Growth rate and decay of magnetospheric ring current

0032 0633,‘85 $3.00+0.00 Pergamon Press Ltd.

Phnrr Space Sri.. Vol. 33, No. IO, pp. 1097 I 102, 19X5 Printed m Great Britam

GROWTH RATE AND DECAY OF MAGNETOSPHERIC RING CURRENT M.1.PUDOVKIN Institute

of Physics, Leningrad

and S. A. ZAITSEVA

University,

Leningrad-Stary

Petergof

198904, U.S.S.R.

and L. Z. SIZOVA

IZMIRAN,

Troitsk,

142092, U.S.S.R.

(Rrceioed injinalfbrm

26 March 1985)

Abstract--The rate of energy input to the ring current is studied as a function of solar wind parameters. The ring current dissipation rate is also examined. The decay constant 5 in the main phase of a storm has been shown to be independent of its intensity and to equal (4 k 2) h. In the recovery phase z rises with increasing storm intensity.

1. INTRODUCTION

The processes of magnetospheric ring current injection and decay were studied in numerous works (Yacob, 1964 ; Davis and Parthasarathy, 1967 ; Pudovkin et al., 1968; Zaitseva and Alekseeva, 1976; Burton et al., 1975; Sizova and Shevnin, 1978; Bobrov, 1977; Murayama, 1982a ; Zaitseva and Glazhevska, 1972 ; Tverskaya, 197 I). Davis and Parthasarathy (1967)and Pudovkin et al. (1968) have shown that the ring current and the polar magnetic disturbances are intensified simultaneously. Pudovkin and Shumilov (1969) argued theoretically that the solar wind electric field penetrated the magnetosphere and that its dawndusk Y-component (EY = -B,V) increasing in the storm time was responsible for the development of aurora1 disturbances. Considering the conclusions drawn by Davis and Parthasarathy (1967) and Pudovkin et al. (1968) one may expect that the same electric field facilitates the formation of the DR-current. Based on this concept, Tverskaya (1971) and Zaitseva and Glazhevska (1972) have demonstrated the feasibility of magnetospheric plasma acceleration and trapping to quasiclosed trajectories around the Earth. Their calculations have yielded quite reasonable parameters of the ring current. The E, field as function determining the rate of energy input to the Dr-current was tested, as applied to concrete disturbances, by Burton et al. (1975) Bobrov (1977) Murayama (1982a, b), Zaitseva and Ponyavin (1979) who largely obtained a fairly good agreement with experimental data. In some cases, however, the calculated D,, values were much different from observations, or the experimental energy input rate Q

was in better correlation with other empirical functions of injection composed of solar wind parameters than with E, (Murayama, 1982a). The differences between the calculated and observed D,, values may be accounted for by several explanations, in particular, by the incorrect allowance for the contribution to the D,, variation from quiet-day ring current and quiet magnetopause currents and by the choice of the DR-current decay constant r the estimates of which are somewhat contradictory (Yacob, 1964; Davis and Parthasarathy, 1967; Zairseva and Alekseeva, 1976; Burton et al., 1975; Sizova and Shevnin, 1978). The aim of the present work is to study (on the basis of mean-hourly data) the variations in r of ring current decay during different phases of geomagnetic storms and to estimate the effectiveness of some functions describing the energy input to the DR-current.

2. CONTRIBUTION CURRENTS

OF THE MAGNETOPAUSE TO /&,-VARIATION

The DR ring current field may be found from the D,, index : 2/3D,$, = DR,+DCF,-DR,

-DCF,,

(1)

where DCF is current field on the magnetopause ; the subscripts d and y are for disturbed and quiet periods respectively; the factor 2/3 takes into account the currents induced in the Earth. We assume that DR, = const., i.e. the processes of the quiet ring injection and decay are in equilibrium. Since DR, = DR,, + DR, (where DR,, is the field of the current formed during a

1097

1098

M.

I.

PUDOVKIN

et

ul

storm), we obtain from (1) :

3. THE

CHARACTERISTIC RING

DR,, = (2/3)0,,-ADCF.

(2)

The value of ADCF may be found if the solar wind parameters are known : ADCF = b(P:” -Pi”),

(3)

where P (eV cm-“) = lo-’ n (cme3) [V (km s-‘)]’ is solar wind dynamic pressure. The values of the constant “b” obtained by various authors differ significantly (Burton et al., 1975; Pudovkin et al., 1975). According to our preliminary estimates the value of “6” depends on the DR-current intensity and varies from 0.35~ (eV cm-3)~‘/2 when IDRl< 10~ to 0.1~ (eV cm-3)m1i2 when IDRl> 60~.However, experimental data is scarce, so we shall use in the next study an average value h = 0.16~ (eV cm-3)-112. It should be noted that, in their calculations of the quiet fields DR, and DCF,,Burton et al. (1975) allowed an inaccuracy. They believe the DR,-current intensity (or D,,, in their designations) to trend to zero by the end of the recovery phase while in reality it has to trend to the DR-current intensity at the quiet time (DR,) :

D,,, E DR, = (D,,-hP1'2 +c) + DR,, where c = DR, + DCF,.Thus the constant obtained by Burton et nl. (1975)--D&,, = 20?;-corresponds not to the value of “c” but to (c - DR,)= DCF, that is to the value of the DCF field at the quiet period. To make allowance for the quiet magnetopause current’s contribution to the D,,-variation, Shevnin et al. (1983) examined the variability of such currents in solar activity cycle. Figure 1 shows the annual means of DCF, calculated from quiet solar wind pressure at h = 0.16y (eV cmm3)- lj2. From Fig. 1 it is seen that the variation amplitude of the DCF, annual means in the studied period was _ 67.

TIME

CURRENT

The ring current field variations are described by the expression dDR/dt

OF

DECAY

throughout

a storm

= Q - DR/z,

(4)

where DR = DR,,;below we shall miss the subscript “st”. The value of z during storm recovery was found from (4) using 3-8-h intervals when B,(IMF) > 0 and (T< (B,(, i.e. the additional energy input to the ring current could be neglected (c is the IMF variability). Figure 2 shows theDR field variations in the recovery phase of the 10-11 January 1976 storm. The shaded area at the bottom of the plot (22.00-06.00 U.T.) corresponds to the period of energy input to the DRcurrent; the IMF data in the 14.0&18.00 U.T. interval are absent. From Fig. 2 it is seen that in the 06.00-14.00 U.T. period of zero additional energy input the DRcurrent decay occurs at a constant z. The values of z in such periods were found for 13 magnetic storms (see Table 1). The values of z obtained for each of the storms are shown in Fig. 3 vs the DR-current in the main phase maximum. Despite a small number of dots and their scatter, Fig. 3 shows clearly that z rises with increasing IDRI,,,. It should be noted that this result contradicts the conclusions drawn by Yacob (1964), Zaitseva and Alekseeva (1976) and Feldstein et al. (1984) who found that T decreases with increasing DR and is at variance with the works where z was adopted to be constant (Davis and Parthasarathy, 1967; Burton et al., 1975). The contradictions arose probably from the fact that, for example, Yacob (1964), Davis and Parthasarathy (1967), Zaitseva and Alekseeva (1976) neglected the additional injections to the DR-current in the recovery phase, while Yacob (1964), Davis and Parthasarathy (1967), Zaitseva and Alekseeva (1976), Burton et nl.

7

s a

IO -

b=O.

01,964 “‘1”““‘1’11”’ 1968 FIG.

1. THE

CALCULATE”

ANNUAL

(eV

cm-3)-“2 30

I972

MEANS

FROM QUIET-DAY

16 7

1976

OF MAGNETOPAUSE SOLAR WIND

1980 AT h = 0.167

(ev

PRESSUKES

~m-~)-(“~~.

22

I980

0

2

4

U.T.

CUKKENTS IN 1963%

6

FIG.

2. THE

DR-FIELD THE

VAKIATIONS

I@11

JANUAKY

I

I

I

8

IO

12

7717 14

7

16

(hl IN THE RECOVEKY 1976~~0~~.

PHASE

OF

Growth

rate and decay of magnetospheric ring current

1099

Table I. Nos.

Date

Interval

1 2 3 4 5 6 7 8 9 10

14 January 1967 23 February 1967 20 January 1968 5-6 April 1968 15 January 1972 22 February 1973 26 September 1973 13-14 October 1974 21 April 1975 18 November 1975 11 1I January 1976 12 8 December 1976 13 4 April 1979

(U.T.)

10.0~19.00 2O.OC24.00 02.OCO5.00 23.OC02.00 19.OCk22.00 02.00-04.00 17.0&23.00 22.0~01 .oo 02.00-05.00 00.0&08.00 06.0@ 12.00 14.0& 19.00 12.0~20.00

(1975) disregarded (or made a not quite correct allowance for) the current field variations on the magnetopause. Besides that, Zaitseva and Alekseeva (1976) erroneously introduced a correction for quiet ring current DR,, whereas the processes of strengthening and decay of the steady-state DR, must be in equilibrium and cannot affect the D,,-field reference level. The disagreement with the results by Feldstein et al. (1984) may be caused by the fact that the value of T obtained by them concerned a D,, storm at the whole that is both the main and the recovery phases simultaneously. At the same time, as will be shown further, the charactetistic times “T” greatly differ at the two phases; in particular, at the main phase T does not depend on the DR current intensity and equals -4_t2 h. Thus, the dependence of z on IDRI,,,illustrated by

IDRI!L,

7 (h)

112 51 22 93 54 92 75 79 55 60 117 50 125

14.2 11.2 7.8 10.8 9.3 12.4 9.5 11.9 7.7 12.7 17.2 14.4 16.1

Fig. 3 seems to be sufficiently reliable and corroborates the trend of T to increase with DR noted earlier by Sizova and Shevnin (1978). The calculations of the DRfield variations made by Bobrov (1984) for several storms at different z indicate also that T = l&15 h satisfies quite well the decay phase of the 8 March 1970 storm. whereas a less intensive storm of 31 December 1967-l January 1968 decayed with 5 near 5 h. Now we shall make an attempt to understand the physical meaning of the increase of the ring current decay characteristic time with rising storm intensity. To this purpose we shall examine the ring current ion lifetimes for the following charge-exchange processes : H++H+H+H+ He++ +H+He++H’ He++H

+ He+H+

(5)

O++H+O+H’.

. 15 -

. . .

IO ~

i

ti = (WJaK)_‘,

. .

.

. .

.

5p

I 20

0

I

1

40

60

Imm,,

F~i.3. THEKING RECOVERY

80

I

I

100

120

(Y)

CURRENTDB(‘AYCF~ARACTERISTICT~MEINTHF

PlfASEVS

IDRI,,,

RING

Considering the ring current ions to be lost due to charge exchange, one may calculate their characteristic lifetime 5i as

. .

2

.

Al-THE

MOMENTSOPTHEMAX,M"M

CURRENTINTENSITY.

(6)

where ~1is number density of neutral hydrogen atoms; r~,,is the io+hydrogen atom charge-exchange collision cross-section ; V,is the mean velocity of ions. Formula(6)wasused tocalculateTion the basisofthe experimental cross-sections and the numerical models of the hydrogen geocorona inferred from the OGO-4 and 6 observations (Smith and Bewtra, 1978 ; Tinsley, 1976). The calculations were made in the prevailing current ring ion energy range from 1 to 300 keV and for the exospheric tcmpcratures of 750, 850, 950, 1000, I100,1300 and 1500 K. The characteristic ring current ion lifetime on L = 2.5-5 proved to depend little on

1100

M. I.

FIG. 4.THE

RING CURRENT POSITION

T=llOO

K

H’,

He++, Of-keV

He+,

PUDOVKIN et al.

ION LIFETIMESvs RING CURRENT

IN THE EQUATORIAL

PLANE.

exospheric temperature, i.e on solar activity level. Figure 4 shows the lifetime of the ring current ions of various energies vs L-shell at 1100 K. Let the calculated zi be compared with the observed t of DR-current decay. From Fig. 4 it follows that on L > 4 (the position of weak and moderate DR) zi = 415 h is characteristic of the 2-30 keV hydrogen ions and the l&100 keV He’+ ions. The high values of ri = 15-30 h on low L (strong storms) correspond to the SO-100 keV hydrogen ions, 30-300 keV helium ions, and low-energy (2-10 keV) oxygen ions. The available ion composition data for the L-shells characteristic of the DR-current are still quite insufficient. Nevertheless, together with the values of ~~ presented in Fig. 4, they make it possible (Williams, 1981) to assume that the rise of z of the DR-current decay with increasing storm intensity is accounted for by the ion composition variations with changing the value (and hence position) of the ring current and/or by a rise of energetic proton fraction on low L.

4.

STRENGTHENING VARIATIONS

OF DR-CURRENT

DUE TO

IN SOLAR WIND PARAMETERS

The rate of energy input to the ring current, Q, was determined, for example, in Burton et al. (1975);

Bobrov (1977); Murayama (1982a, b). The values of Q calculated from ground-based data were compared with either individual solar wind parameters or the various functions composed of the parameters. Bobrov (1977) assumes that the energy injected to the DRcurrent can be described best by the function (BL-a)V, where u is the IMF modulus variability. Murayama (1982a, b) has concluded that, out of three functions E = B*V sin4(0/2) (0 is the angle between the IMF vector in Y.&plane and Z-axis), B,K and B,V2 examined by him, B,V is on the average (at z = 12 h) in the best correlation with the DR-field. He is of the opinion, however, that the function (B,VP"3), whose physical meaning is not quite clear, suits even better. At the same time, Bobrov (1977) and Murayama (1982a, b) disregarded DCF, when calculating the DRfield on the data of D,,, whereas Fig. 1 shows that the quiet DCF field varies from year to year. Burton et al. (1975) describe the DR-current injection by a function proportional to the E,-component of the interplanetary electric field. Their calculations of the D,,-field for several storms have yielded the values close to the observed D,5,. The differences in the behaviour of the experimental and calculated D,,values occurring as arulein therecoveryphasemay bedueinpart to :(l)not quite correct inclusion of the quiet ring current field (its decay was included, but the steady energy input to DR, was disregarded) and (2) a fairly rough estimate of T in the recovery phase (T was assumed to be constant and equal to 7.7 h, whereas Fig. 3 shows that it rises with increasing storm intensity). In the present work we continued studying the functions describing the rate of energy input to the ring current. With this purpose, 44 2-h intervals of the DRcurrent development phase were selected during which the DCF field variations did not exceed 5y and lAB,l d 2~. The value of Q = (dDR/dt)+(DR/z) on the selected intervals was calculated making allowance for the decay at z = 6 h. This value oft was taken on the basis of Fig. 3 as corresponding to a certain extreme at IDRI,,, = 0. The reason for that is the following: the small values of IDRI,,, correspond usually to the short duration of the storm main phase. So the DR belt plasma composition cannot significantly change from the onset of the storm till the beginning of the recovery phase. Then the characteristic time of the DR current decay at the recovery phase (7,) of such a storm has to be close to corresponding to the main phase (7,). We shall see below that in reality r,,, z 4 h instead of 6 h ; however, this affects the result of the calculation of Q insignificantly. The Q variations were compared with the injection functions corresponding to the E,-component of the solar wind electric field, namely VB,, V(a-B,),

Growth

rate and decay of magnetospheric

...

50

c I

40

l

.

. .zda*

_

l

r = 0.96

,. ,. 0

/

2

, 4

/

,

6

,

,

8

u (0.50-Bz)

,

,

IO

, 12

(mV mm’)

FIG.5. THERATEOFENEKGYINPUTTOTHER~NGCURRENTINTHE MAINPHASEVSTHEY-COMPONENTOFTHESOLARWINDELECTRIC FIELD.

V(0.5o-BJ, 1/(0.30-B,). The solar wind data were taken from J. H. King’s catalogues (1977, 1979, 1983). The best function of the above four proved to be 1/(0.5~~- B,) calculated with a l-h shift prior to dDR/dt. The respective dependence is of the form Q = -3.5+4.3I’(0.5a-BB,)x

10-3,

(7)

where V is in km s- I, B, and g are in gammas, Q is in y/h, and the correlation coefficient r = 0.96 (see Fig. 5). At the moment of the DR-current maximum intensity, Q = IDRlma&,_ where T,,,is the characteristic decay time. Having calculated Q from (7) for 88 storms an hour prior to the IDRI,,, moment, we found r, (see

.. .

8

r

-

6

0

1101

ring current

Fig. 6). From Fig. 6 it is seen that r of the main phase is independent of IDRI,,, and that its mean value is _ 4 h. Since T,,, = const., (DRI,,, may be assumed to be proportional to Q. Making use of this we continued studying the relationships of Q for 88 values of IDRI,,, to the following functions composed of the solar wind parameters : F, = B*V sin4 (o/2) [the energy coupling function by Akasofu (1979)], F, = B, V sin’ (O/2) (the value proportional to the Y-component of the electric field generated in polar cap and at the nose of the magnetopause), F, = B$sin3 (8/2)ln- liz [the value proportional to the potential difference produced by the merging field across polar cap (Pudovkin and Zaitseva, 19831, F, = E, = B,V (the azimuthal component of the solar wind electric field), F, = V18,1 [the function determining the Y-component of the reconnection electric field at B, (IMF) close to zero], F, = (Oh-B,)V (the same as F, with its highfrequency component). The results of the comparison are presented by the following regression equations :

IDRImx = 35.8+5.610-4F, IDRL

= 2.0+ 14.3 10_3F,

r = 0.81 (a) r = 0.86 (b)

I~RI,,, = 40.4 + 0.8 F,

r = 0.63 (c)

IDRIm,,= 7.3 + 14.7 1O-3 F,

Y = 0.87 (d)

ID%,,, = 52.9 + 5.4 lo- 3 F,

r = 0.26 (e)

= 5.6+ 11.7 10e3 F,

r = 0.86 (f)

IDRI,,,

.

.**

I

I

20

40

60

80

I

I

I

100

120

140

160

180

IDRIm,, (Y) FIG. 6. THE RING CURRENT

DECAY

CHARACTERISTIC

(8)

1

The relations (8) give IDRI,,, in gammas if in the functions F, to F, V is expressed in km s-i and B,, B, and c are in gammas.

.*

.

I

TIME IN THE MAIN PHASE VS STORM INTENSITY

1102

M. 1. PUD~VKIN

Obviously, out of all the functions examined, the reconnection electric field F, and the E, field (F, or F6) are most suitable when describing the rate of energy input to the DR-current. The correlation with the Akasofu E function (8a) proves to be somewhat lower. To specify the role of the merging field in the process of ring current strengthening, we examined in addition to the function F, the value VIB,I which was shown (Stern, 1973) to be one of the merging field components. However, from the expression (8e) it is seen that the correlation between (DRI,,, and VIE,, is very weak (Y = 0.26). Besides, it may be caused by the relation between JVB,,I and IVB,I (r = 0.23). The close correlation (r = 0.86) between IDRI,,, and the reconnection electric field (FJ seems to be a result of the relation of F, with &-field (r = 0.97). Therefore, the merging field does not in practice affect the ring current formation. CONCLUSIONS

The

results

conclusions

presented

above

permit

the

following

:

(1) the characteristic

time of ring current decay in the recovery phase increases with storm intensity ; (2) the characteristic time of DR-current decay in the main phase is independent of storm intensity and equals (4 k 2) h ; (3) the storm-time energy input to the ring current occurs mainly due to the Y-component of the solar wind electric field which directly penetrates the magnetosphere apart from the merging processes. The electric field of merging seems to be much weakened in the magnetospheric tail and fails to play an essential role in the DR-current formation. REFERENCES

Akasofu, S.-I. (1979) Relationship between the growth of the ring current and theinterplanetaryquantityc. Planet. Space Sci. 27, 1039. Bobrov, M. S. (1977) Solar wind parameters responsible for plasma injection to the region of magnetospheric ring current. Asfron. J. 54, 1335. Bobrov, M. S. (1984)The ring current field variations when the Earth is within a flare-generated flux. Geornuyn. Aeron. 24,

84. Burton, R. K., McPherron, R. L. and Russell, C. T. (1975) An empirical relationship between interplanetary conditions and D,,. .J. geophys. Rex 80, 4204.

et al.

Davis, T. N. and Parthasarathy, R. (1967) The relationship between polar magnetic activity DP and growth of the geomagnetic ring current. J. geophys. Res. 72, 5825. Feldstein, Y. I., Pisarsky, V. Yu., Rudneva, N. M. and Grafe, A. (1984) Ring current simulation in connection with interplanetary space conditions. Plunet. Space Sci. 32,975. King, J. H. (1979) fnterplanefar~ Medium Data Book, Supplement I. WDC-A. (Magnetic tape.) King, J. H. (1983) Interplanetary Medium Data Book, Supplement 2. WDC-A. (Magnetic tape.) Murayama,T.( 1982a)Couplingfunctions between solar wind parameters and geomagnetic indices. Rev. Geophys. Space Phys. 20, 623.

Murayama, T. (1982b) Comparison of the observed values of the D,, index with the predicted values by the coupling functions B, V, B, V’, C, and P”B, V. Sol. Terr. Environ. Rex Japan 6, 39. Pudovkin, M. I., Shumilov, 0. I. and Zaitseva, S. A. (1968) Polar storms and developments of the DR-currents. Planet. Space Sci. 16, 89 1. Pudovkin, M. I. and Shumilov, 0.1. (1969) On the theory of polar substorms. Ann. Grophys. 25, 125. Pudovkin, M. I., Raspopov, 0. M. and Kleimenova, N. G. (1975) Disturbances qf the Earth’s Electromagnetic Field, Part 1. Leningrad State University, Leningrad. Pudovkin, M. I. and Zaitseva, S. A. (1983) Electric field in the polar cap. Geomayn. Aeron. 23,285. Shevin, A. D., Sizova, L. Z., Afanasyeva, V. 1. and Shevnina, N. E. (1983) Cyclic variability of solar wind parameters on geomagnetically quiet days, in Maynetospheric Studies, N 2, pp. 89-92. Nauka, Moscow. Sizova, L. Z. and Shevnin, A. D. (1978) On the problem of the time constant of magnetospheric ring current decay, in Interplanetary Plasma Streams and Magnetospheric Disturbances, pp. 64-71. IZMIRAN, Moscow. Smith, P. and Bewtra, N. K. (1978) Charge exchange lifetimes for ring current ions. Space Sci. Rev. 22, 301. Stern, D. P. (1973) A study of the electric field in an open magnetospheric model. J. geophys. RPS. 78, 7292. Tinsley, B. (1976) Evidence that the recovery phase ring current consists of helium ions. J. geophys. Rex 81, 6193. Tverskaya, L. V. (1971) On the charged particle acceleration by unsteady-state electric field in the Earth’s magnetosphere. Guomqn. Aeron. 1 I, 521. Williams, D. T. (198 1) Ring current composition and sources : an update estimate. Planer. Spuce Sci. 29, 1195. Yacob, A. (1964) Decay rate of recovery phase of geomagnetic storms and dissipation ofassociated ring currents. IndianJ. Meteorol. Geophys. 15. 579. Zaitseva, S. A. and Glazhevska, A. (1972) Formation of the DR-current belt. Geomngn. Aeron. 12, 296. Zaitseva, S. A. and Alekseeva, N.-E. (1976) The DR-current decay as a function of solar activity level, in Geomagnetic Research, N 18, pp. 86- 88. Nauka, Moscow. Zaitseva, S. A. and Ponyavin, D. 1. (1979) The DR-current formation during the storm of May 30-31, 1966, in Geoma