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Plane? Spacr Sci., Vol. 32, No. 8, pp. 975-984, Printed in Great Britain.

1984

0032&O633/84$3.00+0.00 Pergamon Press Ltd.

RING CURRENT SIMULATION IN CONNECTION INTERPLANETARY SPACE CONDITIONS
Y. I. FELDSTEIN Academgorodok, Moscow Region, U.S.S.R

WITH

IZMIRAN,

Institute

V. YU. PISARSKY and N. M. RUDNEVA of Applied Geophysics, Goscomhydromet, Moscow,

U.S.S.R.

Zentralinstitut

A. GRAFE Solar-Terrestrische Physik, DDR 1199, Berlin 1983) on the Earth's

(Receioed injinalform 20 December

Abstract-A ring current model has been obtained which permits calculations of D,, variations surface during magnetic storms. The changes in D,, are described by the equation

$

B,,, = F(EM) - +

where B,,, = D,,-bp"* +c"; p = tnd is solar wind pressure; F(EM) is the function, controlled by the electromagnetic parameters of interplanetary medium, of injection into ring current ; Tis the constant of ring current decay. c = C-rrp = 18 nT, where C is the level of the D,,-variation field measurements; 4" is the injection function characterizing the quasisteady-state injection of energy into the ring-current region. The constant c is determined from the condition that the change of the ring current energy from magnetic storm commencement to end should equal the difference between the injected and dissipated energy throughout the storm. The values of the factors b and z were found by the method of minimizing the sum of the quadratic deviations of the calculated D,, from the values observed throughout the storm : h = 0.23 nT/(eV cm- 3)1'2, 5 = 8.2 h at D,, > - 55 nT and 5 = 5.8 h at - 120 < D,, < - 55 nT. The injection function F(EM) is of the form F(EM) = d(E,- A) at the values of the azimuthal component of the solar wind electric field E, > A, and F(EA4) = Oat A > E,.d = - 1.2 x 10-3nTs-`(mV/m)~`andA = -0.9mVm-`.Thus,theinjectiontoring current is possible at the northward E, component of the IMF.

1. INTRODUCTION

The existence of the magnetospheric ring current and its relevance to geomagnetic field variations during magnetospheric storms have been confirmed by numerous experimental data and theoretical calculations (Akasofu and Chapman, 1972; Nishida, 1978). However, the energy sources and the mechanisms of plasma injection into the ring current have not been determined yet (Williams, 1981 ; Kamide, 1980). According to Rostoker and Falthammer (1967), Russell and McPherron (1973), Burton et al. (1975), Kamide (1980),Hareleta1.(1981), Wolfetal.(1982), thesupplyof plasma to the ring current is due to penetration of the solar wind electric field E = I/ x Bs (V is solar wind velocity, Bs is the southward (B, < 0) component of IMF) into the magnetosphere and subsequent plasma motion from the magnetotail plasma sheet to the ring current. According to Akasofu (1978), the supply of energy to the ring current is relevant to the function E depending on the value of the Poynting vector in solar wind.
975

The ring current geomagnetic effect averaged over low-latitude observatories is described by the D,,-index after subtracting from the latter the magnetic field of currents on the magnetopause (Burton et al., 1975)
DR = D,,, = D,,where p = nm V2 is the dynamic bp"' -I-C (1)

pressure of solar wind ; h is a constant characterizing the relation between P and D,, ; C is the level of D,,-variation measurement on a given magnetically quiet day. The relation of DR to the total energy of particles U, in a closed magnetosphere and to the total energy of the Earth's magnetic field over the Earth's surface U, is given by the following simple expression : DR(nT) = ROg m where B, is the intensity of the Earth's magnetic field at the Equator (Dessler and Parker, 1959). If the D,-index is used, the energy balance equation for the ring current takes the following form (Akasofu and Chapman, 1972 ; = 2.5*1O-"U, (erg)


916 Burton et al., 1975; Akasofu, 1981a):

Y.

I. FELDSTEIN al. et

$

D,,, = F(EM) - +-

where D,,, is found from (1); F(EM) is the rate of energy supply to the ring current (the injection function) controlled by the electromagnetic parameters of interplanetary medium ; z is a constant of ring current decay. The decay is assumed to follow an exponential law. The D,,-variation was simulated at different injection functions F(EM) and values of the factors z, b, c by Burton et al. (1975), Akasofu (1981b), Bobrov (1981), Murayama (1982a, b). It is known that in magnetically quiet periods the ring current fails to dissipate completely and that its magnetic effect (DR,) takes on the value -20 nT > DR, > -40 nT (Hoffman and Bracken, 1965; Schield, 1969; Porchkhidze and Feldstein, 1979). There should exist, therefore, an injection into the ring current cpOwhich will balance its dissipation in quiet periods. In this paper, D,, and DR are simulated on the basis of equation (2) with the following modifications compared with the earlier works : (1) A constant injection to the ring current cp (such injection was designated cpO above for the magnetically quiet periods) was included. (2) A new form of the function F(EM) was determined at which the relation (2) permits D,, to be approximated to within a high accuracy. (3) The decay constant z was assumed to be variable throughout a storm. Allowance was made in the simulation for the requirement that the difference between the injected and dissipated energies throughout a storm should equal the ring current energy variation which was measured by the difference between the values of D,, prior to the commencement and immediately after a storm. The condition of the minimum value of 6, the sum of the deviations of the calculated D,, from the observed values, was used as criterion of determination of the model parameters.

the plasma parameters were interpolated to intervals of durations not exceeding 6 min. The values of D,, were determined with a 2.5-min resolution from the magnetograms of 11 middlelatitude observations which were used in Burton et al. (1975) to find D,,. The geomagnetic field variations recorded on 31 January 1967 were taken to be the D,,-variation measurement level.

3. QUASISTEADY-STATE RING CURRENT

The ring current which satisfies the conditions ;(D,,-bp1~2) = 0; F(EM) = 0;

AE < 100 nT;

ID,1 < 10 nT

(3)

2. INITIAL DATA

We used the following solar wind parameters averaged over a 163 s interval: the velocity, V and density, n, of solar wind and the IMF component B, inferred from the Explorer-33 data. The observation results were kindly granted by WDC-A (principal investigators : in plasma J. Binsack, in IMF N. Ness). During two magnetic storms of February 1967 examined below, the interplanetary data were sufficiently comprehensive, and the values of the field and

during a period of at least 3-5 h will be called quiet quasisteady-state ring current. The conditions (3) are satisfied rather frequently. When they are realized, the ring current delay is obviously compensated by the injection whose nature differs from that adopted in Burton et al. (1975), Akasofu (1981b), Bobrov (1981) and Murayama (1982a, b). Let q,, be the rate of energy supply to the quiet quasisteady-state ring current. The quiet ring current may be sustained by the corotation mechanism proposed by Lee et al. (1982). It is also possible that quasiviscous interaction gives rise to continuous plasma injection from the tail to the ring current region. In this case the convection intensity, hence the energy injected to the ring current, is a function of the solar wind plasma parameters V2 and nV2 (Afonina et al., 1979; Levitin et al., 1982). The analysis of the A&C, AE-D and S3-3 measurements of the potential drop through polar cap (Reiff et al., 1981) is also indicative of the existence of a constant potential component independent of the electromagnetic parameters of interplanetary medium. Such a component of the potential gives rise to continuous energy supply to magnetospheric region with closed force lines (Wolf et al., 1982). Under magnetically quiet conditions, V and n in solar wind vary insignificantly and, therefore, the rate ppoof energy supply to the quiet ring current may be considered, for a first approximation, to be constant. During magnetic disturbances, cp seems to vary, but its variations are inconsiderable compared with the variations of the function F(EM). Therefore, the value of cp is taken below to be a constant. In such a case, the equation (2) will take the form $ D,,, = F(EM)+cp _I - +.

(4)


Ring current

simulation

in connection

with interplanetary
4. THE FUNCTION

space conditions
F(EM) OF ENERGY INJECTION ON THE OF PARAMETERS MEDIUM

971
INTO

Let us introduce

the designations &,, = fis',,-bp"`+Z;.
(5)

e = C--cpz;

THE RING CURRENT DEPENDING ELECTROMAGNETIC INTERPLANETARY

Then, the balance equation the form

for the ring current will be of

; 8,,, = F(EM)-

J+.
(7) (8)

The function F(EM) was calculated on the following assumptions : (1) On the Earth's surface the magnetic field from the magnetopause currents H,, is proportional to solar wind pressure: (eV cme3). H,, = bpl" at 100 < & < 200

When (3) is satisfied, it follows from (6): B,, = 0, i.e. D,,- bp"`+ Obviously, C = q,,z.

q,,r = HFc = DR, and, therefore, = H4,,+H;c-~(Po~ = Hi, the are Let the (5)

e = C-cp,z

i.e. c corresponds to the geomagnetic effect of magnetopause currents when the conditions (3) satisfied. The value of e may be found in the following way. equation (6) be integrated over an interval equaling storm duration (0, T), and the expression ofB,,, from be substituted. Then.
T

(2) H,, is independent of & at p < lo4 eV cmm3. Such an assumption has to be used to coordinate the observed and calculated D,, in the initial phase of the storm of 23-24 February 1967 and, probably, may be confirmed by the results obtained in Gosling et al. (1982). Like Burton et al. (1975), we assumed that F(EM) was of the form at E > A atA>E (10)

(D,,-bp1'2)

T= F(EM)dt+T I0 s0 -~[~~~Ds~d~-bS:p"`dt]. (9)

where E is the solar wind electric field ; d and A are constants. The values of Q, the rate of D,, change considering the ring current decay (i.e. the rate of energy supply to the ring current), were calculated for each 25-min interval :

The left part of (9), which represents the ring current energy variation, and all the integrals in the right part, which represent the difference between the injected and dissipated energies, may be calculated using the observation data at a given injection function P(EM). It should be noted that, if z and rp are not constants throughout the storm, the value of c obtainable from (9) is an approximate estimate which was specified by minimizing the deviations of the calculated D,, from the observed values. The value of c may also be found from the solar wind parameters under quiet conditions (c = bp'12 = H&J. Within the errors, the values of C determined by different methods coincide with each other and equal c = 18 nT. The magnetic effect of the quiet ring current may be found from ground-based observations of the Earth's magnetic field if the value of the D,,-index measurement level is known (the constant C). If this level is considered to equal the external geomagnetic field discriminated in the main geomagnetic field (Cain, 1966) by spherical harmonic analysis (C = -20 nT), then H$ = DR, x -40 nT; if, however, C = 0, then, according to the results of Feldstein and Porchkhidze (1983), H$ = -20 nT.

Q = $(D,-bp':`)

+ ;(D,,-bp"`).

(11)

Figure la shows the mean-hourly values of Q as a function of E, for the storm of 23-24 February 1967. Allowance was made for a 25-min delay of Q with respect to E,. It was adopted that r = 8.2 h at D,, > - 55 nT and r = 5.8 h at D,, < - 55 nT. A linear dependence of Q on E, can be seen at E, > -0.4 mV m-i. At the same time, the examination ofthe values of Q not averaged for each hour is indicative of a more accurate boundary of the linear dependence, namely E, > -0.9 mV m- `. The proportionality factor found by the method of least squares in the regression equation of the form Q = dE, + y at E, > -0.4 mV m-l is - 1.2 x 10e3 nT s-l (mV/m)-`. The functional form of the dependence of the rate of energy injection into the ring current on E, is the same as that obtained by Burton et al. (1975) and does not confirm the results of Lee et al. (1982) who obtained on the basis of theoretical considerations that in the disturbed periods the rate of energy supply to the ring current is proportional to squared potential drop through polar cap, i.e. to EC. The data presented in Fig. la show a large spread of


978

Y. I. FELDSTEIN et al.

Q at the same values of E, outside the domain of the linear dependence of Q on E,. Such a spread may be accounted for by various disregarded factors. In particular the contribution from the magnetic field of the field-aligned magnetospheric currents, which are

Dusk .

to dawn . . .

: . .
,.

I -3

-2 .

I

-I

l

01

,
Ey(

I

I

2
mV-mm')

3

I

I 4

.
.

.2

II
(8)

opposite in sign to the magnetic field ofthe DR-current, to the D,,-variation may prove to be significant in these intervals. A possible dependence of the function cp on solar wind parameters other than electromagnetic field is not excluded either ; the injection and precipitation of particles as a result of the ionosphere-magnetosphere interaction is also possible. The sufficiently high values of Q in the periods with E < A indicate that the above discussed additional injection rp to the ring current took place during those intervals. The'existence of such an additional injection at E, < 0 mV m- 1can also be seen in the experimental dependence of Q on E, found by Bobrov (1977). Figure lb shows the values of Q as a function ofE, for the storm of 7-8 February 1967. All the above discussed features of the storm of 23-24 February 1967 are observed also during this, more intensive, magnetic storm. Thus, the ring current model is proposed which requires that but two parameters (z and b) of six should be set independently. These parameters were determined by minimizing the sum of quadratic deviations of the calculated D,, from the observed values during the storm period (6). The parameters e, d, A found from the relations (9), (lo), (11) were also specified when minimizing 6. The value of 6 can be much reduced if the parameter z characterizing the ring current decay intensity is assumed to be not constant but variable throughout a storm and dependent on D,,. The following values of the factors in (6) were inferred from the data on the storm of 23-24 February 1967 : 8.2 h at D,, > -55 r= nT

. . . ./ .
. . .

i 5.8hatD,,<

-55nT,

b = 0.23 nT (eV/cm3))`iz, d = -1.2x 10e3 nT s-l (mV/m)-`, c = 18 nT, A = -0.9 mV m-`.

.
l

.'

Dawn to dusk

5.

COMPARISON

BETWEEN THE OBSERVED AND VALUES OF D,

/

CALCULATED

.
.
1 1
.

S
l

/ 3

/ 5

/
7

Ey

I mV- WI-`)

.

.

-; . (b)

FIG. 1. INJECTION INTO THE RING CURRENT Q AT VARIOUS VALUESOF THE AZIMUTHAL COMPONENT(E,) OF ELECTRICFIELD INSOLARWIND: (a) THE MAGNETIC STORM OF 23-24 FEBRUARY 1967, (b) THE MAGNETIC STORMOF 7-8 FEBRUARY 1967.

Figure 2 presents the observed Dzp and the values of calculated from (6) for the storm of 23324 February 1967 at the values of the various factors indicated above. Allowance is made here and below for a 25-min delay of D,, relative to the solar wind parameters. The calculated and observed 2.5-min values of D,, were averaged over l-h intervals to facilitate their plotting. An extremely good agreement between Dip and 02 can be seen in all the phases of the storm. The sum of quadratic deviations for the 48-h values is 6 = 26 nT. ThechangeofthevalueofAfromA = -0.9mVm-' to A = 0.5 mVm_ ' with preserving the values ofall the
0:


Ring current simulation in connection with interplanetary space conditions

979

FIG.2. THEOB.SERVED@(DOTS)ANDMODEL-CALCULATEDD~ (CROSSES)VALIJES D,, FOR THE MAGNETIC STORM OF 23-24 OF FEBRUARY~~~~.

rest factors gives rise to a significant increase of 6 and to a difference between D$ and Dfj' during the storm recovery phase (see Fig. 3). Besides that, the recovery phase in the model Dff proves to be an absolutely "smooth" exponent, whereas relatively short-term variations are observed in Dzr during the exponential rise of the field in the recovery phase. The proposed model was tested using the observed D,,-variation of the storm of 7-8 February 1967. From Fig. 4 it is seen that D$ and 0: are in sufficiently good agreement; 6 = 58 nT.

6.ABOUT

A POSSIBLE RELATIONSHIP OF SOLAR WIND VELOCITY

ENERGY INJECI-ION INTO RING CURRENT TO

As was shown above, energy injection into ring current is permanent. According to the results of works by Afonina et al. (1979) and Levitin et al. (1982), the parameters V2 and nVZ may be responsible for the energy supply to the magnetosphere in the absence of an electric field directed from dawn to dusk. In this connection, the coefficients of correlation of Q with Vz and nV2 were calculated for the l-h intervals in which E, < -0.5 mV m-' for the first storm and E, < -0.9 mV m-l for the second and Q < 0 nT s- `. The regression lines for Q and Vz are presented in Figs. 5a and 5b for the storms of 23-24 and 7-8 February respectively. The corresponding regression equations are Q=[-O.O8(A)`+oO3] x 10-3nTs-1

Q=[-0.15(&~+0.81]

x 10-3nTs-1

FIG.~.THEsAMEASINFIG.~,BUTA=

+0.5mVm-`.

at the correlation coefficients I = - 0.4 and r = -0.73. The coefficients of the correlation of Q with nV2 are x0.1. It can be seen from the plot presented, however, that the available data are still insufficient for accurate quantitative relations to be obtained. The relationships between the permanent energy injection into ring


980

Y. I. FELDSTEIN et al.

T* -3

$,y -2
P G

-I';

(a)

.
: .
15

.
. 25
.

-I

l q-'

&_/----. . .
20

c m0

7

_6-

(b)

.
I I

15

25 ccl )' ( km2se') 100

35

Fm.5. INIECTIONINTOTHERINGCURRENTQFORTHESOLARWINDELECTRICF~ELDSFROMDUSKTODAWNASA FCJNCTIONOFSOLARWINDVELOCITY:(~)THESTORMOF 23-24 FEBRUARY~~~~,(~)THESTORMOF 7-8 FEBRUARY
1967.

current and solar wind parameters studied.
7.SOME REGULARITIES DYNAMICS INFERRED

have still to be

expression (15) gives the relation hourly values of DR :

for calculating

the

OF THE RING CURRENT FROM NUMERICAL

DR(t,+ 1) = [DR(ti)+(~i+~)~(efi+~`r-eef~`r)]e~cri+l-*a)'~, (16) The values of DR(t,+ J were calculated for r = 8.2 h at DR 2 -85 nT and t = 5.8h at -85 nT > DR > - 180 nT and at invariable values of rp throughout the storm for cp = cpO= -2.4 nT hh' and cp = `p,, = -4.9 nT h- `, which corresponds to DR, = -20 and -40 nT. Figure 6 presents the given values of E,i and the calculated DR at cp = -4.9 nT h-l. Shown with the dashed line for comparison are the values of DR calculated at the same &, but at cp = 0 in the recovery phase. It is seen that after the increase in E, the ring current rises abruptly during 5 h. During the sixth hour, the dissipation processes got dominant over injection, so the DR recovery phase began. Considering the injection cp, the DR recovery is slower and stops as soon as DR = DR,, whereas at rp = 0 the recovery lasts up to DR=O. It is only natural that the determination of r from experimental data disregarding cp will give overestimated values of the decay constant. It is probably for this reason that Bobrov (1981) obtained somewhat overestimated values of r.

SIMULATION

Here, we shall demonstrate the dependence of the ring current intensity on the conditions in interplanetary medium by making numerical simulation on the basis of equation (4). The solution for (4) will be sought to be of the form DR(t) = K(t) eC'/' at the initial condition DR(t = 0) = DR,. After simple transformations DR(T) = { Let us set now: F(EM) = pi -4.35(&,+0.9) 0 at EYi > -0.9 at EYi < -0.9 mV m-l mV m-l. nT h-' DR,+ we get : et" dt eMTlr. (15) (13)

T[F(EM)+q] s0

If F(EM) = pi on the segment [te ti+ i] of l-h duration,


Ring current simulation in connection with interplanetary space conditions

981

t
IO I

(hr)
20 I I-30 I

?,/ -5

G $

-10

-15

-18

FIG. 6.

-2c )O VARIATIONS OF DR FOR THE E, SEQUENCE SHOWN WITH IN THE A CONSTANT

I
OF PART

UPPER PART OF THE FIGURE FOR THE DECAY INJECTION Cp,THE SOLID LINE (1) AND WITHOUT DASHED LINE@); DR, =

FIG. 7. VARIATIONS THE UPPER

DR

FOR Two

SEQLJNCES OF E, SHOWN

IN

INJECTION rp, THE

OF THE FIGURE

DR, = - 20 nT, cp= - 2.4

-40 nT, cp = -4.9 nT h-`.

nT

h-l.

Figure 7 shows convincingly that the extremal intensity of DR-current depends not only on the extremal value of E,i attained during the storm but also on the duration of the interval during which the electric field is sufficiently high in the dawn-dusk direction. From Figs. 6 and 7 it is seen that DR = DR,,, - 180 = nT may be attained at both the maximum E, = 20 mV m-l and the maximum E, = 10 mV m-`. Let us estimate the maximum value of DR,,, which will be observed at a given permanent injection at the moment when the rates of energy injection and dissipation in the ring current get equal (dR/dt = 0): DR,,, Figure -4.9 nT variations equation - 85 nT = CF(EM) +

8. DISCUSSION

OF

RESULTS

(1) The concept has been introduced of quasisteadystate quiet ring current (DR,) which may be observed under relatively quiet geomagnetic conditions when the ring current decay is compensated for by a certain level ofinjection `pO.Such a quasisteady injection, which may vary during a storm, gives rise to the change of the

cp1'5.

(17)

8 presents DR,,, a function of E, at rp = as h- `. The bend of the straight line is due to the of r in different intervals of DR,,,. The of the straight line in the plot for the interval > DR,,, (where z = 5.8 h) is of the form DR,,, = -25.2E,-51. (18) obtained
FIG.

I O

I 0

I I

I 2

I 3

I 4

I 5

I 6

E (mVm~`l 8. THE MAXIMUM STEADY-STATE DECREASE DR,,, VALUES OF THE OF THE AT GEOMAGNETIC AZIMUTHAL FIELD ATTAINABLE cp = AT VARIOUS

The relation (18) is close to the expression earlier by Porchkhidze et al. (1976).

ELECTRIC FIELD COMPONENT

E, IN SOLAR WIND

-4.9 nT h-l.


982

Y. I.FELDSTEIN et

al.

constant in equation (6) by the value rrp, (e = C - rrp,). This circumstance makes it possible to avoid the difficulties with which Burton et al. (1975) were faced when giving physical interpretation ofthe constant C in equation (2). The value of the constant C = 20 nT adopted by Burton ef al. (1975) corresponds to the quiet ring current on the Earth's surface DR, = H$ = 5 nT. (2) The ring current model has been proposed which is of the form of an ordinary differential equation with a set of factors permitting the magnetic storms with explicitly expressed expansion phase to be sufficiently accurately described with a 2.5-min resolution. The correctness of determining the factors in equation (6) is confirmed by a good agreement between the calculated and observed values of D,,and by the fact that the simulation was made using the energy relation which states that the change of the ring current energy at the end and commencement of the storm should equal the difference between the energies supplied to and dissipating from the ring current. Obviously, this requirement must be satisfied in any model of the ring current. At the same time, from the data presented by Burton et al. (1975) it follows that their model fails to satisfy such an energy relation. If satisfaction of this relation is required and the values ofthe parameters r, b, d,A adoptedin Burtonetal.(1975)areused, thefactor C calculated from (9) will prove to be C = 38. Figure 9 presents the values of&`: and @for the storm of 23-24 February 1967 calculated with r, b, d, from Burton et A al. (1975) and C = 38. A good agreement between D$

and Dff[which is better compared with Burton et al. (1975)] can be seen; the value of 6 = 31 nT. (3)The injection into the ring current has been shown to start at E, = -0.9 mV m- `, which corresponds to positive B, equaling - 1.8 nT at V = 500 km s-l. The injection at B, < 1.8 nT seems to be due to the enhancement of magnetospheric convection. In fact, Hardy et al. (1981) have shown that the equatorial boundary of the region of diffusive electron precipitation, whose position is determined by the intensity of the large-scale magnetospheric convection, starts shifting monotonically to lower latitudes beginning from B, = 1 nT. This means that the plasma convection and supply to the ring current region commence not at B, < - 1 nT [as was assumed by Burton et al. (1975)] but at B, < - 1 ++ 2 nT. (4) The conclusions about the parameters of the model are obtained under an assumption that the injection function into the ring-current is of a definite form. In particular, this function can be presented as a sum of two parts: the continuous injection cp and function F(EM), depending linearly on electric field in solar wind E, = B, - V. It should be noted, that a choice ofinjection function is not unique. Again, as in the case ofpolar cap potential drop, cp+ F(EM) can be defined by some other combination of the solar wind parameters. For example, Wygant et al. (1983) have shown that along with E, = B, - V = I3 * Vcos 0 the following combination may be used :

E, = B,- vsin"(0/2),

E, = B,* vsin'(0/2),

24 February

1967

FIG.~.THEOBSERVEDD;~(DOTS)ANDCALCULATEDINlXRMSOF THE MODEL OF BURTON et al.(1975) (CROSSES) VALUES D,, FOR OF THE STORM OF 23-24 FEBRUARY1967. The factor C = 38 nT is adopted to realize the condition of energy balance during magnetic storm.

where B = J(B: +Bz), B, = the magnetic field component transverse to the magnetopause and 0 = polar angle between transverse component of the IMF B and geomagnetic field at the magnetopause. Any other form of injection function into the ring current will lead to a change of parameters set used in the ring current model. In particular, there will be no need of cp(V) term. E, # 0 and E, # 0 under any B, direction if B, # 0, that means a presence ofcontinuous injection into the ring current, even at the northern direction of IMF B, component. There will be no need of A-parameter, characterizing F(EM) # 0 when E, > A. Functional dependence of F(EM) on E, or E, suggests continuous injection under any direction of IMF B, component. The ring current models for other forms of injection function will be developed in future. At present it would be rather difficult to prefer some definite function of plasma injection into the ring current. (5) The decay rate of the ring current has been shown to depend on its intensity and to vary as a magnetic storm develops. The data presented in Shevnin


Ring current

simulation

in connection

with interplanetary

space conditions

983

(1973a, b) and Zaitseva and Alekseeva (1976) show that the ring current decay time depends on its maximum intensity in a given storm, whereas it follows from the data presented by Akasofu (1981a) that the decay time depends on the value of the energy flux E injected into the magnetosphere. According to Shevin (1973a, b) the ring current decay time increases, but according to Zaitseva and Alexeeva (1976) it decreases, with increasing D,, variation. In Shevnin (1973a, b), t = 4.6, z = -0.04 D,, + 1, which corresponds to 7 = 0.4 h at D,, = - 20 nT and T = 1.1 h at D,, = - 100 nT. Such small values of z and the character of the dependence of T on D,, are consequences of incorrect method for determining z used in Shevnin (1973a, b). The method is based on erroneous concepts concerning the structure of magnetic disturbance field at low-latitude stations. According to Akasofu (1981a), 7 may significantly vary throughout a storm and equal 7 = 20 h at E < 5 andz=lhatE>5xlO'*ergs-`.In x 10" erg s-l the model proposed here, the decay time 7 = 8.2 h at D,,a -55nTandz=5.8hat-120
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