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The effect of the ring current on whistler propagation in the magnetosphere
Planet. Space Sci. 1972, Vol. 20, ~pp.731
to 746.
permmon
Press. Printed in Northern Ireland
THE EFFECT OF THE RING CURRENT ON WHISTLER PROPAGATION IN THE MAGNETOSPHERE J. L. SACRED0 and K. BULLOUGI-I Physics Department, University of Sheffield, Sheffield, England (Received 26 November 1971)
Abatraet-The propagation of whistlers in a disturbed ~~et~p~~ is studied. The disturbance is that produced by a ring of charged particles encircling the Barth with a maximum in energy density at three earth radii. The ring current model adopted (Sozou and Wmdle, I969a, 1969b) takes into account the self-effect of the magnetic field of the ring current particles in their own motion. It is found that the presence of the ring current changes both the nose frequency, $, and the travel time at the nose frequency, tn, of a whistler. The distortion of the magnetic field alters the relationship between thef. of a whistler, the equatorial distance of its path of propagation and the geomagnetic latitude at which the field line is anchored. It is shown that this may account,-at leas? in part, for the apparent decrease in electron density during disturbed periods deduced from whistler analysis bv Carnenter 0962a). In addition. account should be taken of the effect of field line d~t~~ion,whe~ determining the location of the knee during disturbed periods. Thus, the discrepancy found by Rycroft and Thomas (1970) between the position of the medium latitude trough and that, determined from whistler analysis, of the plasmapause is probably due to this effect. 1. INTRODUCPION
In most whistler studies, the Earth’s magnetic field is approximated by a perfect dipole. This assumption represents an adequate approximation to the Earth’s magnetic field for ~gnetically quiet periods. During geomagnetic storms, however, the Earth’s magnetic field deep within the magnetosphere departs from a dipole field by a substantial amount due to the injection, during the main phase of the storm, of a body of charged particles deep into the magnetosphere, near the equatorial plane. The injected particles become trapped in the Earth’s magnetic field and drift in longitude across the L-shells, producing a ring current which encircles the Earth. This ring current becomes axisymmetric in a period of the order of 12 hr and then slowly decays during the recovery phase of the geomagnetic storm. The purpose of this paper is to present the results of an investigation into the propagation of whistlers in a disturbed magnetosphere such as that existing during the recovery phase of a geomagnetic storm when the ring current slowly decays during a period of one day or more and hence a quasi-stationary situation can be assumed. The first suggestion of the existence of a ring current encircling the Earth at several earth radii equatorial distance was made by Chapman and Ferraro (193111933). They attributed the observed depression of the Earth’s magnetic field at the Earth’s surface during the development of a geomagnetic storm to the existence of a ring current. The discovery of belts of charged particles in the Earth’s magnetic field (Van Allen et aI,, 1958; Van Allen and Frank, 1959), confirmed predictions by Singer (1957) arising from the work of Chapman and Ferraro. Cahill (1966) studied the development of the ring current during two geomagnetic storms from data provided by the magnetometer on board the Explorer 26 satellite. He was able to determine the rates of growth and decay. During the main phase of the storm an asymmetric ring current was formed, caused by a body of charged particles injected into the evening sector of the magnetosphere. During the recovery phase the ring current 731
732
J. L. SAGREDO
and
K. BULLOUGH
became axisymmetric and was centred at 3*5RE in the equatorial plane. By measurement of both the inclination and declination of the magnetic field it was deduced that, during the symmetric period of the storm, the magnetic field lines were stretched away from the Earth. The drift period of the injected particles was deduced and their energy estimated to be less than 100 keV. A more detailed analysis of the energy spectrum of the particles which constitute the ring current has been made by Frank (1967, 1969) from data from the OGO 3 satellite. It was found that the energy density of the ring current was predominantly shared by protons in the energy range 3-50 keV. For the magnetic storm of July 9 1966, the peak proton energy density at the equator varied from 9 x 10-s erg cm-3 at L = 6.8 (pre-storm quiet conditions) to 5 x lo-’ erg cm-3 at L = 3.3 (storm main phase), while at L ‘u 7 the energy density changed only slightly throughout the whole development of the storm. Previous theoretical studies of whistler propagation in a disturbed magnetosphere include that of Spreiter and Briggs (1962) who considered a simple ring current model of infinitesimal cross-section and used a ‘gyrofrequency’ model (N ccfH) for the distribution of ionisation along the field lines. Molchanov (1968) has developed a model of the disturbed magnetosphere in which both the currents at the outer boundary of the magnetosphere due to the flow of the solar wind and the currents in the magnetospheric tail have been included. The inflation of the magnetic field is symmetric up to about 5 earth radii but beyond 6 earth radii the field lines are compressed on the dayside of the magnetosphere. Likhter and Molchanov (1968) subsequently studied whistler propagation for this model assuming a ‘gyrofrequency’ model of the ionisation distribution. They found, like ourselves, an increase in the travel time at the nose frequency, and, a decrease in the nose frequency for propagation along a field line anchored at a particular geomagnetic latitude. 2. THE
RING
CURRENT
MODEL
Several studies have attempted to describe, theoretically, the perturbation of the Earth’s magnetic field due to the presence of a ring current axisymmetric with respect to the dipole field. In most of the works, a gaussian distribution of charged particles in the equatorial plane is assumed and the current produced by their drift across the L-shells is deduced from the theory, developed by Parker (1957), which describes the behaviour of a plasma permeated by a magnetic field. In the linear case, charged particles in a stationary radiation belt move under the influence of the dipole field alone, i.e. the self-effect of the magnetic field of the particle belt is ignored, This case has been investigated by Akasofu and Chapman (1961) and Kendall et al. (1966). The model adopted in the present work has been derived by Sozou and Windle (1969a, 1969b). In this model, the energetic particles move in the combined field of the Earth’s dipole and the field due to the currents of the particle motions in the combined field. The number density distribution of particles at the geomagnetic equator is given by n,,(R)
= n, exp [-k2(R
-
RJ2]
(1)
where R is the geomagnetic distance in earth radii, n, the peak number density (at R,,), and k a constant. The values considered were, R, = 3 k = 2.99 k = 0.419
for for
R<3 R > 3.
EFFECT
OF THE RING
CURRENT
ON HISSER
PROPAGA~ON
733
The components in the I and 3 directions of the total. magnetic field can be expressed in terms of the magnetic stream function Y? (Kendall et al., 1966) by,
(2) (3) andY,
expressed in terms of spherical harmonics, is Yp = 7
+ B%rA,(r)P,‘(sin
where M is the moment of the Earth’s dipole field, magnetic latitude, and
F
0) cos 6
the geocentric distance, 8 the gee-
where P, is the Legendre polynomial of degree n and x = sin 8, The computation of A, (n = 1,2,3, . . .) IS * p er formed by successive iteration, equating the current density, 3, given by
to the current due to the gyration of the particles round the lines of force and to their drift across the magnetic field (Sozou and Windle, 1969a). Following Sozou and Windle (1969a), it is assumed that the stream function Y may be approximated by the first eight non-vanishing terms of the series (4) and that both the particle and current densities are zero outside the region 1 < A < 10. Following Chapman et al. (1968) and Sozou and Windle (1969b), a set of different values for the peak kinetic energy density of the particles is considered. These are, (a) (b) (c) (d)
E. = E, = E. = E,, =
150 keV 300 keV 600 keV 900 keV
cm-s cm-3 cm-3 cm-s.
Case (a) is representative while case (d) represents a distribution at the equatorial storm of moderate intensity 1967).
of a ring current generated during a weak geomagnetic storm, very severe one. Figure I shows the kinetic energy density plane for cases (a)-(d) together with that for the geomagnetic on July 9 1966, as determined from the OGO 3 data (Frank,
The depression of the Earth’s magnetic field in the equatorial plane is shown in Fig. 2 for all the cases (a)-(d). At the Earth’s magnetic equator, the depression, BsT, varies from -25~ for & = 150 keV cm3 to - 1287 for E,, = 900 keV cmA, The geometry of the magnetic field is illustrated in Fig, 3 where several field lines are shown together with the corresponding dipolar geld lines anchored on the Earth’s surface at the same geomagnetic latitude. The distortion of the field lines is also depicted in Fig. 4, 7
734
J. L. SAGREDO
c
I
I
3
I
and K. BULLOUGH
I
5
1
I
I
7
,
9 Earth radii
Fro. 1. ENEMY DENSITY OF THE RINQ CURRENT PARTWLESIN SHOWN
THJIEQUATORIAL PLANE. hii0 IS THE ENERGY DENSITY DWIRIBIJTION OF THE RING CURRENT PARTICLES DIJRINC3THE ~~OMA~~~STORM~F JULY91966.
5'1
0 s z 4 -50
-100
-150
-ml
Fm.2.
MACWHTCPIELD,
AB,OPTHE RIN~CURRENTINTHEEQUATORIALPLANB(~R AND WINDLE,1969b).
Sozou
EFFECT
OF THE RING
CURREMT
ON WHISTLER
PROPAGATION
135
1
1
2
3
L
5
6 Earth
FX3.
3.
bLD
LINES
OF THE TOTAL
MAGNETIC FIELD
c
FIELD
AND
THE CORRl?.WONDING
DIPOLE
(----).
I -I
Equatorial FIG.
( -)
I
radii
4.
ORDINATE: SPONDING
GEOMAGNETIC J%‘ALUE.
LATITUDE hSCISSA:
dislancr
(earth
radii)
OF THE FOOT OF THE FIELD EQUATORIAL
DISTANCE
LINE
AND
ITS IXRRE-
OF FTELD LINE.
where the geomagnetic latitude of the foot of the field line and its corresponding L-value is plotted versus the equatorial distance. The straight line corresponds to the dipole field and it is observed that the departure from dipole configuration increases with the energy of the ring current. Up to about L = 3 there is no significant variation in the geometry of the field. 3. WHISTLER
PROPAGATION
A study of the propagation of whistlers in the disturbed magnetosphere, described above, has been carried out. The usual approximations adopted in whistler propagation, such as that of a cold plasma and strictly longitudinal propagation, have been adopted here.
J. L. SAGREDO
736
and K. BULLOUGH
Two models of the distribution of the neutral plasma along the field lines have been considered (Angerami and Carpenter, 1966; Angerami, 1966; Sagredo, 1971): (i) Inside the plasmapause, a diffusive equilibrium model where the magnetospheric plasma, composed of electrons and Of, He+ and H+ ions, is controlled by diffusion processes along the field lines; (ii) beyond the plasmapause, the electron density distribution corresponds to that of a collisionless plasma of protons and electrons. On low L shells the model of a disturbed magnetosphere in diffusive equilibrium and a steady ring current is open to criticism. Thus, Park (1970) has found evidence, from whistler observations, that the protonosphere is probably never fully in equilibrium with the ionosphere but, for most of the time, is recovering from depletion which occurred during previous magnetic disturbances. Clearly, the deviation from equilibrium will depend on the relative magnitudes of the lifetime of the ring current particles against precipitation and the time constant for the establishment of diffusive equilibrium. Thus the observed lifetime of the ring current particles is about 3-4 days at L = 5 and 1 day at L = 3.5 (Swisher and Frank, 1968) while the diffusion time of the ambient particles along the field lines is of the order of 1 day (Bauer, 1969). Inside the plasmapause the lifetime of the ring current may be as little as 1 hr due to rapid ion-cyclotron precipitation (Cornwall et al., 1970). These lifetimes and diffusion times may be compared to the longitudinal drift period of the ring current protons which is a few hours and, of course, the 24 hr diurnal variation in the upper ionosphere and the plasmapause location. According to Carpenter (private communication) during storms when DST I -50~ the plasmapause is usually near or inside L = 3. In the region of the evening bulge near 1800 L.T. the plasmapause is not usually well defined in the ground data. To compute the whistler propagation time the base of the magnetosphere has been assumed at 900 km altitude where a model for the topside ionosphere, derived by Rycroft and Alexander (Alexander, 1971) has been adopted. In this model the fractional proton abundance at 900 km altitude was deduced from the proton cyclotron whistlers observed by the VLF receiver on board the Injun 3 satellite and the data fitted to a cubic polynomial in invariant latitude squared. Electron density, plasma temperature and oxygen ion fractional abundances were derived from data from the Alouette I satellite. Cubic TABLE 1. PARAMETER:P = A + BV + CW + DtV Parameter at 900 km altitude, P EIectron density, N (~rn-~) Plasma temperature, T (OK) Fractional hydrogen ion abundance, 7x+ Fractional oxygen ion abundance, r]o+ Fractional helium ion abundance, vHe+
Summer day
Winter night
A
B
C
D
A
+4 +3.921 $32
+1 -1.567 Ti.876
-1 +3.847
-4 -2.333
-3 +2-555 -4 -1.379 -8 +6.006
-10 -5.951 -8 +I*690 -12 -6.010
+4 +1.564 t2 +7.822 -1 +8.339
TIO+ =
exp (0.016606’ - 1.132)
rllief = 1 - (%i+ + qo+)
B 0 1-3.201 -2 +1.205 -5 -7.072
C -3 -4.949 -5 +4.592 -8 +1*817
D -7 +8*650 -11 +3*863 -12 -8.870
TO+ = exp (0.14686’ - 10.12) IjIIe+= 1 - (?Ia+ + rlo+)
Parameter values at 900 km altitude in the model ionospheres. In the first four rows, the lower figure in each block gives the value of the parameter multiplied by ten raised to the power of the upper figure. For example, the first entry in the table reads: N = +3.921 x 10+4. . . cm-*. 0’ is the geom. lat. (deg.) at 900 km altitude.
EFFECT OF THE RING CURRENT ON WHISTLER PROPAGATION
731
polynomials were fitted except for the oxygen abundance which is approximated by an exponential function. Two extreme models are used corresponding to the data obtained for the summer day (SD) and winter night (WN) ionosphere (Table 1). These extreme models probably encompass the normal diurnal, seasonal and secular variations in tube content (Carpenter, 1962b; Park, 1970). Since the dispersion of a whistler is particularly sensitive to conditions at the apogee of the field line along which it propagates, the comparison of the spectrum of a ‘ring current’ whistler with that of a ‘dipolar’ whistler is made by selecting pairs whose paths of propagation intersect the equatorial plane at the same distance. This is preferable to comparing those which propagate along field lines anchored on the earth’s surface at the same geomagnetic latitude. Figures 5 and 6 show the spectrogram of several one-hop whistlers for both the diffusive equilibrium and the colhsionless models and the corresponding ‘dipolar’ whistlers for comparison, In all cases, the ‘ring current’ whistlers are those which propagate along the field lines whose geomagnetic latitudes at 900 km are 52*5”, 55’, 58”, 60” and 61”. An upper cut-off frequency, at half the equatorial electron gyro-frequency, has been assumed. The values of the dispersion at the nose frequency (0, = &Z/S;;) of the ‘ring current’ and the ‘dipolar’ whistlers, for a wide range of nose frequency, are listed in Table 2, for the diffusive equilibrium and collisionless models respectively. It is observed that, in the equilibrium condition, only moderate changes in dispersion occur even for a large ring current. 4. DISCUSSION
The disto~ion of the field lines due to the presence of the ring current should be taken into account when interpreting the observed decrease in whistler dispersion. Figures 7 and 8 show the whistler nose frequency versus the equatorial distance of the corresponding path of propagation for the diffusive equilib~um and collisionless models respectively. Curves corresponding to the four ring current intensities and the dipole approximation are shown. It is observed that the use of the dipole approximation in determining the equatorial distance of the field line associated with a given nose frequency can lead to an error which may be as large as 0*6R,, Also, from Figs. 7 and 8 there is only a small difference between the summer day (SD) and winter night (WN). This is important since it is clearly possible to correct for the ring current effect, when determining the plasmapause position for an individual whistler event, without having a very precise knowledge of the ion densities and temperature at 900 km altitude. At a particular nose-frequency, the equatorial distance of the associated field line and the geomagnetic latitude at which it is anchored both decrease when the ring current energy increases. Clearly it is incorrect to assume that the nose-frequency may be used to identify a particular field line irrespective of the level of disturban~. The correct procedure therefore must be to include the distortion due to the ring current and hence to determine the tube content and equatorial electron density along the actual path of propagation i.e. along a field line anchored at a lower latitude with a smaller equatorial distance than the undisturbed field line yielding the same nose frequency. For example (Fig. 7a) forfn = 4 kl3z the equatorial intersection is reduced from 4.4R, for the dipole field to 3.8RE for ring current (d) corresponding to field lines anchored at geom. lat. 61.5” and 56.9’. From Table Z(b) the dispersion, L),, is reduced from 127 to 105 sec112for SD ionospheric conditions and a collisionless magnetosphere. Since the equatorial electron density is proportional to Dm2on an undisturbed field line this change in dispersion would be interpreted,
738
J. L. SAOREDO and K. BULLOUGH
-Z
-c
-.
J 0
EFFECT OF THE RING CURRENT
I
I
!
1
I
ON WHISTLER PROPAGATION
I
1
-L___-4’ I
N
I
I m
I
I
-a
I
739
I
N-
I
I (D
t
I *
I
740
J. L. SAGREDO
and K. BULLOUGH
EFFECT OF THE RING CURRENT ON WHISTLER PROPAGATION
I
I
/
I
-
1 I I __
1
I-l--
,
(;_Al --
d w
% &
r-7
---
--
-----
‘C/’
’
/
/
J. L. SAGREDO
742
and K. BULLOUGH
TASL~ 2(a). DJSPERSION OF WHALERS (SEC?/*)FOR A DIPPUSIVE EQUILIBRIUM MACJNETOSPHERE Ring current (keV cm-3 Dipole
3 4 z 7 8 9 10
320 256 215 190 170 155 143 133 162 127 108 96 89 8”: 77
E. = 150 64
E,,= 300 (b)
E,, = 600
cd
Summer day ionospheric conditions 279 310 320 250 230 262 216 200 228 180 190 206 174 165 197 155 161 171 143 149 155 134 140 143 Winter night ionospheric conditions 164 153 175 129 133 142 115 120 124 109 105 114 101 98 104 92 98 ;: 89 93 89 88 90
E,=900 (4 251 211 185 169 157 148 140 133 145 125 112 101 95 90 88 87
TABLE 2(b). DISPERSION OF WHISTLKRS (sEc"~) FOR A ~OLLISIONLESS MAQNETOSPHERE Ring current (keV cm-*) (kkz)
Dipole
E. = 150
E. = 300
E. = 600
E. = 900
(a)
(b)
(c)
(d)
Summer day ionospheric conditions 133 122 142 120 112 127 103 110 103 98 108 115
115 105 93 98
3 4 z
142 127 107 114
7 8 9 10
101 95 90 86
3
56
4 : :
48 43 40 39
48 45 43 40 41
46 44 42 40
44 42 41 39
f: 40 38
:;
40 39
39
38 39
38 39
1:
98 94 102 90 96 ;: 87 92 87 84 88 Winter night ionospheric conditions 51 48 54
90 87 84 82 46
on the assumption of a dipole field, as a one-third decrease in equatorial electron density. This is much smaller than the decrease of up to 4 to 1 during magnetic storms (Carpenter, 1962b). However, if, as seems probable-particularly in the evening sector-the field is inflated in a time short relative to the time constant for the establishment of diffusive equilibrium then the apparent decrease in electron density may be enhanced. For example, in the case cited above, the electron tube contents for the undisturbed dipole field and
EFFECT
OF THE RING r-m--
r7---.--
CURRENT , SD
/
1
I
I
J
5
6
7
EQUILlERlUM Conditions
1 4
3
Earth
FIG. 7(a). GRAPH CURRENT’
OF ~HETLER
WHISTLERS
(LIBRIUM
NOSE
) AND
FREQUENCY
‘DIPOLAR’
MODEL
AND
DIFFUSIVE WN
Ti
SD
VERSUS
WHISTLERS
radii EQUATORIAL
(-
IONOSPHERIC
- - -),
FOR
DISTANCE THB
FOR
DIFFUSIVE
kINQ BQUI-
CONDITIONS.
EQUILIBRIUM Conditions
-
zc Y
743
PROPAGATION /
I
DIFFUSIVE
L
ON WHISTLER
5-
,c
2-
\
/ _l._II FIG. 7(b). As
1
I
5
4
3 FIG.
7(a)
EXCEPT
m
Earth
radii
IONOSPHERIC
I
6
7
CONDITIONS.
field lines anchored at geom. lat. 61-5” and 56.9” are in the ratio of about 2.6: 1 for a SD ionosphere and diffusive equilibrium (Sagredo, 1971). This ratio may, of course, be greatly increased in the vicinity of the plasmapause. The dispersion of a whistler of given nose frequency is reduced by less than 20 per cent even for ring current (d) (see Table 2). This small reduction indicates that both the spectrum of the whistler and the ratio tn/fn are not very sensitive to the distortion of the magnetic
744
3. L. SAGREDO
and K. ~~LOUG~
I
I
I
I
COLLISIONLESS SD
PLASMA
Conditions
20-
‘1
10 z Y ,=
_ 5..
2
I
t
3
I
I
4
5
I 6 Earth
FIG.
8(a). AsFm7(a)~xcwr
20
WN
I 3
Fm.8(b).
I
!
4
As
FIG.
_--__J
I
radii
FORTHECGLLISIONLSSSMODEL.
Ccnditions
1
I 5
8(a)mc~pT WN
I
1
Earth
radii
.-.-L-..
6
--I 7
IONOSPHF!RICCONDITIONS.
field (see Figs. 5 and 6) and therefore it is not possible, from whistler analysis alone, to make a detailed study of temporal and spatial variations in the ring current. The nose frequency of a whistler, propagating along a field line which intersects the equatorial plane at a given distance, is very dependent upon the intensity of the ring current (see Figs. 7 and 8). This is of particular importance when mapping the position of the plasmapause in the equatorial plane. The approximation of the disturbed magnetic field
EFFECT OF THE RING CURRENT ON WHISTLER PROPAGATION
745
to a dipole field can lead to an over-estimation of as much as 0*6R, of the equatorial position of the plasmapause. For moderate disturbed periods (K, = 2-4), the mean position of the plasmapause in the equatorial plane is at 35R, and extends to 5R, in the evening bulge (Carpenter, 1966). Due to the distortion of the field lines, these distances should be corrected and reduced [using, for instance, ring current (b)] by O*lR, and O-JR, respectively. The discrepancy found between the position of the medium latitude electron-density trough and that of the plasmapause during disturbed periods can now be explained by considering the distortion of the fieId lines. Rycroft and Thomas (1970) observed a departure from perfect one-to-one correlation between the knee and the trough positions as KS takes on large values. The centre of the trough (position of minimum electron density at about 1000 km altitude) fell at a systematically lower L value (I,,) than the geocentric distance (R,) to the centre of the plasmapause (as deduced by Carpenter, 1966). For example it was found that, for K, = 4, L, = 3.5 and R, = 4.1 Earth radii. This discrepancy can clearly be explained by observing that, if the distortion of the field lines is taken into account, the equatorial position associated with the trough is further away from the Earth than it is in the dipole configuration. There is also supporting evidence in the work of Carpenter et al. (1968) who found a systematic small offset between the plasmapause position calculated from whistlers and the invariant latitude of the whistler cut-off or noise break-up observed on the low altitude satellites Alouette 1 and 2. They suggested that this offset might be due to a magnetospheric plasma current. ~c~~~~~e~ge~~~~-We are partic~arly indebted to Drs. C. Sozou and R. W. Windie for making the results of their ring current computation available and for helpful discussions, We are also grateful to Drs, M. J. Rycroft and P. D. Alexander for permission to reproduce Table 1. We also wish to thank Professor T. R. Kaiser for encouragement and advice and are grateful to Dr. D. L. Carpenter of Stanford University for helpful comments on the contents of this paper prior to submission for publication. One of us (J. L. S.) wishes to acknowledge financial support received from the Spanish National Commission for Space Research and the Spanish Ministry of Education and Science. REFERENCES AICASOFU, I. and CRAPMAN, S. (1961). The ring current, geomagnetic disturbance and the Van Allen radiation belts. J. geophys. Res. 66,1321. ALRXA~ER, P. D. (1971). Computation of ray paths for very low frequency radio waves propagat~g through the magnetospheric plasma. Ph.D. Thesis, University of Southampton. ANGERAMI,J. J. (1966). A whistler study of the distribution of thermal electrons in the magnetosphere. Tech. Rpt. No. 3412-7, Stanford El. Lab., Stanford Univ. ANGER, J. J. and CARPE~R, D. L. (1966). Whistler studies of the plasmapause in the ~~etospher~ 2; ebxtron density and total tube content near the knee in magnetospheric ionisation. J. geophys. Res. 71,711. BAUER,S. J. (1969). Diffusive equilibrium in the topside ionosphere. Proc. IEEE 57, 1114. CAHILL,L. J. JR. (1966). Inflation of the inner magnetosphere during a magnetic storm. J. geophys. Res. 71,450X CARPENTER, D. L. (1962a). New ex~rimentaI evidence of the effect of magnetic storms on the magnetosphere. J. geaphys. Res. 67, 135. C~PE~R, D. L. (1962b). Electron-density variations in the magnetosphere deduced from whistler data. J. geophys. Res. 67,334s. CARPENTER, D. L. (1966). Whistler studies of the plasmapause in the ma~etosphere; temporal variations in the position of the knee and some evidence on plasma motions near the knee. J. geophys. Res. 71,693. CARPENTER, D. L., WALTER,F., BARRINGTON, R. E. and MCEWEN,D. J. (1968). Alouette 1 and 2 observations of abrupt changes in whistler rate and of VLF noise variations at the plasmapause-a satellite ground study. J. geophys. Res. 73,2929. CHAPMAN, S. and FERRARO, V. C. A. (1931,1932, 1933). A new theory of magnetic storms. Terr. Magn, atmos. Elect. 36,77,171; 37,147,421; 38,79. CHAPMAN, S., I&NDALX,, P. C., SWARTZTRAIJEIER, P. N. and W~NDLB,D. W. (1968). The magnetic field and energy of an axisymmetric Van Alien belt. Geophys. J. R. as&. Sot. 15, 317.
746
J. L. SAGREDO
and K. BULLOUGH
CORNWALL,J. M., C~RONITI,F. V. and THORNE, R. M. (1970). Turbulent loss of ring current protons. Rep. R59 Plasma Physics Group, Department of Physics, University of California. FRANK, L. A. (1967). On the extraterrestrial ring current during geomagnetic storms. J.geophys. Res. 72, 3753. FRANK, L. A. (1969). Direct detection of the asymmetric injection of extraterrestrial ‘ring current’ protons. Res. Rep. 69-39 University of Iowa. KENDALL, P. C., CHAPMAN,S., AKASOPU,S.-I. and SWARTZTRALJBER, P. N. (1966). The computation of the magnetic field of any axisymmetric current distribution-with magnetospheric applications. Geophys. J. R. astr. Sot. 11,349. LIKHTER,YA. I. and MOLCHANOV,0. A. (1968). Change in whistler characteristics in the disturbed magnetic field of the magnetosphere. Geomag. Aeronomy 8,899. MOLCHANOV,0. A. (1968). Structure of the magnetic field in the magnetosphere during the recovery phase of a magnetic storm. Geomag. Aeronomy 8,868. PARK, C. G. (1970). Whistler observations of the interchange of ionisation between the ionosphere and the protonosphere. J. geophys. Res. 75,4249. PARKER,E. N. (1957). Newtonian development of the hydromagnetic properties of ionised gases of low density. Phys. Rev. 107, 924. RYCROPT, M. J. and THOMAS,J. 0. (1970). The magnetospheric plasmapause and the electron density trough at the Alouette I orbit. Planet. Space Sci. 18, 65. SAGREDO,J. L. (1971). VLF goniometer observations at Halley Bay, Antarctica, and the effect of the ring current on whistler propagation in the magnetosphere. Ph.D. Thesis, University of Sheffield. SINGER, S. F. (1957). Trans. Am. Geophys. Un. 38,175. Sozou, C. and WINDLE, D. W. (1969a). A self consistent ring current in the Earth’s dipole field. Planet. Space Sci. 17, 375. Sozou, C. and WINDLE,D. W. (1969b). Non-linear symmetric inflation of a magnetic dipole. Planet. Space Sci. 17, 999. SPRJGTER, J. R. and BRIGOS,B. K. (1962). Analysis of the effect of a ring current on whistlers. J. geophys. Res. 67, 3779. SWISHER,R. L. and FRANK, L. A. (1968). Lifetimes for low-energy protons in the outer radiation zone. J. geophys. Res. 73, 5665. VAN ALLEN, J. A. and FRANK, L. A. (1959). Survey of radiation around the earth to a distance of 107,400 km. Nature 183,430. VAN ALLEN,J.A.,LUDWIG, G. H., RAY, E. C. and MCILWAIN, C. E. (1958). Observations of high intensity radiation by satellites 1958 Alpha and Gamma. IG Y Bdl. 39,767.
to 746.
permmon
Press. Printed in Northern Ireland
THE EFFECT OF THE RING CURRENT ON WHISTLER PROPAGATION IN THE MAGNETOSPHERE J. L. SACRED0 and K. BULLOUGI-I Physics Department, University of Sheffield, Sheffield, England (Received 26 November 1971)
Abatraet-The propagation of whistlers in a disturbed ~~et~p~~ is studied. The disturbance is that produced by a ring of charged particles encircling the Barth with a maximum in energy density at three earth radii. The ring current model adopted (Sozou and Wmdle, I969a, 1969b) takes into account the self-effect of the magnetic field of the ring current particles in their own motion. It is found that the presence of the ring current changes both the nose frequency, $, and the travel time at the nose frequency, tn, of a whistler. The distortion of the magnetic field alters the relationship between thef. of a whistler, the equatorial distance of its path of propagation and the geomagnetic latitude at which the field line is anchored. It is shown that this may account,-at leas? in part, for the apparent decrease in electron density during disturbed periods deduced from whistler analysis bv Carnenter 0962a). In addition. account should be taken of the effect of field line d~t~~ion,whe~ determining the location of the knee during disturbed periods. Thus, the discrepancy found by Rycroft and Thomas (1970) between the position of the medium latitude trough and that, determined from whistler analysis, of the plasmapause is probably due to this effect. 1. INTRODUCPION
In most whistler studies, the Earth’s magnetic field is approximated by a perfect dipole. This assumption represents an adequate approximation to the Earth’s magnetic field for ~gnetically quiet periods. During geomagnetic storms, however, the Earth’s magnetic field deep within the magnetosphere departs from a dipole field by a substantial amount due to the injection, during the main phase of the storm, of a body of charged particles deep into the magnetosphere, near the equatorial plane. The injected particles become trapped in the Earth’s magnetic field and drift in longitude across the L-shells, producing a ring current which encircles the Earth. This ring current becomes axisymmetric in a period of the order of 12 hr and then slowly decays during the recovery phase of the geomagnetic storm. The purpose of this paper is to present the results of an investigation into the propagation of whistlers in a disturbed magnetosphere such as that existing during the recovery phase of a geomagnetic storm when the ring current slowly decays during a period of one day or more and hence a quasi-stationary situation can be assumed. The first suggestion of the existence of a ring current encircling the Earth at several earth radii equatorial distance was made by Chapman and Ferraro (193111933). They attributed the observed depression of the Earth’s magnetic field at the Earth’s surface during the development of a geomagnetic storm to the existence of a ring current. The discovery of belts of charged particles in the Earth’s magnetic field (Van Allen et aI,, 1958; Van Allen and Frank, 1959), confirmed predictions by Singer (1957) arising from the work of Chapman and Ferraro. Cahill (1966) studied the development of the ring current during two geomagnetic storms from data provided by the magnetometer on board the Explorer 26 satellite. He was able to determine the rates of growth and decay. During the main phase of the storm an asymmetric ring current was formed, caused by a body of charged particles injected into the evening sector of the magnetosphere. During the recovery phase the ring current 731
732
J. L. SAGREDO
and
K. BULLOUGH
became axisymmetric and was centred at 3*5RE in the equatorial plane. By measurement of both the inclination and declination of the magnetic field it was deduced that, during the symmetric period of the storm, the magnetic field lines were stretched away from the Earth. The drift period of the injected particles was deduced and their energy estimated to be less than 100 keV. A more detailed analysis of the energy spectrum of the particles which constitute the ring current has been made by Frank (1967, 1969) from data from the OGO 3 satellite. It was found that the energy density of the ring current was predominantly shared by protons in the energy range 3-50 keV. For the magnetic storm of July 9 1966, the peak proton energy density at the equator varied from 9 x 10-s erg cm-3 at L = 6.8 (pre-storm quiet conditions) to 5 x lo-’ erg cm-3 at L = 3.3 (storm main phase), while at L ‘u 7 the energy density changed only slightly throughout the whole development of the storm. Previous theoretical studies of whistler propagation in a disturbed magnetosphere include that of Spreiter and Briggs (1962) who considered a simple ring current model of infinitesimal cross-section and used a ‘gyrofrequency’ model (N ccfH) for the distribution of ionisation along the field lines. Molchanov (1968) has developed a model of the disturbed magnetosphere in which both the currents at the outer boundary of the magnetosphere due to the flow of the solar wind and the currents in the magnetospheric tail have been included. The inflation of the magnetic field is symmetric up to about 5 earth radii but beyond 6 earth radii the field lines are compressed on the dayside of the magnetosphere. Likhter and Molchanov (1968) subsequently studied whistler propagation for this model assuming a ‘gyrofrequency’ model of the ionisation distribution. They found, like ourselves, an increase in the travel time at the nose frequency, and, a decrease in the nose frequency for propagation along a field line anchored at a particular geomagnetic latitude. 2. THE
RING
CURRENT
MODEL
Several studies have attempted to describe, theoretically, the perturbation of the Earth’s magnetic field due to the presence of a ring current axisymmetric with respect to the dipole field. In most of the works, a gaussian distribution of charged particles in the equatorial plane is assumed and the current produced by their drift across the L-shells is deduced from the theory, developed by Parker (1957), which describes the behaviour of a plasma permeated by a magnetic field. In the linear case, charged particles in a stationary radiation belt move under the influence of the dipole field alone, i.e. the self-effect of the magnetic field of the particle belt is ignored, This case has been investigated by Akasofu and Chapman (1961) and Kendall et al. (1966). The model adopted in the present work has been derived by Sozou and Windle (1969a, 1969b). In this model, the energetic particles move in the combined field of the Earth’s dipole and the field due to the currents of the particle motions in the combined field. The number density distribution of particles at the geomagnetic equator is given by n,,(R)
= n, exp [-k2(R
-
RJ2]
(1)
where R is the geomagnetic distance in earth radii, n, the peak number density (at R,,), and k a constant. The values considered were, R, = 3 k = 2.99 k = 0.419
for for
R<3 R > 3.
EFFECT
OF THE RING
CURRENT
ON HISSER
PROPAGA~ON
733
The components in the I and 3 directions of the total. magnetic field can be expressed in terms of the magnetic stream function Y? (Kendall et al., 1966) by,
(2) (3) andY,
expressed in terms of spherical harmonics, is Yp = 7
+ B%rA,(r)P,‘(sin
where M is the moment of the Earth’s dipole field, magnetic latitude, and
F
0) cos 6
the geocentric distance, 8 the gee-
where P, is the Legendre polynomial of degree n and x = sin 8, The computation of A, (n = 1,2,3, . . .) IS * p er formed by successive iteration, equating the current density, 3, given by
to the current due to the gyration of the particles round the lines of force and to their drift across the magnetic field (Sozou and Windle, 1969a). Following Sozou and Windle (1969a), it is assumed that the stream function Y may be approximated by the first eight non-vanishing terms of the series (4) and that both the particle and current densities are zero outside the region 1 < A < 10. Following Chapman et al. (1968) and Sozou and Windle (1969b), a set of different values for the peak kinetic energy density of the particles is considered. These are, (a) (b) (c) (d)
E. = E, = E. = E,, =
150 keV 300 keV 600 keV 900 keV
cm-s cm-3 cm-3 cm-s.
Case (a) is representative while case (d) represents a distribution at the equatorial storm of moderate intensity 1967).
of a ring current generated during a weak geomagnetic storm, very severe one. Figure I shows the kinetic energy density plane for cases (a)-(d) together with that for the geomagnetic on July 9 1966, as determined from the OGO 3 data (Frank,
The depression of the Earth’s magnetic field in the equatorial plane is shown in Fig. 2 for all the cases (a)-(d). At the Earth’s magnetic equator, the depression, BsT, varies from -25~ for & = 150 keV cm3 to - 1287 for E,, = 900 keV cmA, The geometry of the magnetic field is illustrated in Fig, 3 where several field lines are shown together with the corresponding dipolar geld lines anchored on the Earth’s surface at the same geomagnetic latitude. The distortion of the field lines is also depicted in Fig. 4, 7
734
J. L. SAGREDO
c
I
I
3
I
and K. BULLOUGH
I
5
1
I
I
7
,
9 Earth radii
Fro. 1. ENEMY DENSITY OF THE RINQ CURRENT PARTWLESIN SHOWN
THJIEQUATORIAL PLANE. hii0 IS THE ENERGY DENSITY DWIRIBIJTION OF THE RING CURRENT PARTICLES DIJRINC3THE ~~OMA~~~STORM~F JULY91966.
5'1
0 s z 4 -50
-100
-150
-ml
Fm.2.
MACWHTCPIELD,
AB,OPTHE RIN~CURRENTINTHEEQUATORIALPLANB(~R AND WINDLE,1969b).
Sozou
EFFECT
OF THE RING
CURREMT
ON WHISTLER
PROPAGATION
135
1
1
2
3
L
5
6 Earth
FX3.
3.
bLD
LINES
OF THE TOTAL
MAGNETIC FIELD
c
FIELD
AND
THE CORRl?.WONDING
DIPOLE
(----).
I -I
Equatorial FIG.
( -)
I
radii
4.
ORDINATE: SPONDING
GEOMAGNETIC J%‘ALUE.
LATITUDE hSCISSA:
dislancr
(earth
radii)
OF THE FOOT OF THE FIELD EQUATORIAL
DISTANCE
LINE
AND
ITS IXRRE-
OF FTELD LINE.
where the geomagnetic latitude of the foot of the field line and its corresponding L-value is plotted versus the equatorial distance. The straight line corresponds to the dipole field and it is observed that the departure from dipole configuration increases with the energy of the ring current. Up to about L = 3 there is no significant variation in the geometry of the field. 3. WHISTLER
PROPAGATION
A study of the propagation of whistlers in the disturbed magnetosphere, described above, has been carried out. The usual approximations adopted in whistler propagation, such as that of a cold plasma and strictly longitudinal propagation, have been adopted here.
J. L. SAGREDO
736
and K. BULLOUGH
Two models of the distribution of the neutral plasma along the field lines have been considered (Angerami and Carpenter, 1966; Angerami, 1966; Sagredo, 1971): (i) Inside the plasmapause, a diffusive equilibrium model where the magnetospheric plasma, composed of electrons and Of, He+ and H+ ions, is controlled by diffusion processes along the field lines; (ii) beyond the plasmapause, the electron density distribution corresponds to that of a collisionless plasma of protons and electrons. On low L shells the model of a disturbed magnetosphere in diffusive equilibrium and a steady ring current is open to criticism. Thus, Park (1970) has found evidence, from whistler observations, that the protonosphere is probably never fully in equilibrium with the ionosphere but, for most of the time, is recovering from depletion which occurred during previous magnetic disturbances. Clearly, the deviation from equilibrium will depend on the relative magnitudes of the lifetime of the ring current particles against precipitation and the time constant for the establishment of diffusive equilibrium. Thus the observed lifetime of the ring current particles is about 3-4 days at L = 5 and 1 day at L = 3.5 (Swisher and Frank, 1968) while the diffusion time of the ambient particles along the field lines is of the order of 1 day (Bauer, 1969). Inside the plasmapause the lifetime of the ring current may be as little as 1 hr due to rapid ion-cyclotron precipitation (Cornwall et al., 1970). These lifetimes and diffusion times may be compared to the longitudinal drift period of the ring current protons which is a few hours and, of course, the 24 hr diurnal variation in the upper ionosphere and the plasmapause location. According to Carpenter (private communication) during storms when DST I -50~ the plasmapause is usually near or inside L = 3. In the region of the evening bulge near 1800 L.T. the plasmapause is not usually well defined in the ground data. To compute the whistler propagation time the base of the magnetosphere has been assumed at 900 km altitude where a model for the topside ionosphere, derived by Rycroft and Alexander (Alexander, 1971) has been adopted. In this model the fractional proton abundance at 900 km altitude was deduced from the proton cyclotron whistlers observed by the VLF receiver on board the Injun 3 satellite and the data fitted to a cubic polynomial in invariant latitude squared. Electron density, plasma temperature and oxygen ion fractional abundances were derived from data from the Alouette I satellite. Cubic TABLE 1. PARAMETER:P = A + BV + CW + DtV Parameter at 900 km altitude, P EIectron density, N (~rn-~) Plasma temperature, T (OK) Fractional hydrogen ion abundance, 7x+ Fractional oxygen ion abundance, r]o+ Fractional helium ion abundance, vHe+
Summer day
Winter night
A
B
C
D
A
+4 +3.921 $32
+1 -1.567 Ti.876
-1 +3.847
-4 -2.333
-3 +2-555 -4 -1.379 -8 +6.006
-10 -5.951 -8 +I*690 -12 -6.010
+4 +1.564 t2 +7.822 -1 +8.339
TIO+ =
exp (0.016606’ - 1.132)
rllief = 1 - (%i+ + qo+)
B 0 1-3.201 -2 +1.205 -5 -7.072
C -3 -4.949 -5 +4.592 -8 +1*817
D -7 +8*650 -11 +3*863 -12 -8.870
TO+ = exp (0.14686’ - 10.12) IjIIe+= 1 - (?Ia+ + rlo+)
Parameter values at 900 km altitude in the model ionospheres. In the first four rows, the lower figure in each block gives the value of the parameter multiplied by ten raised to the power of the upper figure. For example, the first entry in the table reads: N = +3.921 x 10+4. . . cm-*. 0’ is the geom. lat. (deg.) at 900 km altitude.
EFFECT OF THE RING CURRENT ON WHISTLER PROPAGATION
731
polynomials were fitted except for the oxygen abundance which is approximated by an exponential function. Two extreme models are used corresponding to the data obtained for the summer day (SD) and winter night (WN) ionosphere (Table 1). These extreme models probably encompass the normal diurnal, seasonal and secular variations in tube content (Carpenter, 1962b; Park, 1970). Since the dispersion of a whistler is particularly sensitive to conditions at the apogee of the field line along which it propagates, the comparison of the spectrum of a ‘ring current’ whistler with that of a ‘dipolar’ whistler is made by selecting pairs whose paths of propagation intersect the equatorial plane at the same distance. This is preferable to comparing those which propagate along field lines anchored on the earth’s surface at the same geomagnetic latitude. Figures 5 and 6 show the spectrogram of several one-hop whistlers for both the diffusive equilibrium and the colhsionless models and the corresponding ‘dipolar’ whistlers for comparison, In all cases, the ‘ring current’ whistlers are those which propagate along the field lines whose geomagnetic latitudes at 900 km are 52*5”, 55’, 58”, 60” and 61”. An upper cut-off frequency, at half the equatorial electron gyro-frequency, has been assumed. The values of the dispersion at the nose frequency (0, = &Z/S;;) of the ‘ring current’ and the ‘dipolar’ whistlers, for a wide range of nose frequency, are listed in Table 2, for the diffusive equilibrium and collisionless models respectively. It is observed that, in the equilibrium condition, only moderate changes in dispersion occur even for a large ring current. 4. DISCUSSION
The disto~ion of the field lines due to the presence of the ring current should be taken into account when interpreting the observed decrease in whistler dispersion. Figures 7 and 8 show the whistler nose frequency versus the equatorial distance of the corresponding path of propagation for the diffusive equilib~um and collisionless models respectively. Curves corresponding to the four ring current intensities and the dipole approximation are shown. It is observed that the use of the dipole approximation in determining the equatorial distance of the field line associated with a given nose frequency can lead to an error which may be as large as 0*6R,, Also, from Figs. 7 and 8 there is only a small difference between the summer day (SD) and winter night (WN). This is important since it is clearly possible to correct for the ring current effect, when determining the plasmapause position for an individual whistler event, without having a very precise knowledge of the ion densities and temperature at 900 km altitude. At a particular nose-frequency, the equatorial distance of the associated field line and the geomagnetic latitude at which it is anchored both decrease when the ring current energy increases. Clearly it is incorrect to assume that the nose-frequency may be used to identify a particular field line irrespective of the level of disturban~. The correct procedure therefore must be to include the distortion due to the ring current and hence to determine the tube content and equatorial electron density along the actual path of propagation i.e. along a field line anchored at a lower latitude with a smaller equatorial distance than the undisturbed field line yielding the same nose frequency. For example (Fig. 7a) forfn = 4 kl3z the equatorial intersection is reduced from 4.4R, for the dipole field to 3.8RE for ring current (d) corresponding to field lines anchored at geom. lat. 61.5” and 56.9’. From Table Z(b) the dispersion, L),, is reduced from 127 to 105 sec112for SD ionospheric conditions and a collisionless magnetosphere. Since the equatorial electron density is proportional to Dm2on an undisturbed field line this change in dispersion would be interpreted,
738
J. L. SAOREDO and K. BULLOUGH
-Z
-c
-.
J 0
EFFECT OF THE RING CURRENT
I
I
!
1
I
ON WHISTLER PROPAGATION
I
1
-L___-4’ I
N
I
I m
I
I
-a
I
739
I
N-
I
I (D
t
I *
I
740
J. L. SAGREDO
and K. BULLOUGH
EFFECT OF THE RING CURRENT ON WHISTLER PROPAGATION
I
I
/
I
-
1 I I __
1
I-l--
,
(;_Al --
d w
% &
r-7
---
--
-----
‘C/’
’
/
/
J. L. SAGREDO
742
and K. BULLOUGH
TASL~ 2(a). DJSPERSION OF WHALERS (SEC?/*)FOR A DIPPUSIVE EQUILIBRIUM MACJNETOSPHERE Ring current (keV cm-3 Dipole
3 4 z 7 8 9 10
320 256 215 190 170 155 143 133 162 127 108 96 89 8”: 77
E. = 150 64
E,,= 300 (b)
E,, = 600
cd
Summer day ionospheric conditions 279 310 320 250 230 262 216 200 228 180 190 206 174 165 197 155 161 171 143 149 155 134 140 143 Winter night ionospheric conditions 164 153 175 129 133 142 115 120 124 109 105 114 101 98 104 92 98 ;: 89 93 89 88 90
E,=900 (4 251 211 185 169 157 148 140 133 145 125 112 101 95 90 88 87
TABLE 2(b). DISPERSION OF WHISTLKRS (sEc"~) FOR A ~OLLISIONLESS MAQNETOSPHERE Ring current (keV cm-*) (kkz)
Dipole
E. = 150
E. = 300
E. = 600
E. = 900
(a)
(b)
(c)
(d)
Summer day ionospheric conditions 133 122 142 120 112 127 103 110 103 98 108 115
115 105 93 98
3 4 z
142 127 107 114
7 8 9 10
101 95 90 86
3
56
4 : :
48 43 40 39
48 45 43 40 41
46 44 42 40
44 42 41 39
f: 40 38
:;
40 39
39
38 39
38 39
1:
98 94 102 90 96 ;: 87 92 87 84 88 Winter night ionospheric conditions 51 48 54
90 87 84 82 46
on the assumption of a dipole field, as a one-third decrease in equatorial electron density. This is much smaller than the decrease of up to 4 to 1 during magnetic storms (Carpenter, 1962b). However, if, as seems probable-particularly in the evening sector-the field is inflated in a time short relative to the time constant for the establishment of diffusive equilibrium then the apparent decrease in electron density may be enhanced. For example, in the case cited above, the electron tube contents for the undisturbed dipole field and
EFFECT
OF THE RING r-m--
r7---.--
CURRENT , SD
/
1
I
I
J
5
6
7
EQUILlERlUM Conditions
1 4
3
Earth
FIG. 7(a). GRAPH CURRENT’
OF ~HETLER
WHISTLERS
(LIBRIUM
NOSE
) AND
FREQUENCY
‘DIPOLAR’
MODEL
AND
DIFFUSIVE WN
Ti
SD
VERSUS
WHISTLERS
radii EQUATORIAL
(-
IONOSPHERIC
- - -),
FOR
DISTANCE THB
FOR
DIFFUSIVE
kINQ BQUI-
CONDITIONS.
EQUILIBRIUM Conditions
-
zc Y
743
PROPAGATION /
I
DIFFUSIVE
L
ON WHISTLER
5-
,c
2-
\
/ _l._II FIG. 7(b). As
1
I
5
4
3 FIG.
7(a)
EXCEPT
m
Earth
radii
IONOSPHERIC
I
6
7
CONDITIONS.
field lines anchored at geom. lat. 61-5” and 56.9” are in the ratio of about 2.6: 1 for a SD ionosphere and diffusive equilibrium (Sagredo, 1971). This ratio may, of course, be greatly increased in the vicinity of the plasmapause. The dispersion of a whistler of given nose frequency is reduced by less than 20 per cent even for ring current (d) (see Table 2). This small reduction indicates that both the spectrum of the whistler and the ratio tn/fn are not very sensitive to the distortion of the magnetic
744
3. L. SAGREDO
and K. ~~LOUG~
I
I
I
I
COLLISIONLESS SD
PLASMA
Conditions
20-
‘1
10 z Y ,=
_ 5..
2
I
t
3
I
I
4
5
I 6 Earth
FIG.
8(a). AsFm7(a)~xcwr
20
WN
I 3
Fm.8(b).
I
!
4
As
FIG.
_--__J
I
radii
FORTHECGLLISIONLSSSMODEL.
Ccnditions
1
I 5
8(a)mc~pT WN
I
1
Earth
radii
.-.-L-..
6
--I 7
IONOSPHF!RICCONDITIONS.
field (see Figs. 5 and 6) and therefore it is not possible, from whistler analysis alone, to make a detailed study of temporal and spatial variations in the ring current. The nose frequency of a whistler, propagating along a field line which intersects the equatorial plane at a given distance, is very dependent upon the intensity of the ring current (see Figs. 7 and 8). This is of particular importance when mapping the position of the plasmapause in the equatorial plane. The approximation of the disturbed magnetic field
EFFECT OF THE RING CURRENT ON WHISTLER PROPAGATION
745
to a dipole field can lead to an over-estimation of as much as 0*6R, of the equatorial position of the plasmapause. For moderate disturbed periods (K, = 2-4), the mean position of the plasmapause in the equatorial plane is at 35R, and extends to 5R, in the evening bulge (Carpenter, 1966). Due to the distortion of the field lines, these distances should be corrected and reduced [using, for instance, ring current (b)] by O*lR, and O-JR, respectively. The discrepancy found between the position of the medium latitude electron-density trough and that of the plasmapause during disturbed periods can now be explained by considering the distortion of the fieId lines. Rycroft and Thomas (1970) observed a departure from perfect one-to-one correlation between the knee and the trough positions as KS takes on large values. The centre of the trough (position of minimum electron density at about 1000 km altitude) fell at a systematically lower L value (I,,) than the geocentric distance (R,) to the centre of the plasmapause (as deduced by Carpenter, 1966). For example it was found that, for K, = 4, L, = 3.5 and R, = 4.1 Earth radii. This discrepancy can clearly be explained by observing that, if the distortion of the field lines is taken into account, the equatorial position associated with the trough is further away from the Earth than it is in the dipole configuration. There is also supporting evidence in the work of Carpenter et al. (1968) who found a systematic small offset between the plasmapause position calculated from whistlers and the invariant latitude of the whistler cut-off or noise break-up observed on the low altitude satellites Alouette 1 and 2. They suggested that this offset might be due to a magnetospheric plasma current. ~c~~~~~e~ge~~~~-We are partic~arly indebted to Drs. C. Sozou and R. W. Windie for making the results of their ring current computation available and for helpful discussions, We are also grateful to Drs, M. J. Rycroft and P. D. Alexander for permission to reproduce Table 1. We also wish to thank Professor T. R. Kaiser for encouragement and advice and are grateful to Dr. D. L. Carpenter of Stanford University for helpful comments on the contents of this paper prior to submission for publication. One of us (J. L. S.) wishes to acknowledge financial support received from the Spanish National Commission for Space Research and the Spanish Ministry of Education and Science. REFERENCES AICASOFU, I. and CRAPMAN, S. (1961). The ring current, geomagnetic disturbance and the Van Allen radiation belts. J. geophys. Res. 66,1321. ALRXA~ER, P. D. (1971). Computation of ray paths for very low frequency radio waves propagat~g through the magnetospheric plasma. Ph.D. Thesis, University of Southampton. ANGERAMI,J. J. (1966). A whistler study of the distribution of thermal electrons in the magnetosphere. Tech. Rpt. No. 3412-7, Stanford El. Lab., Stanford Univ. ANGER, J. J. and CARPE~R, D. L. (1966). Whistler studies of the plasmapause in the ~~etospher~ 2; ebxtron density and total tube content near the knee in magnetospheric ionisation. J. geophys. Res. 71,711. BAUER,S. J. (1969). Diffusive equilibrium in the topside ionosphere. Proc. IEEE 57, 1114. CAHILL,L. J. JR. (1966). Inflation of the inner magnetosphere during a magnetic storm. J. geophys. Res. 71,450X CARPENTER, D. L. (1962a). New ex~rimentaI evidence of the effect of magnetic storms on the magnetosphere. J. geaphys. Res. 67, 135. C~PE~R, D. L. (1962b). Electron-density variations in the magnetosphere deduced from whistler data. J. geophys. Res. 67,334s. CARPENTER, D. L. (1966). Whistler studies of the plasmapause in the ma~etosphere; temporal variations in the position of the knee and some evidence on plasma motions near the knee. J. geophys. Res. 71,693. CARPENTER, D. L., WALTER,F., BARRINGTON, R. E. and MCEWEN,D. J. (1968). Alouette 1 and 2 observations of abrupt changes in whistler rate and of VLF noise variations at the plasmapause-a satellite ground study. J. geophys. Res. 73,2929. CHAPMAN, S. and FERRARO, V. C. A. (1931,1932, 1933). A new theory of magnetic storms. Terr. Magn, atmos. Elect. 36,77,171; 37,147,421; 38,79. CHAPMAN, S., I&NDALX,, P. C., SWARTZTRAIJEIER, P. N. and W~NDLB,D. W. (1968). The magnetic field and energy of an axisymmetric Van Alien belt. Geophys. J. R. as&. Sot. 15, 317.
746
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