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Geomagnetic and ionospheric effects of magnetospheric motions
Journal of Atmospheric nnd Terrestrial Physics, 1066, Vol. 28, pp. 1111-1123. P ergamon Press Ud. Printed in Northern Ireland
Geomagnetic and ionospheric effects of magnetospheric motions H. PoEVERLEIN Air Force Cambridge R esearch Laboratories, B edford, Mass.
(Received 14 July 1965; in revised form 19 May 1966) Abstract-A section of the magnetosphere is subject to a varying pressure of the sola r plasma wind during its rotation with the E a rth and in the course of disturbances, in which the plasma wind intensity is increased. The expected motions of the m a gnetospheric plasma are discussed in t erms ofhydromagnetic-wave theory. Crude estimates indicate the importance of the motions for varia tions of the geomagnetic fi eld and of the ionosph eric plasma den sity.
1. INTRODUCTION THE SUDDEN COMMENCEMENT and the initial phase of a geomagnetic storm are the immediate effect of an enhanced compression of the magnetosphere due to an increase of the solar plasma wind intensity (MATSUSHITA, 1964). The descent of the magnetospheric boundary necessarily entails a descending motion of plasma in the magnetosphere. Plasma in rotation with the Earth, moving from the night side to the day side and back to the night side, undergoes a diurnal variation of its compressional state. Vertical motions of the plasma are to be expected also in connection with this diurnal variation. It is in general assumed that a major part of the magnetosphere participates in the Earth's rotation (HINES, 1963 and 1964). The ionosphere at low and temperate latitudes apparently co-rotates with the Earth. The theorem of a joint motion of plasma and magnetic force lines requires then that the plasma along an entire force line performs the same rotary motion. A section of the co-rotating magnetosphere changes its vertical extension in accordance with the varying incidence of the plasma wind at its top. The atmospheric plasma, filling the magnetosphere in its entire vertical extension, has to descend during one half of the day and to ascend during the other half. The question arises what effect magnetospheric motions might have on the ionosphere . One expects variations of the plasma density and currents in the iono ~ sphere and variations of the magnetic field at all altitudes down to the ground. A number of authors have postulated that currents and motions generated in various ways in the ionosphere have some influence on the magnetosphere. The reversed connection has been proposed by FEJER (1964a) and PIDDINGTON (1964) in consideration of various mechanisms by which the solar plasma wind might affect the ionosphere. The present paper deals with magnetospheric processes of a fundamental hydromagnetic nature, which are caused by the solar plasma wind and become evident also in the ionosphere. Ionospheric phenomena believed to be independent of magnetospheric processes are ignored. For observational facts of the ionosphere and theories developed previously it is referred to the existing extensive literature. 1111
1112
H.
POEVERLEIN
The methods employed now arc those of hydromag netic-wavc theory, although the frequency of t he oscillations may be as low as one cycle per day. H ydromagnetic waves in atmospheric conditions were treated by FEJER (1960), FRANCIS and KARPLUS (1960) , K.AHALAS (lOGO) and KAHALAS and McNEILL (1964). More references are given elsewhere (PoEVERLTHN, 1064). PIDDING'l'ON (1059) m some paper included freq uencies nearly as low as under consideration now.
D
L
Fig. 1. Planely stratified model m agnetosphere. Curved lines are magnetic force lines. The plasma density, indicated by the density of dashed lines, decreases with height in the interval D .
2. PROCESSES IN A PLANELY STRATIFIED MEDIUM The effects of an increasing compression or gradual expansion of the magnetosphere are most easily studied in the idealized case of a planely stratified magnetosphere, in which plasma density and magnetic field are functions of height only (Fig. 1). A theory of coupled hydromagnetic waves in a plane stratification was the subj ect of an earlier paper (POEVERLEIN, 1964). In Fig. 1 it is assumed that the plasma is homogeneous in most heights, but of a different density at high and low a ltitudes. The fairly narrow transitional interval D wi ll lat er be interpreted as the region between F2 maximum and 1000 or 2000 km height. Motions in tho medium and the accompanying electromagnetic field are governed by Maxwell's equations and the equations referring to a medium of high conductivity (POEVERLEIN, 1964), Po
av = J X B at
0 -
E
+ v X B0 =
V(a 2 p),
(1)
0.
(2)
Subscript 0 denotes unperturbed quantities. The plasma velocity is v and the ion-acoustic wave velocity a. At first the pressure force V(a 2 p) is neglected. The equations then determine the plasma velocity normal to the force lines at all heights, once such a velocity is given at a boundary.
Geomagne tic a.nd ionospheric effects of m agnetospheric mo t ions
1113
A compression of the medium is obtained from a descending motion normal to the force lines at the top. Neglecting V(a 2 p), a descent normal to the force lines is derived for all altitudes . A perfect refl ector at the bottom of tho medium leads to suppression of E and v at this place and consequently to a compression of the medium. The theorem of a joint motion of plasma and force lines, whi ch follows from equation (2) and rel at es to motion normal to the force lines, postulates an increase of the magnetic field strength in connection with a compression. An oscillatory motion at the top yields an oscillatory state of motion throughout the medium, which corresponds to a standing modified Alfven wave. The plasma velocity v in modified Alfven waves is normal to B 0 and in the plane of B 0 and the wave normal (now the vertical). The electric field is normal to this plane (the plane of drawing in Fig. 1). The perfectly conducting bottom is the location of nodes of E and v and of an antinode of B_ (the oscillatory part of the magnetic field). No nodes or antinodes are expected inside the medium, whose vertical extension is well below a quarter of a wavelength. From the hydrodynamic continuity condition and equation (1} with inclusion of the pressure gradient term it follows that remarkable coupling between modified Alfven waves and ion-acoustic waves occurs in a strong gradient of the plasma density (POEVERLEIN, 1964). Ion-acoustic waves consequently originate in the interval D of Fig. 1. They involve plasma motion parallel to the force lines with a velocity comparable to that normal to the force lines. The ray direction of modified Alfven waves is the wave normal, but ion-acoustic waves have a ray direction parallel to B 0 (POEVERLEIN, 1964). An oscillatory motion in a lateral interval of limited width thus should produce modified Alfven waves remaining in this interval (C in Fig 2), whereas the ion-acoustic waves are confined to a force-line tube (S in Fig 2). Hydromagnetic-wave theory can be transferred to nonperiodic processes (cf. the treatment of a step function by BAZER and FLEISCHMAN, 1959). Nonperiodic or monotonic wave functions may be decomposed into Fourier components, to which the wave theory obviously applies. In the following the word 'waves' will be used with reference to sinusoidal and nonsinusoidal wave functions. In the earlier study it was found that above the coupling area ion-acoustic waves and modified Alfven waves have the same sign of v. (the vertical component of the plasma velocity), but below the coupling area v. in the ion-acoustic wave is opposite. For a monotonically increasing compression this means a plasma flux in the ion-acoustic wave that is directed toward the coupling area and is accompanied by a reduction of the plasma density, briefly a 'suction effect'. A primary compression in the space C of Fig. 2 causes a suction effect in the space S. The plasma motion normal to the force lines, at present attributed to modified Alfven waves, is frequently termed 'electrodynamic drift'. The motion parallel to the force lines, which is characteristic of ion-acoustic waves, would become 'diffusion' if the free path length of the ions exceeded the wavelength. In more complicated situations, in which the wave nature does not become evident, this motion may still be called 'diffusion'. Transport of plasma to other latitudes as the result of a combination of electrodynamic drift and diffusion is assumed to be the cause of some phenomena in the F2-layer (see Section 7).
H.
1114
POEVERLEIN
I Fig. 2. Ion-acoustic suction effect. D- height interval of the plasma density decrease, C-space of the primary compressional effect, S- space in which the suction effect is propagated.
3.
L
REGULAR MAGNETOSPHERIC MOTION
The vertical extension of the magnetosphere is smallest at the subsolar point and largest on the opposite side of the Earth. In rotation with the Earth the plasma consequently descends in the forenoon and ascends in the afternoon. Figures 3 and 4 represent two different models of the magnetosphere. The long tail with the neutral sheet of the magnetic field is not shown and no distinction is made between magnetic and .rotational axes of the Earth and the axis of the ecliptic. Plasma and force lines are supposed to be in joint motion. Rotation of the force lines with the Earth seems to require that the force line through the poles is the rotational axis and reaches the magnetospheric boundary in two neutral points (Fig. 3). However, the magnetic field can to a good approximation be derived from the dipole of the Earth and a current system at the magnetospheric boundary without taking rotation into account; no currents of significance are expected within the rotating magnetosphere (cf. Section 6). In a magnetosphere at rest, on the other hand, there is no obvious reason why the neutral points should lie on the polar force line. Figure 4 shows the field of a magnetosphere at rest according to computations by MEAD (1964) with slight modifications. The assumption that the force lines rotate with the Earth and preserve their bodily existence presents some difficulty in this field model. The polar force line, believed to be at rest, forms a loop. A wide surrounding tube afforce lines (shaded in the figure) then describes a 'twiddling motion' with a rotation opposite to the Earth's rotation in the outer area (HINES, 1963 and 1964). Two arguments against this motion model will be brought forward in the subsequent paragraphs. Beforehand it may be noted that the insulating space between
Geomagnetic and ionospheric effects of m agnetospheric motions
--
~~~
~~-
Fig. 3. Magnetosphere with a polar rotational axis.
Fig. 4. Magnetosphere with neutral points on a nonpolar forc e line. Hatching marks the area of the proposed twiddling motion.
1115
111 6
H.
POEVERLEI N
Earth and ionosphere was ignored. The theorem of a joint motion of force li11es and medium , which assigns a bodily existence t o t he force lines is, however , applicable only in highly condu ctive media . In t he insulating space the force lines lose their identi ty as GoLD (1959) has pointed out. This leaves more freedom for the choice of a sta te of motion. The solar plasma wind exerts some sort of viscous or friction force on the magnetosphere, pulling the force lines a long distance outward in the t ail. The same force tends t o suppress a rotary or t widdling motion that reaches the boundary of th e magnet osphere . The condi t ion (3)
E + vXB = O
prohibits a rotary mot ion at t he neutral points of the magneti c field. In a coordinate system at rest no oBjot is seen and from equation (3) with th e second Maxwell equati on one obtains (4) \7 X (v X B) = 0 or (B · \?)v - B(\7 · v) - (v · \?)B
= o.
(5)
Near the neutral points th e relative variation of B is much faster th an that of v. Thus the last term of equation (5) is predominant unless v disappears. This is consequently required at the neutral points. The force line reaching the neutral points, in Fig. 4 a nonpolar force line, has to stay at rest with the neutral points. A rotation around this force line as the axis t ogeth er with the given shape of the magnetosphere does not permit force lines to be anchored at invariable locations on the E arth, although the field has to be continuous at the bottom of the magnetosphere. During the course of a day force Jines are urged out of the magnetosphere at th e bottom and re-enter. Thus t he vertical motion of force lines and plasma extends down to the lowest altitudes. A suppression of rotary mot ion in the t ail of the magnetosphere would mean no rotation in a wider space around the force line leading to the neutral points ; but t here is no objection toward t he assumption of a rotation around this force line at not t oo high latitudes. In th e subsequent notes the part of t he magnetosphere under consideration is supposed to perform this rotary motion. Later on, hydromagnetic waves will be looked at in a reference system rotating with the E arth, in whi ch no unidirectional plasma flux is assum ed. The height of the magnetospheri c boundary varies one E arth radius per hour or approximately 2 km jsec at some t ime of the day (cf. CAHILL, Hl64). Plas ma in the outer magnet osphere has to follow this vertical displacement, if it is in rotary mot ion. An estimate of the verti cal velocity (v.,) at arbitrary altitudes can be obtained by assuming that t here is no alternat ing horizontal velocity . Wit h nearly no diurnal variation of the magneti c field, t he theorem of a joint motion of plasma and force lines leads t o the continuity condition (6)
Goo m u.gnotio a nd ionos p heri c effects of magnetosph eric m otions
1117
in whi ch r denotes t he distance from the Ear t h's center (geocentri c height) and Bh the horizontal component of B. In t he dipole field equation (6) yields (7)
A velocity of 2 km fsec at 10 earth radii thus corresponds t o 20 m jsec at low altitudes . This value may not be definitive, but it agrees with estimates in the literature, which arc based on completely difl'crcnt ideas. 4. COUPLED .WAVES IN THE MAGNETOSPHERE The velocities under discussion in t he last section are normal to the force lines a nd relate in the present interpret a tion to a st anding-wave field of Alfven waves and modified Alfven waves. These two types of waves, both fast waves, are not separable in the nonpl ane wave field, in which a wave norm al is not clearly defined. In consideration of a plane stratification it was found that ion-acousti c (slow) waves are generat ed in a st eep gradient of the plasma density by coup ling (cf. Section 2). This remains true in the existing situati on. Starting at F 2 maximum the plasma density decreases rapidly with height, approximately from 10 6 ions (or electrons) per cm 3 at 300 km (in daytime) to 10 4 per cm 3 at 1000 km . The stratifi cation of the plasma is presum ably spherical. The magnetic field is nearly a dipole fi eld. The processes in a vertical column of the magnetosphere are now not independent of those in a neighboring column. An estimat e of the plasma velocity in ion-acoustic waves was for plane stratification obtained by means of substituting an abrupt variation of the plasma density for a rapid decrease with height (PoEVERLEIN, 1964). Use of this procedure in the nonplane stratification leads to the same relationship between plasma velocities across and along the magnetic field lines. A descending motion in fast waves again causes ion-acoustic waves carrying plas ma into the coupling region and accompanied by a density reduction . Some more deviations from the idealizations of Section 2 are noticed. The gravity force affect s ion-acoustic waves . Collisions between ions and neutrals modify the characteristics of the various waves and enforce the neutral gas to follow the motion of the plasma p artially. The reflection of hydromagnetic waves at the bottom of the magnetosphere is imperfect. Equati on ( 1) wi t h gravity fm·ce b ecomes Po
av at =JX
B0
~ Y'(a 2 p)
+ gp.
(8)
R eplacement of V' by - i wja shows that gravity is in ion-acoustic waves significant for (9) aw < g, i.e. for angular frequencies below approximately I0- 2 sec-1 • The imaginary refractive indices derived from equation (8) with inequality (9) may lead to a poor definition of rays in some conditions. The frequency of collisions of ions (protons) with neutrals at an altitude of 1000 km is estimated as of the order of I0- 4 sec- 1 (from theoretically derived formulas, cf. HANSON, 1965). Below 1000 l
1118
H.
POEVERLEIN
angular frequencies and can not be ignored. Collisions lead not only to attenuation of waves but also to a decrease of the Alfven velocity, thus increasing the gradient of the Alfven velocity and presumably supporting the coupling effect. Toward lower altitudes the neutral gas participates in the motion in an increasing degree. The Tejlector at the bottom of the magnetosphere consists of the conductive ground and the lower ionosphere in combination. It is an imperfect reflector, leaving a small horizontal electric field component and a corresponding plasma velocity at low altitudes. The phase and amplitude relationships between E and B~ or between v and B~ should be obtainable from a study of the reflection characteristics of the compound reflector. 5. DISTURBANCE EFFECTS The increase of the horizontal magnetic field component in the initial phase of a geomagnetic storm, resulting from an increased plasma wind intensity, is described by the classical Chapman- Ferraro theory. Wave-theoretical formulations of the theory, concerned with Alfven ~·. ·wes and modified Alfven waves, were presented in recent years (MATSUSIII'l'A, 190 ; HINES and REID, 1965). In the present paper ion-acoustic (slow) waves, ori5 in. ~.ing from coupling with the fast waves, are introduced and the same wave-th· · t,ical methods are applied to disturbances and diurnal variations caused by varyi1. ""posure of a section of the magnetosphere to the plasma wind. Many statements t . ' will be made later with reference to diurnal processes are transferable to disturban · • In the above Sections 2 and 4 it was . . d that the ion-acoustic waves generated during an increasing compression of the · ;netosphere represent a suction effect with a motion of plasma toward the altitudeg t which the plasma density decreases rapidly with height (the coupling area). Plasrr. is removed from the regions below and above the coupling area. The reduction oc l,.e plasma density in the F2-layer may be identifiable with the depression of the J. 'tical frequency observed in geomagnetic storms, usually after a short increase of t.~"' critical frequency (SOMAYAJULU, 1963; 0DAYASIII, 1964). The short initial incre •,se 1 .,1ight be attributed to the descent of force lines in the fast waves, which entails a shortening of force line tubes with a compression of the plasma. This is the effect described by PIDDINGTON (1964}. The plasma motion in the ion-acoustic process at F2 altitudes is upward along the force lines and should lead to a lift of the F2-layer. Upward displacements, amounting to approximately 200 km in the maximum, have bemL found in geomagnetic storms (BECKER, 1961; SOMAYAJULU, 1963). 6. DIURNAL PROCESSES CORRESPONDING TO FAST WAVES A force line in its entire length pushed away by the solar plasma wind appears deformed in the way shown for noontime in Fig. 5. Only velocity and displacement components normal to the force lines are referred to in fast waves or in the joint motion of plasma and force lines. Ignoring the other component, it can be said that in Fig. 5 the middle section of the force line was moved downward (toward the Earth), each end section upward. The electric field connected with the motion is westward in the middle and eastward in the end sections. The electric field is supposed to extend through most of the altitude range
Geomagnetic and ionospheric effects of m agnetospheric motions
1119
occupied by the magnetosphere. The second Maxwell equation with the stationary magnetic field (seen by an observer at rest with the Sun) requires
pE · ds = 0.
(10)
Neglect of vertical E components leads to the conclusion that E is roughly inversely proportional to geocentric height. At ten earth radii a velocity of 2 kmfsec with a magnetic field of 50 y corresponds to 0·1 mVfm. At low altitude equation (10} postulates ten times this field strength or 1 mVfm. The velocity derived from this field is roughly 20 m fsec in accordance with the estimate at the end of Section 3 (POEVERLEIN, 1965).
/ I
I
"
"' "'
I I I
I I I
\
\
\
., \
' ' .... .... Fig. 5. Ideal force line (solid) and deformed force line at noon (dashed).
If the reversal of E with increasing latitude persists down to low heights, a surface curl of E appears at the bottom of the magnetosphere. The adjacent conductive surface, in fact, may permit a surface curl, but nearly no surface divergence, which would cause a too large accumulation of charge (DUNGEY, 1958). An energy flux into the imperfect conductor below the magnetosphere requires a northward (southward) B_ in connection with a westward (eastward) E. The diurnal variation of the geomagnetic field is known to have opposite sign at low and high (or temperate) latitudes. Currents in a hydromagnetic medium become in general significant only in dimensions comparable to a wavelength, which are, however, not available for the slow oscillation under consideration. Without currents of significance the first Maxwell equation approximately yields
fB_ • ds
=
o.
(11)
Currents due to peculiar phenomena (e.g. particle drifts in radiation belts) are now ignored. With the assumption that the vertical B_ component is negligible, equation (11} determines the height variation of the oscillatory field B_. An amplitude of 6
H.
ll20
POEVERLEIN
15 y at ten Earth radii would entail 150 y at low heights. The observed diurnal variation of the magnetic field is of the order 20 y (VESTINE, 1960). Application of equation (11) to a closed path at constant height indicates an E - W component comparable in size with the N-S component. Sign and time d ependence of this component correspond to a horizontal displacement of force lines a.way from the Sun in their middle section. The reduction of the horizontal B_ component below the estimate given in the la.st para.graph necessitates a vertical B_ component. The current system associated with the ma.gnetic field B_ is prima.rily one a.t the magnetospheric bounda.ry, where the incoming protons and electrons are deflected in opposite directions. Mea.d and Bea.rd (MEAD and BEARD, Hl64; l\IEAD, 1964) computed the currents at the boundary and the resulting ma.gnetic-field variations. The field varia.tions obta.ined for low altitude show a qualita.tive similarity to the observed variations, but they are of smaller magnitude. Ma.ximum horizontal Bat equatorial latitudes appears at noon. It should be recalled that a second current system, tending to enhance tho variations, has to be expected in the reflector at the bottom of the magnetosphere (PoEVERLEIN, 1965). Despite the qualitative agreement between theoretically derived and observed field variations it remains uncertain which fraction of the observed variations might be the immediate result of the plasma wind. A sizeable reduction of hydromagnetic field variations could occur in the reflection process in the lower ionosphere. On the other hand, rocket data. prove the existence of a. current system in the lower ionosphere such as postulated by the dynamo-electric theory (SINGER, MAPLE and BOWEN, 1952; CAHILL, 1964; BURROWS and HALL, 1965). The continuation of magnetospheric motions into the ionosphere leads also to currents there. Collisions of ions with neutrals cause currents that reduce the magnetic-field variation on the ground. Equation ( 1) with a collision frequen cy v; of the ions and without pressure gradient term becomes Po
av at + V;PoV =
J X B0 •
( 12)
The current density obtained with neglect of the acceleration term is of a. sense such as to diminish the horizontal B component underneath in the case of a descending velocity. A joint motion of charged particles and neutrals has to be expected in a height interval of the ionosphere in which the collision frequency of neutrals against ions Vn = Vtptf Pn
I0- 4
sec-1 ).
(13)
exceeds w (now approximately Joint motion of plasma and neutral gas was considered by various authors (e.g. FEJER, 1960; HINES, 1963; Krno a.nd KoHL, 1965). It could be imagined that at low altitudes a joint downward or upward motion continues, while the electric field is largely suppressed by the vicinity of a reflector. Presence of a v X B 0 without a corresponding E would cause currents of the type dealt with in the dynamo-electric theory. They should arise at the altitude at which the dynamo-electric currents are expected (near 120 km). Vertical velocities
Geomagnetic and ionospheric effects of magnetospheric motions
1121
of 20 mjsec are sufficient for magnetic-field variations of the observed magnitude (FEJER, 1964b). Thus it appears that there are different ways in which the solar plasma wind in connection with magnetospheric motions might lead to a variation of the geomagnetic field on the ground. 7. DIURNAL VARIATION
OJJ'
THE PLASMA DENSI'l'Y
111agnetic-field variations accompany fast waves, in which the plasma velocity is normal to the force lines; the plasma density, however, varies in particular in ionacoustic (slow) waves (PoEVERLEIN, 1964). Both types of waves were found to be strongly coupled in the gradient of the plasma density from F2 maximum up. The general rule that a descending motion of plasma in fast waves causes ascending motion and density reduction in ion-acoustic waves below the coupling region holds also for the processes on a regular day. Inversely, ascending motion in fast waves should lead to a density increase in ion-acoustic waves. The plasma velocity is expected to be in the ion-acoustic wave of the same order of magnitude as in the fast wave. A vertical velocity of 20 mjsec, on the other hand, is capable of changing the plasma density considerably, regardless of the exact characteristics of the ion-acoustic waves. Within 3 hr this velocity produces a vertical displacement of 200 km. A height interval of this size obviously would be evacuated if the velocity were stopped at a specific height. It is mainly compression and expansion what modifies the plasma density in vertical motion, but various processes may be thought of as contributing. A variation of the recombination rate with altitude, for example, may be of influence. If neutral gas and plasma move jointly, the arriving gas may have a ratio of ion to neutral concentration corresponding to its altitude of origin. In descent a more strongly ionized gas will be brought in. It is commonly believed that the behaviour of the F2-layer is to some extent determined by motion of the plasma. In explanations of F2-layer features such as the equatorial trough and the noon minimum of the electron concentration in summer one resorts to the combined effect of two types of motions, which now appear as expression of two types ofwa ves (MARTYN, 1956; DUNCAN, 1960; BRAMLEY and PEART, 1964). 'l'he present theory ascribes the motions to the varying pressure of the solar plasma wind on the magnetospheric boundary. An increasing compression of the magnetosphere at low latitudes is supposed to take place in the forenoon, an expansion in the afternoon. The general motion in the fast waves at low latitudes hence should be a descent in the forenoon and an ascent in the afternoon. The time of reversal may not exactly be noon. It depends on the phase relationship between E and B at the reflecting bottom (the lower ionosphere together with the ground). Because descending motion leads to density reduction ('suction') in the ion-acoustic waves, a plasma density minimum is expected in the middle of the day. This suggests to relate the equatorial trough and the noon minimum of the electron concentration in F2 with the ion-acoustic suction. The suction effect may cover a wider interval of latitudes than the compression in the fast waves because of its propagation along force lines (discussed in Section 2). The process is similar to that called for in events of disturbances (in Section 5). It
1122
H.
PoEvEuL:J<;IN
remains an open question why the noon minimum exists only in summer. It is believed that this has to do with the asymmetry of the compression effect and with the shorter length of propagation paths for ion-acoustic waves on the summer hemisphere. An essential supposition of the present theory is that the ion-acoustic waves are propagated down to the middle of the F2-layer, but not much further. On the other hand, the plasma that is carried away must re-appear somewhere. If fast waves reach lower heights, they may deposit plasma at E-layer height, where it forms sporadic-E (possibly of the equatorial type) and ultimately is removed by recombination. Some of the existing theories invoke a diurnal oscillation in which the phases of the motions differ from those of the present theory. It should be noticed that also in the present theory the vertical velocity component in the fast waves appears reversed at latitudes beyond 35° (cf. Fig. 5). Ion-acoustic waves consequently may show a reversed phase at higher latitudes. A complete theory, of course, would have to take into account all kinds of sources of motions, also temperature gradients, tides, and plasma density gradients not conesponding to a state of equilibrium. The various theories in which plasma motions across and along force lines are separated can account for a geomagnetic control of the F2-layer as it is observed in the dependence on geomagnetic inclination. EYFRIG (1062) found that the character of the diurnal variation of the F2 critical frequ ency varies with the sign of the geomagnetic declination. An earlier or later timing of the suction effect in accordance with the deviation of magnetic force lines from the north- south direction yields an effect of the right sense, but possibly not of sufficient magnitude. In conclusion, the qualitative nature of this paper and the fact that many simplifications were made may be emphasized. Nonlinear effects were ignored, but they aro expected to play a role both in outer areas of the magnetosphere, where the relative variation of the magnetic field is large, and at low heights, where amplitudes of displacements may exceed the scale height. High-latitude (auroral) phenomena, in general being of a more complicated character, were not considered.
Acknowledgements-The author gratefully acknowledges stimulating discussions with Mr. R. J. CORMIER, Dr. R. EYFRIG, Dr. P. NEWMAN, Professor Dr. K. RAWER, Dr. K. ToMAN and many unnamed colleagues in the field. REFERENCES J. a nd FLEISCHMAN 0. W. BRAMLEY E. N. and PEART .M. BunRows K. and HALL S. H. CAUILL L. c.
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R. A. DUNOEYJ. W.
1960 1958
llAZER
DE CKER
DuNCAN
J. Fluid llfech. 2, 366.
Arch. Elekt. Obertr. 15, 569. J. Geophys. R es. 69, 4609. J. Geophys. Res. 70, 2149. Space Physics (Edited by D. P. LoGalloy and A. Rosen), pp. 301349, John Wiley, Now York. J. Atmosph. T err. Phys. 18, 89. Cosmic Electrodynamics, p. 156, Cam· bridge University Pross, Cambridge, England.
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EYFRIG R. FEJER J. A. FEJEit J. A. FEJER J. A. FRANCIS W. E. and KARPLUS R. GOLD T. HANSON w. B.
1962 1960 1964a 1964b 1960 1959 1965
J. Geophys. Res. 67, 1678. J. Atmosph. Terr. Phys. 18, 135. J. Geophys. Res. 69, 123. Rev. Geophys. 2, 275. J. Geophys. Res. 65, 3593. J. Geophys. Res. 64, 1219. Satellite Environment Handbook (Edited by F. S. Johnson), 2nd edition, pp. 23-49, Stanford University Press, Stanford, California.
HINES C. 0. HINES C. 0. HINES C. 0. and REID G. C.
1963 1964 1965
K.AHALAS s. L K.AH.ALAS S. L. and McNEILL D. A. KING J. W. and KoHL H. MARTYN D. F. MATSUSHITA S.
1960 1964 1965 1956 1964
MEAD G. D. OBAYASHI T.
1964 1964 1964
PIDDINGTON J. H. PIDDINGTON J. H. POEVERLEIN H. POEVERLEIN H. SINGERS. F., MAPLE E. and BowEN W. A. SOMAYAJULU Y. v. VESTINE E. H.
1959 1964 1964 1965 1952 1963 1960
Q. JlR. Met. Soc. 89, l. Space Sci. Rev. a, 342. Physics of the Earth's Upper Atmosphere (Edited by C. 0. Hines, I. Paghis, T. R. Hartz and J. A. Fejer), pp. 334362, Prentice-Hall, Englewood Cliffs, N.J. Physics Fluids a, 372. Physics Fluids 7, 1321. Nature, Land. 206, 699. Aust. J. Phys. 9, 161. Research in Geophysics (Edited by H. Odishaw), Vol. 1, pp. 455-483, M.I.T. Press, Cambridge, Mass. J. Geophys. Res. 69, 1181. J. Geophys. Res. 69, 1169. Research in Geophysics (Edited by H. Odishaw), Vol. 1, pp. 335--366, M.I.T. Press, Cambridge, Mass. Geophys. JlR. Astr. Soc. 2, 173. Planet. Space Sci. 12, 553. Phys. Rev. 1a6, A 1605. Nature, Lond. 206, 604. Nature, Lond. 170, 1093. J. Geophys. Res. 68, 1899. Physics of the Upper Atmosphere (Edited by J. A. Ratcliffe), pp. 471512, Academic Press, New York.
]\'lEAD G. D. and BEARD D. B.
Geomagnetic and ionospheric effects of magnetospheric motions H. PoEVERLEIN Air Force Cambridge R esearch Laboratories, B edford, Mass.
(Received 14 July 1965; in revised form 19 May 1966) Abstract-A section of the magnetosphere is subject to a varying pressure of the sola r plasma wind during its rotation with the E a rth and in the course of disturbances, in which the plasma wind intensity is increased. The expected motions of the m a gnetospheric plasma are discussed in t erms ofhydromagnetic-wave theory. Crude estimates indicate the importance of the motions for varia tions of the geomagnetic fi eld and of the ionosph eric plasma den sity.
1. INTRODUCTION THE SUDDEN COMMENCEMENT and the initial phase of a geomagnetic storm are the immediate effect of an enhanced compression of the magnetosphere due to an increase of the solar plasma wind intensity (MATSUSHITA, 1964). The descent of the magnetospheric boundary necessarily entails a descending motion of plasma in the magnetosphere. Plasma in rotation with the Earth, moving from the night side to the day side and back to the night side, undergoes a diurnal variation of its compressional state. Vertical motions of the plasma are to be expected also in connection with this diurnal variation. It is in general assumed that a major part of the magnetosphere participates in the Earth's rotation (HINES, 1963 and 1964). The ionosphere at low and temperate latitudes apparently co-rotates with the Earth. The theorem of a joint motion of plasma and magnetic force lines requires then that the plasma along an entire force line performs the same rotary motion. A section of the co-rotating magnetosphere changes its vertical extension in accordance with the varying incidence of the plasma wind at its top. The atmospheric plasma, filling the magnetosphere in its entire vertical extension, has to descend during one half of the day and to ascend during the other half. The question arises what effect magnetospheric motions might have on the ionosphere . One expects variations of the plasma density and currents in the iono ~ sphere and variations of the magnetic field at all altitudes down to the ground. A number of authors have postulated that currents and motions generated in various ways in the ionosphere have some influence on the magnetosphere. The reversed connection has been proposed by FEJER (1964a) and PIDDINGTON (1964) in consideration of various mechanisms by which the solar plasma wind might affect the ionosphere. The present paper deals with magnetospheric processes of a fundamental hydromagnetic nature, which are caused by the solar plasma wind and become evident also in the ionosphere. Ionospheric phenomena believed to be independent of magnetospheric processes are ignored. For observational facts of the ionosphere and theories developed previously it is referred to the existing extensive literature. 1111
1112
H.
POEVERLEIN
The methods employed now arc those of hydromag netic-wavc theory, although the frequency of t he oscillations may be as low as one cycle per day. H ydromagnetic waves in atmospheric conditions were treated by FEJER (1960), FRANCIS and KARPLUS (1960) , K.AHALAS (lOGO) and KAHALAS and McNEILL (1964). More references are given elsewhere (PoEVERLTHN, 1064). PIDDING'l'ON (1059) m some paper included freq uencies nearly as low as under consideration now.
D
L
Fig. 1. Planely stratified model m agnetosphere. Curved lines are magnetic force lines. The plasma density, indicated by the density of dashed lines, decreases with height in the interval D .
2. PROCESSES IN A PLANELY STRATIFIED MEDIUM The effects of an increasing compression or gradual expansion of the magnetosphere are most easily studied in the idealized case of a planely stratified magnetosphere, in which plasma density and magnetic field are functions of height only (Fig. 1). A theory of coupled hydromagnetic waves in a plane stratification was the subj ect of an earlier paper (POEVERLEIN, 1964). In Fig. 1 it is assumed that the plasma is homogeneous in most heights, but of a different density at high and low a ltitudes. The fairly narrow transitional interval D wi ll lat er be interpreted as the region between F2 maximum and 1000 or 2000 km height. Motions in tho medium and the accompanying electromagnetic field are governed by Maxwell's equations and the equations referring to a medium of high conductivity (POEVERLEIN, 1964), Po
av = J X B at
0 -
E
+ v X B0 =
V(a 2 p),
(1)
0.
(2)
Subscript 0 denotes unperturbed quantities. The plasma velocity is v and the ion-acoustic wave velocity a. At first the pressure force V(a 2 p) is neglected. The equations then determine the plasma velocity normal to the force lines at all heights, once such a velocity is given at a boundary.
Geomagne tic a.nd ionospheric effects of m agnetospheric mo t ions
1113
A compression of the medium is obtained from a descending motion normal to the force lines at the top. Neglecting V(a 2 p), a descent normal to the force lines is derived for all altitudes . A perfect refl ector at the bottom of tho medium leads to suppression of E and v at this place and consequently to a compression of the medium. The theorem of a joint motion of plasma and force lines, whi ch follows from equation (2) and rel at es to motion normal to the force lines, postulates an increase of the magnetic field strength in connection with a compression. An oscillatory motion at the top yields an oscillatory state of motion throughout the medium, which corresponds to a standing modified Alfven wave. The plasma velocity v in modified Alfven waves is normal to B 0 and in the plane of B 0 and the wave normal (now the vertical). The electric field is normal to this plane (the plane of drawing in Fig. 1). The perfectly conducting bottom is the location of nodes of E and v and of an antinode of B_ (the oscillatory part of the magnetic field). No nodes or antinodes are expected inside the medium, whose vertical extension is well below a quarter of a wavelength. From the hydrodynamic continuity condition and equation (1} with inclusion of the pressure gradient term it follows that remarkable coupling between modified Alfven waves and ion-acoustic waves occurs in a strong gradient of the plasma density (POEVERLEIN, 1964). Ion-acoustic waves consequently originate in the interval D of Fig. 1. They involve plasma motion parallel to the force lines with a velocity comparable to that normal to the force lines. The ray direction of modified Alfven waves is the wave normal, but ion-acoustic waves have a ray direction parallel to B 0 (POEVERLEIN, 1964). An oscillatory motion in a lateral interval of limited width thus should produce modified Alfven waves remaining in this interval (C in Fig 2), whereas the ion-acoustic waves are confined to a force-line tube (S in Fig 2). Hydromagnetic-wave theory can be transferred to nonperiodic processes (cf. the treatment of a step function by BAZER and FLEISCHMAN, 1959). Nonperiodic or monotonic wave functions may be decomposed into Fourier components, to which the wave theory obviously applies. In the following the word 'waves' will be used with reference to sinusoidal and nonsinusoidal wave functions. In the earlier study it was found that above the coupling area ion-acoustic waves and modified Alfven waves have the same sign of v. (the vertical component of the plasma velocity), but below the coupling area v. in the ion-acoustic wave is opposite. For a monotonically increasing compression this means a plasma flux in the ion-acoustic wave that is directed toward the coupling area and is accompanied by a reduction of the plasma density, briefly a 'suction effect'. A primary compression in the space C of Fig. 2 causes a suction effect in the space S. The plasma motion normal to the force lines, at present attributed to modified Alfven waves, is frequently termed 'electrodynamic drift'. The motion parallel to the force lines, which is characteristic of ion-acoustic waves, would become 'diffusion' if the free path length of the ions exceeded the wavelength. In more complicated situations, in which the wave nature does not become evident, this motion may still be called 'diffusion'. Transport of plasma to other latitudes as the result of a combination of electrodynamic drift and diffusion is assumed to be the cause of some phenomena in the F2-layer (see Section 7).
H.
1114
POEVERLEIN
I Fig. 2. Ion-acoustic suction effect. D- height interval of the plasma density decrease, C-space of the primary compressional effect, S- space in which the suction effect is propagated.
3.
L
REGULAR MAGNETOSPHERIC MOTION
The vertical extension of the magnetosphere is smallest at the subsolar point and largest on the opposite side of the Earth. In rotation with the Earth the plasma consequently descends in the forenoon and ascends in the afternoon. Figures 3 and 4 represent two different models of the magnetosphere. The long tail with the neutral sheet of the magnetic field is not shown and no distinction is made between magnetic and .rotational axes of the Earth and the axis of the ecliptic. Plasma and force lines are supposed to be in joint motion. Rotation of the force lines with the Earth seems to require that the force line through the poles is the rotational axis and reaches the magnetospheric boundary in two neutral points (Fig. 3). However, the magnetic field can to a good approximation be derived from the dipole of the Earth and a current system at the magnetospheric boundary without taking rotation into account; no currents of significance are expected within the rotating magnetosphere (cf. Section 6). In a magnetosphere at rest, on the other hand, there is no obvious reason why the neutral points should lie on the polar force line. Figure 4 shows the field of a magnetosphere at rest according to computations by MEAD (1964) with slight modifications. The assumption that the force lines rotate with the Earth and preserve their bodily existence presents some difficulty in this field model. The polar force line, believed to be at rest, forms a loop. A wide surrounding tube afforce lines (shaded in the figure) then describes a 'twiddling motion' with a rotation opposite to the Earth's rotation in the outer area (HINES, 1963 and 1964). Two arguments against this motion model will be brought forward in the subsequent paragraphs. Beforehand it may be noted that the insulating space between
Geomagnetic and ionospheric effects of m agnetospheric motions
--
~~~
~~-
Fig. 3. Magnetosphere with a polar rotational axis.
Fig. 4. Magnetosphere with neutral points on a nonpolar forc e line. Hatching marks the area of the proposed twiddling motion.
1115
111 6
H.
POEVERLEI N
Earth and ionosphere was ignored. The theorem of a joint motion of force li11es and medium , which assigns a bodily existence t o t he force lines is, however , applicable only in highly condu ctive media . In t he insulating space the force lines lose their identi ty as GoLD (1959) has pointed out. This leaves more freedom for the choice of a sta te of motion. The solar plasma wind exerts some sort of viscous or friction force on the magnetosphere, pulling the force lines a long distance outward in the t ail. The same force tends t o suppress a rotary or t widdling motion that reaches the boundary of th e magnet osphere . The condi t ion (3)
E + vXB = O
prohibits a rotary mot ion at t he neutral points of the magneti c field. In a coordinate system at rest no oBjot is seen and from equation (3) with th e second Maxwell equati on one obtains (4) \7 X (v X B) = 0 or (B · \?)v - B(\7 · v) - (v · \?)B
= o.
(5)
Near the neutral points th e relative variation of B is much faster th an that of v. Thus the last term of equation (5) is predominant unless v disappears. This is consequently required at the neutral points. The force line reaching the neutral points, in Fig. 4 a nonpolar force line, has to stay at rest with the neutral points. A rotation around this force line as the axis t ogeth er with the given shape of the magnetosphere does not permit force lines to be anchored at invariable locations on the E arth, although the field has to be continuous at the bottom of the magnetosphere. During the course of a day force Jines are urged out of the magnetosphere at th e bottom and re-enter. Thus t he vertical motion of force lines and plasma extends down to the lowest altitudes. A suppression of rotary mot ion in the t ail of the magnetosphere would mean no rotation in a wider space around the force line leading to the neutral points ; but t here is no objection toward t he assumption of a rotation around this force line at not t oo high latitudes. In th e subsequent notes the part of t he magnetosphere under consideration is supposed to perform this rotary motion. Later on, hydromagnetic waves will be looked at in a reference system rotating with the E arth, in whi ch no unidirectional plasma flux is assum ed. The height of the magnetospheri c boundary varies one E arth radius per hour or approximately 2 km jsec at some t ime of the day (cf. CAHILL, Hl64). Plas ma in the outer magnet osphere has to follow this vertical displacement, if it is in rotary mot ion. An estimate of the verti cal velocity (v.,) at arbitrary altitudes can be obtained by assuming that t here is no alternat ing horizontal velocity . Wit h nearly no diurnal variation of the magneti c field, t he theorem of a joint motion of plasma and force lines leads t o the continuity condition (6)
Goo m u.gnotio a nd ionos p heri c effects of magnetosph eric m otions
1117
in whi ch r denotes t he distance from the Ear t h's center (geocentri c height) and Bh the horizontal component of B. In t he dipole field equation (6) yields (7)
A velocity of 2 km fsec at 10 earth radii thus corresponds t o 20 m jsec at low altitudes . This value may not be definitive, but it agrees with estimates in the literature, which arc based on completely difl'crcnt ideas. 4. COUPLED .WAVES IN THE MAGNETOSPHERE The velocities under discussion in t he last section are normal to the force lines a nd relate in the present interpret a tion to a st anding-wave field of Alfven waves and modified Alfven waves. These two types of waves, both fast waves, are not separable in the nonpl ane wave field, in which a wave norm al is not clearly defined. In consideration of a plane stratification it was found that ion-acousti c (slow) waves are generat ed in a st eep gradient of the plasma density by coup ling (cf. Section 2). This remains true in the existing situati on. Starting at F 2 maximum the plasma density decreases rapidly with height, approximately from 10 6 ions (or electrons) per cm 3 at 300 km (in daytime) to 10 4 per cm 3 at 1000 km . The stratifi cation of the plasma is presum ably spherical. The magnetic field is nearly a dipole fi eld. The processes in a vertical column of the magnetosphere are now not independent of those in a neighboring column. An estimat e of the plasma velocity in ion-acoustic waves was for plane stratification obtained by means of substituting an abrupt variation of the plasma density for a rapid decrease with height (PoEVERLEIN, 1964). Use of this procedure in the nonplane stratification leads to the same relationship between plasma velocities across and along the magnetic field lines. A descending motion in fast waves again causes ion-acoustic waves carrying plas ma into the coupling region and accompanied by a density reduction . Some more deviations from the idealizations of Section 2 are noticed. The gravity force affect s ion-acoustic waves . Collisions between ions and neutrals modify the characteristics of the various waves and enforce the neutral gas to follow the motion of the plasma p artially. The reflection of hydromagnetic waves at the bottom of the magnetosphere is imperfect. Equati on ( 1) wi t h gravity fm·ce b ecomes Po
av at =JX
B0
~ Y'(a 2 p)
+ gp.
(8)
R eplacement of V' by - i wja shows that gravity is in ion-acoustic waves significant for (9) aw < g, i.e. for angular frequencies below approximately I0- 2 sec-1 • The imaginary refractive indices derived from equation (8) with inequality (9) may lead to a poor definition of rays in some conditions. The frequency of collisions of ions (protons) with neutrals at an altitude of 1000 km is estimated as of the order of I0- 4 sec- 1 (from theoretically derived formulas, cf. HANSON, 1965). Below 1000 l
1118
H.
POEVERLEIN
angular frequencies and can not be ignored. Collisions lead not only to attenuation of waves but also to a decrease of the Alfven velocity, thus increasing the gradient of the Alfven velocity and presumably supporting the coupling effect. Toward lower altitudes the neutral gas participates in the motion in an increasing degree. The Tejlector at the bottom of the magnetosphere consists of the conductive ground and the lower ionosphere in combination. It is an imperfect reflector, leaving a small horizontal electric field component and a corresponding plasma velocity at low altitudes. The phase and amplitude relationships between E and B~ or between v and B~ should be obtainable from a study of the reflection characteristics of the compound reflector. 5. DISTURBANCE EFFECTS The increase of the horizontal magnetic field component in the initial phase of a geomagnetic storm, resulting from an increased plasma wind intensity, is described by the classical Chapman- Ferraro theory. Wave-theoretical formulations of the theory, concerned with Alfven ~·. ·wes and modified Alfven waves, were presented in recent years (MATSUSIII'l'A, 190 ; HINES and REID, 1965). In the present paper ion-acoustic (slow) waves, ori5 in. ~.ing from coupling with the fast waves, are introduced and the same wave-th· · t,ical methods are applied to disturbances and diurnal variations caused by varyi1. ""posure of a section of the magnetosphere to the plasma wind. Many statements t . ' will be made later with reference to diurnal processes are transferable to disturban · • In the above Sections 2 and 4 it was . . d that the ion-acoustic waves generated during an increasing compression of the · ;netosphere represent a suction effect with a motion of plasma toward the altitudeg t which the plasma density decreases rapidly with height (the coupling area). Plasrr. is removed from the regions below and above the coupling area. The reduction oc l,.e plasma density in the F2-layer may be identifiable with the depression of the J. 'tical frequency observed in geomagnetic storms, usually after a short increase of t.~"' critical frequency (SOMAYAJULU, 1963; 0DAYASIII, 1964). The short initial incre •,se 1 .,1ight be attributed to the descent of force lines in the fast waves, which entails a shortening of force line tubes with a compression of the plasma. This is the effect described by PIDDINGTON (1964}. The plasma motion in the ion-acoustic process at F2 altitudes is upward along the force lines and should lead to a lift of the F2-layer. Upward displacements, amounting to approximately 200 km in the maximum, have bemL found in geomagnetic storms (BECKER, 1961; SOMAYAJULU, 1963). 6. DIURNAL PROCESSES CORRESPONDING TO FAST WAVES A force line in its entire length pushed away by the solar plasma wind appears deformed in the way shown for noontime in Fig. 5. Only velocity and displacement components normal to the force lines are referred to in fast waves or in the joint motion of plasma and force lines. Ignoring the other component, it can be said that in Fig. 5 the middle section of the force line was moved downward (toward the Earth), each end section upward. The electric field connected with the motion is westward in the middle and eastward in the end sections. The electric field is supposed to extend through most of the altitude range
Geomagnetic and ionospheric effects of m agnetospheric motions
1119
occupied by the magnetosphere. The second Maxwell equation with the stationary magnetic field (seen by an observer at rest with the Sun) requires
pE · ds = 0.
(10)
Neglect of vertical E components leads to the conclusion that E is roughly inversely proportional to geocentric height. At ten earth radii a velocity of 2 kmfsec with a magnetic field of 50 y corresponds to 0·1 mVfm. At low altitude equation (10} postulates ten times this field strength or 1 mVfm. The velocity derived from this field is roughly 20 m fsec in accordance with the estimate at the end of Section 3 (POEVERLEIN, 1965).
/ I
I
"
"' "'
I I I
I I I
\
\
\
., \
' ' .... .... Fig. 5. Ideal force line (solid) and deformed force line at noon (dashed).
If the reversal of E with increasing latitude persists down to low heights, a surface curl of E appears at the bottom of the magnetosphere. The adjacent conductive surface, in fact, may permit a surface curl, but nearly no surface divergence, which would cause a too large accumulation of charge (DUNGEY, 1958). An energy flux into the imperfect conductor below the magnetosphere requires a northward (southward) B_ in connection with a westward (eastward) E. The diurnal variation of the geomagnetic field is known to have opposite sign at low and high (or temperate) latitudes. Currents in a hydromagnetic medium become in general significant only in dimensions comparable to a wavelength, which are, however, not available for the slow oscillation under consideration. Without currents of significance the first Maxwell equation approximately yields
fB_ • ds
=
o.
(11)
Currents due to peculiar phenomena (e.g. particle drifts in radiation belts) are now ignored. With the assumption that the vertical B_ component is negligible, equation (11} determines the height variation of the oscillatory field B_. An amplitude of 6
H.
ll20
POEVERLEIN
15 y at ten Earth radii would entail 150 y at low heights. The observed diurnal variation of the magnetic field is of the order 20 y (VESTINE, 1960). Application of equation (11) to a closed path at constant height indicates an E - W component comparable in size with the N-S component. Sign and time d ependence of this component correspond to a horizontal displacement of force lines a.way from the Sun in their middle section. The reduction of the horizontal B_ component below the estimate given in the la.st para.graph necessitates a vertical B_ component. The current system associated with the ma.gnetic field B_ is prima.rily one a.t the magnetospheric bounda.ry, where the incoming protons and electrons are deflected in opposite directions. Mea.d and Bea.rd (MEAD and BEARD, Hl64; l\IEAD, 1964) computed the currents at the boundary and the resulting ma.gnetic-field variations. The field varia.tions obta.ined for low altitude show a qualita.tive similarity to the observed variations, but they are of smaller magnitude. Ma.ximum horizontal Bat equatorial latitudes appears at noon. It should be recalled that a second current system, tending to enhance tho variations, has to be expected in the reflector at the bottom of the magnetosphere (PoEVERLEIN, 1965). Despite the qualitative agreement between theoretically derived and observed field variations it remains uncertain which fraction of the observed variations might be the immediate result of the plasma wind. A sizeable reduction of hydromagnetic field variations could occur in the reflection process in the lower ionosphere. On the other hand, rocket data. prove the existence of a. current system in the lower ionosphere such as postulated by the dynamo-electric theory (SINGER, MAPLE and BOWEN, 1952; CAHILL, 1964; BURROWS and HALL, 1965). The continuation of magnetospheric motions into the ionosphere leads also to currents there. Collisions of ions with neutrals cause currents that reduce the magnetic-field variation on the ground. Equation ( 1) with a collision frequen cy v; of the ions and without pressure gradient term becomes Po
av at + V;PoV =
J X B0 •
( 12)
The current density obtained with neglect of the acceleration term is of a. sense such as to diminish the horizontal B component underneath in the case of a descending velocity. A joint motion of charged particles and neutrals has to be expected in a height interval of the ionosphere in which the collision frequency of neutrals against ions Vn = Vtptf Pn
I0- 4
sec-1 ).
(13)
exceeds w (now approximately Joint motion of plasma and neutral gas was considered by various authors (e.g. FEJER, 1960; HINES, 1963; Krno a.nd KoHL, 1965). It could be imagined that at low altitudes a joint downward or upward motion continues, while the electric field is largely suppressed by the vicinity of a reflector. Presence of a v X B 0 without a corresponding E would cause currents of the type dealt with in the dynamo-electric theory. They should arise at the altitude at which the dynamo-electric currents are expected (near 120 km). Vertical velocities
Geomagnetic and ionospheric effects of magnetospheric motions
1121
of 20 mjsec are sufficient for magnetic-field variations of the observed magnitude (FEJER, 1964b). Thus it appears that there are different ways in which the solar plasma wind in connection with magnetospheric motions might lead to a variation of the geomagnetic field on the ground. 7. DIURNAL VARIATION
OJJ'
THE PLASMA DENSI'l'Y
111agnetic-field variations accompany fast waves, in which the plasma velocity is normal to the force lines; the plasma density, however, varies in particular in ionacoustic (slow) waves (PoEVERLEIN, 1964). Both types of waves were found to be strongly coupled in the gradient of the plasma density from F2 maximum up. The general rule that a descending motion of plasma in fast waves causes ascending motion and density reduction in ion-acoustic waves below the coupling region holds also for the processes on a regular day. Inversely, ascending motion in fast waves should lead to a density increase in ion-acoustic waves. The plasma velocity is expected to be in the ion-acoustic wave of the same order of magnitude as in the fast wave. A vertical velocity of 20 mjsec, on the other hand, is capable of changing the plasma density considerably, regardless of the exact characteristics of the ion-acoustic waves. Within 3 hr this velocity produces a vertical displacement of 200 km. A height interval of this size obviously would be evacuated if the velocity were stopped at a specific height. It is mainly compression and expansion what modifies the plasma density in vertical motion, but various processes may be thought of as contributing. A variation of the recombination rate with altitude, for example, may be of influence. If neutral gas and plasma move jointly, the arriving gas may have a ratio of ion to neutral concentration corresponding to its altitude of origin. In descent a more strongly ionized gas will be brought in. It is commonly believed that the behaviour of the F2-layer is to some extent determined by motion of the plasma. In explanations of F2-layer features such as the equatorial trough and the noon minimum of the electron concentration in summer one resorts to the combined effect of two types of motions, which now appear as expression of two types ofwa ves (MARTYN, 1956; DUNCAN, 1960; BRAMLEY and PEART, 1964). 'l'he present theory ascribes the motions to the varying pressure of the solar plasma wind on the magnetospheric boundary. An increasing compression of the magnetosphere at low latitudes is supposed to take place in the forenoon, an expansion in the afternoon. The general motion in the fast waves at low latitudes hence should be a descent in the forenoon and an ascent in the afternoon. The time of reversal may not exactly be noon. It depends on the phase relationship between E and B at the reflecting bottom (the lower ionosphere together with the ground). Because descending motion leads to density reduction ('suction') in the ion-acoustic waves, a plasma density minimum is expected in the middle of the day. This suggests to relate the equatorial trough and the noon minimum of the electron concentration in F2 with the ion-acoustic suction. The suction effect may cover a wider interval of latitudes than the compression in the fast waves because of its propagation along force lines (discussed in Section 2). The process is similar to that called for in events of disturbances (in Section 5). It
1122
H.
PoEvEuL:J<;IN
remains an open question why the noon minimum exists only in summer. It is believed that this has to do with the asymmetry of the compression effect and with the shorter length of propagation paths for ion-acoustic waves on the summer hemisphere. An essential supposition of the present theory is that the ion-acoustic waves are propagated down to the middle of the F2-layer, but not much further. On the other hand, the plasma that is carried away must re-appear somewhere. If fast waves reach lower heights, they may deposit plasma at E-layer height, where it forms sporadic-E (possibly of the equatorial type) and ultimately is removed by recombination. Some of the existing theories invoke a diurnal oscillation in which the phases of the motions differ from those of the present theory. It should be noticed that also in the present theory the vertical velocity component in the fast waves appears reversed at latitudes beyond 35° (cf. Fig. 5). Ion-acoustic waves consequently may show a reversed phase at higher latitudes. A complete theory, of course, would have to take into account all kinds of sources of motions, also temperature gradients, tides, and plasma density gradients not conesponding to a state of equilibrium. The various theories in which plasma motions across and along force lines are separated can account for a geomagnetic control of the F2-layer as it is observed in the dependence on geomagnetic inclination. EYFRIG (1062) found that the character of the diurnal variation of the F2 critical frequ ency varies with the sign of the geomagnetic declination. An earlier or later timing of the suction effect in accordance with the deviation of magnetic force lines from the north- south direction yields an effect of the right sense, but possibly not of sufficient magnitude. In conclusion, the qualitative nature of this paper and the fact that many simplifications were made may be emphasized. Nonlinear effects were ignored, but they aro expected to play a role both in outer areas of the magnetosphere, where the relative variation of the magnetic field is large, and at low heights, where amplitudes of displacements may exceed the scale height. High-latitude (auroral) phenomena, in general being of a more complicated character, were not considered.
Acknowledgements-The author gratefully acknowledges stimulating discussions with Mr. R. J. CORMIER, Dr. R. EYFRIG, Dr. P. NEWMAN, Professor Dr. K. RAWER, Dr. K. ToMAN and many unnamed colleagues in the field. REFERENCES J. a nd FLEISCHMAN 0. W. BRAMLEY E. N. and PEART .M. BunRows K. and HALL S. H. CAUILL L. c.
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DuNCAN
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Geomagnetic and ionospheric effects of magnetospheric motions
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1963 1964 1965
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1960 1964 1965 1956 1964
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]\'lEAD G. D. and BEARD D. B.