the following, this case w i l l be called an .'electrostatic f i e l d ' . The real situation l i e s between these two extreme cases. In the case of an electromagnetic wave the ratio of £ to ^  is given by -y ~ 1 • (25) Substituting equation (18) into equation (12), and noting that L^ ^  by equation (14), the order of magnitude of E^d) i s given by f . ( S 6 ) This shows that E (d), and hence the degree of the effect of h ionospheric screening, depends not only on w - the time scale of the. phenomenon, but also on L - the scale of the phenomenon i n space, and on k - the degree of magnetostatic property of the observed f i e l d . Magnitudes of S (d) for - 74 -various values of k are related by (27) Since I » ( E k ^ V magnetostatic, which is the basis of estimation by Sugiura (1950), i s the smallest value of by assuming the f i e l d in the neutral atmosphere to be magnetostatic, the ionospheric screening effect has been given the least possible significance. If the actual f i e l d is different from the magnetostatic f i e l d in the sense defined above, the ionospheric screening effect i s more important than was formerly concluded. In the preceding discussion, no reason has been found why the f i e l d in the neutral atmos-phere i s a magnetostatic f i e l d . Therefore a general expression of the near source f i e l d given by equations (12) and (13) w i l l be used in calculating the f i e l d in the upper atmosphere associated with the observed f i e l d . The validity of the magnetostatic f i e l d approximation w i l l be checked afterwards by the results. In the case of an electromagnetic wave, ^ s given by various possible values of k. This means that (28) since 14^ — in this case. From equations (26) and (28) we have Hence the degree of ionospheric screening i s the same for an electromagnetic wave as for a magnetostatic f i e l d . This might explain why similar results are obtained by Sugiura (1950) and by Francis and Karplus (1960) in spite of the differences in t h e f i e l d representation in the neutral stmosphere - b o t h of them concluding that the screening effect i s insignificant for changes with a time scale longer than about a second. 2. Field in the ionosphere Above the height of several tens of kilometers the following relationship holds: where i s the conductivity, and in this region the dis-placement current can be neglected in comparison with the conduction current. The electromagnetic f i e l d i s then determined by, (29) (30) c (31) (32) - 76 -(33) (34) and (35) hi (36) where the dielectric constant and the permeability are set equal to unity, j i s the electric current density, q the electric charge density, and b^ the unit vector in the direction of the geomagnetic main f i e l d BQ. The subscripts ± and f| denote components perpendicular and parallel to b Q respectively, and 0 " , , and <r0 are conductivities in the three specified directions. An equation for E can be derived from these equations as the region where uu i s smaller than fo: a half of the c o l l i s i o n frequency of an ion with neutral particles (which i s below 500 or 400 Jan for u) - 10~2 or 10" 1 sec" 1), the medium behaves as a conductor with conductivity given by (Francis and Karplus, 1960, and Appendix II' (37) where A — Q- 'L and o~ the conductivity matrix. In - 77 -We^e-r^*1) J, ( 3 8 ) tA><2 W i. where i s the number density of charged pairs, mQ and m^  are the masses of electrons and positive ions, e i s the electron charge, {/JQ and OJ^ are the electron and ion cyclo-tron frequencies, and i s the c o l l i s i o n frequency of an electron. It i s assumed in deriving these expressions for the conductivity that the static magnetic f i e l d B q i s uniform, the pressure and the gravitational force are negligible, and the ionosphere consists of electrons, one kind of positive ion and one kind of neutral molecule with the same mass, as the co-existent positive ions. The present discussion i s concerned with middle and low latitude regions, and the ionosphere is assumed to be horizontally s t r a t i f i e d , and the inclination <|/ of the geo-magnetic f i e l d i s taken as constant. Equation (37) can be written in components as - 78 -(39) V where j is given by Equation (39) may be integrated upwards with respect to z to obtain E in the ionosphere from the given values of E and -7-r at the boundary. Since (<r) i s assumed to depend o i only on z, the dependence of E on x and y does not vary with height: i f the f i e l d is represented by a harmonic ^AUXtfo'j) ^ n t j i Q n e u ^ r a i atmosphere i t w i l l also be proportional to £ V in the ionosphere. The f o l -lowing calculations w i l l be made for a harmonic K^-KO-U ^ ^ t o t a l f i e l d i s derived by summing this over j), m and w . - 79 -From the last of equation (39) i t follows that « III ) (41) 4T''^ <) / ( Substituting equation (41) into the f i r s t two of equation (39) we have -Hp^jV.tr, j j e * (42) - 80 -and These are ordinary differential equations giving E and E as functions of z. The magnetic f i e l d i s obtained from 7 E by equations (31) and (41) as f l#f i f - - i f ^ ( o W f ^ » ) ^p-' (43) - e l -and (43) Since the following condition holds in most parts of the ionosphere, equation (42) can be approximated as and (45) - 82 -And equation (45) as (46) and 0 E at the boundary i s given by equation (12) -rr- at the boundary may be obtained from B (d) and E. (d) a i "~h -~h by means of equation (46). It was shown in the preceding section that for given E , B i s largest in the 'magneto-h' h & static' case and i s then given by 0\ * °~) ' Hence the a "Pi. / order of magnitude of -j-g- at the boundary i s given by d3\ nitude of The variation of E^ with height can be evaluated by separ-ating i t into two parts. The f i r s t can be estimated from the gradient of E^ at the boundary given by equation (47). This w i l l result in the variation A, E^ across the iono-sphere : A , Et, Z ( ^ - ) J L I „ f o ^ I U) / (48) where h i s the thickness of the ionosphere which i s of the order of 10 7 cm. With. li^yf 1 0 ~ 8 cm.-1. A E n &oe3 not exceed E^(d) and the variation coming from this source can be neglected. The second part i s due to the - 83 -variation of inside the ionosphere given by equation ( 4 5 ) . Here terms proportional to jf are negligible, since the variation in due to these terms i s of the order of J l ^ n ? & y y - , which is smaller than y r ^ by an order of 10 . The largest value of i s then expected at the height of maximum conductivity. Approximating this region by a layer of thiclcness 100 km with o^io* cgs, A y ^ across this region i s estimated as HT^ M . The variation in E resulting from this amount of change in y r / - i s When i s smaller than 10"" 1 s e c - 1 , or when the time scale of the change i s longer than about 10 sec, A2ir/. does not exceed bj, . The contribution to A~d2 from other parts of the ionosphere i s also negligible. Thus the varia-tion of E with height can be neglected inside the iono-~h sphere for cases of world-wide changes where a time scale is longer than about 10 sec. In the range of where the variation of E across the ionosphere i s appreciable, the ~h ionospheric screening effect may be more significant than estimated here. Hence in the relevant range of u; , the electric f i e l d 1!^  inside the ionosphere and S^ 0) a t t n e upper boundary of the ionosphere z = D are equivalent and can be - 84 -written as = \~l {*> = ^ k U ) / (49) and -Tp^ at z = D i s given from equation (45) by A H . 1 i f J„( 1 1 O- I Substituting equations(49) and (50) into equation (46) and neglecting terras of small order, we have and (51) - 85 -where 21, and 211 a r e integrated conductivities given by t> X , — cr, A? ^ ID'3 and p = r - - i o ' 3 . Thus the ionosphere can be approximated by a metallic shell with anisotropic conductivity. 3. Field in the magnetosphere Above a certain height, ranging from about 400 km for t^ v 10" 1 Sec" 1 to about 500 km for UK 10" 2 sec" 1, ^ is larger than Vl . In this region, the el e c t r i c a l con-ductivity i s given by(Francis and Karplus, 1960: and Appendix II.) <r, = £ 6 ^ 1 o - . - - ^ ; - . ( M ) In this region the following relationships hold between the magnitudes of CT; . In contrast to the ionospheric conductivity given by - 8 6 -equation (58), the conductivity given above depends on °^ . This part of the upper atmosphere behaves as a magnetohy-drodynamic medium. In terms of the Alfven wave velocity: 7~-= J ^ T C N J f YVll > * C d n b e b i t t e n a s 01 = J 0«>) W ' 4-7L I T / The Alfven wave velocity V varies significantly with 7 -1 height: i t increases from 2 x 10 cm sec at a height of 8 - l 500 Ina to 5 x 10 cm sec at a height of 5000 km and then decreases towards the outer boundary of the magnetosphere (Dessler et a l , 1960). In the following discussion, however, V w i l l be approximated by 1 x 10° cm sec . Then for [i\y^ ~ 10~ 8 cm"1 and for UJ £ 10" 1 sec - 1 , the follow-ing relationships hold. (54) Using equations (55) and (54), equations (42) can be approximated by Q (55) - 87 -and —(-• tif/tif-y. ^  = - i IH C/©^f Mv^y t-\ti J V ; where E and E are assumed to vary as e~ with height. From these equations, a dispersion equation may he obtained. where (56) y = - i Nl A * M f - ; £ G o f , Y •=" - * K) <*» ^ +- A j? ^ ^ and E and E are related by ~x ~y Equation (56) can be solved to give (57) For a l l four modes, |M/ i s of the same order as H ot 'in- , and hence equation (41) can be approximated as , (59) This shows that the electric f i e l d in this region i s approximately perpendicular to the direction of the magnetic lines of force as a result of the high conductivity in - 88 -that direction, E i n the magnetosphere can now be written as + 1 M 3 At^l V — In the f i r s t two modes, the electric f i e l d varies exponen-t i a l l y with height. Of these two modes, mode 1, which diverges as z &> , represents the f i e l d incident from above, and mode 2, which converges to zero as -^>©<. , represents the one reflected from below. The second two modes represent wave propagations in ± z directions with an amplitude determined as a function of the x, y and z - 8 9 -coordinates. In the northern hemisphere where ^>0 , mode 3 corresponds to an incident wave propagating downwards, and mode 4 to the reflected wave propagating upwards. In the southern hemisphere where ty<0 , the roles of modes 3 and 4 are interchanged. The magnetic f i e l d B can be derived by substituting equation (60) into equation (43) under conditions (53) and (54) ~ 1 M,w t E U, *i, ;jz>f)— r,—-' t\ KT c<* Y • £ 0 The present solution i s different from the 'magne-tohydrodynamic wave' usually adopted. This comes from the second of the relationships (54) which, in terms of the magnetohydrodynamic wave length A- , can be written as - 90 -ZTC < X showing that the observed f i e l d varies in space with a scale shorter than the wavelength. This i s the situation analogous to what existed in the neutral atmosphere. (61) i s related to the observed f i e l d in the neutral atmos-phere through equations (49) and ( 5 1 ) , where 1^(0) and B_k(D)are given by substituting z = D into equations (60) and ( 6 1 ) . The effect of the ionospheric screening i s considered for the ease where j£l ~| to | , i.e. where the scale of the variation of the observed f i e l d i s similar for both north-south and east-west directions. The orders of magnitudes of the incident f i e l d in the northern hemisphere are then given by The magnetospheric f i e l d given by equations(60) and b, -(62) - 91 -where terms which always appear in a certain combination are written in brackets, and I X , I j^ xand ^ y are related to and £.j by T v - — r ~ — ' -z. M t < ^ £ * i ? J — ~ Z , ^ A ^ A / 2 J ML 1*-Details of the derivation are presented in Appendix B . With H, U, 41" IP"8 C4vr* , £ ^ lP'Jc-f* > d~ lDn c*» and V *s \ C** A u ; _ / ) the orders of magnitudes of the terms in the f i r s t of equation (62) are estimated as follows: Similarly, the magnitudes of the terms in the second of equation (62) are - 92 Since I0 H£, IA) Z \0 Se~z-~l and 1 k, equation (62) can then be approximated b j r , _ 4-71" H> U; two a , > ( 6 S ) . ± Z L LT + _^L- « Written below each term i s i t s order of magnitude. The observed magnetic f i e l d £ consists of the incident f i e l d and the f i e l d b due to the ionospheric current, where b is given by U , 4-TT T b - — z - J- ( 6 4 ) I f b i s smaller than the observed f i e l d , the ionospheric screening effect can be neglected since the observed f i e l d must approximately be the same as the incident f i e l d . But i f on the other hand b i s comparable with, or larger than the observed f i e l d , b must have cancelled the significant part of the incident f i e l d , i.e. the screening i s effective. Hence a comparison with unity of the ratio of b to p can be used as a criterion of the significance of the ionospheric screening effect. Now l e t us consider the case where only the f i e l d of mode 1 i s i n c i d e n t on the ionosphere. Then from equa-tions (63) and (64) i t follows that - 93 -Hence we have b ~ -J=fp A/ uo ^ (66) Since \j0 £ {O^.yVLC* » i t ; follows then that that i s , the f i e l d due to the ionospheric current i s smaller than the observed f i e l d . Thus for the incidence of the f i e l d of mode 1, the ionospheric screening effect w i l l not be significant. The order of magnitude of k in this case can be seen from equations (63) and (65) to be h ~ 1 . (67) This shows that the f i e l d in the neutral atmosphere i s 'magnetostatic', and the approximation adopted by earlier work is correct in this case. But when the f i e l d of mode 3 i s incident on the ionosphere, from equations (63) and (64) we have (68) It follows then for any w ranging from 10""1 sec""1 to IO""2 sec" 1. In this case, the ionospheric screening effect cannot be ignored. (69) - 94 -Due to the anisotropy of the inospheric conductivity, this amount of b can produce a significant difference in the direction, i f not in the magnitude^, between the incident and the observed magnetic f i e l d . The order of magnitude of k i s then £ ~/ UJ i.e. I < T ^ £ £ I O - 1 F ( Y as can be seen from equations (63) and (68). This shows that the observed f i e l d i s not 'magnetostatic'. The pre-sent result i s in accordance with the discussion given in section 1 that ionospheric screening may be effective when the observed f i e l d is sufficiently different from the 'magnetostatic f i e l d ' . The above deviation of the observed f i e l d from the magnetostatic f i e l d i s , however, practically impossible to detect by observation: from equations (19) and (70) i t follows that 10~ 6 £ k' £ 10" 5 and accordingly five to six figure accuracy i s required in the determination of | curl | , and hence in the observation of B to detect this difference. The situation in the southern hemisphere can be discussed in a similar way by solving equations (49) and (51) for E^ and E^, instead of E^ and E^. The present result i s obtained for the special case where l w | , but i t w i l l be seen in the next section that a similar conclusion may be derived for the case where U l ^ l w l • Hence i t may generally be - 95 -concluded that ionospheric screening can be effective for changes in the geomagnetic f i e l d with a time scale of IO - 1 - 10" 2 sec""-1-. The degree of screening depends not only on the time scale, but also on the scale in space and on the mode of the incident f i e l d , and w i l l have to be estimated in each individual case. It i s also found that the observed f i e l d can not always be represented by a magnetostatic f i e l d , and an underestimation of the screen-ing effect can sometimes result i f the observed f i e l d i s always approximated by a magnetostatic f i e l d or an electro-magnetic wave. After completion of the present calculations, i t became known that Dr. J. W. Dungey had estimated the magni-tude of the ionospheric current based on similar ideas to those presented above (private communication). But his calculations are carried out for the extreme case which is called 'electrostatic f i e l d ' in this paper, for which the magnitude of the ionospheric current i s the largest as can be seen from equation (27). Since the actual f i e l d i s quite different from the electrostatic f i e l d as shown above (k': 10" ~ i o while k' ^  1 for the case of an electro-static f i e l d ) , his results w i l l lead to an overestimation of the screening effect. - 96 -APPENDIX A For changes with, a time scale of 10 - 10 sec, the earth may be approximated as a perfect conductor for the following reason. Due to the finiteness of the conductivity of the earth, the horizontal component of the electric f i e l d at the ground does not vanish completely, and s t r i c t l y speaking equation (10) must be replaced by (Al) Accordingly the electric f i e l d in the neutral atmosphere is given, instead of by equation (12), by (A2) r A C^'M,W m a y D e neglected, and the earth may be approxi-mated by a perfect conductor, i f / since under this condition the f i e l d i n the upper atmosphere may approximately be determined independently of ±k £ is related to ^  by equation (18) as f ( A 4 ) - 97 -As d i s c u s s e d i n t h e l a t t e r p a r t o f s e c t i o n 1, t h e r a t i o —^-i s s m a l l e s t when the f i e l d i s m a g n e t o s t a t i c , i . e . when k - 1, Hence t h e l o w e r l i m i t o f 6 i s g i v e n b y I/O ( A 5 ) Then the l e f t - h a n d s i d e o f (A3) i s n*<tr-* * i"-5^f ( A 6 ) w i t h L , ~ \03 ajad ^ I D * 1 O v . O b s e r v a t i o n s show t h a t ^ i s o f t n e o r d e r o f 1 m V / j , i . e . 10" 6 cgs i n the r e l e v a n t r a n g e o f i . e . A Ifc - | D p (A7) (A6) and (A7) show t h a t t h e t h e o o n d i t i o n (A3) i s s a t i s f i e d f o r icT^H oo £ I D - ' A J L O - ' , and the e a r t h may be a p p r o x i -mated b y a p e r f e c t c o n d u c t o r . - 98 -APPENDIX B Derivation of equation (68) From equations (49) and (51) i t follows that (BI) E , + ^ t L — - ^-t rrj ' H + i wrcp^ /ufo - i j ft w ) ^ _ U-^^^t+PJIw,)^ + — rrr^—— - l^ ^— H<L ^ 1^ + ^ ^ (B3) — —— TE | 'E.^ — -f-TT i v j -r x.'w x5 (B4) -LJL i ~ - " " c 1 / - 99 -where L = r ' "2->M+ • —• ^ \BQ) 4 At/* 4- f ' (B6) and ;, -L^V j£) | / (B7> The summation over 1 ,w and u are dropped, and In the following c a l c u l a t i o n , terms of the order of i j p /1, w i l l he ignored. Subtracting (B2) from(Bl) we have Equation (B4) can be written as (B9) ,Vc«^f (-E,^^)^ J ^ Z E ^ (BIO) - 100 -Subtracting (B4) from ( B 3 ) , we have (B 11) From (B2) and (Bll), i t follows that (B 12) Eliminating (Eg - E 4) in (B9) by (B12), we have /. i - -> (B 13) - 101 From (B9) and (BIO) i t follows that Then ( E ^ E g) and (E^ - Eg) can be given as (B14) (B15) ,W ( - £ 1 7 ) ] where IAJ - 102 -and * ( i»Wf>jt 7 (An!)J (B16) Hence under the condition that , orders of magnitude and Eg are given as, (B17) Now, from (Bl) and (B2), we have - 103 --H /u^^fi • — 1 '• t j + ( ^ + + ^ ± > ^ \ E + < B 1 8 ) -= —-L\/*\<k Vy+- — — £ ^ J and (BH) leads to ^ = I { ( '^ -V^ T » ' * ^ * (B19) From (B17), (B18) and (B19), orders of magnitude of E 3 and E 4 are given as, (B20) - 104 -CHAPTER IV THEORY OF WORLD-WIDE CHANGES It follows from the discussion in Chapter III that the screening effect of the ionosphere may be appreciable for vrorld-wide changes. Hence the observed f i e l d which i s analyzed in Chapter II must be corrected for the modula-tion by the ionosphere before we can infer the cause of the phenomenon which i s supposed to operate at the magnetospheric boundary. The main change of world-wide changes has a time scale of a few minutes. As illustrated in Figure 19b, i t s magnitude changes but l i t t l e with local time, but varies with latitude, in middle and low latitudes, with a Q characteristic scale of the order of 10 cm. Hence for this part of the change we have, OJ "V IO"1 MAT* T ji ^ ID CA^ i 14141 « [ t I On the other hand, the preceding reverse change, which has a time scale of several tens of seconds, i s observed only in a limited range of local time as shown by Figure 19a. In middle and low latitudes, the characteristic distance of variation of i t s magnitude i s of the order of 10 cm both - 105 -latitudinally and longitudinally. However, to avoid the mathematical complexity encountered in the preceding chapter (see Appendix B), the variation with local time is neglected, and for the preceding reverse change we take \*J, £ and W as The change in the horizontal component of the electro-magnetic f i e l d at the upper boundary of the neutral atmos-phere (z = d) is given by fl, rt f where S n ^ d ^ $ — h ^ ° ^ :• change observed on the ground, and (71) c — U l c2 * . From the condition that | t n l « l « | , the expressions (60) and (61) for the electromagnetic f i e l d in the magnetosphere can be simplified to give - 106 -I t - - -a, w> + E ^ ( i « i / . - - i i n - w - w t ; - , £ l c * - p > ( 7 3 ) For modes 1 and 2, the .electric f i e l d i s perpendicular to the meridian, and for modes 3 and 4 i t is in the meridi-onal plane. In the magnetosphere where the conductivity is i n f i n i t e , the following relationship holds: = - J - IA- A B o where jA i s the velocity of the plasma and B Q is the main geomagnetic f i e l d which i s in the meridional plane. This - 107 -shows that modes 1 and 2 are associated with a plasma motion in the meridional plane (poloidal), while modes 3 and 4 are accompanied by a plasma motion perpendicular to the meridian (toroidal). The incident f i e l d is composed of modes 1 and 3 in the northern hemisphere, and of modes 1 and 4 in the southern hemisphere. The electromagnetic f i e l d in the neutral atmos-phere and that in the magnetosphere are connected by equations (49) and (51) * E z = -2-\Q\ <A Al\ ^  ("EJ -+• E F /) = ^\£\L<i%/ where prefixes are omitted. Hence the amplitudes E ^ , Eg and E ^ of the incident f i e l d can be related to and £^ by ~ ^ p x ^ Z 7 - ^ 4 " ! ^ ^ (75) - 108 -where I 3 = - ^ - 2 l ^ M ^ + . From these equations the change in the f i e l d at ground level resulting from the incidence of each mode may-be obtained. When only the f i e l d of mode 1 i s incident, i t follows from equation (75) that in the northern hemisphere, Vgd c <+TlV T zAo¥ c r h (76) and 2 ^ = - T - T — ^ ~ ^ ~ U ' ° in the southern hemisphere. With l~ \Q~S om~\ d~ I pic,** > 1 0 " ' ^ uo £ » o " V ^ > V / v j o ? wHAto"* , and /d^Wf |~ | , orders of magnitude of the terms in equation (76) may be estimated f i r s t term m~' £y second term £ x £^ third term ^ , ^  ^ Hence i t follows that - 109 -i . e . A ^ f 0 ' (77) i n b o t h h e m i s p h e r e s . T h i s shows t h a t £ x and 1^ a r e o f t h e same o r d e r o f m a g n i t u d e . D e n o t i n g t h i s by i , t h e m a g n i -tude o f t h e o b s e r v e d m a g n e t i c f i e l d may be w r i t t e n f r o m e q u a t i o n (71) a s The o r d e r o f m a g n i t u d e o f t h e m a g n e t i c f i e l d due t o t h e i o n o s p h e r i c c u r r e n t i s g i v e n by c I t f o l l o w s f r o m t h e s e e s t i m a t e s t h a t _ i 4 ^ 2 2 0 1 ^ w (78) S i n c e | 0_lX *-o ^  I 0° A*-^-1 f o r t h e p r e s e n t c a s e , e q u a t i o n (78) shows t h a t t 4 ^ : 'the c o n t r i b u t i o n f r o m t h e i o n o s -p h e r i c c u r r e n t to t h e o b s e r v e d change i n t h e m a g n e t i c f i e l d i s n e g l i g i b l e . Thus f o r t h e i n c i d e n c e o f t h e f i e l d o f mode 1, i o n o s p h e r i c s c r e e n i n g i s n o t e f f e c t i v e . S u b s t i t u t i n g e q u a t i o n (77) i n t o e q u a t i o n (71), we have (79) - 110 -for both hemispheres. With w£,nf,Au7l and IT, | ~ IT,!, i t follows that ie, the observed direction of the change in the magnetic f i e l d i s approximately in the meridional plane. Substi-tuting equations (77) and (79) into the f i r s t of equation (75), we have -> / \ o \ A ^  ni^u u. i \ -iii« ( 8 0 ) ^ 2 TieT P* . This shows that to an observed increase in the horizontal component ( Pe (i^ j?x) = iE?e (^J< 0 ) corresponds an incidence of the f i e l d with IZ^< 0 in both hemispheres. The incident electric f i e l d i s then directed westward, and the associated motion of the magnetospheric plasma is compressional, A decrease in the horizontal component, on the other hand, implies E^> 0; the incident electric f i e l d is directed eastward and the associated plasma motion i s expanding. Vectors of the incident and the observed f i e l d for the case of incidence of mode 1 are illustrated in Figure 21. The screening current in middle and low latitudes is given by equations (76) and (79) as, - I l l -Figure 21. Vectors of the observed and incident fields when"the f i e l d of mode 1 is incident. E: incident electric f i e l d , u : Velocity of the associated plasma-motion, B^o) : horizontal component of the observed f i e l d , and Bo: geomagnetic main f i e l d . - 112 -T = T ^ ZllU ^ (81) 2.TCT X, - P X in the northern hemisphere, in the southern hemisphere, When the fields of mode 3 (in the northern hemis-phere) and mode 4 (in the southern hemisphere) are incident, i t follows from equation (75) that in both hemispheres. The orders of magnitude of each term are given by f i r s t term ~ | 0 ~ ' 4.^ , second term -~ io / ^ / third term ~ £.\^  Hence for equation (82) to hold, must be of the order of u) H £y as given by *7r,''° z/?U £t +- Z-W = 0 (83) - 113 -Since u> ^jcr , A*t-~* , i t follows that l £ j | « |Ixl , and £JL gives the order of magnitude of the incident f i e l d £ . From equations (71) and (83) we have (84) in both hemispheres. With ~2Z ~ - I O13 Ogs , £ ^  icT^o*"-1 , J A- \Q1 OM and to £ \o~* Atcr' , i t can be seen that (fx I » (^1 and the order of magnitude of the observed change in the magnetic f i e l d is given by n „ . J J L L M J £ \ c The order of magnitude of the magnetic f i e l d produced by the ionospheric current i s given by where Hence i t follows that - 114 -This shows that the contribution from the ionospheric current to the observed change in the magnetic f i e l d is not negligible: the ionospheric screening effect has to be taken into account in this case. Substituting equation (84) into equation (75), i t may be seen that the incident f i e l d in the northern hemis-phere i s characterized by a factor Eg given by I ' d and in the southern hemisphere by The increase in the horizontal component ( f^x < 0 ) thus corresponds to E^<o and £*<f. < 0 . The horizontal component of the incident electric f i e l d i s directed north-wards in the northern hemisphere and southwards in the southern hemisphere. The associated motion of the magneto-spheric plasma i s toroidal and i s directed westwards in both hemispheres, as illustrated in Figure 22. In both hemispheres, the incident magnetic f i e l d i s directed perpendicular to the meridian; eastward in the northern and westward in the southern hemisphere, while the observed change in the geomagnetic f i e l d is approximately in the meridional plane. Thus in the case of incidence of modes 3 and 4, the direction of the change in the magnetic - 115 -North South Figure 22. Vectors of observed and incident fields when the f i e l d of mode 3 (in the northern hemisphere) and of mode 4 (in the southern hemisphere) i s incident. Symbols are the same as in Figure 21. 116 f i e l d i s rotated through 90° by the screening effect of the ionosphere. The screening current in middle and low latitudes is given from equations (75) and (84) by (87) in both hemispheres. Thus the incident f i e l d of both modes i s found to give rise to a change in the meridional component of the geomagnetic f i e l d . The change in the t-lV component i s found to be small compared to that in the meridional com-ponent. Since this result i s closely related to the condition that « If I , the direction of the change in the magnetic f i e l d actually observed may not necessarily be in this way i f i s not negligible compared with |0| , as i t is for the preceding reverse change. Hence In relating the observed f i e l d to the inoident f i e l d in the magnetosphere using the present results, i t may be reason-able to take note only of the meridional component of the magnetic f i e l d . The main change is an increase (for a positive change) or a decrease (for a negative change) in the horizontal component of the geomagnetic f i e l d a l l over the world. If this part of the change is assumed to result from the incidence of the f i e l d of mode 1, It follows that - 117 -the magnetospheric plasma i s contracting (for a positive change) or expanding (for a negative change) everywhere at the time of a main change. This i s consistent with the generally accepted idea that the main change of sudden commencements (which has the same characteristics as positive changes) i s due to the compression of the magneto-sphere resulting from the sudden increase in the impact pressure of the solar corpuscular stream. Negative changes may then be related with a sudden decrease in i t . I f , on the other hand, we assume that the main change i s related to the incidence of modes 3 and 4, i t follows that the magnetospheric plasma i s rotating westwards (for a positive change) and eastwards (for a negative change) everywhere at the time of the main change. The incident electric f i e l d i s then directed outwards (for a positive change) or inwards (for a negative change) with respect to the magnetospheric boundary. This seems also to indicate a sudden change in the impact pressure of the solar corpuscular stream. Due to their larger inertia, protons in the stream may penetrate farther into the magnetosphere than electrons, and this causes a polarization directed outwards at the magnetospheric boundary. When"the physical state of the corpuscular stream i s kept stationary, the electric f i e l d due to this polarization may be neutralized by the displacement of the magnetospheric plasma. But when the impact pressure of the stream suddenly changes, the polari-zation produced by the stream plasma is also suddenly - 118 -changed, and u n t i l i t is neutralized by the resulting displacement of the magnetospheric plasma i t w i l l cause an electric f i e l d with the sense indicated above. It seems therefore that the main change of world-wide changes i s the result of a change in the size of the magnetosphere result-ing from a change in the impact pressure of the solar corpuscular stream. The preceding reverse change is a decrease (for a positive change) or an increase (for a negative change) in the horizontal component observed immediately preceding the main change in most parts of the afternoon side of the Earth. If interpreted as a result of the incidence of mode 1, the appearance of a preceding reverse change indicates the occurrence of an expansion (for a positive change) or of a compression (for a negative change) of the afternoon side of the magnetosphere immediately preceding i t s world-wide compression (for a positive change) or expansion (for a negative change). This model i s , however, hard to accept since the afternoon side of the magnetosphere is the very region where the influence of the stream i s f e l t in the f i r s t place, as can be seen by the distribution of the time of onset illustrated in Figure 12. The change conveyed to the ground on the afternoon side of the Earth by mode 1 must be in the same sense as that transmitted to the remaining parts of the Earth. If , on the other hand, we relate this part of the - 119 -change to the incidence of modes 3 and 4, the associated flow of the magnetospheric plasma w i l l be directed east-wards (for a positive change) or westwards (for a negative change) on the afternoon side. Such a flow seems probable, since as the corpuscular stream flows by the magnetosphere, a shear stress is exerted on i t , bending the lines of force towards the night side. An increase in the impact pressure may be associated with an increase in the shear stress, and lines of force, together with the magneto-spheric plasma, w i l l be brought further towards the night side. When the impact pressure is weakened, the shear stress w i l l also be weakened, and the lines of force, together with the magnetospheric plasma, w i l l return to the sunward side. Hence positive changes are associated with eastward flow and negative changes with westward flow of the magnetospheric plasma on the afternoon side. The absence of preceding reverse changes on the morning side is consistent with this idea, because the direction of flow on this side i s opposite to that on the afternoon side, and the resulting change of the geomagnetic f i e l d on the ground has the same sense as that of the main change. Thus the preceding reverse change seems to result from a sudden change in the shear stress of the solar corpuscular stream exerted on the magnetosphere. A similar idea was presented by Parker (Wilson and Sugiura, 1961) to explain the regularity in the sense of rotation of the - 120 -i n i t i a l part of sudden commencements. But his idea, which ignores the inospheric screening effect, f a i l s to explain the appearance of the preceding reverse change in the horizontal component only on the afternoon side of the Earth. According to his model, the direction of the i n i t i a l variation of the magnetic vector of sudden commence-ments should be longitudinal everywhere, in contradiction with observations. The regularity in the sense of rotation i s not discussed here since (1) In the present model which neglects the variation of the magnitude of the change with local time, the longitudinal component of the change i n the geomagnetic f i e l d can not be reliable and (2) A strong objection i s presented by Matsushita (1962) to the results of analysis given by Wilson and Sugiura. Since the characteristic distance in which the Alfven wave velocity varies is shorter than the wave length -1 -2 -1 corresponding to an angular frequency of 10 10 sec (see Appendix II), the estimation of the time of propagation of the change from the magnetospheric boundary to the ground on the basis of ray theory i s misleading. Hence the distribution of the times of onset given by Figure 12 can not readily be explained. The preceding reverse change precedes the main change possibly because the deformation of the magnetosphere by a shear stress may be achieved in an interval of time short compared with that required for a change of i t s size by the impact pressure. - 121 -CHAPTER V CONCLUSIONS Summarizing the results of this thesis, the influence of the solar corpuscular stream on the geomag-netic field, can be described as follows. The upper atmosphere of the Earth is composed of plasma with the geomagnetic f i e l d frozen into i t . The impact pressure of the corpuscular stream which i s always flowing out from the sun confines the geomagnetic f i e l d , together with the Earth's atmosphere, in a space of f i n i t e dimensions called the magnetosphere. At the same time, the solar corpuscular stream exerts a shear stress on the magnetosphere as i t passes by, and geomagnetic lines of force are bent towards the night side. Thus in a stationary state the configuration of the geomagnetic lines of force may be illustrated in Figure 23. The intensity of the solar corpuscular stream i s as variable as the physical state of the solar atmosphere. A sudden change in i t s intensity gives rise to a sudden change in the impact pressure and the shear stress which i t exerts on the magnetosphere, and this w i l l result in a sudden change in the configuration of the geomagnetic lines of force. The result i s observed at ground level as a sudden, world-wide change in the geomagnetic f i e l d . Such - 122 -changes are observed quite frequently: almost every day around sunspot maximum. A few of these changes are followed by an interval of increased activity and are known as sudden commencements of a magnetic storm. But most of these changes are not associated with the beginning of a magnetic storm. This difference may result from the difference in the energy spectrum of the relevant flow of the solar corpuscular stream. If the intensity of the corpuscular stream i s suddenly strengthened, the impact pressure and the shear stress are suddenly increased, and the geomagnetic lines of force w i l l be further compressed, and further dragged towards the night side of the Earth from the stationary configuration as shown in Figure 23. After being modulated by the screening effect of the ionosphere, the effect of this process i s observed in the horizontal component of the geomagnetic f i e l d as a decrease immediately followed by an increase (in a region covering most of the afternoon side of the Earth) or as an increase (in the remaining regions). If the intensity of the stream i s suddenly weakened, on the other hand, the resulting sudden decrease in the impact pressure and the shear stress changes the stationary configuration of the magnetosphere to the form illustrated in Figure 23. The effect of this process on the horizontal component of the geomagnetic f i e l d at ground level produces a sudden increase immediately followed by a INCREASE STATIONARY DECREASE SOLAR CORPUSCULAR STREAM Figure 23. Schematic illustration of the configuration of lines of force. Dotted curves represent the projection on the equatorial plane of representative lines of force. Center: stationary configuration. Left: after an increase in intensity of the corpuscular stream. Right: after a decrease in i t . - 124 -decrease (in a region covering most of the afternoon side of the Earth) or a sudden decrease (in the remaining regions) . The present model seems to give a reasonable explanation for such observed features as (1) the frequent occurrence of world-wide changes in the geomagnetic f i e l d , (2) the existence of positive and negative changes which are morphologically identical, (3) the world-wide occurrence of the main change and (4) the occurrence of the preceding reverse change In a limited region covering most of the afternoon side of the Earth. But in the present treatment, (1) the horizontal uniformity of the physical state of the ionosphere and the geomagnetic main f i e l d is assumed, and given physical parameters are representative of the state in middle and low latitudes, and (2) variation in the magnitude of the preceding reverse change with local time i s neglected. Further considerations without making these assumptions are necessary to explain (1) the regularity in the sense of rotation of the magnetic veotor and (2) the equatorial enhancement of the main and preceding reverse change. The cause of the following reverse change also remains to be explained. - 125 -APPENDIX I Classification of sudden impulses in the geomagnetic f i e l d Committee No. 10 (on rapid variations and Earth currents) of the International Association of Geomagnetism and Aeronomy (I.A.G.A.) issued a special report at the 1957 meeting of the International Union of Geodesy and Geophysics (I.U.G.G.) in Toronto. This report contained the resolu-tions of an earlier meeting held that year in Copenhagen. Three kinds of sudden impulses in the geomagnetic f i e l d were defined. ssc A sudden impulse followed by an increase in activity lasting at least one hour. The more intense activity of the storm may appear immediately or i t may be delayed a few hours. ssc* This i s similar to an ssc, except that the sudden impulse i s immediately preceded, on at least one component, by one or more small reverse oscillations. In case the reverse movement has approximately the same amplitude as the principal movement, i t w i l l be reported as ssc (not ssc 4 8 -). s i If the observer sees an important sudden impulse during a storm, but doubts that i t represents the beginning of a new storm, he should report i t as s i . - 126 -As knowledge of the world-wide morphology of these changes i s accumulated, the incompleteness of the present classification has become more apparent. The main defect i s the lack of regard of world-wide features of the phenomenon. This i s perhaps natural, since the above specifications were given as indications for the c l a s s i f i c a -tion of phenomena at an individual station. Hence phenomena are classified only by characteristics observed at a single station regardless of world-wide features of the phenomena. This makes the terminology used in the present classification inadequate for the description of the overall features of the phenomenon. For example, the present definition of ssc* could apply to four different types of changes. Since these four types of changes are entirely different in character, confusion i s unavoidable i f the same terminology ssc* i s used for their description. According to the present definition of s i , sudden impulses which do not occur during a magnetic storm are not counted as s i , although both in reports from stations and in published papers such occurrences are usually called s i ' s . Actually si's are observed quite frequently, and since they show the same morphology as sc's, they must be classified in the same way as sc's. (To make the revision in termin-ology as small as possible, the terminology s i i s retained, although in the main part of this thesis these are called 'world-wide changes' since they are not always impulse-shaped.) - 127 -These indicate that we are now in a position to try and revise, on the basis of our accumulated knowledge, the present classification of sudden impulses in the geomag-netic f i e l d . * * * * * The observed features of sudden impulses in the geomagnetic f i e l d are summarized below. Descriptions always refer to the horizontal component, since consider-able c l a r i t y can be attained by noting this component only. 1. There are sudden changes in the geomagnetic f i e l d which are observed a l l over the world with certain features in common within a time interval of about one minute. The sense of the change i s either an Increase or a decrease. The part of the phenomenon which i s observed on a world-wide scale w i l l be called the main impulse. The overall phenomenon i s called positive or negative according to the sign of the main Impulse. The overall morphology of the phenomenon i s independent of the sign of the main Impulse. 2. A sudden impulse may be classified into two categories - those which mark the beginning of a magnetic storm and those which do not. Their overall morphology i s identical in both cases. - 128 -3. The main impulse may he accompanied, in some regions, by a reverse impulse. These are of two types. The f i r s t , which precedes the main impulse, w i l l be called a preceding reverse impulse. 4. The second, which follows the main impulse, w i l l be called a following reverse impulse. The possible confusion inherent in the present classification i s shown in the following example. Con-sider the changes shown in Figure 24a and 24b. The change illustrated in Figure 24a may be either (1) A positive main impulse preceded by a preceding reverse impulse, or (2) A negative main impulse followed by a following reverse impulse. The change illustrated in Figure 24b may be either (1) A positive main impulse followed by a following reverse impulse, or (2) A negative main impulse preceded by a preceding reverse impulse. - 129 -Figure 24. Examples of sudden impulses. A l l these four cases are apparently different. But a l l of them are sudden impulses which are accompanied, on at least one component, by one or more small reverse oscillations. Hence i f they are followed by an interval of 'an increase in activity lasting at least one hour', then a l l of them must be called ssc*, thus losing any distinction between them. The same d i f f i c u l t y i s encountered i f we try to classify sudden impulses in the same way as sudden commencements into s i and s i * . Moreover, a l l of them must be called ssc i f |H,| is comparable with or larger than IhUl ( i t is not rare that following reverse change i s smaller than main change), since then the 'reverse movement has approximately the same - 130 -amplitude as the principal movement'. This introduces further confusion. It i s impossible to identify the nature of the phenomenon using only the two terms - ssc and ssc*. # * 45- -55- ¥r Hence an attempt i s made to improve the present classification. The terminology used by Matsushita (1957, 1960, 1962) i s adopted as a basis. This i s preferred to the terminology used by Akasofu and Chapman (1960), since this can be extended to the case of negative change in a simpler way. This i s extended in the following respects. 1. A clear distinction i s made between the terminology for the phenomenon as a whole and that for the phenomenon as seen in various parts of the world. 2. Since their morphologies are the same, similar c l a s s i f i -cation and symbols are used for the four following cases - a positive impulse preceding a period of increased activity, for a negative impulse preceding a period of increased activity, for a positive impulse not preceding a period of increased activity, and a negative impulse not preceding a period of increased activity. Sudden impulses w i l l f i r s t be divided into two categories: those which are observed within about one minute a l l over the world, although the shape, of the impulse may not - 131 -be exactly the same, and those which are not. Only the •first of these two categories are studied in this thesis. World-wide sudden impulses are then classified according to their relationship with the interval of increased activity and the sign of the main impulse, as follows: 1. sc (positive sudden commencement). A phenomenon which is observed as a sudden increase in the horizontal component a l l over the world, and which precedes the increase in activity lasting at least one hour a l l over the world. In some regions the sudden increase i n the horizontal component i s accompanied by a decrease. 2. (sc) (negative sudden commencement). A phenomenon similar to an sc but with the sign of the overall impulse reversed. (This class of phenomena has not been clearly identified in records.) 3. s i (positive sudden impulse). A phenomenon which i s similar to an sc but which does not precede the increase in activity in the manner specified in 1. 4. (si) (negative sudden impulse). A phenomenon which is similar to an s i but with the sign of the overall impulse reversed. The above are the classifications of the phenomena as a whole. Each of these w i l l appear in various shapes in - 132 -different parts of the world, and w i l l he denoted in the following way. 1.1 SC At a place where only the main impulse i s observed at the time of the sc, the phenomenon w i l l be called SC, 1.2 SC At a place where the main impulse and a preceding reverse impulse are observed at the time of the sc, the phenomenon w i l l be called ""SC. 1.3 SC~° At a place where the main impulse and a following reverse impulse are observed at the time of the sc, the phenomenon w i l l be called SC~~. 1.4 ~SC~" At a place where the main impulse, preceding reverse impulse and following reverse impulse are observed, the phenomenon w i l l be called "~SC~"". 2.1 (SC) Replace sc in 1.1 by (sc) 2.2 (~"SC) Replace sc in 1.2 by (sc) 2.3 (SC""*) Replace sc in 1.3 by (sc) 2.4 (*~SC"~) Replace sc in 1.4 by (sc) 3.1 SI Replace sc in 1.1 by s i 3.2 "~SI Replace sc in 1.2 by s i 3.3 SI"" Replace sc in 1.3 by s i - 133 -3.4 ~SI~~ Replace sc In 1.4 by s i 4.1 (SI) Replace sc In 1.1 by (si) 4.2 (~SI) Replace sc in 1.2 by (si) 4.3 (SI~) Replace se in 1.3 by (si) 4.4 ("~SI~") Replace sc in 1.4 by (si) Since the above detailed classification i s impossible using data from only one station, the present o f f i c i a l term-inology ssc and ssc* might have to be retained for reporting. But in an investigation of sudden impulses, the terminology suggested above is preferable. - 134 -APPENDIX II THE OHMIC LAW IN THE UPPER ATMOSPHERE 1. Introduction In electromagnetic theory, the property of the medium i s expressed by the following three equations: (1) an equation representing the relationship between the magnetic Induction B and the magnetic f i e l d intensity H, (2) an equation representing the relationship between the electric displacement D and the electric f i e l d Intensity E and (3) an equation relating the eleotric current density j, to the electric f i e l d intensity E. In the upper atmosphere of the Earth the f i r s t two of these relationships are given by B = H and D = E to a good order of approximation. The third,, which may be called the Ohmic law in a generalized sense of the word, i s derived from the equation of motion, the equation of continuity and the equation of state of the gas, and i s expressed either as, j = # E or as I X - A - o ) ' where v i s the velocity of the center of mass of the gas, and B_0 is the geomagnetic f i e l d , o1 and are conductivity matrices consisting generally of operators. - 135 -The difference between these two representations l i e s in the frame of reference in which j[ i s derived. In the f i r s t , j_ i s derived in a frame in which E i s observed. In the second j_ i s derived in a frame which i s moving with velocity v with respect to the frame in which E i s observed, and since the r e l a t i v i s t i c variation in j i s small for the values of v to be discussed later, jj_ i s approximately the same as J_ observed in the same frame as E. From a mathe-matical point of view, in the f i r s t representation, the variable v i s already eliminated, and the property of the medium Is sufficiently expressed by a conductivity matrix 'cr . In the second representation, on the other hand, v is s t i l l included, and hence to express the property of the gaseous medium, equations relating v to the electromagnetic f i e l d must also be used together with the Ohmic law. In.spite of the greater simplicity of the f i r s t expression of the Ohmic law, the second representation i s usually adopted by most workers, because i t has been found that in most cases studied in geomagnetism and aeronomy, the behaviour of a gas under an electric f i e l d i s expressed as a d r i f t of the center of mass in a direction perpendicular both to the geomagnetic main f i e l d and to the direction of the electric f i e l d , with a velocity given by, and the second representation of the Ohmic law i s then - 136a -simplified as, I + I A B 0 = 0 (Alfven, 1950; Cowling, 1957; Dungey, 1958; and others). But, in the ionosphere, this simple expression does not always hold. Particularly for angular frequencies 1 —3 —1 ranging from 10" to 10 sec , which correspond to a time scale of 6 to 6000 seconds and include much of the phenomena treated in geomagnetism and aeronomy, this expression can not be used (Watanabe, 1962). In this situ-ation, the seoond expression seems to lose i t s advantage, and might only add to the complexity of the problem by including the variable v e x p l i c i t l y and thus increasing the number of basic equations. Hence for a study of world-wide changes, sckand micropulsations in the geomagnetic f i e l d , which have a time scale of one second to several minutes, i t seems preferable to use the f i r s t formulation of the Ohmic law without including v e x p l i c i t l y . Ionospheric data are tabulated in Table 6. 2* Fundamental equations The equations of motion for the three constituents (electron, singly ionized positive ion and neutral particle) of the model Ionosphere are given by - 136b -Table la. Ionospheric data Altitudo (km) ^ n N. T Kn ven v; vie 80 2-8414 1-003 168 3-53-12 1-986 6-874 2-561 90 3-9013 3-804 176 9-75-10 2-785 9-473 6-802 100 6-0012 1-805 208 3-00"8 4-484 1-483 2-483 120 6-3011 2-005 390 3-18-' 9-783 1-602 118 3 140 1-0711 2-405 662 2-24~6 1-953 2-821 8-852 160 400 1 0 3 005 926 7-50-6 4-432 1-011 4-982 180 2 00 1 0 4 005 1115 2-00-5 2-222 5-46° 5-052 200 107 1 0 6 005 1230 5-60-5 111 2 2-97° 6-772 220 6-609 8-605 1305 1-30-4 6-391 1-87° 8-832 240 4-609 1-306 1356 2-84~4 3-941 1-32° 9-552 260 3-309 1-806 1400 5-45~4 2-581 9-65-1 1-633 280 2-359 2-206 1430 9-37~4 1-751 6-92-1 1-923 300 1-829 2-606 1455 1-43-3 1-141 5-42-1 2-213 350 8-308 2-146 1488 2-58-3 4-77° 2-52-1 1-753 400 4-708 1-536 1500 3-26-3 1-66° 1-46-1 1-573 450 2-508 1-336 1500 5-33-3 7-25"1 7-90-2 111 3 500 1-438 9-525 1500 6-65-3 3-12-1 4-61-2 8-202 600 4-737 7-395 1500 1-56-2 6-35-2 1-55-2 6-302 700 1-647 617 5 1500 3-76-2 1-95-2 5-52-3 5-302 800 5-818 4-915 1500 8-46-2 5-75-3 2 05- 3 4-252 T means the ionospheric temperature. Table 6. Ionospheric Data (after Watanabe, 1962). N n: the number density of neutral particles, N Q: the number density of electrons, Kf= , T: the ionospheric temperature, and Vz.-l^d-r \>e,„, : the electron c o l l i s i o n frequency, and V; : the co l l i s i o n frequency of an ion with neutral particles. - 137 -- V Pe - e M e ( § + - L - ^ e ^ E . ) / (1) M;IM (2) |W*-H»l' R (.<A« -K! )+• N/.U»e = - VP* (3) where m Q , m^  and are the masses, , u^ and u n the average v e l o c i t i e s , N , and N n the number densities, and P Q, P.j_ and P n the p a r t i a l pressures, of an electron, an ion and a neutral p a r t i c l e r e s p e c t i v e l y . The second and t h i r d terms on the l e f t hand side of each equation represent the exchange of momentum due to c o l l i s i o n s between d i f f e r e n t kinds of - 138 -p a r t i c l e s , , ye« , and represent c o l l i s i o n frequen-cies of an ion with electrons, an electron with neutral p a r t i c l e s and an ion with neutral p a r t i c l e s respectively. Three other c o l l i s i o n frequencies are related to them by the equations NcVe; = N'.Ue, M i * — N..VV, N*»«., ( 4 ) (In deriving these c o l l i s i o n frequencies, ! i t i s assumed that the d i r e c t i o n of r e l a t i v e v e l o c i t y between c o l l i d i n g p a r t i c l e s becomes completely random a f t e r each c o l l i s i o n . ) The equations of continuity r e l a t i n g the u's and N Ts are 2*± + (_N;U; ) = ' (? , (6) JN= 4- <J<V IN* ^ ) = D (V) Let us assume that when a changing electromagnetic f i e l d i s not present, the v e l o c i t y of each constitutent i s zero and that the density and p a r t i a l pressure are constant and homogeneous. Pressure P_ and number density N_ (s = e, S o i and n) are replaced by P s + p s and Ns+- n g , where c a p i t a l - 139 -letters denote the value corresponding to the state before the changing electromagnetic f i e l d is introduced, and small letters denote the perturbation associated with the changing electromagnetic f i e l d . As the gas should be e l e c t r i c a l l y neutral in the stationary state, EL = N-, and w i l l be denoted by Np. Magnitudes of perturbing quantities are assumed to be small enough to allow the linearization of the above equations. Neglecting also terms of the order ^- Q/^ or m e / m n (in comparison to the remaining terms), equations (1) - (7) become (IM = _ v>p. (SM - 140 -(3») | i where V;^ .-=-j- ^ i * (assuming m^  - n^) , -t- Ni|» 4iV J/U -= 0 r (5t ) i ! i + ^ <J.V*M = 0 (7«) ?t -where denotes the main geomagnetic f i e l d which is far stronger than the changing magnetic f i e l d . Assuming that the change in state takes place adiabatically, p and n_ (s m e, i and n) are related by the equations ft = b-lWeK*, (k= J - ^ 1 , (8) f. = At* ft.'Hi, (9) - 141 -rn*. (10) ( N o t e : K = B o l t z m a n c o n s t a n t ; k = m a g n i t u d e o f wave v e c t o r . ) The a b o v e e q u a t i o n s c a n be s o l v e d i n t h e f o r m , 7 = <r E where (11) (12) and ^ i s a c o n d u c t i v i t y m a t r i x . F rom M a x w e l l ' s e q u a t i o n i n a medium where £. and jt> c a n be a p p r o x i m a t e d by u n i t y : ~b 3 C^ AX 1 = £ -pjT £ - ^ i -4 r c a t ; (13) (14) (15) (16) where (17) - 142 -i t follows that i V ^ _ _ L . ^ = <^U .Jir* f ^ - 5 T " _ (18) The right hand side of equation (18) includes the effects of the presence of a charged medium on the propaga-tion of electromagnetic waves. The f i r s t term represents the effect due to the inhomogeneity produced in the charged medium, and the second term represents the effect due to the presence of electric currents. From equations (5') and (6') i t follows that Hence using equation(15)we have, J.V±5- -r 4-TT A* ± — 0 . (18') This i s not an independent equation,however. It follows directly from equation (18)by taking the divergence of both sides, since E and j are time-dependent. The electric f i e l d E can be derived from equations (11) and (18). The associated magnetic f i e l d B can be derived from equations (13), (14) and (16). 3. The Ohmic law Equations (1) - (10) w i l l be solved to derive 'tr . Let us assume that every variable in the preceding equations has the form: e . Then equations - 143 -(IM - (3') can be written as, and using equations (5') - (7 T), (8) - (10) become, fe = We Wr ~f {k • IA.) ( - 1 4 4 -It can be shown that the terms representing the pressure gradient in equations ( 1 " ) - ( 3 " ) , viz. ifcfe/ i ^ f * and A ^ ' j ' v may he neglected in comparison with other terms under certain conditions which are f u l f i l l e d in the present problem. These conditions are, | Hj> v^ vwu,: |, i N f Ve« toe JA* |y (19) (so) " U J — — / / i N ^ I W I J i l l , I ^ ^ W e J A . . ! > ( 3 D These may be summarized as, - 145 -t - f f » J [ K T j ^ _ H r r IAJ ^rKT j r K T IM: / y<* w. , tw* , v% N)f ml , (22) From the ionospheric data shown in table 6, i t can be seen that on the right hand side of the inequality (22), the term ti\t l s t i l e l a r S e s , b a t a n 7 height. Hence the condition (22) may be represented by X ^ *KT I (22') It can be seen that the condition (22) can be satisfied for UJ = 10~ 2 sec""1 only i f [ 1 (23) This means that there should be l i t t l e difference in the characteristics of the phenomenon over distances of about 30,000 km (300° along a meridian). This i s a rather severe condition that does not seem to be f u l f i l l e d in the case of world-wide changes. But i t can be seen that a l l terms appear-ing In the condition (22) other than the largest are smaller than (^ ") i f ^ in; wtf* . - 146 -This can be satisfied when ( \jj - 10 -2 sec" ) (23' ) i.e., when features of the phenomena are similar over distances of 1000 km (10° along a meridian), which seems to be true in the present case. Hence i t may be said that when the condition (235) i s f u l f i l l e d , a l l the terms in equations ( ! ' ) _ ( 3 ? ) are larger than the pressure gradient terms with the exception of one term - that which i s related to the largest term on the right hand side of (22). This i s Np ))en BigU^ on the l e f t hand side of equation (3'), which is the smallest among the non-pressure gradient terms. Hence equations (1') - (3') may be approximated consistently by condition (23') by dropping, in addition to the pressure gradient terms, the term N mQ u^ in equation (3'). The upper limit of the error introduced by this approximation is given by the ratio of the largest of the dropped terms to the smallest of the retained terms, i.e. by which is small enough - ranging from 10 at 80 km to 10~ at 500 km. This estimation of the upper limit of the error i s quite s t r i c t , and the real order of magnitude of the error could be considerably smaller than that given here. (23'') - 147 -Equations (1") - (3* 1) are solved under this approximation. The components of u and u. perpendicular e ~ * i to the main magnetic f i e l d B are denoted by u^ and u^ ", and O —9 ~1 written as, (25) where ^ (»^r+ ^ ( . ^ j + ^ , where s = e or X , Mp" NJ* M« , - 148 -Np N« Me 0; H„ V;, - fop N« w; m„ , - Np* Kl* IV; v>/» , - Nf* A/* m .'At*, - 149 -I)? me w; y<>» Vi*, ty1 w wu, Mp1 J\Jn Me &U 1 4 A , hip A/»t W e A/pl A/* W« m« , - 150 -Prom equations (24) and (25) i t follows that i 1 — zr(^ = - ^ ^ V J L ( ^ + ^ i ) - r 6 J ' A ^ (26) — r - — > ^< -t- 1 + c 1 A 2 \ - (27) — a — e The components of u e and Uj[ p a r a l l e l to B Q, denoted hy u' 1 and u 1 1 ^ are given by R" _ -±i-e ( 2 8 ' — ^ — ' u" =- e 5 " . <29> The solution of equations (26) - (29) can, in general, be written in the form, A. p (I'I*/)u+ • A (|V)'+ • -p--1- J 3 ° ) ( i i ^ J + + - • -- 151 -l . V ) + • - - -(31) where C^)$H represents a power series in ( ) of order S, and are non-zero constants. The complete expression must be derived i f we wish to find out the characteristics over the entire frequency range. But in the present problem, we are interested in a limited range of frequency, and further approximation i s possible. The following condition holds between 80 and 500 km -1 -2 -1 for ranging from 10 to 10 sec Mi* ( vK \>i, Vu ) ^ ^ This is equivalent to v;„ >> w >> j p j u a k i i k ' N * VVe Then A , A , A ' $ and A ^ may be approximated as, - 152 -A = fi/i; iv\e iHn ye„ (to; (| • L i . - N 7 Nn in; 6 k ; i + „ . — A; — Mp" N* Me w„ Pe* (.UJ) , (33) A ; ' = - Np*N/» P i > (-'^ ) / ^ i " — N i p 7 W\ f W» V e » (-'^ ( • + ~ £ ^ f ) Above the 120 km. level, where ^ ^ ^ , equations (26) - (29) can be solved to give, ^ = ^ E - A | L 4 ^ b ( 5 4 ) ,1 = N/f ^ " (35) - 153 -where bedenotes a unit vector in the direction of B c. Between 80 and 120 km, where uj« vU , the solution i s , (37) Thus the conductivity below the 500 km level i s real and inde-pendent of IAJ . The ionosphere behaves like a conductor with anisotropic conductivity given by cr • / cn <r2 0 \ V 0 0 where the z-axis i s taken in (38) 80 to 120 km, <T\ — - pn; w; <T"» •=• f1— and from 120 to 500 km, - 154 -Q~0 =. U - • These are tabulated in table 7, and illustrated in figure 25. Above the 500 km l e v e l , either of the following conditions is satisfied: y'*, ^ ^ « i 4 * , p/e , (39) or V.t , )>t* « uJ <<: (40) -1 -2 -1 u> taken to l i e between 10 and 10 sec does not exceed Ue anywhere, because Me i s of the order of 1 0 2 sec" 1 with a magnetospheric temperature of 10 °K and a plasma density of 1 0 2 cm - 3. Under the condition ( 3 9 ) , A , As> , As may be written as — - N)^Mr rw.'w* d V ; \ A e " = Np~ W« Me ("v ) . ( 4 1) A ' / = - Np l t - 155 -Table 7. Ele c t r i c a l conductivity in the ionosphere.*" iitude (km) 07 07 101 1 80 3.104 1.10* 3.104 90 6.106 5.104 8.105 100 1.108 2.105 3.106 120 g 3.10s 4.106 5.106 140 7.109 7.105 1.105 160 3.10 1 0 5.105 4.104 180 3.10 1 0 2.105 6.103 200 5.10 1 0 9.104 2.103 250 1.10 1 1 4.104 2.102 300 1.10 1 1 2.104 4.101 350 1.10 1 1 8.103 8.10° 400 1.10 1 1 4.103 2.10° 450 1.10 1 1 2.103 6.10" 500 1.10 1 1 1.103 2.10"' *Cgs Gauss units are used. These may be transformed into other systems of units by, 10 rr - 157 -Substituting these into equations (26) - (29) i t follows that, i « » - ^ 1 — * \ ( 4 3 ) (44) Under condition (40) we have, A — N/^ iwe | M W e ( \ J^)*/ A e - - blfM*M.'W* ( ' V ) * , A / = _ Wpx ^ „ C i ' " / , A € " = A/^ A/n Mn he Wfc (iw) , A ( ' = Mi m'e A-; = - M , y,v ( i " ' ; , A;'«=. K/^  A/* ft* W« C ^ ) . It follows then that, ^ = j ^ * h ^ _ ^ ^ ^ ^ f ^ c e Li„f ^ ( 4 5 ) - 158 -Hence above 500 km the conductivity i s given by 0\ C i v / (47) The main difference between the conductivity matrix given by (38) and that given by (47) l i e s in the dependence of T ; on \jJ. Below about 500 km, oi i s a constant independent of w , and the medium behaves as an anisotropic conductor. Above the 500 km level, on the other hand, o~, i s propor-tional to . Substituting this into the Maxwell equation i t can be seen that this has an effect equivalent to alter-nating the dielectric constant. Hence the phase velocity of the propagation of the electromagnetic f i e l d becomes entirely different from c. This mode of propagation of the electro-magnetic f i e l d i s called a magnetohydrodynamic wave. Equation (48) has been solved in the case of transverse propagation by Spitzer (1956). But i t is more customary to rewrite j as, (13); ( OUAP I ) -f I J IU/TE (48) (49) - 159 -^ / T i s the velocity of the center of mass of the gas and <r is the conductivity matrix as determined in a frame which i s moving with the velocity v, v, defined by, _ typHi \Al -tune JA<) + N/wfth (50) is given from equations (1) - (3) by where p = Mp (M;-t- Wt ) -t N/* vrt* . Substituting equations (42) or (45) into equation (1) and noting that Np^Nl* in the magnetosphere, we have, Ms--. ^ ( - ^ ( M i t f c f ^ ) ( 5 2 ) It follows from equations (49) and (52) that, — c — — — — , where vJ^ i s the proton plasma frequency defined by (53) Hence 0\ = (54) CP* — (7~o - 160 -As VJ«U)L inside about ten earth r a d i i for vo .* |0~*«/ io"a rcc"' | o V | « 1 ° ^ • a n d It follows that, | g V ^ X A P . l = |-£-l* J*| « 1^1. (55) Hence J - X A ^ V 0 . (56) The theory of magnetohydrodynamic wave propagation i s constructed from this equation which implies that the mag-netic lines of force are virtually frozen into the conductive medium (Alfven, 1950: Cowling, 1957; Dungey , 1958). But i t must be noted that the applicability of the theoretical ray treatment adopted by most previous workers is quite limited for problems in geomagnetism and aeronomy. Ray theory i s valid only when the medium i s sufficiently uniform within a distance of a wavelength? i.e., i t is appropriate only for phenomena whose characteristic period of variation T satisfies « 1 , where V i s the Alfven velocity and L a characteristic distance of variation in V" . Table 8 shows that this condition requires ~\~ <•< \ tec In most parts of the magnetosphere. Hence for most phenomena studied in geomagnetism and aeronomy, theoretical ray treatment i s inadequate. - 161 -Table 8. Check of the uniformity of the magnetosphere. 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