Ionospheric Electric Fields, Currents, and Resulting Magnetic Fields Variations
Junhu Du
A thesis submitted for the degree of Doctor of Philosophy . Ill - The Faculty of Science and Technology
The University of New South Wales Sydney, 1998 CERTIFICATE OF ORIGINALITY
1 lleteby declare that this submission is my own work and to die best of my knowledge it conllins no materials previously published or wriam by -tbcr person, nor material which ID a substantial extent bas been accepted for die awanl of any other degree or diploma at UNSW or any other educational insti1ution, except where due acknowleclgement is llllde in the thesis. Any contribution lllldc ID the research by odlers, with whom I bave worlted at UNSW or elsewllcre, is explicitly acknowledged in lbe thesis. l also declare that lbe intellec1ull content of this thesis is lbe product of my own ..t, except ID die extent that ISSis1ance from others in lbe project's design 111d c:mc:eption or in style, ~talion and linguistic expression is acknowledged. (~) ...... Abstract
This thesis uses an equivalent circuit model to calculate ionospheric electric fields, current densities and introduced magnetic fields variations on the ground. The winds used as input are adjusted to yield values of the calculated parameters close to those which have been measured experimentally. The role of the field aligned current is examined. MSIS-90 and IRl-86 are adopted in the program to represent the neutral atmosphere and the ionosphere. The flux tube integrated conductivities in the E and F region are compared. It is found that the ionospheric electric dynamo process is controlled by the E region during daytime but by the F region during nighttime. The F region has a larger effect on the dynamo processes during solar maximum than at solar minimum, and during equinox than in solstice. The different wind models are included and their contributions to the ionospheric electric fields are discussed. We studied the electric field variations with altitude, season and solar activity. In equatorial area, the ionospheric eastward electric field changes very little within the whole ionosphere. The southward(equatorward) electric field is large and changes quickly with height in the E region although it is nearly constant in the F region. The prereversal enhancement of the eastward electric field is produced by the F region dynamo. We conclude that the Forbes and Gillette tidal wind omitting the semidiurnal eastward component can repro duce most features of the Jicamarca experiment and the AE-E and DE-2 satellite observations of the electric fields. The HWM90 empirical wind model failed to produce the observed electric field and it seems the semidiurnal wind in HWM90 is too strong. The changes of the field aligned current with altitude, UT, season and solar ac tivity are examined. We find that the field aligned current is sensitive to the arithmetic method used and is located mainly in the E and low F region. The non-coincidence of the geomagnetic and geographic equators has a strong effect on the field aligned current in the equatorial zone. The solar activity does not much influence the field aligned current distribution pattern but changes its magni tude and introduces considerable field aligned current at night. The field aligned currents driven by Forbes' winds for March equinox and December solstice flow mainly from the southern to northern hemisphere in the morning and vice versa in the afternoon at F region heights. The observed magnetic field variations on the ground are well reproduced in our simulations. It was shown that the field aligned current is the main contributor to the eastward magnetic field component in the equatorial zone. The longitudinal inequality of the northward magnetic field is introduced mainly by the variations of the local magnetic field intensity. The electric field variations have only a mi nor effect. The northward magnetic field variations with the solar activity are introduced by changes of the E region equatorward electric field and the Hall conductivity. The difference in the seasonal dependence between simulations and observations in the equatorial zone is pointed out. It seems that a more accurate wind model is needed. Acknowledgments
The work described in this thesis was carried out in the School of Physics at the University of New South Wales under the direction of Associate Professor Robert J. Stening. I would like to take this opportunity to express my most heartfelt gratitude to my supervisor, Associate Professor Robert J. Stening, for allowing me use his equivalent circuit codes, for his unflagging encouragement, constant reassurance, careful supervision, and patient guidance both during the research and prepara tion of this thesis. Thanks must also go to my fellow student Scott, who has provided me with mis cellaneous help and useful discussions concerning the ionospheric physics. Great thinks also go to Weihong Zheng, who has helped me with computer graphing. I am very grateful to my wife Wei Sun and my son Johnny Du for their support and understanding throughout the course of my study. I also acknowledge the financial support provided by an Australia Commonwealth Government Overseas Postgraduate ·Research Scholarship scheme, and another scholarship provided by Associate Professor Robert J. Stening which makes my research possible. Contents
1 Introduction 1
1.1 Introduction . 1
1.2 Simulation models 2
1.2.1 No feedback between the electrodynamics and the neutral motions ...... 3
1.2.1.1 Equivalent Circuit Network 3
1.2.1.2 Differential Equation .... 4
1.2.2 Feedback between the Electrodynamics and the Neutral Motions 8
1.3 Experiments . . 10
1.3.1 Rockets 10
1.3.2 Incoherent Scatter Radar . 10
1.3.2.1 Equatorial Region. 10
1.3.2.2 Low and Middle Latitude 14 1.3.2.3 Empirical Drift Model 15
1.3.3 HF Coherent Scatter Radar 15
1.3.4 Satellite ...... 17
2 Simulation Model 21
2.1 Introduction .. 21
2.2 Equivalent Circuit 21
2.3 Perpendicular Current Density . 26
2.3.1 No Dynamo in F Region 27
2.3.2 No Dynamo in E Region 28
2.4 Scale Factor . . . . 28
2.5 Equipotential Lines • • I • • • • • • • • • • • • • • • • • • • • • 31
2.6 Field Aligned Current 32
2.7 Magnetic Field Variations on the ground 33
3 Conductivity and Background Atmosphere 38
3.1 Conductivity .... 38
3.2 Collision Frequency . 39
3.3 Electron Temperature 42
3.4 Neutral Atmosphere . 44
11 3.5 Ionosphere ...... 46
3.6 Internal Magnetic Field . 47
3. 7 Atmospheric Wind 48
3.7.1 History ... 48
3.7.2 The (1, -2) Tidal Winds in E Region and Measured F Re gion Zonal Winds ...... 49
3.7.3 Forbes Diurnal and Semidiurnal Tidal Winds 51
3. 7.4 HWM90 ...... 53
4 Flux Tube Integrated Conductivity 55
4.1 Introduction . 55
4.2 Equations .. 57
4.3 Flux Tube Integrated Conductivity 58
4.3.1 Altitude distribution . 58
4.3.2 Local Time Variation . 60
4.3.3 Solar Activity Dependence . 60
4.3.4 Longitudinal Variation 70
4.3.5 Seasonal Variation 70
4.4 Discussion 71
4.5 Summary 72
lll 5 Electric Fields and Currents 74
5.1 Introduction ...... 74
5.2 Electric Field and Current Produced by the (1, -2) mode in the E region and the F Region Winds 75
5.2.1 E Region alone . . 76
5.2.2 Whole Ionosphere . 77
5.2.2.1 Dynamo in the E region only 77
5.2.2.2 Dynamo in the F Region only 78
5.2.2.3 Dynamo Operating Throughout the Whole Ionosphere 79
5.2.3 Altitude Variation 80
5.2.3.1 Daytime . 80
5.2.3.2 Nighttime 82
5.2.4 Solar Activity Dependence . 83
5.3 Electric Field Produced by Forbes' Tidal Winds 84
5.3.1 Altitude Variation 86
5.3.2 Seasonal Variation 86
5.3.3 Solar Activity Dependence . 87
5.4 Electric Field Produced by HWM90 Winds . 88
5.5 Comparison and Conclusion ...... 88
lV 6 Field Aligned Current 111
6.1 Introduction .... 111
6.2 Altitude Variation 112
6.3 Universal Time Effect . 115
6.4 Solar Activity Effect 119
6.5 Seasonal Variation . 120
6.6 Discussion and Summary . 121
7 Magnetic Fields Variations on the Ground 136
7.1 Introduction ...... 136
7.2 Magnetic Fields Variations without Field Aligned Current 137
7.2.1 Latitudinal Variation . 137
7.2.2 Longitudinal Variation 139
7.2.3 Seasonal Variation . 140
7.2.4 Solar Activity Effect 140
7.3 Magnetic Fields Variations Introduced by Field Aligned Current 141
7.4 Conclusion ...... 145
V Chapter 1
Introduction
1.1 Introduction
Models of the ionospheric wind dynamo are useful for several purposes. They can help us to elucidate the characteristics of the dynamo mechanism, and show where and how the electric field and current were generated in the electrically conducting ionosphere. The dynamo model can also be used to infer properties of the local and global scale thermospheric winds by comparing calculated electric fields, currents and generated magnetic field variations with experimental values. The dynamo model certainly has the potential to predict upper atmospheric electrodynamic properties which we have not measured yet, such as field aligned currents. In this chapter, we will review the dynamo simulation models and discuss the experiments concerning the electric fields and currents measured by incoherent and coherent scatter radars, rockets and satellites.
1 CHAPTER 1. INTRODUCTION 2
1.2 Simulation models
The electric fields and currents produced by dynamo action in the ionosphere have been investigated and computed by many workers. It is not easy to solve the relevant equations without any assumptions and simplifications since we have the wind dynamo process, the anisotropic inhomogeneous conductivity of the ionosphere plasma, and the feedback between the electrodynamics and the neutral winds all involved in the process. The once used assumptions are
1. the vertical currents generated by the dynamo in the ionosphere are inhib ited,
2. the geomagnetic field lines are electrical equipotentials,
3. the east-west current is divergence free,
4. the vertical current vanishes at the upper boundary of the dynamo region,
5. the electric currents driven by the ionospheric dynamo do not significantly influence the plasma density distribution,
6. the plasma E x B drift does not modify the generating wind field.
Generally, all of the electrodynamic parameters, such as conductivities, neutral winds, electric fields and currents, have mutual physical interactions. These in clude the feedback from the electric fields to the winds and conductivities, as well as from the winds to the conductivities(Cole, 1969). We will divide all the theoretical modeling into two groups according to whether the feedback between the electrodynamics and the neutral motions has been in cluded. CHAPTER 1. INTRODUCTION 3
1.2.1 No feedback between the electrodynamics and the neutral motions
Up to now, most theoretical models exclude the feedback between the electro dynamics and the neutral winds. There are two prevailing procedures used to calculate the electric fields and currents.
1.2.1.1 Equivalent Circuit Network
Stening(1968) developed a equivalent circuit method to calculate the ionospheric electric fields and currents. In his model, the ionosphere is divided into a latitude vs longitude mesh. Each section( or block) of his mesh defines a particular area of the ionosphere. The boundaries of each block are taken to extend along the magnetic field lines of the earth, thus defining a tube of force. Currents in the first instance are then computed with components taken along this tube of force, normal to the tube of force in the eastward direction and at the right angles to both these vectors. Using the equivalent circuit method, Stening(1969a, 1969b, 1970, 1971, 1973, 1977a, 1981, 1985, 1989) examined the efficiency of various tidal modes to generate electric fields and currents. Although simple electron and neutral density models were employed in his calculation, he still successfully predicted the electrostatic field increasing near sunset(Stening, 1973). By using the equivalent circuit method, Walton and Bowhi11(1979) studied the seasonal variations in the low latitude dynamo current system near sunspot maximum, Reddy and Devasia(1981) investigated the local wind effects on the equatorial electrojet and the height structures of the electric fields and currents that are generated by the east-west winds in the electrojet region. Both groups only focused on the E region and used a simple ionospheric model. CHAPTER 1. INTRODUCTION 4
1.2.1.2 Differential Equation
The differential equation governing the ionospheric currents and electric fields is the condition of current continuity
(1.1)
The central equation relating the winds, electric fields, and electric currents is Ohm's Law
(1.2) where J is the current density; Ej, and E-:_ are the components of the electric field parallel and perpendicular to the geomagnetic field .B; U is the wind velocity; bis a unit vector in the direction of B; u0 is the conductivity parallel to .B; O'p is the
Pedersen conductivity; and O'H is the Hall conductivity. The detailed coordinates system is introduced in section 2.4. Also, the electric field is assumed to be the electrostatic
(1.3) where \l1 is the electrostatic potential. Sugiura and Cain(1966) used the theory developed by earlier workers to study the height and latitude structure of the equatorial electrojet in various longitude sectors. Their model assumed that the vertical currents in the ionosphere were completely inhibited. Untiedt(1967) advanced the state of electrojet modeling significantly by pointing out that a self-consistent physical model must allow for some vertical currents flow. His model was refined somewhat by Sugiura and Poros(1969) and applied to different longitude sectors. Richmond(1973a, 1973b) examined in detail the physical features of the equato rial electrojet with the aid of his numerical model which includes neutral winds and the two stream instability. He found that the model currents and resul tant magnetic field variations are relatively unaffected by assuming the parallel CHAPTER 1. INTRODUCTION 5
conductivity, u0 , to be infinite. This assumption permits a closed mathematical solution for the electric fields and currents. He showed that the electric field and current at a given point are strongly dependent on conditions along the entire magnetic field line, but are relatively independent of conditions along neighboring field lines. He also compared his calculations with rocket measurements and with the magnetometer records of !:iH, the northward magnetic field variation, on the ground. His model includes wave-like winds, such as the (1, 1) tidal mode but no F region was included. Introducing the current function, Tarpley(1970a, 1970b) obtained the dynamo equation which describes the currents that flow in the dynamo region in response to a horizontal wind and discussed the efficiency of the solar and lunar tide to gen erate the electric current. Similar to Baker and Martyn(1953), Tarpley's model is two dimensional and only valid from 90 to 150 km. Forbes and Lindzen(1976a, 1976b, 1977) constructed a three dimensional global numerical model of the electrodynamics of solar tides in the E region of the ionosphere. Using their thin shell dynamo model, they calculated the electric currents and ground magnetic field v~iations and compared them with measure ments. They concluded that the F region dynamo should be included, especially at nighttime. If orthogonal magnetic coordinates(p, q, ) are selected, the electric field E can be expressed in terms of an electrostatic potential(Crain et al., 1993a)
.... 1 aw 1 aw E = - \7 'ii! = ------(1.4) hp 8p h,j, 8
Also, the current continuity equation becomes
here, p is directed perpendicular to iJ in the meridional plane, q is along B, and represents longitude, hp, hq, h,J, are scale factors, the detailed coordinate system CHAPTER 1. INTRODUCTION 6 is introduced in section (2.4) and
Jp = upEp - UH Er/> + upUrf>B + uHUpB (1.6)
Jr/> = up Er/> + UH Ep - upUpB + uHUr/>B (1.7)
Assuming that no field aligned current flows in or out at the base of the iono sphere, we have the following dynamo equation by integrating equation (1.5) along the magnetic field line from the base of the southern to the base of the northern hemisphere
(1.8)
where qb is the value of q at the base of the ionosphere and
Jwp = upUrf>B + UHUpB (1.9)
Jwrf> = UHU,f>B - upUpB (1.10)
Mohlmann(1977) solved the ionosphere potential equation of the dynamo theory by a perturbation method. Using the wind model presented by Salah and Evans(l977), Takeda and Maeda (1980) calculated the current structure in the ionosphere from 90 to 400 km pro duced by the diurnal (1, -2) mode and then that due to the semidiurnal (2, 2) and (2, 4) modes(Takeda and Maeda, 1981) in the range of 90 - 200 km, and finally the field aligned current generated by asymmetric dynamo action in the iono sphere(Takeda, 1982). He also simulated magnetic field variations and the equiv alent current system generated by an ionospheric dynamo at the solstice(Takeda, 1990) by use of the IRI-86 for the ionospheric model and the results of Forbes and Garrett(1978a) for the wind model . Singh and Cole(l987a, 1987b, 1987c) discussed the boundary conditions and transferred the equations to an initial values problem. They computed the elec trostatic fields and currents produced by an assumed tide-like wind and a local CHAPTER 1. INTRODUCTION 7 periodic wind. Crain et al.(1993a, 1993b) presented the integrated field line Hall and Pedersen conductivities and discussed the roles of the F region in the low latitude dynamo. By using the (1, -2) tidal wind in the E region and, in the F region, the winds derived by Blum and Harris(l975) for the meridional component and the winds measured by Herrero and Mayr(1986) for the zonal component, they solved equa tion (1.8) and derived the electrostatic potential and electric field distributions and compared their results with earlier theoretical calculations and experiments. Their results lead to the conclusion that the F region dynamo is a very important source of electric fields at low latitudes at all local times. They also proposed that the postsunset enhancement of the vertical ion drift at Jicamarca is primar ily due to the local time gradient in the F region zonal wind in conjunction with the conductivity gradient at the dusk terminator. In contrast to the theories of Tarpley, Forbes and Richmond which included only an E region dynamo, Rishbeth(1971a) first investigated the ion drift, current system and magnetic field arising from F region winds. He pointed out that neu tral winds blowing across the magnetic field may cause a transverse drift of the ions and this sets up an electric polarization field which can only be neutralized by currents flowing along magnetic field lines and through the E layer. Follow ing the same procedure, Heelis et al. (1974) studied the electrical coupling of the E and F regions and its effect on F region drifts and winds. Their results agree generally with the incoherent scatter radar data from Jicamarca. Farley et al.(1986) investigated the cause of the prereversal enhancement, a phenomenon of the enhancement of the zonal electric field in the equatorial ionosphere just before the change from eastward to westward in the evening, and confirmed that the F region wind blowing eastward at the time of E region sunset is the main cause of the prereversal enhancement. Richmond and Roble(1987) simulated the ionospheric electric fields and cur rents and the associated ground magnetic field variations, generated by the dy- CHAPTER 1. INTRODUCTION 8 namo action of winds simulated with the National Center for Atmospheric Re search(NCAR) Thermospheric General Circulation Model(TGCM). Two TGCM wind simulations/ are used, one of which includes lower boundary forcing that mimics the effects of upward propagating semidiurnal tides and another does not. Their results show that the addition of tidal forcing improves the agreement between calculated and observed electric fields and magnetic field variations on the ground.
1.2.2 Feedback between the Electrodynamics and the Neutral Motions
There are two kinds of feedback in the dynamo process which might be taken into account in a thermosphere/ionosphere model
1. the feedback from the electric fields to the neutral winds, and the electron density;
2. the feedback from the neutral winds to the electron density.
One of the main feedback mechanisms is the effect that electric fields have on the neutral wind distribution. The electric currents driven by the electric fields exert an Ampere force on the ions. This force can be comparable to other forces in the horizontal direction. Rishbeth(1971b) demonstrated that the neutrals and ions at F region height can move rapidly together in the east-west direction at equatorial latitudes at night because of ion drag. Anderson and Roble(l974) examined the effects of vertical E x B ionospheric drifts on F region neutral winds and electron density in the low latitude thermo sphere using two assumed E x B drift patterns, one without and one with the postsunset Ex B drift enhancement. CHAPTER 1. INTRODUCTION 9
Volland(1976a, 1976b) and Volland and Grellmann(1978) also examined the feed back from the electric fields and ion drifts to the neutral winds by including the modification of the neutral pressure in the simplified global dynamo model. They found the horizontal and vertical structures of an atmospheric tidal model are al tered when the atmosphere is electrically conducting. The effects of the electric fields and neutral winds on the distributions of elec trical conductivities were discussed by Cole(1969). He showed that in the F re gion the Pedersen conductivity is proportional to the product of electron and neutral density. A raising(lowering) of the bottom side F layer by equator ward(poleward) winds or by eastward(westward) electric fields will produce a reduction( enhancement) of the conductivity. To improve the prediction accuracy of electric fields, current densities and the re sulting magnetic fields on the ground, NCAR developed a Thermosphere/Ionosphere General Circulation Model with coupled Electrodynamics(TIE-GCM), which com putes self-consistently the coupled thermospheric/ionospheric dynamics, the as sociated dynamo electric fields and currents, and the electrodynamic feedback on the neutral and plasma motions as di~cussed by Roble et al.(1988) and Richmond et al.( 1992). They clearly showed the differences of electron density, zonal neu tral wind and zonal ion drift which occurred between a fully coupled simulation and the lack of an ionospheric dynamo. Namgaladze et al. ( 1991) presented a self-consistent numerical model of the thermosphere ionosphere-protonosphere system. Although their model had low resolution, they demonstrated that coupled simulations are possible, and they could reproduce at least the gross structure and dynamics of the thermosphere, ionosphere and protonosphere. CHAPTER 1. INTRODUCTION 10
1.3 Experiments
1.3.1 Rockets
In-situ studies of the equatorial electrojet have been carried out during the last five decades using probes on sounding rockets. The main results originate from the launching sites of Peru and India. The rocket observations in the equatorial electrojet have been summarized by Pfaff(1991), who also proposed seven out standing scientific problems in equatorial electrojet plasma physics some of which can be resolved by future rocket experiments. The observations reveal that the maximum current density of the equatorial electrojet at midday off the coast of
Peru and over Thumba in India is about 10 µA/m2 (Richmond,1973b; Sampath and Sastry, 1979). From six rocket launches performed in 1970 near noon at Natal, Brazil, Musmann and Seiler(1978) measured the equatorial meridional current system experimen tally. They discussed the variations of the declination and explained the discrep ancy between prediction and the observation by current flowing at 5 degrees off the magnetic equator in a direction which is opposite to the direction of the main electrojet on both sides.
1.3.2 Incoherent Scatter Radar
1.3.2.1 Equatorial Region
The equatorial ionosphere has been extensively studied with Incoherent Scat ter(IS) radar measurements at the Jicamarca Radio Observatory(12° S, 76.9°W, magnetic dip 2° N). It has provided detailed information on equatorial iono spheric electrodynamics and plasma instabilities(Balsley, 1969a, 1969b, 1970a, 1970b, 1973). Most of the F region drift studies have concentrated on the vertical CHAPTER 1. INTRODUCTION 11 component of the drift which plays an important role in the height/latitudinal distribution of ionization at low latitudes and constitutes an important input parameter for equatorial and low latitudes, and for global ionospheric density models(Anderson et al., 1987; Walker and Chan, 1989) because it relates directly to the eastward electrostatic field. The east-west drift velocity of the F region ionosphere also has been measured since 1970 in order to better understand the dynamics of the ionosphere and their effect on the dynamics of the neutral atmo sphere. The F region vertical drift measurement technique used in Jicamarca has been described by Woodman and Hagfors(1969) and Woodman(1970). The method involves the determination of the Doppler shift of incoherently scattered signals from the F region ionization when the propagation vector is directed normal to the earth's magnetic field. The drifts are measured from 200 - 600 km where they usually do not change much with altitude. Most of the published results were obtained by averaging the drifts between 300 and 400 km, where the signal to noise ratio is the highest. The integration time is about 5 minutes and the accuracy of the measurements is usu~lly 1 - 2 m / s. The procedure used to measure the F region east-west drift velocity is similar to that of the vertical velocity. The only difference is the antenna pointing di rection. The large Jicamarca antenna is split into two beams, which are both perpendicular to the magnetic field and point 2.45° to the east and 4.33° to the west of vertical, giving a net split of 6. 78°. The line of sight drifts from these two directions are then combined to give the F region vertical and east-west drifts. Different from the vertical measurement accuracy of 1 - 2 m/ s, the uncertainty of the east-west drift may reach 12m/s. The detail has been described by Wood man(1972). The measurement technique for the E region drift is quite different from that of the F region. The data are obtained by determining the mean Doppler shift of oblique radar returns from a type of electron density irregularity embedded in CHAPTER 1. INTRODUCTION 12 the equatorial electrojet. These irregularities drift with the electrons so that a measurement of the irregularity drift velocity is equivalent approaximately to the measurement of the electron motion itself. As the mean Doppler shifts obtained from the oblique echo spectra are a composite of the shifts from irregularities over the complete height range of the echoing region, and the electron drift velocity is strongly height dependent within the region, the resulting drifts represent a weighted average value for all heights(Balsley, 1973).
Vertical Plasma Drift Woodman et al.(1977) analyzed the data of 1968 to 1975 and discussed the solar cycle effects on the east-west electric fields( vertical drifts) in the equatorial iono sphere. They concluded that the reversal of the electric field from west to east near sunrise is not affected by the solar cycle, but the evening reversal is found to occur about one hour earlier during low sunspot years. Fejer et al. (1979) and Fejer(1981) examined all the available data from 1968 to 1976 and further pointed out that the daytime drift velocities during sunspot minimum are usually larger than during the maximum, while the opposite is true for nighttime periods. The evening prereversal enhancement is much more common and pronounced at sunspot maximum. To investigate the height variation of the equatorial F region vertical plasma drifts, the integration time is changed to only 1 minute during the experiment of 1986. The preliminary results indicated a small change of the vertical drift velocity with altitude between 200 and 700 km but with considerable day-to-day variation(Pingree and Fejer, 1987). The experiments confirmed that the iono spheric electric field is irrotational. Fejer et al.(1989) further studied the effects of large solar fluxes and magnetic activity on the F region vertical plasma drifts. The average drifts from the two solar maximums are almost identical except in the late afternoon-early evening sector where their variations with solar flux and magnetic activity are strongly season dependent. Using extensive IS radar oh- CHAPTER 1. INTRODUCTION 13 servations from Jicamarca during 1968-1988, Fejer(1991) and Fejer et al.(1991) showed that the amplitude of the evening prereversal enhancement of vertical drift increases linearly with solar flux during equinox but tends to saturate for large fluxes during southern hemisphere winter. Typical Jicamarca vertical drifts can be found in figure 5.20.
Zonal Plasma Drift The initial results(Woodman, 1972) showed that there is a super-rotation of the F region ionization which can be interpreted as experimental evidence of the super-rotation of the neutral atmosphere as proposed by Rishbeth(1971b). The neutral atmosphere movement is mainly determined by ion-drag frictional forces balancing the pressure gradient forces and its velocity can be inferred from the zonal plasma drift data. The general characteristics of the zonal plasma drift were described by Fejer et al.(1981) and Fejer(1981). The drifts are westward during the day and eastward at night. The daytime drift velocities are about 50 m/ s and change very little with season or solar cycle. The evening reversal occurs at about 16 h,: local time. Considering the measurements of both the IS radar and the radar interferometer, Fejer et al.(1981) discussed the zonal plasma drifts changes with altitude. A thoughtful summary of the zonal plasma drifts was given by Fejer (1991). They concluded that the amplitude of the late afternoon and nighttime zonal drifts are strongly dependent on the 10. 7cm solar flux. The seasonal effects on the zonal drifts are most pronounced in the midnight-morning sector. The night time eastward drift shows an increase in amplitude with solar flux for all seasons but decreases slightly with magnetic activity. The daytime westward drifts are essentially independent of season, solar cycle and magnetic activity. CHAPTER 1. INTRODUCTION 14
1.3.2.2 Low and Middle Latitude
Ionospheric plasma drifts have also been extensively measured at Arecibo (18°N, 67°W), Shigaraki (34.9°N, 136.1°E), Millstone Hill (42.6°N, 71.5°W) and Saint Santin (44.6°N, 2.2°E). The Arecibo observations have been summarized by Behnke et al.(1973). Fe jer(1993) and Berkey et al.(1990) showed the solar, seasonal, and magnetic activ ity effects of F region plasma drifts. The E region ion drifts and the neutral wind measurements have been discussed by Harper et al.(1976) and Harper(1977b ), who also studied the ionospheric currents and magnetic variations at Arecibo(1977a). At mid-latitude, at the altitude of the Flayer peak, the following four velocities are approximately equal in magnitude(Kelley, 1989)
E g vl -rvurv_,-..,_ B - - Vin - L where g is the gravitational field, u is the meridional neutral wind, llin is the ion-neutral collision frequency, v is the ion thermal velocity, l is the ion mean free path, and L is the plasma pressure gradient scale length. The Arecibo observatory is well suited to the study of these interrelated forces since the magnetic field is inclined at an angle of about 45° to the vertical. This geometry allows each of the important forces an equal vote in the control of the vertical motions of the F layer plasma. Behnke et al.(1974) and Burnside et al.(1983) studied the effects of the different processes and explained the F layer plasma drift measurements. The Middle and Upper atmosphere(MU) radar of Kyoto University at Shigaraki, Japan, is the most recent of the large atmosphere radars capable of detecting incoherent scatter from the electrons in the ionosphere. The radar configuration and the observational technique have been discussed in several papers(Fukao et al., 1985a, 1985b; Sato et al., 1989; Takami et al., 1991). Oliver(1993) analyzed MU radar observations of electric fields over the period September 1986 to Jan uary 1991 and compared his results with the existing electric field model and CHAPTER 1. INTRODUCTION 15 measurements of Jicamarca and Arecibo. A good agreement existed between them and the existence of a large semidiurnal component in the perpendicular eastward drifts and its possible relation to the enhanced tidal propagation at the MU radar location have been concluded. The earlier Millstone Hill observations have been published by Evans et al.(1970) and Evans(l971a, 1971b), Carpenter et al.(1974), Kirchhoff et al.(1976) and Wand et al.(1981). Buonsanto et al.(1993) analyzed the experiments in the pe riod February 1984 to February 1992 and constructed, for the first time at this station, average quiet time E x B drift patterns for both solar cycle maximum and minimum and for the summer, winter, and equinox sea.sons. The Saint Santin ionospheric E x B drifts have mainly appeared in Blanc et al.(1977, 1979).
1.3.2.3 Empirical Drift Model
With the substantial collections of ionospheric electric field data from Jicamarca, Arecibo, Saint Santin, and Millstone Hill, Richmond et al.(1980) constructed a model of the middle and low latitude ion drifts for solar minimum conditions. The detail can be found in Richmond et al.(1980). This model has been widely used as the input for simulating ionospheric structure and relevant research(Haerendel et al., 1992; Chan et al., 1984,; Walker et al., 1989)
1.3.3 HF Coherent Scatter Radar
The HF coherent Doppler radar is a valuable means to gain information on the ionospheric plasma drift. It is composed of an HF pulse transmitter, a phase coherent receiver and transmitting and receiving antennas. The use of a fre quency synthesizer for both transmitter and receiver guarantees the system is phase coherent. The information of Doppler shift and spread, signal strength can CHAPTER 1. INTRODUCTION 16 be 'picked up' from the received pulse after it has been transmitted to and then reflected from the ionosphere. To investigate the ionospheric electrostatic field which drives the equatorial elec trojet, a coherent backscatter radar was operated regularly at Trivandrum(8.5°N, 77.6°E, Geographic) in south India since 1964 to measure the horizontal iono spheric drifts in E and F regions of the ionosphere. The early observations were summarized by Rastogi et al. (1966). They concluded that the E region drifts
. , at Trivandrum, close to the magnetic equator, are consistently westward during daylight hours. Prakash et al.(1981) described the electrostatic field variations during morning and evening periods and showed that the fields over Trivandrum and Jicamarca vary similarly close to the morning and evening reversal times. Jayachandran et al. (1987) reported preliminary observations on the prereversal enhancement in vertical plasma drifts. Namboothiri et al.(1989) presented the measurements conducted during 1984-1986. The results show that the gross di urnal pattern of the vertical plasma drift is similar to observations at Jicamarca. The prereversal enhancement varies with season and solar activity by about the same factors for the two stations. But the magnitudes of the drift velocities, ex cept for the prereversal enhancement period, are found to be generally greater at Jicamarca than at Trivandrum. Under low solar activity and solstice conditions, a weak but finite prereversal enhancement is more often noted at Trivandrum than at Jicamarca. Further, the evening reversals in the drift velocity occur as much as 45 minutes earlier at Jicamarca compared to Trivandrum. The day-to day variations observed at Jicamarca are significantly greater than those noted at Trivandrum. CHAPTER 1. INTRODUCTION 17
1.3.4 Satellite
Satellite measurements of the magnetic field in the near earth environment have provided valuable information on ionospheric electric fields, current distributions and magnetic field variations. The early satellites measured the total magnetic field. These include: Sputnik 3 in the altitude range of 240-800 km, Vanguard 3 in 510 - 3753 km, Alouette in 993 -1025 km, Cosmos 26 in 271- 403 km, and the Polar Orbiting Geophysical Observatories(POGO) series measured the equatorial electrojet as part of their objectives. Onwumechili(1985) has summarized all the measurements of the above satellites. To obtain accurate vector measurements of the near earth geomagnetic field and to use those measurements to identify and model the main( core) and crustal fields, the Magsat spacecraft was launched on October 30, 1979, into a twilight, sun syn chronous, orbit with inclination 96. 76°, perigee 352 km and apogee 560 km. The cesium vapor scalar and fluxgate vector magnetometers together were used to measure the field magnitude to better than 2 nanoTesla(nT) and each compo nent to better than 6 nT(Langel et a!·, 1982, 1985). Magsat data have proven useful in the investigation of the fields from current systems external to the earth. Possibly the most significant discovery of this type has been made by Maeda et al.(1982), who found a distinct variation in the east-west component near the dip equator. The field is westward to the north of the equator and eastward to the south. This occurs on every dusk pass, does not occur at dawn, and shows no correlation with fields measured on the ground. The characteristics of the measured Magsat magnetic fields are reported by Maeda et al. (1985). Langel et al. (1993) re-examined the Magsat data. They calculated current den sities of 1 - 3.6 µA/m2 for horizontal currents at 110km and about 10 - 20 x
10-3 µA/m2 for the vertical currents at 400 km altitude. Their results confirmed and extended earlier results of Takeda and Maeda. Olsen(1997) used two meth- CHAPTER 1. INTRODUCTION 18 ods to determine the F region current density at satellite heights by means of a decomposition of the magnetic field into toroidal and poloidal parts. His results show that an upward current flows at the dip equator and downward currents at low latitudes in the evening. This is, he concluded, the radial component of the meridional currents system of the equatorial electrojet. There is no evidence for such a current system in the morning data. The Dynamics Explorer 2 (DE-2) satellite was ,launched in August 1981 into a 90° inclination orbit with perigee near 280 km and apogee near 1200 km. Two completely different techniques for determining the ionospheric E x B convection velocities were flown on it. One of the techniques, which utilizes an ion drift meter(IDM) and a Retarding Potential Analyzer(RPA), measures the bulk flow velocity vector of the ambient ions. The other, the Vector Electric Field Instru ment(VEFI), uses antenna to measure the electric field directly. Maynard et al. (1988) and Coley and Heelis(l989) have independently published the observed morphological behavior of the equatorial zonal drift based on the VEFI and IDM data respectively. Hanson et al.(1993) compared the measure ments of E and -V x B from DE-2 and found a good agreement in low latitude data. Heelis et al.(1992) described the latitudinal and local time distributions of the east-west drift. By examining the distributions during quiet and disturbed times and contrasting them with the findings of other observational and theoretical studies, they discussed the influence of ionospheric dynamo fields and electric fields from magnetospheric sources. Different from Magsat and DE-2, the Atmosphere Explorer E(AE-E) is a low inclination (19.76°) satellite, which makes it ideally suited for low latitude iono spheric studies. Using the IDM measurements from the AE-E satellite taken from January 1976, through December 1979 (the satellite was in nearly circular orbits with the altitude increasing from 230 to 470 km during this period) Fejer et al.(1995) studied the dependence of equatorial F region vertical plasma drifts on CHAPTER 1. INTRODUCTION 19 solar activity, season, and longitude. They found that the pronounced presunrise downward drift enhancements are often observed over a large longitudinal range but not in the Peruvian equatorial region, the longitudinal variations are largest near the June solstice particularly near dawn and dusk but are virtually absent during equinox. The AE-E vertical drift signatures show consistence with results from ionosonde data(Abdu et al., 1981; Fejer et al., 1991). The San Marco D/L satellite was launched into a low altitude(260x614 km) equa torial orbit with an inclination of 2.9° from Kenya, Africa, in March 1988(Ag gson,1993). Aggson et al.(1995) published the satellite observations of zonal electric fields near sunrise in the equatorial ionosphere. They found a number of sunrise enhancements of electric fields similar to the first Jicamarca studies reported by Woodman(1970). As the San Marco D /L satellite measures simulta neously both the meridional and zonal electric fields, it provides a new dimension to understand the ionospheric electrodynamic process. Maynard et al.(1995) ex tensively studied the average equatorial zonal and vertical ion drifts determined from San Marco electric field measurements and concluded that
1. the daytime westward zonal ion drift increases as F10.1 increases,
2. magnetic activity does not affect either the vertical or the zonal ion drifts,
3. June solstice values for the westward zonal drift in the daytime are higher than equinox values, the vertical drift at equinox is larger than that for June solstice during both the day and night,
4. there are significant longitudinal differences in both velocities during the June solstice, the predawn enhancement in the downward flow is strong in the Indian sector and virtually nonexistent in the Peruvian sector,
5. the F region dynamo is confirmed to be dominant in the 19 to 21 hr LT sector. CHAPTER 1. INTRODUCTION 20
They also pointed out that the offset of the geographic and geomagnetic equators plays a very important role in the local time development of ion drifts and should be included in the relevant simulation models. Chapter 2
Simulation Model
2.1 Introduction
Developed in 1968 by Stening, the equivalent circuit method has been used to calculate the electric fields in the ionosphere. In this chapter, we will introduce Stening's equivalent circuit and discuss the E and F region dynamo effects on the currents distributions flowing in both the E and the F region. The scale factors are introduced. The assumption that magnetic field lines are equipotentials is discussed. The methods to calculate the field aligned current and magnetic field variations on the ground are also presented.
2.2 Equivalent Circuit
If we select a coordinate system in which p, and q are the directions of magnetic southward (equatorward precisely), eastward and along the magnetic field line respectively, we can write Ohm's Law as
21 CHAPTER 2. SIMULATION MODEL 22
up(Ep - U4iB) + uH(E4i + UpB) (2.1) up(E4i + UpB) - uH(Ep - U4iB) (2.2) (2.3) where Jp southward current density, J4i eastward current density, Jq field aligned current density, up Pedersen conductivity,
O'H Hall conductivity,
u 0 parallel conductivity, Ep southward electric field, E4i eastward electric field, Eq field aligned electric field, Up southward wind velocity, U4i eastward wind velocity.
The ionospheric wind system drives charged particles across the magnetic field line of the earth. These motions induce an electric field Ox B (U = (Up, U4i, Uq)). These dynamo induced electric fields then drive currents that depend on the con ductivity components of the ionosphere. In order to satisfy the continuity of J
v. 1 = v. a. (E +ox B) = o (2.4) a polarization electric field E must be set up to satisfy the equation. Since the polarization electric field is an irrotational vector field(V x E = 0), it can not bal ance the generally rotational O x B field at all points, so that a net current must flow in closed circuits. Since the parallel conductivity is very much higher than CHAPTER 2. SIMULATION MODEL 23 the Pedersen and Hall conductivities, the magnetic field lines may be regarded as equipotential lines, and the electric field can map practically unattenuated between the E and F region(Dagg, 1957; Farley, 1959, 1960; Spreiter and Briggs, 1961). Following the method of Stening(1968) the ionosphere is represented by a circuit network and every branch then takes the form shown in figure 2.1.
+ I ...___ _, I I I : ei ~ R : I I I I I I LI ______Vs ______:I
Figure 2.1: The components in every branch of the equivalent circuit network.
Using this notation, Stening(1968) has shown that the total voltage of every branch is given by
(2.5) here
ei dynamo e.m.f.,
eh hall generator, R resistance, I current flowing through the branch, ½ electric voltage across the tube of force.
From Stening(1968), we know that the Hall generators depend on the ionospheric conductances and on the current flowing in the branch in which the Hall genera tor is situated and the perpendicular branch as well as on the differences of the two weighted effective emf's. CHAPTER 2. SIMULATION MODEL 24
Integrating equations (2.1) and (2.2) in the p and
Ip = (Vap + epp)Gpp + (½<1> + e<1><1>)Gp4> (2.6) 14> = (½<1> + e4>p)G4>4> - (Vap + ep4>)Gp4> (2.7) here
k2tl. Gpp '5:k j up sin 0(1 + 3 cos 2 0)d0 Gp - k j un sin 0(1+3cos2 0)½d0 G4>4> - !: j up sin 0d0 epp - -k2tl. j upU4>Bsin4 0(1 +3cos2 0)½d0/Gpp e4>4> - k2tl. j unUpBsin4 0(1+3cos2 0)½d0/Gp4> e4>P - ktl.k j upUpBsin4 0d0/G4>4> ept/> - -ktl.k j unU4>Bsin4 0d0/Gp4> where k is the apex altitude of the magnetic field line, tl.k and tl. are increments of
(2.8)
(2.9)
Substituting equations (2.8) and (2.9) in (2.6) and (2.7), Stening(1968) has shown that
(2.10)
(2.11) CHAPTER 2. SIMULATION MODEL 25
Figure 2.2: The form of the equivalent circuit. Loop currents and emf's contribut ing to the calculation of the loop current Ik are indicated(from Stening,1968).
Using Kirchhoff's law on the ionospheric current network as is shown in figure 2.2, Stening obtained the loop current in the kth branch
lk = [ew,k + ehp,k + e,,,k + eh,,k - epp,k+l - ehp,k+l - e,,.k+p - eh,,k+P + 4-p/G,,,k + Ik-i/Gpp,k + lk+i/Gpp,k+i + Ik+p/G,,,k+p)/[1/Gpp,k + 1/Gpp,k+i + 1/G,,,k + 1/G,,,k+p](2.12)
These equations can be solved by the matrix inversion method(Walton,1979) or an iterative method as discussed by Stening(1968). Then, the current of every cell can be calculated by
Ip= h-lk-1 (2.13) 1_ = Ik - lk-p (2.14)
Finally, the electrostatic fields at any latitude and altitude were obtained by use of simple geom~try and equations (2.10), (2.11) and (2.5). It should be pointed out that the equivalent circuit developed first by Sten ing(1968) was just for the E region. To explore the whole ionospheric electro dynamic process and the effect of the F region dynamo on E region currents, CHAPTER 2. SIMULATION MODEL 26 he developed a two layer ionospheric dynamo model based on the earlier model (Stening, 1981 ). In our model, the equivalent circuit model is appropriate for either the whole ionosphere or part of it. The only changes are the relevant in tegration ranges of G and e. It should be guaranteed that the integration begins from a starting point in the northern hemisphere, goes along the field line, and ends at the relevant point in the southern hemisphere. So the model permits us to investigate the separate roles of the E and F region dynamos. We will study the questions of when the F region dynamo becomes dominant and when the E region gives the major driving force.
2.3 Perpendicular Current Density
After running the equivalent circuit model program, we obtained the eastward and equatorward( southward) electric fields at various magnetic field line apex altitudes or latitudes at the selected reference level(86 or 90 km in our case). During the calculation, we selected the boundaries of the ionosphere to be at 60° S and 60° N for latitude and at 90 km or 86 km and 500 km for altitude. At all boundaries, there will be no currents flow in or out. 15° is selected as the step size of longitude. The step size of latitude is determined in such a way that the equivalent circuit always gives a stable electric field. For example, 0.1 ° within ±20° of the equator and 2° beyond are the values we used as step sizes of latitude while dealing with the Forbes and Gillette tidal wind. The step sizes are 0.2° and 2° in corresponding latitude ranges for the other winds which are used in the thesis. So, for any UT and longitude, we will have enough pairs of(220 or 120) electric fields to present the electric field variations with apex altitude or latitude. Then an interpolation subroutine was used in the program to calculate the electric fields at any point in the ionosphere. In a similar way to Takeda and Maeda(1980), the divergence of the magnetic CHAPTER 2. SIMULATION MODEL 27 field line with height was neglected in our calculation. After the eastward and equatorward electric fields were determined, the perpendicular current densities, the eastward and equatorward current densities, can be calculated directly by using equations (2.1) and (2.2) incorporating the conductivity and wind distribu tion models. Before proceeding to model the ionospheric perpendicular current density quantitatively, we will discuss it under some special situations.
2.3.1 No Dynamo in F Region
In the F region we usually have up > UH. So the F region current density can be expressed as
JpF = (Ep - UpFBF)UPF (2.15)
J"'F = (E"' + u"'FBF)uPF (2.16)
As expected, the F region current density is very small and decreases rapidly with . increasing altitude because the electric fields and winds do not change much, being nearly constant above 200 km(Harper, 1977a, 1977b; Fejer et al., 1985; Pingree et al., 1987). The altitude variations of F region currents are mainly controlled by the Pedersen conductivity and hardly any currents flow at altitudes over 200 km. If there is no dynamo in the F region (UvF = UF = 0), the current densities induced by the E region dynamo can be expressed by
(2.17)
(2.18)
That is, there is still a current flowing in the F region even when no dynamo exists there, but it is very small as up decreases very quickly. CHAPTER 2. SIMULATION MODEL 28
2.3.2 No Dynamo in E Region
This case is very similar to the previous section, the only difference being that the electric field is determined by the dynamo in the F region this time and in the E region in the earlier case. The current density in the E region can be written as
(2.19)
(2.20)
From the early works(Rishbeth, 1971b; Farley et al., 1986), we know that the F region dynamo is short circuited by the E region during daytime. If so, we do not expect that the F region dynamo will affect the current and thus the magnetic field variations on the ground since Ep = Et/> ~ 0. During nighttime, any current flow in the F region was forbidden and a large electric field mapped down to the E region along the magnetic field line. Then the E region current and the magnetic field variations on the ground are completely controlled by the electric field which arises from the F region dynamo. We will discuss this problem in Chapter 5.
2.4 Scale Factor
We introduce coordinates p, q, cp as follows. The coordinate direction q is defined by the magnetic field direction, i.e. q = B/ B, f, is perpendicular to the magnetic field line at every point and J is in the magnetic eastward direction. The set of vectors f,, q and J are orthonormal
Also, we have a set of spherical polar coordinates r, (), cp. To complete the defi nition of the p, q, system, we relate the p, q, coordinate system to the r, 0, CHAPTER 2. SIMULATION MODEL 29
coordinate system by the equations
r0 sin2 0 p= (2.21) r ri cos0 q= (2.22) r2 here, r0 is the height of the field line at the base of the ionosphere.
Although Murphy and Heelis(1986) and Crain et al.(1993b) used the p, q, coordinates, their relationships between p, q, and r, 0, are a little different. Our definitions are exactly the same as those of Takeda and Maeda(1980).
Because of their applicability to the dipole magnetic field geometry, the p, q, coordinate system is a good choice for modeling the ionospheric electric field and current. For the dipole magnetic field model the p value remains unchanged along any magnetic field line. The relationships between the unit vectors of p, q, and r, 0, can be devised as follows from figure 2.3
Figure 2.3: The schematic relationships between the two coordinate systems
In the southern hemisphere CHAPTER 2. SIMULATION MODEL 30
pA - cos If- - sin I 8 (2.23)
qA sin If- - cos JO (2.24) and in the northern hemisphere
pA - cos If-+ sin JO (2.25)
A q - sin I r - cos I 8 (2.26) here, I, not the inclination angle, is the angle between p and -f- and 0 is the colatitude. Using the expression E = - V W and considering the electric field should be the same in the two coordinate systems of (p, q, ) and (r,0, ), we have
8w A 1 8w A 1 8w A 1 8w A 1 8w A 1 8w A 8r r + r 80 8 + r sin 0 8 - hp 8p P + hq 8q q + h"' 8 (2-27) further
8w 8w 8p 8w 8q 8w 84> -=--+--+-- (2.28) 8r 8p 8r 8q 8r 8 8r 8w 8w 8p 8w 8q 8w 8 (2.29) 80 = 8p 80 + 8q 80 + 84> 80 8w 8w 8p 8w 8q 8w 8 (2.30) 84> = 8p 8 + 8q 8 + 8 8
Combining all equations above, the scale factors can be expressed by
r2 hp - (2.31) r0 sin 0(1 + 3 cos2 0) ½ r3 hq - (2.32) ri(l + 3 cos2 O)½ h"' r sin 0 (2.33) CHAPTER 2. SIMULATION MODEL 31 which are exactly the same as Takeda and Maeda(1980) and also the follow rela tionships have been used.
sin0 cos/ - (2.34) (1 + 3 cos 2 0)½ sin/ - I 2cos0 ii (2.35) (1 + 3 cos 2 0)2
2.5 Equipotential Lines
It has been known that the electric fields produced in the lower ionosphere are responsible for the ionization drifts in the F region(Baker and Martyn, 1953). Considering the ionosphere be a finitely conducting, anisotropic, inhomogeneous, but stratified medium, the conductivity of the ionosphere is anisotropic due to the earth's magnetic field, which restricts the motion of electrons and ions per pendicular to the lines of flux but does not affect the motion parallel to these lines. In most of the ionosphere the ratio of the conductivity parallel to the earth's magnetic field to the conductivity perpendicular to the field is very large. For example, the ratios of the parallel conductivity to the Pedersen and the Hall conductivity are larger than 106 and 108 at the altitude of 200 km. It is this fact which has led Martyn(1955) and Dagg(1957) to use the assumption of equipoten tial field lines without quantitative proof. Farley(1959, 1960) developed a theory to describe the idea that in an ionized gas subject to an imposed magnetic field, such as the ionosphere, the lines of mag netic flux are approximately equipotential lines. In his papers, the theoretical electric coupling between the dynamo region and the F region of the ionosphere is examined at polar high geomagnetic latitudes. It is found that, under cer tain conditions, significant coupling between these two regions can occur at all latitudes, even for electric fields with horizontal scale sizes as small as a few kilo meters. The coupling is strongest at the poles and weakest at the equator. Strong CHAPTER 2. SIMULATION MODEL 32 coupling will also occur between magnetically conjugate portions of the F region, while weaker but significant coupling exists between conjugate portions of the dynamo region. Spreiter and Briggs(l961) analyzed the same governing differential equations as Farley, but the boundary condition imposed at infinity and the method of solution is different. They imposed the boundary condition that the current vanishes at infinity, whereas the corresponding boundary condition stated by Farley is that the electric potential vanishes at infinity. They concluded that the attenuation of the electric field is much less than that which would be experienced in a ho mogeneous medium. Richmond(1973a) also demonstrated that the equipotential lines coincide with the magnetic field lines. He concluded that it is reasonable to assume that mag netic field lines are equipotentials. In this thesis, we will use this assumption. In the same way as Takeda and Maeda(1980), Singh and Cole(1987a) and Crain et al.(1993a) have done, the di vergence of the magnetic field lines is also ignored in our program.
2.6 Field Aligned Current
From equation (1.5), we have the field aligned current density at any point(p, q, ) 1 a a Jq = - hph4, lqqo [ap (hqh4,Jp) + 8 (hphqJ4,)]dq (2.36) here, the integration is along the magnetic field line to the point of interest, starting from the lower boundary q0 , corresponding the altitude h0 , where we suppose no current flows in or out of the ionosphere. The magnetic field lines satisfy equation
where() is the geomagnetic colatitude. r = R + h, where R is the Earth's radius and h is the altitude of the magnetic field line from the earth's surface. k is the CHAPTER 2. SIMULATION MODEL 33 apex altitude of the magnetic field line measured from the center of the earth. If we want to calculate the field aligned current at a point P with coordinate (p, q,
(2.37)
(2.38)
All variables with ' refer to the related values at point P', " the values at point P", otherwise at point P. During calculation, we take the colatitude() as a variable for the selected magnetic field line. 0.001 ° was selected as the step size of the integration in equation (2.36) to guarantee a stable solution. The criteria for selecting the adjacent point will be discussed in Chapter 6.
2. 7 Magnetic Field Variations on the ground
Selecting the coordinate system as in figure 2.4 and letting the observation point be O(ro, (2.39) here ar - ax sin() cos a9 ax cos() cos a,t, - -ax sin z y t-,,,...... I ...... ;···~~-::,::- ____ j ...... ,., ...... --· Figure 2.4: The coordinates used for the transformations between the geographic and tilted centred dipole. ay - r0 sin 00 sin az ro cos Bo - r cos 0 (2.45) Suppose the current element is expressed as According to the Biot-Savart law, the magnetic field on the ground produced by the current :flowing in the ionosphere is B--... µ jjf ---dvJ xr' - 41r I r' 13 In our case, we have all the components as follows 2 (2.46) Br =,:: j j j I :rl3 r sin0 dr d0 d 8 2 Bo= ,t: jjj I : l3 r sin0drd0d (2.47) B, = ,:: j j j I :,13 r 2 sin 0 dr d0 d (2.48) here I r' 12 = ri + r 2 - 2rro[cos0ocos0 + sin0osin0cos(o - )] (2.49) CHAPTER 2. SIMULATION MODEL 35 Fr = a In practice, during the calculation, we integrate equations (2.46) to (2.48) from 86 to 500 km for altitude, 00 - 10° to 00 + 10° for colatitude and -Bo (2.53) (2.54) (2.55) These are the components toward the geomagnetic north, east and downward not the geographic directions. In order to change all of these from the geomagnetic CHAPTER 2. SIMULATION MODEL 36 into the geographic x, y, z components, the following equations are used in our model. B'X Bx cos + By sin (2.56) B'y - - Bx sin + By cos (2.57) B'z Bz (2.58) here - sin On sin( - On, 0 BT=X B'X +B:C BT=y B' y + B y0 BT=z B' z +B z0 For convenience to compare with measurements, we also calculated the variations of H, D and Z by !:l.H !:l.D - !:l.Z - B'z The currents were calculated with a step size of 1° for both latitude and longitude. 2 km was used as the step size for altitude. The magnetic field variations were CHAPTER 2. SIMULATION MODEL 37 then determined by adding the fields due to those currents as described above. Chapter 3 Conductivity and Background Atmosphere 3.1 Conductivity The ionosphere is ionized primarily by solar ultraviolet(UV) and X radiation during daytime and starlight and cosmic rays are minor ionization sources in the night side ionosphere. The ionization rates for different sources change with altitude and depend on the intensity of ionizing radiation, atmospheric density and composition and the ionization cross sections of the atmospheric constituents. Theoretical expressions for the conductivities derived from multi:fluid dynamic theory, in which neutrals and the different charged species are treated as separate fluids that interact through collisions, are as the follows(Richmond, 1995). Nee 2 Uo (3.1) me(venll + lleill) Nee ( vinni ven.10e ) Up - (3.2) B vfn + Ol + 11:n.1 + n~ Nee( n~ UH n1 ) (3.3) B v~n.L + n~ vln + n1 38 CHAPTER 3. CONDUCTNITY AND BACKGROUND ATMOSPHERE 39 here, Ne is electron density, v the collision frequency, n the gyrofrequency, the subscript II denotes the direction along Band 1- perpendicular to B. Clearly, conductivity can be divided into three parts, the direct conductivity gives the component in the magnetic field direction, the Pedersen conductivity gives the component in the electric field direction, while the Hall conductivity gives the component perpendicular to both E and B, more precisely in the B x E direction. The conductivity magnitudes are controlled by the magnetic field strength, the electron density and the collision frequencies. 3.2 Collision Frequency The collision frequency of ions and electrons is an important basic quantity re quired to understand several phenomena in the upper atmosphere. In the iono sphere, the propagation of electromagnetic waves is controlled by the collision frequency through the electrical conductivity of the ionosphere. Thermal balance between the electrons, ions and other_ components in the ionosphere is also deter mined by the collision frequency. So, it is a fundamental problem in ionospheric or atmospheric physics to obtain the ion and electron collision frequencies as ac curately as possible. The electron collision frequency was first given by Nicolet(1953) as a sum of neutral and ion terms (3.4) 1 Ven - 5.4 X 10-16 NnTl (3.5) T3 3 Vei [59 + 4.18/og( Ne )]NeTe- 2 X 10-5 (3.6) The ion collision frequency was first derived by Chapman(1956) and was given by (3.7) CHAPTER 3. CONDUCTIVITY AND BACKGROUND ATMOSPHERE 40 (3.8) here M is average mass. As the electrons are so light they have little effect on the ions at ionospheric altitudes and so the ion-electron collision frequency can be neglected, that is Vie= 0 (3.9) Mason(1970) estimated the mobilities of the ions o+, N+, Of, Nt and NO+ in the neutral constituents He, 0, N, 0 2 , and N 2 from Oto 2500° K. He considered the ion mobilities to be dominated by two mechanisms only: elastic collisions between ions and neutrals, and resonant charge exchange collisions between ions and neutrals. The variation of the mobility with temperature can be radically different for different mechanisms. For charge exchange collisions, the mobility decreases with increasing temperature, rapidly at first and then rather slowly. For elastic collisions, the temperature dependence of the mobility depends on the nature of the short range force between ions and neutrals. If this force is repulsive, the mobility rises with increasing temperature to a broad maximum and then decreases. If the force is attractive as in the case of a chemical valence force, the mobility probability decreases slowly with increasing temperature. Although Mason's estimates agree well with the experimental values, most of these experiments are valid for temperatures less than 300° K, where ion-neutral interactions are dominated by induced dipole forces. The collision frequencies are relatively easy to compute if the ion charge and neutral particle polarizability are known. Above 300° K short range quantum mechanical repulsion and resonant charge exchange become dominant, and these effects are more difficult to estimate. Expressions for ion neutral collision frequencies are derived by Richmond(1972) on the base of Mason's estimates 0 06 0 19 Vin(NO+) = [(1.07NN2 + l.06No2 )({o~)- · + 0.60No({o~)- · ] x10-22n(~o+) (3.10) CHAPTER 3. CONDUCTNITY AND BACKGROUND ATMOSPHERE 41 v· (O+) = [1.08N ( Tn )-0.17 + 2.02N. ( Tn )0.37 + 0.61N. ( Tn )-0.019] m 2 N 2 500 °2 500 O 500 x10-22n(~t) (3.11) (o+) [O 89N ( Tn )-0.20 6N. ( Tn )0.05 N. ( Tn )0.361 Vin = . N2 500 + 1.1 02 500 + 0.89 0 500 X10- 22 !1(~+) (3.12) Salah(1993) checked the commonly used value for the ion neutral atomic oxygen( o+ - O)collision frequency based on radar and optical observations of winds in the earth's upper atmosphere and found it is too low by a factor of between 1.3 and 2 and therefore recommended the following term should be used to substitute the relevant term the equation above. v· (o+ - 0) = 1 47 N. ( Tn )0.5 X 10-22 n( o+) (3.13) m • 0 500 B The situation of the electron collision frequency is a little more complex as the magnetic field influences the effective collision frequency. Based on the de rived mobilities for electrons in N2 and 0 2 by Pack and Phelps(1961, 1966) and Itikawa's theoretical values of the electron collision frequency with 0(1971 ), Rich mond(1972) combined all these into a single expression for the electron neutral collision frequency _ [ ( Te )0.90 ( Te )0.55 ( Te )0.83 ] -26 ~ ) Ven - 2.59 300 NN2 + 2.44 300 No2 + 0.83 300 No X 10 F3.14 Later, Richmond found that he erred in applying the laboratory collision frequen cies to the computation of conductivities. The values he used are appropriate for computing the parallel conductivity u 0 but not for the transverse conductivity up and UH. Gagnepain et al.(1977) found it is appropriate to use the values given in Itikawa's(1971) table 2 to compute up and UH which seem to be accurate to within about 10%. So, they derived the following expression to calculate the electron neutral collision frequencies _ [ ( Te )0.95 Te )0.79 ( Te 0.85 ] -26 ~ ) Ven - 4.11 300 NN2 + 2.95( 300 No2 + 1.09 300 ) No X 10 F3.15 CHAPTER 3. CONDUCTNITY AND BACKGROUND ATMOSPHERE 42 Further, they compared different models of the equatorial electrojet with several observed parameters and found that an electron collision frequency four times the values given by equation ( 3.15), or about six times Richmond's values given by equation ( 3.14), yield a model in satisfactory agreement with most of the observed parameters. Equation ( 3.15) has been used in our all calculations. Concerning electron ion collision frequencies, we used equation ( 3.6) when the altitude is over 140 km because near this height Vei has become comparable with Ven although Vei can be neglected in the lower E region. It is noted that the subscript e, i and n stand for electron, ion and neutral particles. All v, defined by equations (3.1)-(3.15), are in unit of Hertz. 3.3 Electron Temperature Assuming that the electron temperature is the same as the neutral temperature is a good approximation below the altitude of 130 km(Richmond, 1973a) but it is quite complicated in the F region of the ionosphere. Various heating, cooling, and energy flow processes determine the electron temperature distribution together. More detail can be found in Schunk et al.(1978)'. Brace and Theis(1978) summarized the measurements of the electron temperature and ion density made by Langmuir probes on Atmosphere Explorer C( AE-C) and concluded that the relationship between electron temperature and ion density at the day side non-aurora ionosphere during solar minimum can be expressed by (3.16) where Pi - 1.051 X 103 P2 1.707 CHAPTER 3. CONDUCTNITY AND BACKGROUND ATMOSPHERE 43 P3 -2746 P4 - -5.122 X 10-4 Ps -6.094 X 10-12 p6 -3.353 X 10-14 here Te is in units of K, Ne is in units of m-3, and his the height and in kilome ters. The first term represents the exospheric gas temperature and a lower limit on the electron temperature. The rest of Equation ( 3.16) introduces a portion of the Te height dependence related to both the neutral and ion cooling rates. The exponential form allows the Ne dependence to vanish at low altitudes. P2 h and P4h include the height dependence of neutral collisions, while P5 Ne and P6 hNe introduce the electron-ion cooling and its variation with height. Later, Brace and Theis(1981) constructed empirical models of the global distri bution of Te at different altitudes by using the measurements from AE-C, ISIS-1 and ISIS-2 satellites. Their results showed that the variations of the electron tem perature with local time at the altit~de of 300 km and 400 km near the equator are different from those at altitudes of 1400 km and 3000 km. In the equatorial area, the electron temperature does not change much with local time at F region altitudes except during 1 - 2 hours around 6 hr LT. Brace and Theis(1984) examined how the electron temperature and electron den sity relationship changed with solar activity on the basis of data from AE-C taken when solar activity was rising, and from Dynamics Explorer-2(DE-2) taken at so lar maximum. They found that the solar maximum Te is about twice as large as the solar minimum Te, The best fit line to describe model values and experiments can be represented by Te= Tem(0.006F10.1 + 0.53) (3.17) where Tern, given by equation ( 3.16), is the model value. So equation ( 3.17) is the formula we used in our model to describe the general solar cycle dependence CHAPTER 3. CONDUCTNITY AND BACKGROUND ATMOSPHERE 44 of Te. Although Brace and Theis(l990) developed global models of Ne and Te in the F region( covering all altitudes between 300 and 1000 km) at solar maximum, based on Langmuir probe measurements from the DE-2 satellite, we will still use equation ( 3.16) to include high solar activity Te as it provides the possibility of studying the effects introduced by F10.7 variations. Titheridge(1993) analyzed 60,000 topside profiles of plasma temperature obtained from Alouette 1 ionograms. This analysis gave the mean plasma temperatures and gradients at heights of 400 and 1000 km. He showed that at mid-latitudes the mean gradient dTe/ dh, at a height of 350 km, is about 0.5 K / km at night and 2.5 K / km near noon. He modeled the variations by the equation dTe G ( dh ) laso L5(l + 0.4+ I G I) (3.18) G cos(0.95X) - 0.3cos(2.85X) - 0.4sin(2X) (3.19) X 90 + A(x- 90) (3.20) here x is the solar zenith angle and A is determined by the condition of X lnoon= 0 when Ix I< 90° or (3.21) X lmidnight= 180 when IX I> 90° (3.22) So, the electron temperature at heights over 350km can be expressed by Te= Te laso +(~~e) laso ·(h - 350) (3.23) 3.4 Neutral Atmosphere The global mean structure of the thermosphere has been studied extensively. The most successful theoretical model is probably the Thermospheric General Circulation Model(TGCM), a self-consistent model of the global mean structure of the thermosphere and ionosphere, of the National Center for Atmospheric CHAPTER 3. CONDUCTIVITY AND BACKGROUND ATMOSPHERE 45 Research(NCAR) (Dickinson et al., 1981, 1984). It uses solar EUV and UV fluxes measured by the Atmospheric Explorer Satellite to obtain the photoion ization and photodissociation rates for 0, 0 2 , and N2 • The neutral gas en ergy equation is solved considering heating from photoelectrons, 0 2 absorption in the Schumann-Runge continuum and bands; excess energy from exothermic ion-neutral and neutral-neutral chemical reactions, ambient electron and ion col lisions, 0 3 absorption in the Hartley bands, and atomic oxygen recombination and cooling from molecular and eddy thermal conduction and NO and C02 IR radiation. Major constituent composition equations are solved for the 0, 0 2 , and N2 number densities by use of the 0 2 photodissociation rates. Also, the minor neutral constituent equations, ionospheric equations, and electron and ion en ergy equations are solved for the number density distributions of N(2 D), N(4S) and NO, for the vertical distribution of o+, NO+, Ot, N:j and N+ as well as o+ of the ionosphere. Generally, the calculated neutral thermosphere tem perature and composition are in a good agreement with values from -the Mass Spectrometer/Incoherent Scatter(MSIS) empirical model if similar conditions are considered(Roble et al., 1987). Hedin et al.(1977a, 1977b, 1979)developed this global neutral thermospheric em pirical model MSIS (Mass Spectrometer and Incoherent Scatter) similar in form to the OGO 6 model but based on a much wider data base provided by six satellite mass spectrometers and four incoherent scatter stations. The MSIS-86 model can give He, 0, N2 , 0 2 , Ar, H, N number densities, total mass density, exospheric temperature and temperature at any altitude for a certain year, universal time, local time, altitude, F10.7, magnetic index Ap, geographic latitude and longitude. The overall good agreement of individual data with the model confirms the ba sic consistency of the various measurements and the correctness of the model. Details can be found in Hedin(1977a, 1977b, 1979). We used MSIS-86 in our simulations. CHAPTER 3. CONDUCTNITY AND BACKGROUND ATMOSPHERE 46 3.5 Ionosphere In contrast to the troposphere, the stratosphere, the mesosphere and the ther mosphere which are defined by lapse rates of temperature, the ionosphere is the region in which sufficient ionization exists to influence the radio wave propagation. The presence of ions and electrons makes the ionosphere an electric conductor and refracting medium for radio waves. The ionosphere is produced by a broad spectrum of solar radiation which dis sociates and ionizes the mixture of gases in the upper atmosphere. Because of the variation of the intensity of solar radiation with the angle of elevation of the sun and the solar activity, the density of electrons exhibits temporal and spatial changes. In contrast to the variability of atmospheric parameters in the troposphere which is usually a small fraction of the average value, ionospheric parameters can change by several orders of magnitude over the period of a day, season, and sunspot cy cle. In addition to the regular variations introduced by solar wave radiation, the ionosphere also experiences irregular variations or ionospheric disturbances which arise from the impact of extraterrestrial, predominantly solar corpuscles. The ionosphere usually is divided into the E and F regions or layers which were used by Sir Edward Appleton to denote the electric fields of the waves reflected from different heights. The various layers can be distinguished by different ion compositions and the ion production in each layer is due to different solar wave lengths. Similarly to the International Reference Atmosphere{CIRA) or the Mass Spec trometer/Incoherent Scatter{MSIS) empirical model, an International Reference Ionosphere(IRI) has been established based on the observed values. IRI uses the 'true height profiles' deduced from ionograms, profiles obtained by incoherent scatter radar(ISR) sounding, and the Alouette topside sounder profiles as the data bases and a set of mathematical expressions suitably linked to the peak CHAPTER 3. CONDUCTNITY AND BACKGROUND ATMOSPHERE 47 densities given by the International Union of Radio Science(URSI) or the Inter national Consultative Radio Committee(CCIR) numerical maps. The topside profiles are essentially based upon a smoothed version of the descrip tive compilation of the Alouette topside sounder results. These were also checked with ISR and satellite data and with electron content measurements from ground based observations of beacon satellites. The profile is normalized to the F2 peak and the shape parameters depend on geomagnetic latitude, F2 peak critical fre quency, and the monthly mean 10. 7 cm solar flux. The model is fully described by a combination of analytical functions. We adopted IRl-86 in our simulations. 3.6 Internal Magnetic Field The International Geomagnetic Reference Field(IGRF) is used to calculate the gyrofrequencies. The version adopted in the program is the POGO 68/10 mag netic field Legendre model, transfor~ation coefficients valid for 1973. Takeda(1996) studied the effects of the strength of the geomagnetic main field strength on the dynamo action in the ionosphere for three extreme cases which may only take place in the geological time scale. During a solar cycle, the geo magnetic main field strength has a very limited change, less than 1/100 roughly and so the selection of any IGRF version has actually no noticeable effects on the ionospheric electrodynamics. CHAPTER 3. CONDUCTIVITY AND BACKGROUND ATMOSPHERE 48 3. 7 Atmospheric Wind 3. 7.1 History Although atmospheric tides have been studied for almost two centuries and most famous scientists such as Newton, Laplace, and Kelvin were involved, the re search into the wind and temperature fields in the mesosphere and thermosphere apart from theoretical and observational analyses of surface pressure and tem perature, only occurred from the 1960's. Kato(1966a, 1966b) and Lindzen(1966a, 1966b) independently investigated the atmospheric tides and later summarized their findings in their books(Chapman and Lindzen, 1970; Kato, 1980). The assumptions, among other approximations used, allow consolidation of the governing momentum, continuity, thermal energy, and state equations for an os cillation of given period into a single separable partial differential equation in latitude and height, and hence formulation of an eigenfunction-eigenvalue prob lem. The solutions to the latitude variations are the so called Hough functions and the relevant eigenvalue are the equivalent depths. The Hough functions are usu ally expressed by an expansion in associated Legendre polynomials. Most of the expansion coefficients relating normalized Hough functions and normalized asso ciated Legendre functions are given by Chapman and Lindzen(1970). They also provide a particularly efficient numerical scheme to solve the vertical structure equation. To model the atmospheric tide, a number of physical processes beyond those in classic tidal theory must be included. Lindzen and Hong(1974), Aso et al.(1981), who exclude mean zonal winds and meridional temperature gradients, Walter scheid and Venkateswaran(1979a, 1979b, 1980) who neglect eddy and molecular dissipation, have worked on this. The extra processes include molecular and eddy diffusion of heat and momentum, Newtonian cooling, hydromagnetic coupling, CHAPTER 3. CONDUCTIVITY AND BACKGROUND ATMOSPHERE 49 composition variations, and interactions with background winds and meridional temperature gradients. 150 .....-----,---,.---.----.-----....---...---..-----,.-----T-----.------.------. 'Southward' -+ 'Eastward' ----· 100 50 -50 ._____,._____., _ __._ _ __._ _ _.__....__...___..___ ,____. _ __,_ _ __._ _ __._ _ _, -70 -60 -50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 Geographic Latitude(degree) Figure 3.1: The (1, -2) tidal southward and eastward wind amplitude variations with geographic latitude. Eastward and southward/equatorward winds are posi tive. 3.7.2 The (1, -2) Tidal Winds in E Region and Measured F Region Zonal Winds Decomposing the heating rates due to insolation absorption by 0 3 and H20 into Hough modes, Forbes and Garrett(1978b) demonstrated that the (1, -2) mode is the most important component of the heating rates in the E region and this is consistent with the result of Chapman and Lindzen(1970). So it is very natural to CHAPTER 3. CONDUCTIVITY AND BACKGROUND ATMOSPHERE 50 200.------,------.------.------r------,,------. 'Zonal' - 150 100 50 0 ····································································································································································································· -50 -100 -150 ,...._ ___.....______._ ____....______._ ____ .....______, 0 4 8 12 16 20 24 Local Time(hr) Figure 3.2: The DE-2 measured F region Zonal neutral wind variations with local time. The eastward is positive(from Herrero and Mayr, 1986). use the diurnal (1, -2) mode as the main wind in the E region. Stening calculated the electrostatic fields in the ionosphere produced by the (1, -2) wind model in the E region(1969a, 1971, 1973) and in the whole ionosphere(1981). Tarpley demonstrated that the solar diurnal mode (1, -2) wind generates currents that resemble the Sq current pattern(1970b). Richmond et al.(1976) studied the roles of different tidal winds and further concluded that the (1, -2)*(includes ion drag influence) is probably the primary generator of ionospheric currents. Forbes and Lindzen(1976b) simulated magnetic field variations on the ground produced by different tidal modes and drew the same conclusion. In our simulation, the tidal winds are expressed by U = A cos[w(t - f)] CHAPTER 3. CONDUCTIVITY AND BACKGROUND ATMOSPHERE 51 here w = 21r /24, t is the local time in hours, f = 22 hr for the southward wind and 4 hr for the eastward wind. A is amplitude. The latitudal variations of the southward and eastward tidal winds are shown in figure 3.1. The F region zonal neutral wind adopted is from the DE-2 WATS measure ment(Herrero and Mayr, 1986). No latitude and altitude variations were included and its variation with local time is shown in figure 3.2. The F region meridional wind is the same as that obtained by Blum and Harris(l975). The neutral winds between 150 and 200 km were calculated by interpolation al though physically this is a questionable procedure, we expect that the errors introduced will not be significant(Crain et al.; 1993b). 3. 7 .3 Forbes Diurnal and Semidiurnal Tidal Winds Although the diurnal (1, -2) wind model can reproduce the main characteristics of the ionospheric electrostatic fields and Sq current pattern, tidal theories and experiments clearly show a more complex structure and the existence of the prop agating (1, 1) tidal mode in the E region(Chapman and Lindzen, 1970; Amayenc, 1974; Lindzen, 1976; Harper, 1977b; Dickinson et al., 1981; Sipler et al., 1983; Tsuda et al., 1988; Manson et al., 1991; Salah et al., 1991; Clark and Salah, 1991; Miyahara et al., 1993, Roble and Ridley, 1994; Hagan et al., 1995; Burrage et al., 1995; Deng et al., 1997). Forbes(1982a, 1982b) included eddy and molecu lar diffusion, mean winds, background temperature structure and hydromagnetic coupling in his model and solved the four coupled partial differential equations in the three velocity components and temperature. Forbes and Hagan(1988) investigated numerically the propagation characteristics of the first symmetric propagating tide (1, 1) mode for a zonally averaged back ground atmosphere characterized by mean winds, meridional temperature gra dients, and mechanical and thermal damping. By comparing with the available observations, they concluded that the joint presence of mean winds and dissipa- CHAPTER 3. CONDUCTNITY AND BACKGROUND ATMOSPHERE 52 tion act to significantly modify the propagation characteristics of the ( 1, 1) mode. Forbes and Vial(1989) used the most recent heating rates provided by Groves(1982a, 1982b ), a zonally averaged wind, temperature and pressure field developed for the new COSPAR international reference atmosphere and new parameters of eddy diffusivity. They calculated the monthly solar semidiurnal tide in the mesosphere and low thermosphere. Although these new results of the solar semidiurnal winds are little different from Forbes's earlier calculations, since Forbes and Gillette(l982) provided explicit simulations from the surface to over 400 km for the solar diurnal, solar semid iurnal and lunar semidiurnal tides for equinox and solstice, we will use their tabulations and graphs as inputs of our model to study the ionospheric electro dynamic process. Ground based meteor wind radars and incoherent scatter radars have provided many observations of the neutral wind in the mesosphere and lower thermo sphere( Amayenc, 1974; Wand, 1976; Harper, 1977b). But the geographic cover age is quite limited as the radar chain is mainly located in the American sector, es pecially in the campaign of the Lower '.l'hermosphere Coupling Study(LTCS)(Salah et al., 1991). All these measurements are usually difficult to cross-calibrate and show large variability that generally was attributed to local influences. Satellites provide a long term and continuous global observation of the middle atmosphere. The launch of the Upper Atmosphere Research Satellite(UARS) in September 1991 makes it possible to measure the wind in situ in the mesosphere and thermo sphere(Reber, 1993). The Wind Imaging Interferometer(WINDII) and the High Resolution Doppler lmager(HRDI) on the UARS will provide a comprehensive global picture of the horizontal tidal winds in mesosphere and thermosphere. The preliminary results of HRDI and WINDII observations of mesosphere winds are quite consistent and both show that the solar diurnal tide is the dominant feature in the meridional wind field. The observed vertical wavelength of 20 km and the maximum amplitude of meridional wind of 75ms-1 at ±22° Nat 95 km(Morton CHAPTER 3. CONDUCTNITY AND BACKGROUND ATMOSPHERE 53 et al., 1993) and 65ms-1 at 90 km(McLandress et al., 1994) are quite consistent with the Forbes [1982] result and makes us believe that the Forbes model should be adopted in the present study. If so, our calculations should give some indi cation of the current form of the thermospheric winds by the success the input winds have in generating the observed electric fields and magnetic variations. The WINDII results have not yet been analyzed into a reasonable climatological model. In what follows, we will use Forbes and Gillette's diurnal and semidiurnal winds and different combinations for the southward and eastward components and we will seek to calibrate the amplitudes of the diurnal and semidiurnal winds against observed ionospheric electrostatic fields, currents structures and the magnetic field variations on the ground. 3.7.4 HWM90 HWM90(Horizontal Wind Model, version 90) is a revised global model of ther mosphere winds using satellite and ground based observations. It can be used to calculate the horizontal neutral wind on any day of year for any time of day(UT), altitude( over 100 km), geographic latitude and longitude, local solar time, 3- month average and previous day value of the 10. 7 cm solar flux index, and either the daily Ap magnetic index or prescribed history of 3-hour Ap indices. The spatial variations in the horizontal wind vector are represented by an expan sion in vector spherical harmonics with each expansion coefficient represented by a Fourier series in universal time and/or day of year as appropriate. The expansion involves two orthogonal vector fields, the irrotational and rotational. Generally, there are four coefficients to be determined for each harmonic order which to gether specify the amplitude and phase of the meridional and zonal winds. Because of the sparsity of data between 130 and 220 km and the wrong scale factor used for the zonal wind values measured between 1988 and 1990(Biondi CHAPTER 3. CONDUCTNITY AND BACKGROUND ATMOSPHERE 54 et al., 1995), the correctness of the HWM90 is doubtful and we will discuss this question in the relevant section. The HWM90 full description can be found in Hedin et al.(1988, 1991). Chapter 4 Flux Tube Integrated Conductivity 4.1 Introduction It has long been known that F region ·polarization fields play an important role in the low latitude dynamo during nighttime (Rishbeth, 1971b; Heelis et al., 1974; Stening, 1981; Takeda and Maeda, 1983). More recently, models considering the conductivity of the entire ionosphere have been developed with no restrictions on where currents may be generated or closed within the region(Richmond and Roble, 1987; Singh and Cole, 1987a; Crain et al., 1993a). With the E region dynamo model, S9 magnetic variations and the general features of the F region plasma drift have been successfully reproduced to a limited extent(Richmond et al., 1976). With the E and F region dynamo model, the agreement between model calculations and experiments has been much improved especially regarding the post-sunset enhancement of the vertical drift. It is therefore concluded that the F region dynamo is very important at night and should be included in ionospheric dynamo models. 55 CHAPTER 4. FLUX TUBE INTEGRATED CONDUCTIVITY 56 When does the F region become a dominant and controlling driver in the middle and low latitude ionospheric dynamo? One of the critical parameters in assessing the importance of the F region polarization field is the ratio between the F and E region electrical conductivities. Harper and Walker(1977) studied not only the Pedersen and Hall conductivities but also their height integrated values. They found that, although the Pedersen and Hall conductivities in the F region are much smaller than those in the E region, the height integrated Pedersen conduc tivities in the F region are larger or nearly equal to that in the E region. The Hall conductivity has its main contribution from the E region, even during night time. The height integrated Hall conductivity of the E region is twice as large as the height integrated Pedersen conductivity of the F or E regions. Furthermore Anderson and Mendillo(1983), after examining the effect of the F region dynamo on zonal drifts at night, concluded that the transition altitude at which the F region becomes dominant is determined by the ratio between the flux tube inte grated Pedersen conductivities of the F and E regions. It is thus very clear that flux tube integrated conductivities are more appropriate than height integrated conductivities for determining currel?-t and electric field distributions. This can be recognized from many works (Stening, 1968; Gagnepain et al., 1976; Duhau et al., 1983; Singh and Cole, 1987b,1987c and Crain et al., 1993b) in which flux tubes were appropriately considered as equipotentials and so simplifying the cal culations. We should point out that both individual conductivity values and their flux tube integrations have separate effects on the current and electric field distributions. The characteristics of the Pedersen and Hall conductivities have been studied extensively but less attention has been given to their flux tube integrated val ues. Detailed work on E and F region flux tube integrated Pedersen and Hall conductivities, including apex altitude distribution, local time variation, seasonal changes and the relationship with solar activity, will be very helpful for our un derstanding of the F and E region dynamo processes. More important, it will CHAPTER 4. FLUX TUBE INTEGRATED CONDUCTNITY 57 provide more insight into some experimental results. 4.2 Equations Using the (p, q, ) coordinates system, we assume that the electric field is curl free and it can be expressed by (4.1) (4.2) (4.3) Using Ohm's law and the condition that the current must be divergence free, the electric field satisfies the follow equation(Gagnepain et al., 1976) a a , au+ au- ap (EphpEP - E"'h"'EH) + a<1> (E"'h"'E p + EphpEH) + ap + a<1> = o (4.4) where 1q2 •h,j, "£,p - Uphhqdq (4.5) q1 p 1q2 hp E'p Uphhqdq (4.6) q1 "' EH 1q2 UHhqdq (4.7) q1 u+ - 1q2 B(upU,f, + uHUp)h,J,hqdq (4.8) q1 u- - 1q2 B(uHU,J, - upUp)hphqdq (4.9) q1 here u+ and u- are integrated emf's. If the magnetic field is presented by a eccentric dipole field and the equation for magnetic field lines can be written as r = k sin2 (} The equations ( 4.5, 4.6, 4. 7) can be simplified into k2f1 182 2 (4.10) "£,p = ilk }81 up sin 8(1 + 3 cos 8)d8 CHAPTER 4. FLUX TUBE INTEGRATED CONDUCTNITY 58 (4.11) (4.12) which are the equations we will use in this chapter and here ( q1 , q2) and ({Ji, 82) are the integration limits of q and 8. We take the ionospheric ranges as 90-150 km for the E region and 150-1000 km for the F region. During calculation, we first determine latitudes where the designed magnetic field line crosses the heights of 90, 150 and 1000 km. The number of integration steps for the equations (4.10) and ( 4.12) in the E and F regions are each taken to be 128. This decision guarantees the stability of the solution and the efficiency of running the program. 4.3 Flux Tube Integrated Conductivity 4.3.1 Altitude distribution The typical altitude distribution of Pedersen and Hall conductivity is depicted in figure 4.1. It is well understood that E region conductivities are larger than those of the F region as the collision frequency is much larger in the E region than in the F region. From figure 4.1, we can see that conductivities at an altitude of 120 km are about 17 and 22000 times as large as those at 300 km for Pedersen and Hall conductivities at 14hr LT respectively. But it is not the case for flux tube integrated conductivities. Figure 4.2 shows the variations of integrated conductivities with the apex altitude of the field line. During daytime, the flux tube integrated Pedersen conductivities in the E and F regions are not so much different when the apex altitude is about 250 km, and increasing the apex altitude, the F region flux tube integrated Pedersen conductivity is about half of the E region. But during nighttime, the F region value is much larger than that CHAPTER 4. FLUX TUBE INTEGRATED CONDUCTNITY 59 1000 ------~------...... ------....-...... ----,----- 900 800 700 600 500 ...... 400 ·------...... 300 --. ·-----... ······ ------, ...... 200 ························································.·.·.·::-::, ··-... ___ ·-··------.,--~---· ------··-······················ .. -_·: .::::,-·-·······-·····-····-. 100 ~-:·: :: ___ :::::, 1e-08 1e-07 1e-06 1e-05 0.0001 0.001 Conductivity(mho/m) Figure 4.1: Height distribution of Pedersen and Hall conductivity at (20.0° N, 116.3° E) in March 1986 for different local times. The solar activity index F10.7 is 75.9. The solid line is for Pedersen at 14 hr, long dash line for Hall at 14 hr, short dash line for Pedersen at 2 hr and dot line for Hall at 2 hr. in the E region. Ei/Ej reaches a maximum at 320 km with a value of 25 and then decreases but is still over 16 at 1000 km apex altitude. Considering that an apex at 1000 km corresponds to about 20.6° geomagnetic latitude at a height of 90 km, there is no doubt that the F region plays a large role in the ionospheric dynamo during nighttime for the middle and low latitude regions. There is not much difference between the variations of the Hall conductivity itself and the flux tube integrated values no matter whether it is in day or night. The main contributions to the Hall conductivity come from the E region at all local times. We have not shown the variations of E~ (Equation 4.6) as it is very similar to CHAPTER 4. FLUX TUBE INTEGRATED CONDUCTNITY 60 Ep and will not do so later for the same reason. 4.3.2 Local Time Variation Although a magnetic field line in the F region is maybe ten times longer than one in the E region, the integrated Hall conductivity in the F region is still much less than that of the E region as the Hall conductivity in the E region usually is about 1000 times larger than that in the F region(at 300 km for example). So both the Hall conductivity and the flux tube integrated Hall conductivity have similar variations with local time. Considering the flux tube integrated Pedersen conductivity, the situation is quite different. For an apex altitude of 510 km, the flux tube integrated Pedersen conductivity of the F region is smaller than that of E region at day times. Similarly, for the apex altitude if 350 km the contribution from the F region is greater than that of E the region at nighttime (17 hr - 07 hr), as figure 4.3 shows. Generally the integrated Pedersen conductivity of the E region is larger than that of the F region during daytime but the opposite is true during nighttime for the magnetic field lines with an apex altitude of over 200 km. The time of change over depends on solar activity, season, longitude and especially, the apex altitude of the field line. 4.3.3 Solar Activity Dependence It is reasonable to think that the ionospheric dynamo is closely related to solar activity. Jicamarca incoherent scatter radar observations of the ion drift velocity near the magnetic equator clearly show the dependence of the electric field on solar activity(Fejer et al., 1979) and so does theoretical work(Heelis et al., 1974). As we know, the higher the solar activity, the higher are the conductivities. Fig- CHAPTER 4. FLUX TUBE INTEGRATED CONDUCTNITY 61 1000 100 I '- ..... I _.-:_--:.:...= ----- I I --., ______:-:__-:_::.. ::--_-:-_-:- -- -_ - .- _- -- _- - - ::_--:-__ 10 I 0 I -~ __ ... ,..---· ...... ·._ .. 8 I ...... -...... I -l;.;J 1 0.1 0.01 0 100 200 300 400 500 600 700 800 900 1000 1000 r', I ..._ 100 --- I ------I ...... I 0 10 ~s :z: -l;.;J 1 ·-·- -·-·------·- --·-·-·-·-·---·-""-·-·- 0.1 4•"'. ~·- ...... _...... _...... --...... --.... -... 0.01 0 100 200 300 400 500 600 700 800 900 1000 Apex Altitude(km) Figure 4.2: The variations of Ep, EH with apex altitude at different local times in March 1986(F10.7 = 75.9) at Asian longitude. The solid line is for E region at 2 hr LT, dot line for F region at 2 hr LT, short dash line for E region at 14 hr LT, dot-short dash line for F region at 14 hr LT. CHAPTER 4. FLUX TUBE INTEGRATED CONDUCTNITY 62 1000 ~-~-~---~-~-~-~-~-~-~--~~ 100 ...... -.. -... -. . .. ---.. -.. -..c:0 8 10 ;f 1 0.1 0 4 8 12 16 20 24 1000 ~-~-~---~-~-~-~-~-~-~--~~ 100 -0 ] 10 'Ji 1 ·-. 0.1 0 4 8 12 16 20 24 Local Time(hr) Figure 4.3: The variations of 'Ep and 'EH with local time for different apex alti tudes. The upper panel is for the apex altitude of 350 km and the lower panel for 510 km. The solid line is for the E region, dot line for F region. Asian longitude and a value of 75.9 for F10.7 are used. CHAPTER 4. FLUX TUBE INTEGRATED CONDUCTIVITY 63 1000 100 -=-=--=-=---:--_7_"7_~-=-=------:.=······· -...... ------.. ---- 0 10 -.c: 8 ---- ...... -~ 1 0.1 0.01 80 100 120 140 160 180 200 1000 ~-~-~-~---~-~~-~-~-~---~~ 100 ------ 10 . ---- .... -...... ------ .. -.... - -- .. ---.. -.... -- 0.1 ...... -.. --- .- .... -- .... -.... - -- .... 0.01 =·--.....- _ __._ _ __._ _ __._ _ _.___....___._____. _ __._ _ __._ _ __._ _ _.___....______. 80 100 120 140 160 180 200 F107 Figure 4.4: The variations of Ep, EH with solar activity index F10.1• The apex altitude of the field line is 510 km. The other conditions are the same as figure 4.2. CHAPTER 4. FLUX TUBE INTEGRATED CONDUCTIVITY 64 100 ~~--=-~...... ------______--- -==-~-:-:....------=-=--=---=-=---=---=----=-----=--=---== .. =-~·-=-- 0 10 -..c: ...... -.. ---.. 8 A, -i:-:i 1 0.1 0.01 0 30 60 90 120 150 180 210 240 270 300 330 360 1000 .,..-,--~-r--~--,---.-~~---r----r----r-----r-----r-~-r--r-,----,-----.--,,--,--,--...... ,. 100 ------ .. .. --..... -.. -.... -...... 0.1 ...... _ .. -- .... -.. -. -. -.... -\, ...... -.. -- ...... -- -__ ... 0.01 0 30 60 90 120 150 180 210 240 270 300 330 360 Geomagnetic Longitude(deg) Figure 4.5: The variations of :Ep, EH with longitude. The other conditions are the same as figure 4.4. CHAPTER 4. FLUX TUBE INTEGRATED CONDUCTNITY 65 140 ...... 120 100 ...... 0 ...... c: . . 13 80 -~ 60 40 20 0 30 60 90 120 150 180 210 240 270 300 330 360 1.4 ...... 1.2 . 1 ...... c:0 0.8 13 0.6 -~ 0.4 0.2 0 0 30 60 90 120 150 180 210 240 270 300 330 360 Geomagnetic Longitude(deg} Figure 4.6: The variations of Ep and EH in the E region with longitude at 14 hr(upper) and 2 hr(lower) LT. The solid line is for Ep and dot line for EH, The other conditions are the same as figure 4.4. CHAPTER 4. FLUX TUBE INTEGRATED CONDUCTIVITY 66 1000 ---~-~-~--~-~-~----~-~-~-~ 100 - - - - _::-.:::------=-=-=--=------_--:.=--. - - - -- ..------0 10 ------.c: e ------·-- .. ------...... --- -~ 1 0.1 0.01 2 4 6 8 10 12 1000 ---~-~-~--~-~-~----~-~-~-~ 100 o 10 ~ J 1------~...-,c..:.·=------~------__ .. ------.. ______-- 0.1 -----··------.. ___ .. ------0.01 ------...... --- 2 4 6 8 10 12 Month Figure 4.7: The variations of Ep, EH with month. The other conditions are the same as figure 4.4. CHAPTER 4. FLUX TUBE INTEGRATED CONDUCTIVITY 67 50 ~-~-~----~-~-~-~~-~-~---~ 40 -..c:0 E 30 _____ ...... -······· ...... -~ ·-. . . 20 ···--... ______-·· 10 2 4 6 8 10 12 70 -..c:0 E 60 J 50 2 4 6 8 10 12 Month Figure 4.8: The daytime variations of Ep(upper) a.nd EH (lower) with month. The solid line is for the E region a.nd dot line for F region. The other conditions a.re the same a.s figure 4.4. CHAPTER 4. FLUX TUBE INTEGRATED CONDUCTNITY 68 :·--- .. i1'..., ... 30. 1,·-·-- ii \ ... ii \ ... \ ... ii \ \ 20 ~ ' ······· \ ·.. \ ~ ' ...... ·· ... j ..... \ ·· .... 10 ...... ~'. i ..... i ..... ·. .. '·.. j 0 L-L-L-L.__JL-L...... ,j:.:..:::l:=::::l~==i:::=1:::~==±=:::t::::=t::...L--1..---1...--1..---1...---1...._J 0 2 4 6 8 10 12 14 16 18 20 22 24 250 r--..--...---.--,---r-...... ,....-,----.--,----..--.---,.--r--....-...---r--r---r--r--,--,----..--,---, 200 - "\ / / \ / ---···. \ / ----- ... \ / ---- ... \ / .-· ... \ / .-· ·.. / ~ ~ 100 ,... - .,., .,., ----- ."\ / -- ~-~-~-=---··- .. ------. 50 /_---·-·····----- 0 .__.__.,__....__.__....L..._,___.__.__.___,____,_____.'--L--.L.-..J.-....L..-_.__....L..._.___.___,____,____,_____. 0 2 4 6 8 10 12 14 16 18 20 22 24 Local Time(hr) Figure 4.9: The variations of Ei/Ej, Ei/Ek in March 1986 with local time for different apex altitude field lines. The solid line is for the apex of 310 km, dot line for 510 km and dash line for 710 km. CHAPTER 4. FLUX TUBE INTEGRATED CONDUCTIVITY 69 ure 4.4 shows the variations of flux tube integrated Pedersen and Hall flux tube integrated conductivities with F10.7. It is interesting that during daytime the flux tube integrated Pedersen and Hall conductivity in both F and E regions only change approximately within a factor of 2 when F10.7 changes from 65 to 185. Moreover, E~/Ek and E~/Ej remain at about 100 and 0.9 for solar maximum for the field line with an apex altitude of 510 km. The situation is quite different during nighttime. The flux tube integrated Pedersen conductivities of the F and E region both increase with solar activity but with a more pronounced effect in the F region. On increasing F10.7 from 65 to 185, at 2 hr LT E~ increased by a factor of 10 while Ej increased by only a factor of 2. E~/Ej increased from 20 to 90, E~/Et decreased from 28 to 3. Obviously the F region will be more significant during solar maximum than minimum in the nighttime ionospheric dynamo. Jicamarca observations show that the zonal eastward drift velocity at night is twice as great as the westward drift during day which can be easily explained by our calculations. As E~ /Ej "' 1 in daytime and is larger than 10 at nighttime, the above conclusion can be drawn immediately even from a very simple iono spheric dynamo using the following equation for the vertical electric field given by Kelley(1989) when dynamo action is dominated by the F region wind(U) (4.13) The solar activity index F10.7 has different effects on the Pedersen and Hall inte grated conductivity during daytime and nighttime. We ascribe this phenomenon to the effects of the ionospheric electron density changes with the solar activity. More details can be found in section 7 .2.4. So any detailed ionospheric dynamo model should include the effect of the F region especially during nighttime. CHAPTER 4. FLUX TUBE INTEGRATED CONDUCTIVITY 70 4.3.4 Longitudinal Variation Figure 4.5 shows the variations of flux tube integrated Pedersen and Hall con ductivity with longitude at a fixed local time. E region value variations are quite similar between day and night. The values in the American longitudes are larger than those in the Asian longitudes. The same is true for the F region values al though the F region flux tube integrated conductivities show wave like variations with longitude. In daytime the fluctuation is about 20 mho for Ep and 1 mho for EH. At nighttime it is more clear that the American region values are larger than those in the Asian and Indian regions. We can see this in figure 4.6 where a . al · d Th t· f I:p(American) d I:H(American) £ d d , ht 1mear sc e 1s use . e ra 10s o I:p(lndian) an I:H(lndian) or ay an mg are both about 1.5. This value is close to the ratio of 8 fjindi~n)) mer,can (1.4). At 2 hr LT the Ep in the American longitudes are about 5 times larger than those in the Asian longitudes, while EH values are 10 times larger. These differences are mainly introduced by the magnetic field strength and the electron density distri bution. Although the flux tube integrated conductivities have a clear longitude dependence as shown in figures 4.5 and 4.6, we do not expect the ionospheric electric field in American and Asian and Indian longitudes will be much different from our simulation results. 4.3.5 Seasonal Variation The flux tube integrated conductivities both in the E and F regions change with season. The F region variations are more pronounced than E region. From fig ure 4. 7, we can see that the flux tube integrated Pedersen conductivity of the F region reaches a high value in spring and autumn, and a low value in winter and summer. Similar characteristics apply to the F region EH, To study the varia tions of the E region flux tube integrated conductivities, the daytime E region integrated conductivities variations are reproduced in figure 4.8 where a linear CHAPTER 4. FLUX TUBE INTEGRATED CONDUCTIVITY 71 scale is adopted. Similar to F region, the E region integrated conductivities reach a maximum in equinox and a minimum in solstice. For example, the daytime E region integrated Pedersen conductivities are 37 mho and 30 mho in March and July. The corresponding F region values are 28 mho and 10 mho respectively. ~ p changes from 0. 7 in March to 0.3 in July. So if the winds in the March and July are the same, we would anticipate a little larger electric field in March than in July from equation (4.13). It is quite understandable that the flux tube integrated conductivity has a maxi mum in equinox and minimum in solstice because the ionospheric electron density varies in this way. The variations of E~/Ej and E~/Ek with month are more pronounced in nighttime than in daytime. The values of E~/Ej in equinox are about 2 ,.._, 3 times as large as in solstice during nighttime. So it seems that the F region plays a more important role in the ionospheric dynamo in equinox than in solstice. 4.4 Discussion The variations of the flux tube integrated conductivities are different from those of the conductivities themselves. Pedersen and Hall conductivities of the E re gion are larger than those of the F region. As with Hall conductivity itself, the integrated Hall conductivity of the E region is still larger than that of the F region during daytime; the integrated Pedersen conductivity of the F region is comparable to or larger than that of the E region according to the apex altitude of the magnetic field line. Furthermore, the F region integrated Pedersen con ductivity is much larger than that of the E region at night. This clearly shows the importance of the F region in the ionospheric dynamo. From figure 4.9, it is clear that E~/Ej is very close to 1 for the field lines with an apex altitude of 300-700 km during 6 -18 hr LT, while at other times it is larger CHAPTER 4. FLUX TUBE INTEGRATED CONDUCTIVITY 72 than 1. The exact values change with apex altitude. At midnight, E~/Ej are 27, 20, 15 for apex altitudes of 310, 510, 710 km respectively. Most importantly, E~/Ej reaches a maximum of over 30 around 19 hr LT for apex altitudes of 510 and 710 km. Compared with the nighttime, the sunset F region is even more important for the ionospheric electrodynamo process and maybe this contributes to the prereversal enhancement of the eastward electric field. The integrated Pedersen conductivity and the ratio of the F and E region values are very important parameters for assessing the F region's importance in iono spheric electrodynamics processes. From day to night, the control shifts from the E region to the F region, driving changes to load. 4.5 Summary • The flux tube integrated Pedersen conductivities in the E and F region have similar magnitudes especially when the apex altitude is over 400 km during daytime. F region values are much larger than those in the E region at night. • The ionospheric electric dynamo process is controlled by the E region during daytime but by the F region during nighttime. Around 19 hr LT, there is a sharp increase of E~/Ej. • Nighttime integrated Pedersen and Hall conductivities are more seriously affected by solar activity than in daytime. The F region has a greater effect on dynamo processes during solar maximum than at solar minimum. • The integrated conductivities show clearly the longitude variations. The integrated conductivities in American longitudes are larger than those in the Asian longitudes. CHAPTER 4. FLUX TUBE INTEGRATED CONDUCTIVITY 73 • The F region will play a more important role in ionospheric dynamo pro cesses during equinox than in solstice. Chapter 5 Electric Fields and Currents 5.1 Introduction Using the equivalent circuit method and different wind models, we will exam ine separately the roles of the eastward and southward winds in the E region and in the F region. As the (1, -2) tidal wind has been widely used in early ionospheric electric field simulations, we will adopt the classic (1, -2) tidal wind between the altitude of 90 - 150 km, the theoretical meridional wind of Blum and Harris(1975) and the zonal wind from satellite measurements(Herrero and Mayr, 1986) between 200 - 500 km. The effects of the F region zonal wind are inves tigated. Then the temporal, altitude variation and solar activity dependence of the electric fields and current densities are summarized. In section 5.3, we use the Forbes and Gillette(1982) atmospheric wind calculation in our program and will discuss the contributions of the solar diurnal and semidiurnal components and the combinations of these. The Horizontal Wind Model(HWM90) is discussed in section 5.4 and it seems that the semidiurnal wind in this model is too strong. A comparison of our simulations with measurements is given last. In this chapter, all the electric fields are calculated at a particular UT(18 hr). We take the local 74 CHAPTER 5. ELECTRIC FIELDS AND CURRENTS 75 time variations to be equivalent to the longitude variation. 5.2 Electric Field and Current Produced by the (1, -2) mode in the E region and the F Region Winds Figure 5.1 shows the procedure used in all the calculations and simulations. The neutral density, electron density, magnetic field and collision frequency, electron temperature model etc. have been discussed earlier as they have been used in Chapter 4. Coaductuce and Equivalent ---~ ci:reuit IRI Bleatric field IQIII' l CUrnnt diatrihatioa and -gnetic field nriati011 Figure 5.1: Schematic of modeling electric field, current and magnetic field vari ation on the ground During the simulation, we used three programs. By the first one we calculate the flux tube integrated conductivities and integrated emfs when the whole iono sphere is divided into a number of blocks according to the geomagnetic latitude and longitude. The southward and eastward electric fields are calculated by the CHAPTER 5. ELECTRIC FIELDS AND CURRENTS 76 second program using Stening's equivalent circuit method. The current den sities( excluding field aligned current) and the magnetic field variations on the ground are calculated by use of Ohm's and Biot-Savart laws operating on the output of program two. In this section, we use the (1, -2) diurnal tidal wind without altitude varia tion. A linear interpolation method is used to calculate the winds between 150 and 200 km. The ionospheric ranges of the E and F regions are taken to be 90 - 150 km and 150 - 500 km respectively. Concerning the amplitude of the (1, -2) diurnal tidal wind, -We have tried us ing different amplitudes of the (1, -2) diurnal tidal wind in our calculations and found that with the amplitude of the southward wind of 35 m/ s at 22° latitude, we can produce close to the experimentally measured electric fields in the F region. Although the E region and the low F region tidal wind always has a very com plicated height structure due to the propagating (1, 1) tidal wind(Tarpley, 1970b; Forbes et al., 1988; McLandress et al., 1994), this wind selection is a reasonable first approximation. The phase is so selected to ensure the maximum southward wind occurs at 22 hr LT and the eastward maximum occurs 6 hr earlier than the southward wind. The solar activity index of F10.1 is selected as 75.9 to stand for the solar minimum, March 1986, unless otherwise stated specifically. 5.2.1 E Region alone If we include the E region only in our calculations and the (1, -2) tidal wind as the only source of the dynamo, the electric field distributions are very similar to previous work(Stening, 1973; Forbes and Lindzen, 1977; Richmond et al., 1976). Figure 5.2 shows the variations of the southward/vertical and eastward electric fields with local time over the geomagnetic equator at the altitude of about 105 km. It is obvious that both the southward and eastward tidal winds contribute to the electric fields but the southward wind is the major contributor. CHAPTER 5. ELECTRIC FIELDS AND CURRENTS 77 The eastward electric field is positive between about 4 and 18 hr LT, and negative otherwise. The southward electric field has an opposite behavior. Concerning the magnitude of the electric field, the southward field is much larger than the eastward. It is because this large downward electric field and the Hall conductivity distribution produce the electro jet phenomenon. The eastward electric field shows a sudden increase, produced by the southward wind, at about 5 hr LT. We will discuss this later. The importance of the southward wind can be further testified by referring to figure 5.3 where the height variation of the eastward current density at noon at the magnetic equator is shown. Although the maximum eastward current densities appear at the same altitude , around 106 km, the current density from the southward wind is nearly 10 µA/m2 which is about 5 times larger than that produced by the eastward wind at 12 hr LT near the geomagnetic equator. 5.2.2 Whole Ionosphere In what follows, we will discuss three quite different cases with the dynamo operat ing in the E region, in the F region and in the whole ionosphere. The contributions of the eastward and southward winds in the F region are also checked. 5.2.2.1 Dynamo in the E region only This is very similar to the first discussed case of the E region alone except that current flow is now permitted in the F region. The main features of the electric field and current density are nearly the same. The only difference lies in the magnitude. At the geomagnetic equator, the maximum eastward current density at noon changes from 12.6 µA/m2 to 9.8 µA/m2 as seen in figure 5.3 and the upper panel of figure 5.4. This is caused by the increase of the flux tube integrated conductivities. From equation (2.12) we know that, with an increase of the flux tube integrated conductivities, the electric fields will decrease if we keep the CHAPTER 5. ELECTRIC FIELDS AND CURRENTS 78 dynamo emfs unchanged. It is as if we have added an extra parallel load into the ionospheric electric circuit and so made the original circuit branch current smaller. 5.2.2.2 Dynamo in the F Region only Figure 5.4 shows the contributions of the F region dynamo to the eastward cur rent density at different local times. The upper panel is at mid-day(12 hr) and the lower at sunset(18 hr). It is clear that the eastward current density driven by the F region dynamo is much larger than that of the E region at sunset. The current density produced by the F region wind is about 6 times larger than that produced by the E region tidal wind. Figure 5.5 shows the electric field variations produced by the F re gion eastward and the combined wind respectively. It is the F region wind, the eastward component precisely, that produces the prereversal enhancement of the eastward electric field which has been studied by many people(Heelis et al., 1974; Anderson and Roble, 1974; Fejer, 1981; Farley et al., 1986; Haerendel and Eccles, 1992; Crain et al., 1993b ). It is clear that the electric fields are nearly fully con trolled by the eastward wind while the southward wind has a very limited effect. This differs from the E region dynamo where the southward wind is the main contributor. It is very important that we have correctly obtained the prereversal enhancement from Stening's equivalent circuit method as it is quite different from other methods which solve the differential equations, such as Crain et al.(1993b ). We have used exactly the same winds as Crain et al. in our calculation. Although the F region zonal wind affects both eastward and southward electric fields between 17 and 6 hr, it has little effect during daytime. This is consistent with the conclusion of Farley et al.(1986) who obtained the prereversal enhance ment of the eastward electric field by use of a simple F region wind model. The other differences between our results arise from the different wind and the electron CHAPTER 5. ELECTRIC FIELDS AND CURRENTS 79 density models adopted. They used a uniform F region wind and a very simple electron density distribution. The more accurate IRI and the satellite measure ments of the F region zonal wind which we used should give a more accurate result. 5.2.2.3 Dynamo Operating Throughout the Whole Ionosphere We have seen that the E region dynamo is the main contributor toward the elec tric field and the current density during daytime, while the F region dynamo is predominant during nighttime, as shown in figures 5.4 and 5.6. During the daytime, the F region dynamo is shorted out by the highly conducting E region and therefore the electric field and current are controlled by the E region dynamo. With the approach of sunset, the E region conductivity falls and the F region dynamo is shorted to a lesser extent and so the F region dynamo becomes more important. Its role reaches a maximum around sunset and decreases later. From 22 to 6 hr, the electric field produced by the E region dynamo is comparable to that of the F region and the electric field and current density are determined by both of them. Near sunset, the E region electron density drops rapidly to the night value which is fairly constant during all the night. But the F region electron density changes slowly compared with that of the E region. Then a very small part of F region dynamo is shorted by the E region and a large electric field will build up to prevent the increase of the F region current. As the night progresses, the F region electron density drops continuously but the E region value nearly stays at a constant level. The consequence is that both E and F region dynamos control the electric field and current density. After sunrise the control reverts back to the E region again. In contrast to the sharp increase of the eastward electric field produced by the E region dynamo at about 5 hr LT, there is a similar decrease produced by the F region dynamo at the same time as shown in figures 5.2 and 5.5. Usually the CHAPTER 5. ELECTRIC FIELDS AND CURRENTS 80 increase will counteract the decrease while the occasional early morning increase of the vertical ion drift measurements(Crain et al., 1993b ) can be explained as a consequence of a stronger than usual E region dynamo. It should be noted that the ionospheric currents are mainly located in the E region no matter which dynamo is the controller. Quite different from the eastward electric field, the southward electric field at the F region height is nearly totally controlled by the F region eastward wind at anytime as shown by equation ( 4.13). The nighttime value of the southward electric field is always about 2 - 3 times larger than that during the daytime. 5.2.3 Altitude Variation To understand how the current density is distributed in the ionosphere, we will examine the roles of the electric field, local dynamo and also the Pedersen and Hall current densities at equinox. We select the magnetic equator in the follow ing discussion for simplicity as the north-south local wind is usually very small at that location. The conclusions are valid for the equatorial area and during both high and low solar activity periods. 5.2.3.1 Daytime The variations of the electric field strength with height are shown in figure 5. 7. We see that the eastward electric field does not change much with altitude which is quite consistent with experiments and other theoretical models(Pingree et al., 1987; Fejer et al., 1989). This is expected as for a curl-free electric field when east-west gradients of model parameters are much weaker than vertical gradients as equation (4.1) shows. The southward(equatorward/vertical) electric field in CHAPTER 5. ELECTRIC FIELDS AND CURRENTS 81 the E region is much larger than that in F region. The magnitude at an altitude of 100 km is about 15 times as large as that at 350 km at noon in our case. The eastward electric field is always larger than the eastward dynamo emf at the equatorial area due to the fact that the eastward dynamo emf at the equator is generated solely by a vertical wind, which is neglected in our model. Below 120 km, the southward/vertical electric field is larger than the local dynamo and vice versa when the altitude is over 200 km. They are nearly the same in magnitude between 120 km and 200 km. So the E region southward/vertical electric field is more important than the local dynamo at and near the magnetic equator. If the global wind system is changed, this may lead to changes in the vertical electric field at the equator. The magnitude of this field at the equator will always be greater than that of local dynamo emfs. Thus, the electric field not the local dynamo is the main contributor to the magnetic field variations on the ground at and near the magnetic equator. But this is not the case in middle and high latitudes. From equation (2.1) and (2.2) we know that the current density is composed of two parts, namely Pedersen and Ha!l current. The calculation shows that the eastward current density in the E region can be approximated with (5.1) From the above discussion it follows that the downward current is controlled by both Hall and Pedersen currents and the eastward by Hall current only. The maximum altitude of Jq, is located at about 105 km and Jp at 120 km. The east ward current is nearly all within the E region because UH and Ep decrease rapidly with altitude. Differently, the downward current has a complex variation with altitude. From the upper panel of the figure 5.8, we can see that the Peder sen conductivity is still the main contributor to the downward current density. The downward current density variations with altitude are associated more with the relative variations of flux-tube-integrated Pedersen and Hall conductivities in the equatorial electrojet. There is nearly no eastward current flow in the F CHAPTER 5. ELECTRIC FIELDS AND CURRENTS 82 region and that is why an E region model or shell model can successfully simulate the magnetic field variations during daytime, especially the horizontal northward component on the ground at and near the equator. 5.2.3.2 Nighttime The electric fields are quite different between midday and midnight as is shown in figure 5.7. The eastward electric field is about -0.75mV/m at midnight but 0.3mV/m at midday. The maximum southward/vertical electric fields are 24mV/m and -l0mV/m respectively. Compared with the maximum eastward current density of 6.8 µA/m2 at noon, the midnight value is only about -0.18 µA/m2 as are shown in figures 5.8 and 5.9. At night also in the equatorial E region the electric fields are always larger than the relevant dynamo emfs. Above 150 km, the southward/vertical electric field is nearly the same as the southward/vertical dynamo emf in magnitude but is op posite in sign. So, the ionospheric east-west electric field is mainly controlled by the F region dynamo as discussed before. Concerning the current density(figure 5.9), the Hall current still is the main contributor to the westward current in the E region and can also be expressed by the equation (5.1). We should note that although there is a westward current flow in the F region, it actually may not have significant effects on the magnetic field variations on the ground even during high solar activity because of its magnitude. The southward/vertical current still shows a very complex variation. Below 120 km, it is controlled by both Pedersen and Hall currents. At greater heights it is fully controlled by the Pedersen current, as the Hall conductivity then becomes very small, the same as in daytime. The east-west current reaches a maximum value at about 100 km at midnight but 105 km at noon. Comparing the magni tude of J,, and J4i, the maximum eastward current density is about 12 times as CHAPTER 5. ELECTRIC FIELDS AND CURRENTS 83 large as the maximum downward current density. All these characteristics can be found in figures 5. 7 and 5.9. 5.2.4 Solar Activity Dependence Figure 5.10 shows the solar activity dependence of the electric fields at equinox. In the calculation, March 1990 and 1986 are used to stand for the solar maximum and minimum. The F10.7 is selected to be 175.9 and 75.9 respectively. As exactly the same winds are used in the two different solar activity periods and the neutral density does not change much and so does not affect the conductivity noticeably, we can attribute the difference to the ion density changes. The main features we wish to emphasize are as follows 1. The higher the solar activity, the higher the prereversal enhancement of the eastward electric field; 2. The evening field reversal occurs earlier during sunspot minimum than dur ing the maximum and the same is true for the morning reversal time; 3. The daytime eastward electric field during high solar activity period is com parable to that during the low solar activity. Although quite a simple wind model is used in our calculation, the above charac teristics of the electric fields are very close to the Jicamarca measurements and other simulations. But there are still quantitative differences between our cal culations and those measurements. The agreement can be further improved by adjusting the amplitude and the phase of the (1, -2) tidal wind but we do not like to pursue this because tidal theory and measurements clearly show the existence of a more complex wind structure and the presence of propagating tidal modes CHAPTER 5. ELECTRIC FIELDS AND CURRENTS 84 in the E region. In the following section, we will use Forbes and Gillette's diurnal, semidiurnal and different combinations of winds to investigate the ionospheric electric fields and currents. 5.3 Electric Field Produced by Forbes' Tidal Winds As Forbes and Gillette(1982) provided explicit simulations from the surface to over 400 km for the solar diurnal, solar semidiurnal and lunar semidiurnal tidal winds, we digitized their extensive tabulations and graphs and inserted their winds in our program to calculate emfs. Figure 5.11 shows the eastward and southward solar diurnal tidal winds distribution in equinox. For meridional wind, the U ARS measurements show that the diurnal tidal is the dominant feature of the wind below 120 km. Morton et al.(1993) compared the UARS measurements with the Forbes and Gillette(1982) predictions and concluded that the inclusion of the solar semidiurnal tidal wind does not improve the comparison with the measurement at about 100 km. The semidiurnal wind appears to be significant only in mid- to high- latitude regions. The U ARS measurements also show the zonal tidal wind can be represented by only the diurnal tidal wind. In our calcu lations, for which the Forbes and Gillette values are interpolated, the maximum meridional diurnal wind amplitude is about 54 m/sat geographic latitude of ±20° at 90 km which is close to the value of 65 m/s measured by WIND II and 70 m/ s by HRDI(McLandress, 1994; Morton et al., 1993; Hays et al., 1994). As there is no reliable semidiurnal tidal wind available from the UARS, we will keep the amplitudes of the diurnal and semidiurnal tidal wind as determined by Forbes and Gillette(1982). The eastward and southward/vertical electric fields at the apex altitude of about 400 km, derived using these winds, are shown in figure CHAPTER 5. ELECTRIC FIELDS AND CURRENTS 85 5.12. Compared with the observations at Jicamarca(Fejer, 1981; 1991; Fejer et al.; 1991) and the AE-E satellite(Fejer et al, 1995) , it seems that only the calcula tions which include the diurnal east-west tidal wind reproduce the features of the experiments, especially the prereversal enhancement of the eastward electric field. Considering the difference between the two different UARS measurements(65m/s and 70m/s) of the meridional wind and the value we used (54m/s), the Forbes diurnal tidal wind produces a very good approximation to both the eastward and southward/vertical ionospheric electric fields. Also we can see, from figure 5.12, that the reversal time changes with different southward and eastward wind combinations. Compared with the quite changeable experiments, it is not easy to conclude which is better. To examine the effect of the semidiurnal wind phase on the electric field we ex perimented with shift of the phase of the semidiurnal tidal wind. We find that the prereversal enhancement of the eastward electric field is enhanced when we shift the phase of the semidiurnal tidal wind ahead by 2-3 hrs as shown in figure 5.13. The changes of the transition time, fr?m westward to eastward in the morning, of the eastward electric field are within 2 hrs. Very similar changes of the transition times are seen in the morning and evening for the southward electric field. It should be mentioned that the maximum evening prereversal enhancement time is changed from around 18 hr to 19 hr local time compared with figure 5.12. Our result is consistent with the theoretical work of Forbes and Gillette(l982) on the uncertainties of the time of the maximum amplitude of the semidiurnal tidal wind which they found to be about ±(2 - 3) hrs. Also we tried to retard the phase of the maximum semidiurnal tidal wind but this failed to reproduce the prereversal enhancement of the eastward electric field. CHAPTER 5. ELECTRIC FIELDS AND CURRENTS 86 5.3.1 Altitude Variation The electric field variations with altitude using the Forbes winds are shown in figure 5.14. Similar to figure 5.7, the eastward electric field nearly remains a constant at all altitudes, from 90 to 500 km, although there is a small change in the E region. It still is a very good assumption that the eastward electric field is constant within the ionosphere. The southward/vertical electric field has a complex variation and it is very large in the E region. At midnight the magnitude at the altitude of 105 km is about 10 times larger than that at F region heights at midnight. The same is true for midday. Different from the lower panel of figure 5. 7, the southward electric field reaches the F · region value at a lower altitude(below 150 km) compared to figure 5. 7(250 km) where an unrealistic wind was used in the calculation. 5.3.2 Seasonal Variation Some indications of the electric field seasonal dependence can be seen from figure 5.15 for the minimum and 5.16 for the maximum solar activity period. During the low solar activity period, the daytime eastward electric fields in March equinox and in December solstice are nearly exactly the same. The nighttime value at solstice is larger than that during equinox. There is no obvious difference for the southward electric field during the daytime. At nighttime, the southward electric field in equinox is larger than that in solstice. During the high solar activity period, both eastward and southward electric fields at the equinox are larger than those at the solstice all the time except around 20 hr LT. That the prereversal enhancement of the eastward electric field occurs between 18 - 19 hr LT in all cases and more obviously at high solar activity period, and the southward electric field at night is about 2 times as large as the northward electric field in daytime is quite consistent with the Jicamarca(Fejer et al., 1981) and satellite CHAPTER 5. ELECTRIC FIELDS AND CURRENTS 87 measurements(Maynard et al., 1995). Concerning the prereversal enhancement of the eastward electric field, our calculation is consistent with the Jicamarca observation at the high solar activity period. That the March equinox value is smaller than that in December solstice during the solar minimum period does not agree with the Jicamarca measurements(Fejer, 1991). Although IRI and MSIS used in our program include a seasonal variation, the Forbes and Gillette winds for equinox and solstice do not show much difference between the two seasons. Furthermore, the wind variations with solar activity are not included in the Forbes wind model. All these contribute the disagreement between our calculations and experiments. 5.3.3 Solar Activity Dependence Figures 5.17 and 5.18 show the differences in the electric fields when F10.7 solar fluxes of 75.9 and 175.9 are used for the December solstice and for the March equinox. The higher the solar activity, the larger is the eastward electric field in both seasons. The southward electric field shows the same trend as the eastward electric field in the solstice. In the equinox, the higher the solar flux, the higher the value of the northward electric field in daytime but there is no difference at nighttime. The most distinctive feature in figures 5.17 and 5.18 is the dependence of the eastward electric field prereversal enhancement on the solar activity index. The higher the F10.7 solar flux, the more pronounced is the prereversal enhance ment. This is because the higher the solar activity, the more important is the F region dynamo. CHAPTER 5. ELECTRIC FIELDS AND CURRENTS 88 5.4 Electric Field Produced by HWM90 Winds The electric field produced by including HWM90 winds in our model is shown in figure 5.19. The calculated electric fields are rather different from both Jicamarca and AE-E satellite measurements when either the total wind or only the diurnal wind is used. Based on the incoherent scatter and Fabry-Perot measurements obtained mostly in mid- and high- latitude, the validity of the HWM90 empirical model is questionable in the low latitude and equatorial area, especially in the altitude region of 130 - 220 km because of the sparsity of measurement data in that region. Comparing the calculated electric field with measurement, we found that the HWM90 can re-produce some characteristics of the electric fields. But the calcu lated eastward electric field decreases too much in the afternoon and the south ward electric field is too large in the evening. After trying to decompose the neutral wind into the diurnal and the semidiurnal components, we conclude that the HWM90 empirical wind model fails to produce the observed electric field distribution, the semidiurnal wind is. too strong or the diurnal component is too weak. 5.5 Comparison and Conclusion From sections 5.2, 5.3 and 5.4, it seems that the Forbes and Gillette tidal wind gives the best approximation to the experiments. So in this section and in the follow two chapters, we will use the Forbes and Gillette diurnal tidal wind as the eastward wind, both diurnal and semidiurnal wind as the southward wind in our calculations and discussions. Note that the eastward semidiurnal component is omitted. To demonstrate the good agreement between our simulations and the measure- CHAPTER 5. ELECTRIC FIELDS AND CURRENTS 89 ments from Jicamarca and satellites(Fejer et al., 1995; Coley et al., 1989), figure 5.20 shows the comparison of the calculated eastward electric fields in March equinox and December solstice. The solar flux index F10.7 of 175.9 was used to stand for the high solar activity condition. Considering the uncertainties of the measurements and the large day-to day variations of the eastward electric fields, our calculations successfully predict the main features of the measurements. The comparisons between our calculations and the DE-2 southward electric field mea surements are shown in figure 5.21. A very good agreement was obtained during daytime. The calculations are smaller than observations at nighttime. We should point out that the local time and season are locked together in the DE-2 data base and our calculations are corresponding to March equinox. The measurements which we used in figure 5.20 are taken from 1978 and 1979. During this period of time, the F10.7 changed from 144 to 192 which are very close to the value we used in the calculation. Also, we approximated the longitudinal change to be equivalent to the local time variation. In the calculation, we take 1 hr as the local time step size in the program for sim plicity. Therefore, we can only infer that the maximum prereversal enhancement lies between 18 and 19 hr LT. Changing the step size to 30 minutes, the results clearly show they will occur at about 18 : 30 hr LT at both seasons which is in good agreement with the measurement. From figure 5.20, it is clear that the Forbes and Gillette wind model can repro duce the electric fields which are in good agreement with Jicamarca and satellite measurements if the semidiurnal eastward wind is excluded. The upper panel is for the March equinox and the lower panel for the December solstice. Considering that the measurements are averaged over two years and there are large day-to day fluctuations, we conclude that the modified Forbes and Gillette wind model is very successful in producing the ionospheric electric fields. Our selection that the zonal tidal wind is composed of the diurnal tidal wind only and the meridional tidal wind is composed of both the diurnal and the semidiurnal components is CHAPTER 5. ELECTRIC FIELDS AND CURRENTS 90 supported by the conclusions of Morton et al.(1993), who compared HRDI mea surements and Forbes calculations at altitudes of about 100 km. In what follows, we will use the diurnal eastward wind combined with the diurnal and semidiurnal southward winds as the real wind in the ionosphere and focus our discussion in the equatorial area, unless otherwise specified. CHAPTER 5. ELECTRIC FIELDS AND CURRENTS 91 2 ,----~--.----..-----,r----r----r------.----,--,-----r------.-----, 1 -8 > '8 ..c: 0 ...... -+> QI) s:: GJ r-. +> Cl.I -1 -2 0 4 8 12 16 20 24 40 ... 20 -8 ~ 8 _., ..c: 0 ,_., -+> bOs:: ------GJ r-. +> Cl.I -20 -40 ..__....__ __._ _ _,___ ,..__...._ _ _.__ _.__ __.'--_ _.__ _ _.__ _.__ __. 0 4 8 12 16 20 24 Local Time(hr) Figure 5.2: Electric field variations with local time at an altitude of 105 km over the geomagnetic equator. Dynamo model operates in E region only. The upper panel is for the eastward and the lower panel for the southward electric field. The solid line is the contribution from both eastward and southward winds, dot line from the southward and dash line from the eastward tidal winds respectively. CHAPTER 5. ELECTRIC FIELDS AND CURRENTS 92 150 -~-~-~~-~--~-~-....-~--.----....-----.--.----,-----, 140 I: I : 130: (_ 1\ I '-. '°;;' I \ .; \ ·· ... ~ \ ·· .. "d 120 , .....E \ .... \ < ' ' \ \ 110 I I I I I I 100 1 I I / I I I •••• •••• 90 IL...... oo<...L._.....____L-____.__ __.__...... _____.__ _.___.,____.__ ___,__ _.______._ __.__ _._____. 0 2 4 6 8 10 12 14 16 Current Density(µA/m2) Figure 5.3: The eastward current density altitude distribution at noon at the ge omagnetic equator. The calculation includes heights from 90 km to 150 km only. The lines definitions are the same as figure 5.2. CHAPTER 5. ELECTRIC FIELDS AND CURRENTS 93 200 180 ...... E 160 ~ Cl) -'O ::s 140 ....+J +J -< / 120 / --- I' ----- ...... 100 ... -4 -2 0 2 4 6 8 10 200 180 ...... E 160 ~ Cl) -'O ::s 140 ....+J +J < 120 :. --:::. 100 -0.2 0 0.2 0.6 0.8 1 Figure 5.4: The eastward current density produced by the E region{90 - 150 km) tidal wind(dot line), F region{200 - 500 km) wind(dash line) and the combined wind{solid line) in the whole ionosphere{90 - 500 km). The upper panel is for 12 hr and the lower for 18 hr local time. CHAPTER 5. ELECTRIC FIELDS AND CURRENTS 94 0.8 -e } 0.4 ~ ~ G) 1-. rn+> -0.4 0 4 8 12 16 20 24 6 -e ~e 4 ..c: -+> ~ s::: G) 2 1-. rn+> 0 -...... 0 4 8 12 16 20 24 Local Time(hr) Figure 5.5: The eastward( upper) and southward/vertical(lower) electric field vari ations with local time at the apex altitude of about 400 km. These were produced by the F region eastward wind only( dot line) and the total wind( solid line) re spectively. CHAPTER 5. ELECTRIC FIELDS AND CURRENTS 95 1.2 .,,. 0.8 .,,. \ \ 8 \ ...... __ _ 0.4 \ l \ \ i 0 1------'------,,...... -'-'------'-,-----'l----';...,,...--1 ~ ...... QJ r------S.. / en -o.4 -0.8 0 4 8 12 16 20 24 6 " " ' -E 4 ~ E ' -...... c: bi) 2 i::: QJ ....S.. I'll 0 -2 0 4 8 12 16 20 24 Local Time(hr) Figure 5.6: The eastward( upper) and southward/vertical(lower) electric field pro duced by the dynamo in the E region, F region and both of them combined. The lines definitions are the same as in figure 5.4. CHAPTER 5. ELECTRIC FIELDS AND CURRENTS 96 480 420 -e 360 ~ Q) -'O 300 ::I ....+> <+> 240 180 120 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 480 420 -] 360 Q) -'O 300 ::I ....+> +> 240 -< 180 •' :::_:_.___ _ 120 ------·------... -16 -12 -8 -4 0 4 8 12 16 20 24 Strength(mv/m) Figure 5.7: The altitude variations of the eastward(upper) and south ward/vertical{lower) electric field over the geomagnetic equator. The solid line is for the 12 hr and dot line for Ohr LT. CHAPTER 5. ELECTRIC FIELDS AND CURRENTS 97 360 120 ____ ,,.,,,,~----~------~===:;:___::: ______~-- ...... ) -1.6 -1.2 -0.8 -0.4 0 0.4 I I I 360 - - - 300 .._ - -8 .II: Cl) -"C - ...,::, 240 - ...,.... < 180 - - ~ 120 .._ - ; I I 0 2 4 6 Current Density(µA/m2} Figure 5.8: The southward/vertical( upper) and eastward(lower) current density distribution near the geomagnetic equator at 12 hr LT. The dot line stands for the contribution of Pedersen, dash line for Hall and solid line is the resultant. CHAPTER 5. ELECTRIC FIELDS AND CURRENTS 98 360 -E 300 ...... lo: Cl> ,:; 240 .....;::l ...... < 180 120 ------.. --- --·------. ------. .:-, r------. -- -0.008 -0.004 0 0.004 0.008 0.012 0.016 0.02 0.024 360 - 300 ...... ] Cl> ,:; 240 .....;::l ...... < 180 120 -0.24 -0.2 -0.16 -0.12 -0.08 -0.04 0 0.04 Current Density(µA/m2) Figure 5.9: The southward/vertical(upper) and eastward(lower) current density distributions near the geomagnetic equator at Ohr LT. The dot line stands for the contribution of Pedersen, dash line for Hall and the solid line is the resultant. CHAPTER 5. ELECTRIC FIELDS AND CURRENTS 99 2 1.6 -e 1.2 ~e 0.8 ..c: -... 0.4 1:11) i::: G) ...s.. 0 ('/) -0.4 -0.8 0 4 8 12 16 20 24 8 6 -e ~e 4 -..c:... tlll i::: 2 G) ...s.. ('/) 0 ...... --- ...... -2 0 4 8 12 16 20 24 Local Time(hr) Figure 5.10: The eastward{upper) and southward{lower) electric field variations at the apex altitude of 400 km. The solid line is for the solar maximum and the dash line for the solar minimum period. CHAPTER 5. ELECTRIC FIELDS AND CURRENTS 100 Eastward diurnal wind c:, 00 ,... I \ N I• I - ! I t I I c:, ! ..... I +I N - I I - ,, I /I' I ' _,,,, I - c:, ' ' ' ..... ___ _/ - E c:, - --~- - ' .. N s-..c; ' I'- - ' en ·.:; ::c f,-- - _.,.------...,._ - - - -:~, c:, "" =----. .,,,.- - -OZ-.;: ---. - of.... ------oc------oz------~------c:, N -60 -50 -40 -.30 -20 -10 0 10 20 .30 40 50 60 Geographic Latitude(deg) Southward diurnal wind .i. ----r• - 'i' ,, c:, ,--.---.-, --·-,r,---.- l 00 ,. ' I I I N I I I I I I I I I I I + + l + T I I I I I I I I I I • I • ., l c:, ' ~ + + I I I I ..... I I + +I ' N I I I I •I I ' t t + l I I I I t t I I : I I I I l I I I I +I I I f ' E 8 I I N ' I I .... I I \ ~ + .c , I• • I "i '\ .5?' j ,l \ ' CU ,, ,, ' ' ' ::c I ' ' ' ,,,., .,,,. I ' ' c:, - ' p ' ' ' ...... ' ' ' ...... "" , _.,.--- - .# ' ' ""--, ..... __ _.,.- ..------_- --- ' --- -..._ --- c:, -- -- N - _ _:.~~ ~ ~ ~ ~ ~=:~-=--:?:=;~~~~~.:.,..,""?=----=--"-'-=-=-=_f_._~_, __~--~---~= .. _,,;-~-==~-!!!1,_:="=----=~=-=;'°::_-_-_-;,;~ - - - - ~~ -oc- -60 -50 -40 -.30 -20 -10 0 10 20 .30 40 50 60 Geographic Latitude(deg) Figure 5.11: The eastward(upper) and southward(lower) wind distributions with latitude and height at 12 hr LT in the equinox. CHAPTER 5. ELECTRIC FIELDS AND CURRENTS 101 0.8 -8 0.4 > '8 -...... c: 0 , .. _ QO ~:::-:-, ...... _...... #'~--~;.-;.::/ \ ... :w-.. i::: ...... / _,,, Cl) ...... / _/ ....rn -0.4 ...... - _;- .. ./ -0.8 0 4 8 12 16 20 24 4 3 -8 ';;- 2 ~ .,, 8 -...... c: 1 '·, -.\ QO i::: Cl) '· .... 0 °'I. ....rn ,, -1 ~::.... ~ .. -·-·-'::-:>·· -2 0 4 8 12 16 20 24 Local Time(hr) Figure 5.12: Electric field variations with local time at the apex altitude of about 400 km. The upper panel is for the eastward and the lower panel for the southward electric field. The solid line stands for results in which we include the diurnal( d) component of both eastward(E) and southward(S) winds, dot line included of S and d+s of E, short dash line for d+s(semidiurnal) of S and d of E, dot short dash line for d+s of Sand E. Equinox and solar minimum conditions are used in this calculation. CHAPTER 5. ELECTRIC FIELDS AND CURRENTS 102 0.8 -s 0.4 ...... s> ..c: 0 -+> bO ~ Cl) rn+>"" -0.4 -0.8 0 4 8 12 16 20 24 4 3 -s ~ 2 '~ ~ ... , s ...... ~ ..c: 1 ,, -+> \,, bi) ... ,·, ~ Cl) ·.. ,·, 0 rn+>"" -1 -2 0 4 8 12 16 20 24 Local Time(hr) Figure 5.13: Electric field variations with local time at the apex altitude of about 400 km. The upper panel is for the eastward and the lower for the southward electric field. The solid line stands for 3 hr, dot line for 2 hr, short dash line for 1 hr, dot short dash line for no phase shift ahead of the Forbes semidiurnal tidal wind. There is no phase change of the diurnal tide wind. The other conditions are the same as in figure 5.12. CHAPTER 5. ELECTRIC FIELDS AND CURRENTS 103 480 420 ...... 8 360 ~ Cl) -"d 300 3.... <+> 240 180 120 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 480 420 ...... 8 360 ~ Cl) -"d 300 ::, ....+> <+> 240 180 .. :. 120 ········································ ------~··· ------... :':.,- -8 -4 0 4 8 12 16 20 Strength(mv/m) Figure 5.14: The altitude variations of the eastward(upper) and south ward/vertical(lower) electric fields produced by Forbes wind in the equinox and solar minimum period over the geomagnetic equator. The solid line is for 12 hr and the dot line for Ohr LT. CHAPTER 5. ELECTRIC FIELDS AND CURRENTS 104 0.8 -8 0.4 ...... '-> 8 -..c: 0 ..QI) i::: a, ri.i1-t -0.4 -0.8 0 4 8 12 16 20 24 4 3 -8 2 ~ 8 -..c: 1 ..bi) i::: a, 1-t 0 ..rn -1 -2 0 4 8 12 16 20 24 Local Time(hr) Figure 5.15: The seasonal variations of the eastward( upper) and southward(lower) electric fields produced by Forbes wind during the solar minimum period. The solid line is for March equinox and the dot line for December solstice. CHAPTER 5. ELECTRIC FIELDS AND CURRENTS 105 0.8 -e 0.4 ...... ';;-e -..c:.... 0 bO c:: G) ~ -0.4 -0.8 0 4 8 12 16 20 24 4 3 -e 2 ';;-e -...... c: 1 bO c:: G) ....,.., 0 I'll -1 -2 0 4 8 12 16 20 24 Local Time(hr) Figure 5.16: Similar to figure 5.15 but for the solar maximum period. CHAPTER 5. ELECTRIC FIELDS AND CURRENTS 106 0.8 -s 0.4 ------. -. - > 'E -:5 0 tlO C: . I) ~ -0.4 -0.8 0 4 8 12 16 20 24 4 3 -s 2 ~s -.c:.... 1 tlO C: I) ....1-, 0 I'll .. -...... --- -1 -2 0 4 8 12 16 20 24 Local Time(hr) Figure 5.17: The solar activity dependence of the eastward(upper) and south ward(lower) electric fields produced by the Forbes wind in the solstice. The solid line is for the high solar activity(F10.7 = 175.9) and the dot line for the low activity(F10.7 = 75.9). CHAPTER 5. ELECTRIC FIELDS AND CURRENTS 107 0.8 -8 0.4 ...... > ...... 8 ..c: 0 -+> 01) ~ Q) ~ -0.4 -0.8 0 4 8 12 16 20 24 4 3 -8 '>- 2 8 ..c: 1 -+> Ill) ~ Q) I-, 0 ... en+> ...... -1 -2 0 4 8 12 16 20 24 Local Time(hr) Figure 5.18: Similar to figure 5.17 but for the equinox. CHAPTER 5. ELECTRIC FIELDS AND CURRENTS 108 0.8 -s 0.4 ...... s> .c: 0 -+> 1:11) d Q) U)S... -0.4 -0.8 0 4 8 12 16 20 24 6 5 -s 4 ~s 3 .c: 2 -+> bO d Q) 1 S... +> ('/) 0 ..... -1 .... -. -.... - -2 0 4 8 12 16 20 24 Local Time(hr) Figure 5.19: The eastward(upper) and southward(lower) electric fields variations at the apex altitude of 400 km which are produced by the HWM90. The solid line is for the total wind and the dot line for the wind with the semidiurnal com ponent excluded. CHAPTER 5. ELECTRIC FIELDS AND CURRENTS 109 0.8 ,,,, / ' I ' I •••••••·•• ·\:· ••• e o.4 , ...- ' 1/ ~ 1/ i 0r------,-,------i;/ tlO 1/ \, ~ f \ ~ -0.4 ..,. /I \ -~ I \ •... " :1. - ~ ...... ,.., -0.8 0 4 8 12 16 20 24 0.8 _.,. __ -13 0.4 .--;,~"·:.,.-.-.-:-:--- ~ ,...... ·.., -·:::·-~.-:-:.:-:-.:-:-...., ___ .. ··.:. _, 13 -1· '- - ..c:: 0 -+' tlO r::: Cl) I-, +' -0.4 rn ...... -0.8 0 4 8 12 16 20 24 Local Time(hr) Figure 5.20: The comparison of the calculated electric fields with the measure ments of Jicamarca and AE-E(Fejer et al., 1995) during 1978 and 1979 magnet ically quiet conditions. The upper panel is for the March equinox and the lower panel for December solstice. The solid line is for the calculation, dot line for Jicamarca and dash line for the AE-E measurement. 175.9 was used as the F10.1 index in the calculation. CHAPTER 5. ELECTRIC FIELDS AND CURRENTS 110 960 840 ...... 720 El ~ II) 600 -"C :I .... 480 < 360 240 120 -- ,,..,..,. -----·------. -· -22 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 2 960 840 ...... 720 El ~ II) 600 -"C ....:I .... 480 -< 360 240 120 · •······· ···• •••• ··· ··•· •••• ··· ···= ::::: ::: zz111• •••• -2 0 2 4 6 8 10 12 14 16 18 20 22 Strength(mv/m) Figure 5.21: The comparison of the calculated southward electric field with the DE-2 observations. The upper panel is for the local time of 15 hr and the lower panel for 23 hr. The dot line is for the calculation and solid line for measurement with error bar. The measurements are from Coley and Heelis(1989). Chapter 6 Field Aligned Current 6.1 Introduction The combination of the Forbes and Gillette diurnal eastward, diurnal and semid iurnal southward tidal winds successfully reproduced the main features of the measured ionospheric electric fields. We will use this combination to investigate field aligned currents. The altitude variations, universal time and solar activity effects are examined in this chapter. The methods used in this chapter are those discussed in section 2.6. We first calculate the electric field by use of the equivalent circuit model and then derive the eastward and southward/vertical current density components by Ohm's law. The field aligned current is calculated by integrating the eastward and southward current density divergences along the magnetic field line. It is found that the tidal winds structure and the displacement between the geo graphic and geomagnetic equators have large effects on the field aligned currents. The field aligned currents are mainly produced and flow in the E region. Our results show that there is a positive( northward) field aligned current flowing in the morning section and a negative(southward) in the afternoon and evening in 111 CHAPTER 6. FIELD ALIGNED CURRENT 112 both hemispheres and in both March equinox and December solstice at F region heights. 6.2 Altitude Variation Figure 6.1 shows the field aligned current, northward positive, over the geomag netic equator. During the calculation, we change the apex altitude of the magnetic field line, find the latitude where it crosses through the base of the ionosphere( 86 km in our case), and then integrate the field aligned current along the field line starting from 86 km to just over the geomagnetic equator. 360 300 !.. j 240 ;.! 180 120 -6 -4 -2 0 2 4 6 Current Denslty(µ.A/m8 ) Figure 6.1: The field aligned current density variations with altitude over the geomagnetic equator at noon at Indian longitude. Equinox and solar minimum conditions apply. There is a very large field aligned current in the equatorial E region and it changes CHAPTER 6. FIELD ALIGNED CURRENT 113 very quickly with altitude. Above the altitude of 200 km, the field aligned current is about 2 x 10-s A/m2 but at an altitude of 101 km it increases to 3 x 10-5 A/m2 • Our field aligned current value is close to Maeda's (1974) maximum value of 3.5 x 10-s A/m2 for asymmetric wind and conductivity but is only about 1/50 of the result of Singh and Cole(1987c) at the altitude of 200 km and above. Most importantly, we confirm Singh and Cole's results that a large field aligned current flows in the E region and it has a wave-like altitude distribution. But we should mention that different winds were used for different authors. Maeda used his deduced ionospheric winds from the Sq variations. Singh and Cole adopted a tide-like zonal wind whose amplitude and phase are dependent on altitude and longitude, but independent of latitude. They also modeled the effects of local periodic winds by ascribing to them properties suggested by a measurements of an internal gravity wave. Our wind model include local time, latitude and altitude but no universal time and solar activity variations. The wave-like structure in the E region maybe is the main feature of the Forbes wind used in the thesis. The small fluctuations in the figure 6.1 probably arise from the adopted arithmetic interpolation for winds and electric ~elds. Figure 6.2 demonstrates how current densities change with altitude along a mag netic field line. The similarity between the southward and the field aligned cur rent, especially in the E region, confirms that the field aligned current is pro duced predominantly from the divergence of the meridional current. Although the southward and eastward currents are mainly located in the E and low F region, there is a considerable field aligned current not only in the E region but also in the F region and even in the magnetosphere. The field aligned current is determined by the southward and eastward current divergences all the way along the field line. The field aligned current variations with latitude (or altitude) at different local times are shown in figure 6.3. At an altitude of 300 km over the geomagnetic CHAPTER 6. FIELD ALIGNED CURRENT 114 250 200 150 ------·------...., 100 so~~~~~~~~~-~~~~~~~~~~~~ -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 Current Density(µ.A/m8 ) Figure 6.2: The current density distributions along a magnetic field line{300 km height over the magnetic equator). The solid line is for the field aligned current, dot line for the eastward and the dash line for the southward current density. The other conditions are the same as figure 6.1. equator, there can be seen a strong positive field aligned current in the morning, weaker at noon and negative in the evening. To investigate the individual contributions of the electric field and of the winds to the field aligned current, we force either the electric fields or the winds to zero calculate the horizontal currents by using Ohm's law and then deduce the field aligned currents. The field aligned current at the altitude of 300 km 10° south of the geomagnetic equator is shown in figure 6.4. Near the base of the magnetic field line, the effect of the electric field is comparable to that of the wind. Approaching the geomagnetic equator along the field line, the contribution of the electric field decreases very quickly. In the low F region, the contribution from wind is much larger than that from the electric field. But, generally, the electric field and wind CHAPTER 6. FIELD ALIGNED CURRENT 115 0.8 0.6 0.4 "a l 0.2 ~ ..c 0 ,! i:i j -0.2 -0.4 -0.6 -0.8 -1 -12 -8 0 4 8 12 Geomagnetic Latitude(deg) Figure 6.3: The field aligned current distributions along a magnetic field line with altitude of 300 km over the magnetic equator at different local times. The solid line is for 8 hr, dot line for 12 hr and dash line for 17 hrLT. have equal influences on the field aligned current. As conductivity, wind and electric field do not change much above the altitude of 200 km, the propagating tidal wind structure in the E and low F region and the equatorial electric field are most important in determining the field aligned current. 6.3 Universal Time Effect It is of interest to examine the universal time effects on the field aligned current. Figures 6.5, 6.6, 6. 7 present the field aligned current distributions with local time and geomagnetic latitude at the altitude of 300 km. It will be seen immediately that there are similar features in the evening, but more varying and complicated situations in the morning during all three universal times. CHAPTER 6. FIELD ALIGNED CURRENT 116 300~-~---~~~-~----~-~---~ 250 I 200 I I I ••• ··~I f< :······· ..... 150 I \ .... __ . 100 ------ so~-~-~-~-~-~-~~-~-~-~-~ -0.2 -0.1 0 0.1 0.2 0.3 Current Density(µ.A/m") Figure 6.4: The contributions towards the field aligned current of the electric field and wind. The solid line is the resultant field aligned current, dot line is the contribution from the winds and dash line from the electric fields. In the afternoon and evening, there.are considerable currents flowing from the northern hemisphere to the southern hemisphere along the magnetic field lines. The most common magnitudes of the field aligned currents are between 2 and 3 x 10-s A/m2• In the morning region, the field aligned currents flow from the southern hemisphere to the northern at most latitudes. The 'island' north ---+ south field aligned currents at several latitude intervals in the morning are caused by the tidal wind structures along the field lines. An example is that of 5 hr UT. For the field line of latitude -24° at the altitude of 300 km, the field aligned currents arising from the electric field and wind are -0.3 x 10-s A/m2 and -1.76 x 10-s A/m2 • But for the -26° latitude field line, these components become -0.7 x 10-s A/m2 and 1.57 x 10-s A/m2• Therefore there is a negative field aligned current around -24° and positive at -26°. A very similar situation occurs at the -34° latitude negative field aligned current contour. Compared CHAPTER 6. FIELD ALIGNED CURRENT 117 with the field aligned currents of the morning and the evening, the magnitude of the field aligned current at noon is small, usually no larger than 0.1 x 10-s A/m2 , and even smaller is the field aligned current at night. The latter confirms the earlier results(Maeda, 1974; Stening, 1977b; Richmond and Roble, 1987) which showed the field aligned current to be a daytime phenomenon in the low solar activity period. Comparing the field aligned current contours of 5 hr, 11 hr and 17 hr UT in fig ures 6.5, 6.6, 6. 7 we can see that the field aligned current distribution at 11 hr UT is very similar to that at 17 hr UT. As the conductivities become negligible around the base, 86 km for example, of the ionosphere, there should be no field aligned current flowing in or out the base of the ionosphere. That means if we integrate the divergence of the transverse current density, starting from the base of the ionosphere in the southern hemi sphere, along the magnetic field line, we should obtain zero field aligned current at the base of the ionosphere in the northern hemisphere. Generally, this is what happens but it is not the case for a low apex magnetic field line, 100 km for example. This is due to the wind distribution in the equatorial area. As the Hall conductivity changes very quickly with altitude in the E region,·even a small change of the wind or its gradient can produce considerable variations of the field aligned current. To increase computational efficiencies, we integrate the divergence of the trans verse current density either starting from the southern base of the ionosphere or the northern depending on the position of the point for which calculations are being made. Thus a more symmetric field aligned current distribution will be found if we perform all calculations beginning the integration from the southern base of the ionosphere. But even so, the main features of the graphs are the same. Broadly there are three main factors which influence the field aligned current. These are CHAPTER 6. FIELD ALIGNED CURRENT 118 1. the tidal winds and their gradients, 2. the conductivities and their gradients, 3. the electric fields and their gradients. The electric fields are determined by both the wind and conductivity distribution worldwide. From our calculations and from the DE-2 measurements(Coley and Heelis, 1989), we know that the electric fields only change slowly with the latitude and longitude except in the low latitude and equatorial region. The E and low F regions are the main sources of the field aligned current in the F region and in the magnetosphere. So we anticipate the E and low F region conductivity and tidal wind structures are the main factors to consider when examining the field aligned current. As IRl-86, which is used in our simulation, includes a UT effect, we will focus our attention on the tidal wind difference be tween the southern and northern hemispheres. The Forbes tidal wind at the equinox is symmetric about the geographic equator as figure 5.11 shows. The geomagnetic field geometry is fixed in a geomagnetic dipole system. The non-coincidence of the geomagnetic and geographic equators will destroy the symmetric wind distribution in the geomagnetic reference frame. The relative position of the geomagnetic equator in the geographic grid has a con siderable influence on the emf direction and magnitude. Another element which contributes to the wind asymmetry is that the opposite end of a field line may be at a different local time. For example, at -40° geomagnetic latitude and 45°E ge ographic longitude, the local time is about 1.2 hr ahead of the opposite northern point which is joined by the field line. Because the Forbes winds are controlled by local time, this time difference can generally lead to a different wind magnitude in the opposite hemisphere and sometimes also to a different wind direction. All these will give rise to a considerable field aligned current flowing. For 5 hr, 11 hr and 17 hr UT, the geographic longitudes with the local time of 8 hr are 45°E, 315°E and 225°E respectively. At 45°E longitude, the geomagnetic CHAPTER 6. FIELD ALIGNED CURRENT 119 equator is about 10° north of the geographic equator. The geomagnetic equator is about 3° south of the geographic equator for both 225°E and 315°E longitudes. In the evening at 17 hr LT, the correspond longitudes are 180°E, 90°E and 0°E where the geomagnetic equators are 10° north of the geographic equator for all three. This explains the very similar field aligned current patterns in the after noon and evening for the three UT and the contours in the morning for 11 hr and 17 hr UT. The southward(equatorward) tidal wind variations with magnetic latitude and altitude at 8 hr LT but different longitudes are shown in figure 6.8. The differ ences of the tidal wind directions and amplitudes between different hemisphere can be easily noticed. 6.4 Solar Activity Effect The solar activity effect on the field. aligned current is mainly via the changes of the ionospheric conductivities as the Forbes winds do not change with the solar activity. With increasing solar activity, the conductivities, southward and eastward current densities and their corresponding gradients become larger. Con sequently a somewhat larger field aligned current will be present in the ionosphere during higher solar activity. The details can be found in figures 6.9, 6.10, and 6.11. Similar to figures 6.5, 6.6, and 6. 7, there is a positive field aligned current flowing from the southern hemisphere to the northern hemisphere in the morning and a negative current in the afternoon and evening. A considerable field aligned current exists at night in contrast to the near zero field aligned current at solar minimum. This large field aligned current is introduced by the changes of the ionospheric conductivity. CHAPTER 6. FIELD ALIGNED CURRENT 120 All the differences between figures 6.9, 6.10, 6.11 and 6.5, 6.6, 6. 7 are introduced by the changes of the ionospheric conductivities. As mentioned above we should note the problems with field aligned currents flowing along very low latitude field lines. 6.5 Seasonal Variation Figure 6.12, 6.13, and 6.14 show the field aligned currents at 300 km computed for 5 hr, 11 hr and 17 hr UT at the December solstice with high solar activity. It seems that there is no distinct difference between figures 6.9, 6.10, 6.11 and 6.12, 6.13, 6.14. respectively In the morning, the field aligned current is from the southern to northern hemi sphere and vice versa in the afternoon. There is still a substantial current at night flowing from southern to northern hemisphere along the field lines during periods of high solar activity. Beyond the general agreement of figures 6.9, 6.10, 6.11 and 6.12, 6.13, 6.14, December solstice pattern is more smooth and symmetric. The equinox abrupt field aligned current reversement, 'island', in the morning sector of 5 hr and 11 hr UT has disappeared in the December solstice. It is very important that the morning field aligned current is quite changeable near the geomagnetic equator. In spite of the often positive field aligned currents, there are negative field aligned currents flowing along those field lines with ends very close to the geomagnetic equator. Our results show that the field aligned current has little dependence on season. As we know the field aligned current is mainly controlled by the conductivities and winds. The conductivity does not change much with seasons and the same is true for the integrated conductivity. Figure 6.15 shows the equatorward tidal winds at the geographic longitudes of 45° E and 315° E at 8 hr LT at solstice. CHAPTER 6. FIELD ALIGNED CURRENT 121 Comparing figures 6.15 and 6.8, we can easily conclude that the similarity be tween the field aligned currents at equinox and solstice arises from the similarity between the winds at the respective seasons. This is important. If the wind at the equinox is different from that at the solstice, we would expect different field aligned current patterns and therefore different eastward magnetic field variations on the ground for different seasons. 6.6 Discussion and Summary Although the field aligned current has been studied by Maeda(1974), Stening(1977b ), Takeda(1982), Richmond and Roble(1987), the conclusions are diversified even between the magnitude and direction of the field aligned current. Maeda(1974) analyzed the field aligned current induced by asymmetric dynamo action in the northern and southern hemispheres using simple ionospheric wind and conductivity models. The non-coincidence of the geomagnetic and geographic equators was excluded. He predicted that the field aligned current flows mainly in the daytime and partly in the morning and evening, that the daytime current flows from the winter hemisphere to the summer hemisphere, that the maximum value of the current density is about 3.5 x 10-s A/m2 for asymmetric wind and conductivity. He also concluded that the wind and conductivity play a different role but the former is more effective in producing the field aligned current. Stening(1977b) calculated the field aligned currents generated by (1, -2) tidal wind. He found that the changes in the current pattern with season are relatively small compared to changes with longitude. Currents at the equinox are of similar magnitude to those at the solstice. He predicted a very large field aligned current, as large as 1.0 x 10-6 A/m2, near the magnetic equator. The winds he used were symmetric about the geographic equator but not about the geomagnetic equator. CHAPTER 6. FIELD ALIGNED CURRENT 122 There was no change of wind with season. Using the same wind as Stening, Takeda(l982) also discussed the field aligned current variations with season and UT. He showed that the maximum magnitude of the current is about 0.5 x 10-s A/m2, that field aligned currents under the solstice condition flow mainly from the summer to the winter hemisphere in the morning and vice versa in the afternoon. Richmond and Roble(1987) simulated the field aligned current at 300 km altitude for equinox solar minimum condition. The pattern of their field aligned current is quite different from the earlier authors. Most importantly, they just draw the vertical component of the field aligned current which is quite different from the field aligned current itself near the magnetic equator. It should be pointed out the field aligned current distributions with latitude and longitude ( or LT) are different at different altitudes. This is the case especially in the E and low F region where most field aligned currents are produced. The substantial difference of the field aligned current pattern between Takeda and Stening is just because a different altitude is selected. Takeda selected heights in the F region or above height but Stening used the interhemispheric values. As the field aligned currents are located mainly close to the ends of the magnetic field lines, Stening's magnitude is quite large and different directions also occur. For a given geomagnetic latitude, the field aligned currents at different altitudes mainly arise from the E and from the low F regions where the electric fields, es pecially the tidal winds and their relevant gradients are different. So the altitude and latitude need to be specified when discussing field aligned currents. Field aligned currents appear to be much more sensitive to the details of the wind model than the patterns of the perpendicular ionospheric currents and electric fields. There are two elements mainly affecting the calculation of the field aligned cur rent. These are the step size of selecting the adjacent apex altitude and the arithmetic interpolation method used to calculate the winds at any location. CHAPTER 6. FIELD ALIGNED CURRENT 123 We tried several step sizes of the apex altitude, namely 5 km, 2 km, 1 km, 0.1 km and 0.01 km. The results are quite different for 5 km and 2 km. But the field aligned currents are very close to each other for last three step sizes. Most impor tantly, the results are very stable for step sizes of 0.1 km and 0.01 km. Therefore, the step size 0.1 km of the apex altitude has been adopted in all the calculations. Another factor affecting the value of the field aligned current is the interpola tion method adopted to calculate the winds in the program. As we selected the boundaries at 86 km and 500 km for altitude and -60° and 60° for geomagnetic latitude, the extrapolation from 400 km to 500 km is not a problem. We just set the winds at the altitude of over 400 km to be exactly the same as the winds at 400 km, this is a simple but also a reasonable procedure as the winds vary little with height over 300 km. A two dimensional interpolation formula is used to calculate the winds at any latitude and altitude. In the program, the southward or eastward wind is de rived from adjacent four wind values in every direction and dimension. Although the middle latitude tidal winds are more effective in generating the ionospheric electric fields and in driving the perp~ndicular current densities(Stening, 1977a), the field aligned currents are closely related to the details of the conductivities and winds along the magnetic field line. The Forbes tidal winds we used in the simulation are presented at every 6° in latitude and at differing height intervals ranges from several kilometers for the E region to several tens kilometers in the F region. As has been shown in figures 6.2 and 6.3, the main field aligned currents arise from the E and low F region where a different interpolation method may produce different values of the winds. Therefore, a different interpolation may change the magnitude of the field aligned current but not the main features of the pattern. It should be pointed that we still only have very limited knowledge of the E re gion tidal structures and further work is certainly needed. For example, that the southward(equatorward) tidal wind is symmetric about the geographic equator is CHAPTER 6. FIELD ALIGNED CURRENT 124 questionable. Also that the southward wind comprises of the diurnal and semid iurnal components while the eastward wind comprises of the diurnal component only seems unphysical although they can reproduce the experimental electric field distributions. The main features of the field aligned current are 1. the field aligned currents are mainly located in the E and low F region and change quickly with the altitude, 2. the displacement between the geomagnetic and geographic equators has a strong effect on the field aligned current as it changes with longitude, 3. the solar activity level does not much influence the field aligned current distribution pattern but changes the magnitude and introduces considerable field aligned current at night, 4. the Forbes winds yield no distinct difference between the March equinox and December solstice field aligned current patterns, 5. the field aligned currents driven by Forbes winds for March equinox and December solstice at geomagnetic longitudes of 45° E, 225° E and 315° E flow mainly from the southern to northern hemisphere in the morning and vice versa in the afternoon at the F region heights. CHAPTER 6. FIELD ALIGNED CURRENT 125 UT=OS hr ~ ,--...,...... ,,...... ,...-,----.-----.--.----.-----.--.----.-----.--,...... ,...--.-----.--,----.---,----,-,----,---.---,--,---.---,----, 0 N r----- 0 1 '"'01 G) ~o G) "Cl ::, :;::;.... 0 ....J 0 0 :;::; Ql C g' 0 E ~ > o I / Ql > (!) ,~ 0 ----- N I ,.,.,0 I .,;;:~.._:-_;_-_-_-__ .;- 0v .__....,__.._.__.__....,_____.__.__....,_____.__.__....,_____.__.__..._____.__.__.....____.__.....__.____.__.....__.____._~ 'o 2 4 6 8 10 12 14 16 18 20 22 24 Local Time(hr) Figure 6.5: The field aligned currents at 300 km computed for 5 hr UT. The contour interval is 20 x 10-9 A/m2 • The solid contours represent south --+ north current, and the dash contours represent north --+ south field aligned current. Equinox and solar minimum conditions apply. CHAPTER 6. FIELD ALIGNED CURRENT 126 UT=11 hr te::,-~-:!-=-::. 0 ----- I") 0 N O'> -CU ~o CU "U ...,::, :;:; .3 0 0 :;:; CU C g' 0 E ~ o I CU C) 0 N I 0 I") I 0,- ~ .____.....____.__L...l.....,___.__...... =-..1-:<:J_..__...,_....L_L-...... _--L_.__...,___.__'--.....__--'-_..__...,___.____, 1 0 2 4 s a 10 12 14 16 18 20 22 24 Local Time(hr) Figure 6.6: The conditions are the same as figure 6.5 except for 11 hr UT. CHAPTER 6. FIELD ALIGNED CURRENT 127 UT=17 hr -.:-: -=-~ _------ -=o- ... -20 - ,, 0 6> u :.:; Q) goC: ~ E ~ o I .; Q) c., .... - 0 N 0 I Figure 6. 7: The conditions are the same as figure 6.6 except for 17 hr UT. CHAPTER 6. FIELD ALIGNED CURRENT 128 Geographic Longitude=45E ~ r--~-_-_..,._-=-~--,--~---.a-~-~-~-~--.--_.,,=-~-~-~-~~ ---- __ ,,, ------.4,• - ---- 0 u, 0 0 ------:.; ====------40 -30 -20 -10 0 10 20 30 40 Geomagnetic Latitude(deg) Geographic Longitude-31 SE ~ ..--~-~------~------~---~-~-----~-~~-~-~-~-~-1r--,-.---~-.---~-----. __ ,,,,.- ' ' ' ------______.,.------, , , , I lzl ' <------~ ------40 -30 -20 -10 0 10 20 30 40 Geomagnetic Latitude(deg) Figure 6.8: The equatorward tidal winds at the geographic longitudes of 45° E and 315° Eat 8 hr LT. The contour interval is 20 m/ s. The solid contours are the geomagnetic equatorward and the dashed contours for the opposite direction. CHAPTER 6. FIELD ALIGNED CURRENT 129 UT=5 hr 0v ,, ... ,, ' 0 I') ,,., I '«-~-----" Ii"-----,,~ 0 v ' ,, io 2 4 6 8 10 12 14 16 18 20 22 24 Local Time(hr) Figure 6.9: Similar to figure 6.5 but for the high solar activity period(F10.7 - 175.9). CHAPTER 6. FIELD ALIGNED CURRENT 130 UT=11 hr 0v I "? ,, ' 0 I") I --- - I '~- 0 N ~ ...... c,, Q) ~o Q) "O :::, :;; -0 ...J 0 0 » :;; Q) C 8' ~ E I 0 Q) c., 0 N -;tP I 0 I") I ,... - - - -- ? -==::ir / 0v --- io 2 4 6 8 10 12 14 16 18 20 22 24 Local Time(hr) Figure 6.10: Similar to figure 6.6 but for the high solar activity period(F10.1 = 175.9). CHAPTER 6. FIELD ALIGNED CURRENT 131 UT=17 hr 0v 0 I') 0 N .-.. OI Q) ~o Q) -0 .....::] :.:; 0 ...J 0 0 :.:; Q) C OI 0 0 ~ E 0 I Q) (!) 0 N I 0 I') I 0v 'o 2 4 6 8 10 12 14 16 18 20 22 24 Local Time(hr) Figure 6.11: Similar to figure 6.7 but for the high solar activity period(F10.1 = 175.9). CHAPTER 6. FIELD ALIGNED CURRENT 132 UT=5 hr 0 ' ,.,0 J. 0 N ----O> QJ ~o ~'l> QJ "'O .,::, :.:; b 0 ....J 0 0 :.:; QJ C g'o E ~ o I QJ c., 0 N I ,.,0 < ', --- J I ,,.-'lfl' ...... -~ .. _------.... _~ 0 I ,_ e ' Local Time(hr) Figure 6.12: Similar to figure 6.9 but for December solstice. CHAPTER 6. FIELD ALIGNED CURRENT 133 UT=11 hr 0 -.t 0 I"') -- -.,,, 0 N ...... Cl> a, ~o > a, -0 ...,:::, :;:; C ...J 0 0 :;:; a, C g' ~ E I 0 a, (!) 0 N I 0 I"') I 0 -.t io 2 4 6 8 10 12 14 16 18 20 22 24 Local Time(hr) Figure 6.13: Similar to figure 6.10 but for December solstice. CHAPTER 6. FIELD ALIGNED CURRENT 134 UT=17 hr 0 " 0 r') I 0 " Figure 6.14: Similar to figure 6.11 but for December solstice. CHAPTER 6. FIELD ALIGNED CURRENT 135 Geographic Langitude=45E 8~-~-N ..... ~-~-~..... --~-~--~-~-- .....-.,-~-~--~-~--,...,...--~~~ I I ' , I \ , .... __ .,..,,,. , , I I , \ , I , , , 0 T I , , 0 N -.a=-- --~------40 -30 -20 -10 0 10 20 30 40 Geamognetic Latitude(deg) Geographic Longitude=315E 0 0 N I I \ I I I ,, I ' ,...__ • I I I ... ., I --- - \ I , I 0 ---.....,. , I I \ ' I I ' ~ ----- I I ' \ ' I I , ' ' 'lb ' \ , I ---- __ , ! I \ ' ' I 0 I ' u, _, , ' ' ------I e-" --- "i;' ,, --- ..., 0 ::, .... i ' 0 N 0 0 ------40 -30 -20 -10 0 10 20 30 40 Geomagnetic Latitude(deg) Figure 6.15: Similar to figure 6.8 but for December solstice. Chapter 7 Magnetic Fields Variations on the Ground 7 .1 Introduction answer magnetic field variations on the ground have been investigated for nearly a century, many answers concerning the magnetic components variations still re main unknown. Today there is no doubt that the ionospheric current is the main contributor toward the daily magnetic field variation recordings on the ground. To analyze the Quiet field (Sq) variations, Spherical Harmonic Analysis( SHA) has been applied to handle data in the X, Y and Z fields from a great number of geomagnetic observations{Matsushita and Maeda, 1965; Winch, 1981; Campbell and Schiffmacher, 1986, 1988) although selecting the local midnight value or the mean for the day as the reference level remains questionable. Three different techniques have been used to analyze the Sq variations. The 'snapshot' method fits the global field observations at a selected fixed universal time. The 'slice' method was used when only observatories in a longitudinal slice were available. The third 'mirror' technique was adopted when observatories from only one hemi- 136 CHAPTER 7. MAGNETIC FIELDS VARIATIONS ON THE GROUND 137 sphere could be used. Once the technique has been selected, the SHA coefficients are obtained from the Fourier components of field at each latitude step. Forbes et al. (1976a, 1976b ), using their global thin shell dynamo and three di mensional model of the equatorial electro jet, reproduced the main features of the magnetic field variation, especially fl.H. Takeda(l990) and Takeda et al.(1986) calculated the magnetic field variations introduced by the different tidal winds in the ionosphere. Richmond and Roble(l987), using the winds generated by the TGCM, simulated the ground magnetic field variations and compared them with observations for equinox solar minimum conditions. Using our own model including the electric field results calculated earlier, we will simulate the magnetic field variations on the ground, discuss the longitudinal variations, seasonal changes and the solar activity effects. Also the contributions of the field aligned currents are assessed. The method has been given in section 2. 7. The same as Takeda(1990) the induced current flowing below the earth is not included in our calculation. Otherwise our calculations should be corrected by a factor of about 1.3 for the northward and eastward magnetic components. 7.2 Magnetic Fields Variations without Field Aligned Current 7.2.1 Latitudinal Variation Figure 7.1 gives the latitudinal variations of fl.X, fl.Y, ll.Z at 1300 hr LT during the March equinox of 1986 for the geomagnetic longitudes of 146° E and 350° E. The other conditions are: F10.7 = 75.9 and Ap = 4. The main features are: 1. The northward component fl.X reaches a maximum at, and decreases sharply away from the geomagnetic equator. For example, fl.X changes from 107 nT CHAPTER 7. MAGNETIC FIELDS VARIATIONS ON THE GROUND 138 at the geomagnetic equator to 78 nT, 35 nT and 25 nT at 2° S, 4° S and 10° S respectively at about 1300 hr LT in the American longitude. There is a sim ilar change at every other longitude. 2. l:,.X changes from the positive to negative at about ±30° geomagnetic lati tude. The exact zero value position changes with the longitude, season, and solar activity. For example, it changes from 34° S at Indian longitudes to 27° S at American longitudes in the southern hemisphere under the equinox solar minimum condition. In the northern hemisphere however, it remains at about 30° N for both longitudes. These results are consistent with those of Matsushita and Maeda(1965). 3. The vertical component l:,.Z has different signs in the northern and south ern hemispheres during the daytime. There is an extreme value at about ±3° and it declines to zero at about 50° - 60° on either side of the geomag netic equator. It has nearly a constant value between 12° and 40° in both hemispheres. 4. l:,.Z is asymmetric about the geomagnetic equator even in equinox. This is expected as symmetry of the Sq current about the equator would imply antisymmetry of l:,.Z. 5. If there is no field aligned current in the ionosphere and at near the geo magnetic equator, the eastward component l:,.Y is controlled by the geo magnetic horizontal component l:,.H. From equation (2.56), it is clear that the l:,.Y depends also on 4>, the angle between the geomagnetic and geo graphic north pole from the observation point. At Indian longitudes(146°, magnetic longitude), the angle 4> is about 5° and it is about -2° at Amer ican longitudes(350°, magnetic longitude). Furthermore, a zero value of l:,.Y at the geomagnetic equator can be expected at Asian longitudes(180°, magnetic longitude). CHAPTER 7. MAGNETIC FIELDS VARIATIONS ON THE GROUND 139 7.2.2 Longitudinal Variation The magnetic field variations have a distinctive longitude variation. !:::..X, !:::..Y, !:::..Z components, beyond the equatorial area, at different longitudes, seasons and solar activity periods are shown from figures 7.2 to 7.9. !:::..X daily changes at the geomagnetic equator at different longitudes are presented in figures 7.10 and 7.11. It is clear that the magnitudes of the magnetic field variation at American longitudes are larger than those at Indian longitudes for both high and low solar activity, and for both March equinox and December solstice. At the geomagne t1c. equa t or, the rat· 10s, .6.X(America).6.X(lndia) , are 1. 57 , 1 .86 £or equmox. and solstice at solar minimum and 1.64, 1.20 for equinox and solstice at solar maximum at 1300 hr LT. To investigate the cause of !:::..X varying with longitude, we examined the local wind, conductivity and the magnetic field. The currents which produce the magnetic field variations are mainly located in the E region and they are controlled by the Hall conductivity as discussed in 5.2.3.1. In the E region near the equator, Ep ~ Ut/>B and so we can calculate the eastward current density by the simple formula (7.1) Our calculations(figure 7.12) show that IEPI has a maximum at about 102 km al though the exact distribution with altitude is a little different at each longitude. The ratio of the maximum Hall conductivity, u~11~e~~)), is close to the ratio a:11~~~)) and this assures us that the Hall conductivity is the decisive factor which gives rise to the distinctive !:::..X difference at different longitudes. At the March equinox and solar minimum condition, uH(1;1~-ic>) 1.40 at 104 which O'H n ,a = km is close to the calculated value 1.57 of a:11~~i~)). The observations at Huancayo and Trivandrum between 1964 and 1965 also show this ratio is 1.57(Patil et al., 1990) as shown in figure 7.13. All details can be clearly identified from the figure 7.12. A careful checking of the Hall conductivity changes with longitude shows the CHAPTER 7. MAGNETIC FIELDS VARIATIONS ON THE GROUND 140 relationship between Hall conductivity and the local magnetic field strength. In the E region, UH ex ½· Although a simple dipole geometry was used in all the calculations, the more exact model IGRF-73 was adopted to calculate the gy rofrequencies used to determine UH. At Indian longitudes, the magnetic field is about 3. 75 x 104 nT but only 2.67 x 104 nT at 350° magnetic longitude. So, we expect that the Hall conductivity at American longitudes to be about 1.40 times as large as at Indian longitudes. The Indian and American longitudes rep resent the maximum difference for the northward magnetic field variations near the magnetic equator. The magnetic field variations at other longitudes will be between the Indian and American longitude values. 7.2.3 Seasonal Variation The magnetic field seasonal variation does not show clearly in our calculation. Under solar minimum conditions and at the magnetic equator, !1X values at the December solstice are larger than at the March equinox at both Indian and American longitudes which does not agree with the observations. The experi ments show the equinox value is larger than that in the solstice. At high solar activity period, the Indian maximum values are nearly the same at both seasons while the American maximum value in March equinox is about 1.4 times larger than in December solstice. It is suggested that a more comprehensive neutral wind model incorporating changes with longitude and solar activity should be developed. 7.2.4 Solar Activity Effect The solar activity effects on the magnetic field variations in our calculations arise mainly from the conductivity and the electric field which in turn, were introduced CHAPTER 7. MAGNETIC FIELDS VARIATIONS ON THE GROUND 141 mainly by the changes of the electron density in the E region. The variation of the neutral density does not change the conductivity noticeably. The reason is that the neutral density changes only a little Increasing the solar activity index F10.7 from 75.9 to 175.9, the ratios, ":~'t:eNs~: , of the neutral density and the electron density at 110 km are 1.13 and 1.36, of the Pedersen and Hall conductivity at 128 km and 104 km respectively are both 1.36, of the southward electric field at 104 km is 1.48, and of the northward magnetic field is 2.27 at American magnetic equator. It should be mentioned that although the electric fields in the ionospheric F region do not change much with the solar activity in equatorial area, the E region southward/vertical electric field does. Noting that the eastward current density is determined approximately by the product of the southward electric field and the Hall conductivity, we may expect a factor of about 2.0 between the northward magnetic field during the high solar activity period and that in the low solar activity period. This result is quite consistent with the observations(Rastogi and Iyer, 1976) which show the ratios, ~~((~~,:,>, are 2.0 at Huancayo and 1.7 at Trivandrum stations as shown in figt1;re 7.14. So we can conclude that the northward magnetic field variations with the solar activity are introduced by the E region southward electric field and the Hall conductivity and all these changes arise mainly from the electron density variation as our wind model does not change with the solar activity. 7.3 Magnetic Fields Variations Introduced by Field Aligned Current The contributions of the field aligned current to magnetic fields variations are simulated. The calculation procedure is exactly the same as before except the field aligned current is included in the program. So, the magnetic fields variations CHAPTER 7. MAGNETIC FIELDS VARIATIONS ON THE GROUND 142 6.X, 6.Y and 6.Z on the ground are produced by the resultant current which comprises of the eastward, southward and the field aligned currents. The field aligned current does not affect noticeably the northward and vertical components 6.X, 6.Z. Its main effect is on the eastward magnetic field compo nent 6.Y or 6.D, especially in the equatorial area and at low latitudes. Figures 7.15 and 7.16 show the magnetic field variations with local time at four different geomagnetic latitudes in American longitude(350° E) for the December solstice and the March equinox respectively. From figure 7.15, it seems that the field aligned current has a little effect on 6.X and 6.Z in the December solstice. It decreases the magnitude of 6.X and 6.Z in the March equinox by a very small amount as shown in figure 7.16. Most importantly, the field aligned current is the main factor determining the eastward magnetic variations at low latitudes. We can see from figure 7.15 that with no field aligned current flowing in the iono sphere, the eastward component 6.Y will be very small. If the field aligned current is included in the calculation, the eastward magnetic variation 6.Y changes from -2.9nT to -11.9nT at 15hr and from 2.1nT to 11.7nT at 08hr at 5° Nin the December solstice. Similar variations occur in the March equinox. Figure 7.17 shows the three magnetic field components variations at a middle latitude( 40° N) for equinox and solstice. Although the field aligned current gives small changes in 6.Y, the general form of the variations remains unchanged. It is clear that the field aligned current has a very strong effect on the magnetic equatorial 6.Y variations on the ground. This is consistent with the conclusion by Schieldge et al.(1973). They pointed out the field aligned current is likely to have its most visible effect on the eastward magnetic variations along the mag netic equator. From section 6.2, we know that the field aligned current has a very complicated structure with altitude, namely the wave-like structure in the E and low F region. This is quite different from the eastward current distribution. During daytime and near the magnetic equator, the eastward current guarantees there is a very CHAPTER 7. MAGNETIC FIELDS VARIATIONS ON THE GROUND 143 large northward magnetic component !::..X on the ground. Although the magni tude of the field aligned current is large, the current direction changes from along B to anti B or vice versa within about 40 km and therefore the contributions of the positive and negative currents to the ground magnetic fields variations cancel each other to some degree. As discussed in section 6.6, the field aligned current is quite changeable and very sensitive to the local variations of the winds and conductivities. So we certainly will anticipate changeable eastward magnetic field variations near the magnetic equator as the tidal wind changes day-to-day. This is consistent with the observations at American longitudes(Hutton, 1967a, 1967b) as shown in figures 7.18 and 7.19. If contributions by the northward field aligned currents are larger than those by the southward field aligned currents, a negative eastward magnetic component !::..Y will be expected, otherwise positive. From figures 7.15 and 7.16. we can conclude that there is a northward net field aligned current in the afternoon and a southward net field aligned current in the morning over the geomagnetic equa tor in both March equinox and December solstice. Excluding the induced earth current, the equatorial eastward mag~etic field variations !::..Y may reach -17 nT in the afternoon and 10 nT in the morning at equinox. The correspond !::..D are -2.3 minutes and 1.5 minutes respectively. The values are -12nT(-l.7min.) and 16nT(2.0min.) at solstice. Compared with the afternoon pattern, !::..Y shows a complicated structure in the morning. It is interesting to compare our results with observations as shown in figure 7.18 even the solar activity indices are different between the two cases. Our calcula tions are reasonably close to the observations at solstice. The morning maximum and the afternoon minimum are the main feature at equatorial stations. Although the experiments show different patterns of !::..Y or !::..D for equinox and the De cember solstice, our results are rather similar for the two seasons. This is because the winds we used in the March equinox and in the December solstice are not so different. CHAPTER 7. MAGNETIC FIELDS VARIATIONS ON THE GROUND 144 We would like to point out that the eastward magnetic component shows a con siderable variability in amplitude and pattern as presented in figure 7.18 and 7.19. The ~y or ~D variation patterns in the March and September equinox are even different( Rastogi and Stening, 1998). Therefore, further work is still needed to simulate quantitatively the equatorial eastward magnetic field variation on the ground. A neutral wind model including LT, latitude, longitude, season and solar activity dependence is crucial to the success and urgently needed. It should be noted that the contributions of the currents only up to 500 km are considered and the contributions of the currents above 500 km are neglected in our calculation. This maybe can explain the difference between our results and those of Richmond and Roble(l987). Their result is about 3 times as large as our result at the latitude of 40° N. If we extend the top of the ionosphere from 500 km to 1000 km in our program, the eastward magnetic field variations on the ground show a significant change although the northward and the vertical components keep nearly unchanged. A similar situation happened when increasing latitude and longitude integration intervals. These clearly show that the field aligned currents flowing in the up per F region and in the magnetosphere have significant roles toward the ground eastward magnetic field variation. From chapter 6 we know that the field aligned currents flow at very large distances. Most importantly, their contributions to ground eastward magnetic field variations decrease very slowly with their dis tance. It is a critical problem mathematically if the integrand of the Biot-Savart law decreases no faster than ~. Physically, the field aligned current must dimin ish with increasing the altitude quick enough to guarantee the contributions of very distant(30, 000 km) current to the ground magnetic field variation become negligible. As discussed earlier, the neutral wind is the main cause of the ionospheric electric fields, transversal currents and the field aligned current. The correct wind model must introduce a field aligned current distribution which diminishes quickly with CHAPTER 7. MAGNETIC FIELDS VARIATIONS ON THE GROUND 145 increasing the altitude. The future work should focus on developing a more ac curate wind model and then simulating the effect of the field aligned current on the eastward magnetic field variation. 7.4 Conclusion The magnetic field observations on the ground have been studied by many authors (Matsushita and Maeda, 1965; Hutton, 1967a; Rastogi and Iyer, 1976; Stening and Hopgood, 1991). But many answers concerning the magnetic field variations, especially the eastward component, still remain unknown. The theoretical work is mainly focused on dX (or dH) (Forbes et al., 1976a; Reddy and Devasia, 1981) and at the middle latitude (Richmond and Roble, 1987). Takeda(1990) calculated the three magnetic components produced by the (1, -2) tidal wind and his results show a very small eastward magnetic field vari ation in the equatorial area. We have calculated the three magnetic components dX, dY and dZ and dH, dD and dZ using the Biot-Savart law and the earlier currents results. The lati tudinal, longitudal, seasonal variations and the solar activity effect are discussed. The roles of the field aligned current are also examined. It is clear that our model successfully reproduces the gross observed features of magnetic field variations on the ground. At and above the geomagnetic middle latitudes in either hemisphere, our simulations, dX, dY and dZ, are similar to other calculations( Takeda et al., 1986; Takeda,1990; Richmond and Roble, 1987), and close to the observed data(Matsushita and Maeda, 1965). For ex ample, the latitude of the current vortex center is higher in summer than in winter at December solstice during solar minimum period. This is consistent with Takeda(1990). Concerning the maximum magnitude of the northward or horizontal magnetic field variation, our dX of 80 nT and 120 nT at the magnetic CHAPTER 7. MAGNETIC FIELDS VARIATIONS ON THE GROUND 146 equator in Indian and American longitudes are close to Takeda's till of 100 nT under solar minimum and solstice condition. Further, Takeda obtained till of 13 nT and we predict tiX of 16 nT at geomagnetic latitude 20° S. But our tiX of 17 nT is smaller than till of 30 nT calculated by Richmond and Roble(l987) at 17° S under solar minimum and equinox condition even if we include effect of the induced earth current. Very similar situation appears at other latitudes if we compare our results with observations. It seems that our simulations underesti mate the magnetic field variations at middle latitudes. But we should remember that the magnetic fields are quite changeable and sensitive at the latitudes close to the current vortex. The northward component tiX is positive within ±30° latitude and changes to negative beyond during daytime. The exact latitude of the current vortex changes with longitude, season and solar activity index. The eastward component tiY shows the characteristics of the morning maximum and afternoon minimum in the northern hemisphere and the reverse in the southern. The negative tiZ in the northern hemisphere and positive in southern hemisphere are well reproduced. It is interesting to note the geomagnetic variations in the equatorial zone. On wumechilli( 1967) studied the northward component tiX and the vertical com ponent tiZ using his assumed ionospheric current density models. Forbes and Lindzen(1976a) calculated the northward magnetic field variations produced by different tidal winds by their thin-shell dynamo model. Takeda et al.(1986) and Takeda(1990) calculated the eastward magnetic field variations at the geomag netic equator but their values are too small. From figures 7.15 and 7.16 we can see that there is still a very large eastward component tiY in the equatorial zone. The difference between morning and afternoon values may be as large as 27 nT at 5° N in Equinox even with no induced earth current included in the calcu lation. Importantly, figures 7.15 and 7.16 show some similarity of the eastward component in the equatorial zone between the March equinox and the December solstice. The large eastward magnetic field variations have been summarized ex- CHAPTER 7. MAGNETIC FIELDS VARIATIONS ON THE GROUND 147 perimentally by Hutton(1967a, 1967b) who explained observations by the shift of the boundary between the northern and southern current vortices but no theoret ical work has been reported up to now. It is clear that these large variations of the eastward magnetic field are introduced mainly by the field aligned current. This demonstrates the correctness of the suggestion that the field aligned currents are likely to have their most visible effect on the eastward magnetic field variations along the magnetic equator(Schiedge et al., 1973). That the vertical component 6.Z has different signs in the northern and south ern hemispheres and reaches maximum and minimum at about 3° S and 3° N is successfully reproduced in our calculation. This is consistent with observa tion( Onwumechilli, 1967). Although Rastogi(1962), and Rastogi et al.(1996) ascribed the longitudinal in equality in the equatorial electrojet to be due to the differences of the ionospheric electric field, Sugiura and Poros(1969) suggested the longitudinal inequality of the electrojet is due to the corresponding variations in electrical conductivity. Our calculation shows the longitudinal inequality of the northward magnetic field is introduced mainly by the variations _of the local magnetic field intensity which affect the Hall conductivity. The electric field only has a minor effect. The difference in the seasonal dependence between our simulations and the obser vations in the equatorial area raises a concern about the accuracy of the Forbes wind model. Although the Forbes tidal winds can produce an electric field dis tribution in the F region which is close to those experimentally obtained, we still have not enough information to judge the accuracy of the E region electric fields structure. Most importantly, the E region electric fields are important factors affecting the equatorial magnetic fields variations on the ground. Any changes of the tidal winds in the E region in the equatorial area will introduce modifications to the E region electric fields and currents although the F region electric fields may remain almost unchanged. Another possible source of error may come from our selection that the eastward CHAPTER 7. MAGNETIC FIELDS VARIATIONS ON THE GROUND 148 tidal wind includes the diurnal wind only while the southward tidal wind includes both the diurnal and semidiurnal winds. Although this selection gives a best fit to the observed F region electric fields, it is clearly unphysical. We expect that diurnal and semidiurnal tidal winds will exist in both the eastward and southward directions. CHAPTER 7. MAGNETIC FIELDS VARIATIONS ON THE GROUND 149 120 100 80 E-t -i:: 60 ..c: -~ bD 40 i:: QJ I-< ~ 20 CJ) 0 -20 -40 -60 -40 -20 0 20 40 60 120 100 80 E-t -i:: 60 ..c: -~ bD 40 i:: QJ I-< ~ 20 CJ) 0 -20 -40 -60 -40 -20 0 20 40 60 Geomagnetic Latitude(deg) Figure 7.1: Magnetic field components variations with latitude at 1300 hr LT. The upper panel is at the Indian longitude(146° E, geomagnetic ) and the lower at the American longitude(350° E). The solid line is for ll.X, dot line for ll.Y and dash line for ll.Z. March equinox and solar minimum conditions are used in the calculation. CHAPTER 7. MAGNETIC FIELDS VARIATIONS ON THE GROUND 150 ax 6Y az 0 0 I() 0 0 ,qt 0 0 t") 0 0 C\I 0 0... 0 ...0 I 0 0 C\I I 0 0 t") I 0 0 ,qt I 40 10 10 0 0 20 0 I() 0 I 0 -10 -20 -20 -10 0 12 24 0 12 24 0 12 24 Local Time(hr) Local Time(hr) Local Time(hr) Figure 7.2: Three magnetic components variations at ten geomagnetic latitudes from 50° S to 50° N. Indian longitude, March equinox and solar minimum condi tions apply. CHAPTER 7. MAGNETIC FIELDS VARIATIONS ON THE GROUND 151 .1.X .1.Y .1.Z 0 0 IO 0 0 -.:I' 0 0 t") 0 0 N 0 ....0 0 0.... I 0 0 N I 0 0 C".) I 0 0 ~ I 40 10 10 0 0 20 0 IO 0 I 0 -10 -20 -20 -10 0 12 24 0 12 24 0 12 24 Local Time(hr) Local Time(hr) Local Time(hr) Figure 7.3: Similar to figure 7 .2 but for American longitude, March equinox and solar minimum period. CHAPTER 7. MAGNETIC FIELDS VARIATIONS ON THE GROUND 152 AX AY AZ 0 0 It:) 0 0 ,i:11 0 0 t") -...... __,,,, 0 0 t\2 ~ 0 0 - .... "-/ 0 ....0 /"--..... I 'V 0 0 /""'-.. t\2 I 0 0 t") ~ I 0 0 ~ ,i:11 I 40 101---.-----.--r----t 10 I 0 0 20 0 1----_-,,c.---=:,--1 ./"'... It:) 0 I 0 -10 -20 -20 ~~__.__..___, -10 I 0 12 24 0 12 24 0 12 24 Local Time(hr) Local Time(hr) Local Time(hr) Figure 7.4: Similar to figure 7.2 but for Indian longitude, December solstice and solar minimum period. CHAPTER 7. MAGNETIC FIELDS VARIATIONS ON THE GROUND 153 11X 11Y 11Z 0 0 IC) 0 0 ' 0 0 C') 0 0 N 0 0.... 0 ....0 I 0 0 N I 0 0 C') I 0 0 ' Figure 7.5: Similar to figure 7.2 but for American longitude, December solstice and solar minimum period. CHAPTER 7. MAGNETIC FIELDS VARIATIONS ON THE GROUND 154 t:.Y t:.Z 0 0 I(,) 0 0 ""' 0 0 t") 0 0 N 0 ....0 0 ....0 I Cl 0 N I 0 0 t") I 0 0 ""'I 40 40 20 0 0 I(,) 0 0 0 I -40 -40 -20 0 12 24 0 12 24 0 12 24 Local Time(hr) Local Time(hr) Local Time(hr) Figure 7.6: Similar to figure 7.2 but for Indian longitude, March equinox and solar maximum period. CHAPTER 7. MAGNETIC FIELDS VARIATIONS ON THE GROUND 155 t:,.Y l:J.Z 0 0 I() 0 0 ~ 0 0 C') 0 0 Cll 0 0.... 0 ....0 I 0 0 Cll I 0 0 C') I 0 0 ~ I 40 40 20 0 0 I() 0 0 0 I -40 -40 -20 0 12 24 0 12 24 0 12 24 Local Time(hr) Local Time(hr) Local Time(hr) Figure 7.7: Similar to figure 7.2 but for American longitude, March equinox and solar maximum period. CHAPTER 7. MAGNETIC FIELDS VARIATIONS ON THE GROUND 156 dX dY dZ 0 0 l(J 0 0 ,:j< 0 0 C':l 0 0 N 0 .....0 0 .....0 I 0 0 N I 0 0 C':l I 0 0 ,:j< I 40 40 20 0 0 l(J 0 0 0 I -40 -40 -20 0 12 24 0 12 24 0 12 24 Local Time(hr) Local Time(hr) Local Time(hr) Figure 7.8: Similar to figure 7.2 but for Indian longitude, December solstice and solar maximum period. CHAPTER 7. MAGNETIC FIELDS VARIATIONS ON THE GROUND 157 flX flY flZ 0 0 LO 0 0 -.:I' 0 0 C') 0 0 C\l 0 ....0 0 ....0 I C, 0 C\l I C, 0 C') I 0 0 -.:I' I 40 40 20 0 0 IO 0 0 0 I -40 -40 -20 0 12 24 0 12 24 0 12 24 Local Time(hr) Local Time(hr) Local Time(hr) Figure 7.9: Similar to figure 7.2 but for American longitude, December solstice and solar maximum period. CHAPTER 7. MAGNETIC FIELDS VARIATIONS ON THE GROUND 158 0 ....N 0 CXJ .. -..... 0 t---,• .,.... .• =--=--=---=--=--=--=--=--=--~_..,.-- ... . 0 4 8 12 16 20 24 ...... 120 ...... 80 40 .. • ...... 0 1--.-..- .. -.. -.. -...- ..- ..-:c ••:-:-o. ,..:;·_· ..:...'· 0 4 8 12 16 20 24 Local Time(hr) Figure 7.10: !Ji..X variations at the geomagnetic equator during the solar minimum period. The solid line is for the Indian longitude and dot line for American. The upper panel is for March equinox and the lower for December solstice. CHAPTER 7. MAGNETIC FIELDS VARIATIONS ON THE GROUND 159 0 ----- ,qt . N .. ····· ...... 0 0 N 0 (0 -0 N -0 CX) 0 ,qt 0 r=------:-:,....:.:_------······------0,qt ,___...... __ _.______._ _ ___.._..___...... __ _.__ ___._ _ ___.__ ...... __....._ _ ___._ _ ___. 'o 4 8 12 16 20 24 240 200 E-< 160 -i;::: .c: -+> 120 QI) i;::: G) 80 +> Cl)"' 40 0 -·------·------.. -...... -. -40 0 4 8 12 16 20 24 Local Time(hr) Figure 7.11: Similar to figure 7.10 but for solar maximum period. CHAPTER 7. MAGNETIC FIELDS VARIATIONS ON THE GROUND 160 0 0 --~-~~~--..-~---,---..--,----,---,--,----,---,--,------,---,----.----, C\I 0 ....in -..... -. ---..... -.. ---.. -.. - ---·····=····=····-~·-··=·· ------.. -.. -.. -.. - •. 0 -.. -· 0.... ------· ------·------ ~ .___.____.__...... __.____.__...... _~___.__.,__~___.__.,____.____.__....____.___._ _.____.____, 0 1 2 3 4 5 6 7 8 9 10 Hall Conductivity(l0-4 mho/m) 200 ,---,--,---,--,---,--,--,---,,--,---,,--,----,--.----,-...... ----,,--,----, 8 150 ~ Cl) -"'C .3 ---.. ------...... ------< 100 so~~-~~-~~~~~~~~~-~~-~~-~~-~~ -16 -14 -12 -10 -8 -6 -4 -2 0 2 Southward Electric Field(mv/m) Figure 7.12: Hall conductivities and downward electric fields over the geomagnetic equator at two different longitudes. The solid line is for the Indian longitude and dot line for American. March equinox and solar minimum conditions are used. CHAPTER 7. MAGNETIC FIELDS VARIATIONS ON THE GROUND 161 Annual Mean Daily Variation of ll H American Sector Indian Sector nT nT 80 80 60 60 40 40 20 20 0 0 00 06 12 18 24 00 06 12 18 24 75°W 75°E Local Standard Time Figure 7.13: Diurnal variations for 1964-65 years. American sector at sta tions at Huancayo(HUA), Fuquene(FUQ) and Indian sector stations at Trivan drum(TRD), Alibag(ABG)(from Patil et al., 1990). 140,------, ADDIS ABABA 120 TRIVANDRUM 100 ~H 80 60 40 20 o~--..---+--; 20 l!::!i)t oi----1--t:-~...,. -·20 00 06 06 00 06 12 18 24 . 06 00 HOUR LOCAL MEAN TIME Figure 7.14: Yearly average daily variations of H-field as well as the rate of change of H-field at Huancayo, Addis Ababa and Trivandrum for low solar activity(1964) and high solar activity(1958)(From Rastogi and Iyer, 1976). CHAPTER 7. MAGNETIC FIELDS VARIATIONS ON THE GROUND 162 t.X t.Y t.Z 0 ....0 ..- ...... 0 .. LO A . 0 LO I 40 10 40 20 0 20 0 0 .... 0 I 0 -10 -20 -20 -20 -40 0 12 24 0 12 24 0 12 24 Local Time(hr) Local Time(hr) Local Time(hr) Figure 7.15: Three magnetic components variations at four different latitudes near the geomagnetic equator. The solid line is for the contributions of the east ward, southward and the field aligned currents. The dot line is for the eastward and southward currents only. The American longitude, December solstice and solar minimum conditions apply. CHAPTER 7. MAGNETIC FIELDS VARIATIONS ON THE GROUND 163 t.X t.Y t.Z 0 ....0 0 It) 0 It) I 40 10 40 20 0 20 0 0 .... 0 I 0 -10 -20 -20 -20 -40 0 12 24 0 12 24 0 12 24 Local Time(hr) Local Time(hr) Local Time(hr) Figure 7.16: Similar to figure 7.15 but for the March equinox. CHAPTER 7. MAGNETIC FIELDS VARIATIONS ON THE GROUND 164 t.X t.Y t.Z 0 0 0 -10 . , \: -20 ,..____.__.____.___. -1 0 ,..___.__.___.____, -5 ,..___.__.____.___. 0 12 24 0 12 24 0 12 24 Local Time(hr) Local Time(hr) Local Time(hr) Figure 7.17: Three magnetic components variations in the March equinox(upper) and December solstice(lower) at 40° N. The solid line is for the contributions of the eastward, southward and the field aligned currents. The dot line is for the eastward and southward currents only. The American longitude and solar minimum conditions apply. CHAPTER 7. MAGNETIC FIELDS VARIATIONS ON THE GROUND 165 hr, 75°W.M.T. hr, 75°W.M.T. hr, 75° W.H.T. Figure 7.18: Daily variations of .6.D for each season for eight S. American stations during the IGY. D-December solstice; E-Equinoxes; J-June solstice(from Hutton, 1967a). CHAPTER 7. 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