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The influence of the recovery phase injection on the decay of the ring current
Planer. Space Sci., Vol. 36, No. 8, pp. 76S773, Printed in Great Britain.
M)32-0633/88 S3.M)+O.o0 PeQa”,On ,hSS pk
1988
THE INFLUENCE OF THE RECOVERY PHASE INJECTION ON THE DECAY OF THE RING CURRENT A. GRAFE
Heinrich Hertz Institute of Atmosphe~c Research and ~oma~etism, G.D.R., II99 Berlin, G.D.R.
Academy of Sciences of the
(Received injinal form 13 January 1988)
Abstra&--CaIculations of the decay parameter of the equatorial ring current are generally made under consideration of the momentary injection, which is calculated from interplanetary parameters. Hereby values of the order of 6 h result. However our investigations of 23 storms from 1966 to 1977 have shown that the ring current decays in a much slower manner. A time constant of about 20 h has been found. This is obviously caused by the fact that the decay event of the ring current is not disturbed by the injection at the beginning of the recovery phase. It is supposed that at this time the ring current region can no longer be reached by the injection. Therefore it is not justified to consider the injection at the beginning of the recovery phase for the calculation of the decay parameter. This is changing within the recovery phase. It increases with decreasing intensity of the ring current and vice versa. Here several storms behave differently which leads to the conclusion of various conditions of the magnetosphere and probably also a different pre-development.
INTRODUCTION
In earlier investigations of the recovery phase of a geomagnetic storm the continuous increase of the magnetic horizontal intensity was only attributed to the regular intensity decrease of a ring current flowing around the Earth in a western direction (Schmidt, 1924-5). The anaiysis of many geomagnetic ring current effects resulted in the well-known “Angenheister law” (Angenheister, 1924), which describes the course of the horizontal intensity during all recovery phases by a time constant, the so-called “ring current decay constant”. This ring current constant reaches smaller values at stronger ring current effects and vice versa, which means strong geomagnetic storms decrease much faster than weaker ones. Later calculations of the decay constant presume additionally that the energy input to the ring current plasma ends at the beginning of the recovery phase, so the decay constant can be calculated from the eth value of the maximal disturbance. It was also concluded that stronger storms are decreasing faster than weaker ones. For a storm intensity of 100 nT a decay constant of 20 h was stated. Yacob (1964) found a similar result. In fact these investigations describe the regular decay of the geomagnetic ring current effect, but they do not inform us about the real course of the decrease in the ring current intensity or about energy loss of the ring current particles. Indeed the course of the ho~zontal intensity during the recovery phase is caused not only by that of the ring current, but also 765
by the temporally variable energy injection from the far magnetospheric tail into the ring current plasma. This must clearly be recognized. Former investigations were not able to consider energy injections during the recovery phase. Satellite observations of interplanetary parameters nowadays, however, allow the calculation of the ring current injection rate (Burton et al., 1975; Feldstein et al., 1984). This possibility has resulted in several recent investigations about the geomagnetic ring current effect using only D,,-indices as initial values but giving contrary results. Pisarsky et al. (1986) found that the decay parameter for a storm is not constant but increases with decreasing ring current intensity and vice versa. Sisova and Zaitzeva (1984) concluded that the decay constant during the recovery phase increases with increasing ring current intensity and vice versa. According to Tin&y and Akasofu (1982) the decay parameter has lower values during the main phase than during the recovery phase. These differing results made it necessary to investigate again the law of the ring current development during the recovery phase of geomagnetic storms. This is intended by the following analysis of 23 storms during the years 19661977. D,, mean values were used.
DERIVATION
OF RING CURRENT
DECAY PARAMETER
The D, indices are for many reasons not ideal values for the description of the activity of the sym-
A. GRAFE
766
-300
-2DD
.. I .
:
L
&I$
-‘Do
AlTERBEGINNlNGOFTHESMRM.
i,‘
DR, = D,,-
DCF,-
D,,
(1)
is used. According to Burton et al. (1975) DCF, = b = 0.3 nT - cm3/*eV- I/*, p = bp ‘I* = 0.03 V* &, solar wind pressure, V = solar wind velocity in km SC’ and n = solar wind density in g cmW3. The value of D,,q was obtained from D, values during extreme quiet days following several investigated storms. The result of this analysis is shown by Fig. 1. Three different groups were chosen giving un-
I -35
I -30
I -23
I -20
I
.
-.
..
.*
5.
.:.:
c’t”’
metric ring current, but they allow the best possible description at present. The influence of the magnetopause current during the disturbed conditions of DCF, is also given by the D, values and must be eliminated. Furthermore it is necessary to obtain DRd values which are free from the influences of the undisturbed ring current DR,, their sum is denoted by DSfq. Therefore the equation
*.
._ -
..**’ .
s
FIG. 1. MEANHOURLY&,-VALLJESONEXTREMELYQCJJETDAYS
.
. . .: *
F:
Days after the beginning of the laststorm befom the extremely quiet day
.
.
,.’
--
.J.
h-‘)
0 (nl
FIG. 2. RELATIONSHIP BETWEEN ADJUSTED D&VALUES Q-VALUES.
AND
disturbed days. Figure 1 shows distinctly that D,, is relatively high on extremely quiet days following a storm. Dsr decreases, then later a storm is followed by extreme quiet days, and aims at a constant value of about 15 nT. This value was taken for Dstq. In this way all mean hourly Dsr values are converted into DRd ones. Mean hourly values of the solar wind velocity and solar wind density of the King catalog were used for the calculation of DCF,. The ring current balance condition is necessary for the calculation
I -15
I -10
I -5
I0
Cl(nT he’) FIG. 3. RELATIONSHIPBETWEENTANDINJECTIONRATE
QFOR
13 DIFFERENTSMRMS.
767
The influence of the recovery phase injection on the decay of the ring current
during
the
recovery
phase
this
means
that
dDR/dt > 0. This corresponds to the negative sign of DR. From (2) it follows that
r = DR/(Q-dDR/dt).
(4)
BEHAVIOUR OF THE DECAY PARAMETER s DURING THE RECOVERY PHASE Statistic results I -50
I -20
I -30
I -40
I -10
According to (4) z is a function of Q as well as of
I0
0 (nT hei) FIG. 4. ~?ELATIONSHIPBETWEEN z AND Q FOR THEBEGINNING OFTHERECOVERYPHASE (dDR/dt= 0).
of the ring current decrease parameter t from the DR values. This condition is given by (DR,is subsequently denoted by DR) dDR/dt = Q-DR/z.
(2)
Here Q is the ring current energy injection rate and I)R/z the ring current loss term. According to the papers of Burton et al. (1975) and Feldstein et ai. (1984), it is supposed that Q is controlled by the interplanetary electric field. Using values of the 2 component of the interplanetary magnetic field B, and those of the solar wind velocity Y the relation of Feldstein et al. (1984) was used for the calculation of 7 according to (2) Q = -4.32(-R,I’+O.9).
(3)
For the South component of the interplanetary magnetic field values of Q < 0 result. Source and loss terms have inverse signs as DR < 0 during the storm. Because the loss term is greater than the source term
DR. Generally it is assumed that a close relation exists between Q and DR in such a form that a strong injection leads to high DR values and vice versa. This
relation is often linear (Sizova and Zaitzeva, 1984). Our analysis has also shown this (cf. Fig. 2). Therefore it has been confirmed that there also exists a certain functional relation between z and Q. Indeed we found a hyperbolic-like relation between both parameters, shown in Fig. 3, for 13 different storm recovery phases. An increasing Q corresponds to a decreasing T and vice versa. It is remarkable that hereby pronounced differences between injection and decay effects are existing for different storms. This points to different development of the storms caused probably by a different previous history. For strong injections we have found a mean value r of nearly 6 h. This is in good accordance with the value given by Pisarsky et al. (1986). In Fig. 4 the z values in dependence from Q for 19 storms are shown which were calculated for the beginning of the recovery phase. Essentially this result corresponds to that of Fig. 3. Now we must ask the question: is such a cakulation of r correct? We have calculated r considering the injection. However, is it definite that this injection which we have calculated by using equation (4) is acting in the ring current region? We believe that a correct estimation of z is possible only by using time
I
17.11.7s Q
200
IS0 = -I c
6.7.74 & loo
I
\ '\I '1
SCJi
-106
‘s *7$:.=_2,,, I
I
0'
OR (nlf FIG. 5. RELATIONSHIP BETWEEN WI~OUTIN~C~ON~R
z AND DR FOR PERIODS ~6D~~~~S~~S.
-300
OR (nTf FIG. 6. ~LATION~PBE~N=AND DR DU~NG~VA~ WI~OUTIN~C~ON~R~~SELEC~DS~~.
768
A. GUFE .
. .
. . .
. ..
.
’
. .
-10
0
-50
Q f nT h-‘) FIG. 7(b). ~LA~ON~P~ 0 (nT h-‘f FIG. 7(a). RELATIONSHIPBETWEEN ADR/At ADJUSTED DR-VALUES.
AND
Q
MR
ANON-~JUS~DR-VALE AND@VALUES.
NON-
intervals of non-existing injections. Fortunately the injection for some time intervals during the recovery phase was zero. So z could be calculated dependent only on DR. The result of this calculation is shown in Fig. 5. Here the hyperbolic-like relation can also be perceived. One recognizes unambi~ously that z decreases when DR increases and vice versa. z is nearly 20 h for high ring current intensities. The relative strong scattering of the points in this figure is caused again by the different decay processes of the storms. This is seen clearly in Fig. 6 showing the relation between r and DR for four storms where during a longer time interval the injection was absent. Tinsley and Akasofu (1982) have found a z of 25 h for a time interval free from injection. With this value our estimated values of T are in good accordance. However, here we must point to the fact that the high value t of 25 h estimated for the missing injection contradicts that of 6 h for the acting injection. How can this contradiction be solved? We think it can be done by supposing that either the acting injection does not frequently reach the ring current region and therefore the ring current cannot be intensified, or Q is not the correct parameter for an energy injection into the ring current. In both cases it must be supposed that the observed effect in the magnetic horizontal intensity during the recovery phase is scarcely or not influenced by the variation of the Q-value. This leads to the question of whether the temporal variations of
DR may be controlled by Q or not. To answer this a calculation of dDR/dt values using non-balanced DR
values is necessary. These were estimated for a 5 h interval in the recovery phase as a mean value of two successive DR values DR-,, D& and DR,, . The two difference quotients follow ARJAt
= (DR,-DR_
,)/At
AR,/At = (DR, , - DR,)lAt
(3 (6)
At is 1 h.
From this it was calculated ADRjAht =
(7)
The relation between the values ADRjAt and Q is shown in Fig. 7(a). It can clearly be seen that there is no functional relation between both parameters. However, as Fig. 7(b) shows there is a linear dependence between the non-balanced DR-values and Q. In this case there hardly exists a difference to the result of the balanced DR values shown in Fig. 2. How can this be explained with regard to Fig. 7(a)? It is guessed that the linear relation between DR and Q is only virtual at the beginning of the recovery phase. The decrease of the injection shows a similar temporal behaviour as the loss process of the ring current. We believe that the decay of the ring current will not often be influenced by the decreasing injection. This will
769
The influence of the recovery phase injection on the decay of the ring current
-I March
1974
OR (nT)
November
1975
OR(nT) FIG.
8.
LEFTSIDE:TWO RING CURRENTEFFECTSWITHOUT XNJECTION IN THE FIRST PARTOF THE RECOVERY PHASE. RXGHTSIDE: RELATIONSHIP BETWEEN 2,AND DROFTHE LEFTSIDERING CURRENT EFFECTS.
clearly be shown in the following by the investigation of special events. Event investigation
In the following Q values are used which were calculated exactly after equation (3). These values were designated as Q*. For intervals with Q* > 0 the injection is zero. Besides the 5-h values of Q* using the balanced DR-values dDR/dt-values were graphically estimated at the same time moments for which Q*-values were calculated. From these values z, = -DR/dDR{dt were derived. In Fig. 8 two ring current effects are shown for which the injection suddenly disappears at the end of the main phase. Q* remains positive during nearly 24 h. Within that time the ring current decay turns out quite uniformly. This also shows the functional dependence of r, on DR at the ant-hand side of the figure. For the March 1974 event such a relation is valid until the time moment 5. Afterwards it is interrupted by a new injection enhancement. The t, values at the beginning of the
recovery phase amount to nearly 20 h. It can clearly be seen that the ring current decay and injection pass similarly during the first day of the recovery phase. Figure 9 shows ring current effects on 11 February 1969 and on 1I December 1977. Here, for these events, the injection indeed diminishes at the beginning of the recovery phase but does not disappear totally. Investigating these four storms (Figs 8 and 9) we find for all the storms, decrease of DR during the 15 h of the recovery phase taking place independently from the acting injection. This is shown in Table I. The decrease of DR is nearly the same during different injections. In the case of the storm on 11 February 1969 the decrease of DR is even greater though the injection continues. A calculation of rr (without consideration of Q*) also gives for both storms shown in Fig. 9 values of nearly 20 h at the beginning of the recovery phase. The decrease of the ring current intensity, however, is interrupted in both recovery phases. In the case of the February event a new ring current
A. GRAFE
o-
O-
I’
>-
-2oc>t3 FIG.~.LEFTSIDE :TWORINGC~~ENT EPFECTSWlTH INJJXTION IN THJiFIRST PART OF THE RECOVERY i’HASE. ~GHTSIDE:RELATIONSHIPBE~EN~, AND~ROFTHELEXTSIDERINGCURR@NTEFF!XTS. TABLE 1 Decrease of Date
11February
1969 16 March 1974 17 November I975 11 December 1977
DR @T) in 15h 75 61 59 58
-20.2 +2.6 -4.4 -48.5
increase is connected with an enhancement of injection. The temporal gradient of DR is positive and therefore negative for r. However, already at the time moment 7 the ring current decreases again without being influenced by the injection. Even the first decay phase at the storm in December 1977 turns out in the same manner as before. However, already at the time moment 3 a new intensification of the ring current begins. This, however, cannot be caused by an injection determined by Q*. It is shown in Fig. 10 how differently the relation between injection and ring current intensity can develop. On the right-hand side of this figure there are
represented two storm events (March 1969, October 1974) showing the ring current recovery phase being controlled extensively by the injection. This is much less the case for both storm events on the left-hand side (February 1967, July 1974) of Fig. 10. However, also for both storms on the right-hand side the ring current decay occurs obviously during the first hours of the recovery phase non-influenced by an existing injection. This was the case for all 23 investigated storm events. As Figs 2 and 7(b) show, a linear relation between injection and ring current intensity actually exists but this is not of correlative nature in such a way that the injection decrease controls the ring current decay. The relation between both parameters is only virtual. Calculating the decay parameter for 10 h after the beginning of the recovery phase by not considering the injection the values of Fig. 1I result. According to that for a ring current intensity of lW200 nT a mean value z, of 25 h follows. The scattering of the points in this figure is caused again by the individual development of the single storms and perhaps also by their different previous histories. It seems that for stronger sto~s(>2~n~~~~~~tol5horeventolOh.
The influence of the recovery phase injection on the decay of the ring current
771
A. GRAFE
772
I
0
I
I 200
loo DR
FIG. 11. ~A~ONS~PBE~N~~AND 10 h AFlER THE BEGINNINGOF
I
300
(nl)
DR CALCULATEDFOR THE REcWJERY PHA.SEFOR 23
STORMS.
DISCUSSION
In former calculations of the ring current decay parameter it was assumed that the energy injection from the tail into the ring current region stopped suddenly at the beginning of the recovery phase (Yacob, 1964; Grafe and Best, 1966). There was no possibility to do otherwise because inte~laneta~ parameters were unknown and therefore also input rates of injection. Due to this lack the calculated characteristic times of the ring current effect were considered as not quite suitable. The determination possibility of interplanetary parameters, however, now permits the calculation of the ring current injection rate which is a function of the inte~laneta~ electric field. The consideration of this injection has led in the past to rather contrary results (for instance Sizova and Zaitzeva, 1984; Pisarsky et al., 1986). What may be the cause? We are of the opinion that the course of the ring current decay is often not influenced by injection. We believe that this is only the case within the beginning of the recovery phase. Therefore it is not correct to always consider injection values like Q for the calculation of the ring current decay parameter r. We suppose the following cause for such a behaviour. The injection energy which drives the ring current toward the Earth diminishes at the beginning of the recovery phase. At this time the energy is too weak to reach the storm time ring current region. Therefore the ring current can decay without influence by injection. Of course sometimes a new injection may appear during the recovery phase. This is shown in Fig. 10. Then the injection energy reaches the ring current region once again. However, it is often too weak. Another investigation result is the following: for one and the same ring current effect the decay process cannot be described by a constant parameter. The
decay parameter changes with the intensity of the ring current. As a rule it increases with the decrease of the ring current intensity and vice versa. The functional relation between these parameters is hy~r~lic-like. A mean value r of 25 h was found for storms in the intensity interval of 100-200 nT. As we have already mentioned this is in good accordance with the results of Tinsley and Akasofu (1982), of Sizova and Zaitzeva (1984) and of Pudovkin et al. (1988). The values given by Pisarsky et al. (1986) are far too small. Since the previous calculations of r did not take into consideration an injection the r values are quite correct. Therefore the r values estimated by Grafe (1967) and Grafe and Best (1966) correspond rather well with those calculated here. A further result is the fact that indeed for all storms a general decay relation is valid, however, there exist remarkable quantitative differences of the ring current decay. We point out that the decay time for ring currents with the same intensity is not constant. As it is shown in Fig. 11, r can be variable from I5 to 3.5 h for a ring current. This means that each storm has its own ring current development. This is not surprising considering that the behaviour of the inner magnetosphere at the beginning of every storm is different concerning the position and intensity of the quiet-time ring current and that consequently the composition of the ring current particles will be different, due to the variability of the ionospheric source for the different storms. This results in different courses of the charge exchange process. Finally the fact that the value r of 25 h is in good accordance with the lifetime of 10 keV protons for L = 3.5 should be noted, assuming that only the charge exchange process is acting (Liemohn, 1961). This shows that protons contribute essentially to the formation of the ring current. The enhancement of the decay parameter during the recovery phase is caused by an increasing lifetime of higher energetic protons after the charge exchange process. It is believed that the observed ring current effect is the sum of many single charge exchange processes with different time constants. This was previously pointed out by Grafe and Best (1966).
REFERENCES
Angenheister, G. (1924) Die erdmagnetischen Stiirungen nach den ~obachtungen des ~rnoa-ob~~ato~~~ 1. Nachrichten der Gesellschaft der Wissenschafteen, Gdttingen., Math. Phys. Kkzsse. 1. Burton, R. K., McPherron, P. L. and Russel, C. T. (1975)
empirical relationshjp between inte~ianeta~ and Ds,. J. geophys. Res. 80,4204.
in
An conditions
The influence
of the recovery
phase injection
Feldstein, Y. I., Pisarsky, V. Y., Rudneva, N. M. and Grafe, A. (1984) Ring current simulation in connection with interplanetary space conditions. Planet. Space Sci. 32, 915. Grafe, A. (1967) Bemerkungen zur Ringstromtheorie. Jahrbuch 1965 dses Adolf-Schmidt-Observatoriums fur Erdmagnetismus in Niemegk, 185. Grafe, A. and Best, A. (1966) Bemerkungen zur Hypothese zweier Sturmzeitringstriime. PAGEOPH 64, 59. __ Liemohn, H. (1961) The lifetime of radiation belt orotons with energies between 1 keV and 1 MeV. J. geophys. Res. 66,3593. Pisarsky, V. Y., Rudneva, N. M., Feldstein, Y. I. and Grafe, A. (1986) About the ring current decay constant. Geomagnetism i Aeronomija H. 3,454.
on the decay of the ring current
713
Pudovkin, M. I., Grafe, A. Zaitzeva, S. A., Sizova, L. Z. and Usmanov, A. V. (1988) Calculating the &-variation field on the basis of solar wind parameters. Gerlands Beitrzge zur Geophysik (in press). Schmidt, A. (1925-5) Das erdmagnetische AuBenfeld. Z. J Geophysik 1, 1. Sizova, L. Z. and Zaitzeva, S. A. (1984) Growth and recovery of ring current (in Russian). Preprint ZZMIRAN 52,463. Tinsley, B. A. and Akasofu, S.-I. (1982) A note on the lifetime of the ring current particles. Planet. Space Sci. 30,733. Yacob, A. (1964) Decay rate of recovery phase of geomagnetic storms and dissipation of associated ring currents. Indian Y. Met. Geophys. 15, 579.
M)32-0633/88 S3.M)+O.o0 PeQa”,On ,hSS pk
1988
THE INFLUENCE OF THE RECOVERY PHASE INJECTION ON THE DECAY OF THE RING CURRENT A. GRAFE
Heinrich Hertz Institute of Atmosphe~c Research and ~oma~etism, G.D.R., II99 Berlin, G.D.R.
Academy of Sciences of the
(Received injinal form 13 January 1988)
Abstra&--CaIculations of the decay parameter of the equatorial ring current are generally made under consideration of the momentary injection, which is calculated from interplanetary parameters. Hereby values of the order of 6 h result. However our investigations of 23 storms from 1966 to 1977 have shown that the ring current decays in a much slower manner. A time constant of about 20 h has been found. This is obviously caused by the fact that the decay event of the ring current is not disturbed by the injection at the beginning of the recovery phase. It is supposed that at this time the ring current region can no longer be reached by the injection. Therefore it is not justified to consider the injection at the beginning of the recovery phase for the calculation of the decay parameter. This is changing within the recovery phase. It increases with decreasing intensity of the ring current and vice versa. Here several storms behave differently which leads to the conclusion of various conditions of the magnetosphere and probably also a different pre-development.
INTRODUCTION
In earlier investigations of the recovery phase of a geomagnetic storm the continuous increase of the magnetic horizontal intensity was only attributed to the regular intensity decrease of a ring current flowing around the Earth in a western direction (Schmidt, 1924-5). The anaiysis of many geomagnetic ring current effects resulted in the well-known “Angenheister law” (Angenheister, 1924), which describes the course of the horizontal intensity during all recovery phases by a time constant, the so-called “ring current decay constant”. This ring current constant reaches smaller values at stronger ring current effects and vice versa, which means strong geomagnetic storms decrease much faster than weaker ones. Later calculations of the decay constant presume additionally that the energy input to the ring current plasma ends at the beginning of the recovery phase, so the decay constant can be calculated from the eth value of the maximal disturbance. It was also concluded that stronger storms are decreasing faster than weaker ones. For a storm intensity of 100 nT a decay constant of 20 h was stated. Yacob (1964) found a similar result. In fact these investigations describe the regular decay of the geomagnetic ring current effect, but they do not inform us about the real course of the decrease in the ring current intensity or about energy loss of the ring current particles. Indeed the course of the ho~zontal intensity during the recovery phase is caused not only by that of the ring current, but also 765
by the temporally variable energy injection from the far magnetospheric tail into the ring current plasma. This must clearly be recognized. Former investigations were not able to consider energy injections during the recovery phase. Satellite observations of interplanetary parameters nowadays, however, allow the calculation of the ring current injection rate (Burton et al., 1975; Feldstein et al., 1984). This possibility has resulted in several recent investigations about the geomagnetic ring current effect using only D,,-indices as initial values but giving contrary results. Pisarsky et al. (1986) found that the decay parameter for a storm is not constant but increases with decreasing ring current intensity and vice versa. Sisova and Zaitzeva (1984) concluded that the decay constant during the recovery phase increases with increasing ring current intensity and vice versa. According to Tin&y and Akasofu (1982) the decay parameter has lower values during the main phase than during the recovery phase. These differing results made it necessary to investigate again the law of the ring current development during the recovery phase of geomagnetic storms. This is intended by the following analysis of 23 storms during the years 19661977. D,, mean values were used.
DERIVATION
OF RING CURRENT
DECAY PARAMETER
The D, indices are for many reasons not ideal values for the description of the activity of the sym-
A. GRAFE
766
-300
-2DD
.. I .
:
L
&I$
-‘Do
AlTERBEGINNlNGOFTHESMRM.
i,‘
DR, = D,,-
DCF,-
D,,
(1)
is used. According to Burton et al. (1975) DCF, = b = 0.3 nT - cm3/*eV- I/*, p = bp ‘I* = 0.03 V* &, solar wind pressure, V = solar wind velocity in km SC’ and n = solar wind density in g cmW3. The value of D,,q was obtained from D, values during extreme quiet days following several investigated storms. The result of this analysis is shown by Fig. 1. Three different groups were chosen giving un-
I -35
I -30
I -23
I -20
I
.
-.
..
.*
5.
.:.:
c’t”’
metric ring current, but they allow the best possible description at present. The influence of the magnetopause current during the disturbed conditions of DCF, is also given by the D, values and must be eliminated. Furthermore it is necessary to obtain DRd values which are free from the influences of the undisturbed ring current DR,, their sum is denoted by DSfq. Therefore the equation
*.
._ -
..**’ .
s
FIG. 1. MEANHOURLY&,-VALLJESONEXTREMELYQCJJETDAYS
.
. . .: *
F:
Days after the beginning of the laststorm befom the extremely quiet day
.
.
,.’
--
.J.
h-‘)
0 (nl
FIG. 2. RELATIONSHIP BETWEEN ADJUSTED D&VALUES Q-VALUES.
AND
disturbed days. Figure 1 shows distinctly that D,, is relatively high on extremely quiet days following a storm. Dsr decreases, then later a storm is followed by extreme quiet days, and aims at a constant value of about 15 nT. This value was taken for Dstq. In this way all mean hourly Dsr values are converted into DRd ones. Mean hourly values of the solar wind velocity and solar wind density of the King catalog were used for the calculation of DCF,. The ring current balance condition is necessary for the calculation
I -15
I -10
I -5
I0
Cl(nT he’) FIG. 3. RELATIONSHIPBETWEENTANDINJECTIONRATE
QFOR
13 DIFFERENTSMRMS.
767
The influence of the recovery phase injection on the decay of the ring current
during
the
recovery
phase
this
means
that
dDR/dt > 0. This corresponds to the negative sign of DR. From (2) it follows that
r = DR/(Q-dDR/dt).
(4)
BEHAVIOUR OF THE DECAY PARAMETER s DURING THE RECOVERY PHASE Statistic results I -50
I -20
I -30
I -40
I -10
According to (4) z is a function of Q as well as of
I0
0 (nT hei) FIG. 4. ~?ELATIONSHIPBETWEEN z AND Q FOR THEBEGINNING OFTHERECOVERYPHASE (dDR/dt= 0).
of the ring current decrease parameter t from the DR values. This condition is given by (DR,is subsequently denoted by DR) dDR/dt = Q-DR/z.
(2)
Here Q is the ring current energy injection rate and I)R/z the ring current loss term. According to the papers of Burton et al. (1975) and Feldstein et ai. (1984), it is supposed that Q is controlled by the interplanetary electric field. Using values of the 2 component of the interplanetary magnetic field B, and those of the solar wind velocity Y the relation of Feldstein et al. (1984) was used for the calculation of 7 according to (2) Q = -4.32(-R,I’+O.9).
(3)
For the South component of the interplanetary magnetic field values of Q < 0 result. Source and loss terms have inverse signs as DR < 0 during the storm. Because the loss term is greater than the source term
DR. Generally it is assumed that a close relation exists between Q and DR in such a form that a strong injection leads to high DR values and vice versa. This
relation is often linear (Sizova and Zaitzeva, 1984). Our analysis has also shown this (cf. Fig. 2). Therefore it has been confirmed that there also exists a certain functional relation between z and Q. Indeed we found a hyperbolic-like relation between both parameters, shown in Fig. 3, for 13 different storm recovery phases. An increasing Q corresponds to a decreasing T and vice versa. It is remarkable that hereby pronounced differences between injection and decay effects are existing for different storms. This points to different development of the storms caused probably by a different previous history. For strong injections we have found a mean value r of nearly 6 h. This is in good accordance with the value given by Pisarsky et al. (1986). In Fig. 4 the z values in dependence from Q for 19 storms are shown which were calculated for the beginning of the recovery phase. Essentially this result corresponds to that of Fig. 3. Now we must ask the question: is such a cakulation of r correct? We have calculated r considering the injection. However, is it definite that this injection which we have calculated by using equation (4) is acting in the ring current region? We believe that a correct estimation of z is possible only by using time
I
17.11.7s Q
200
IS0 = -I c
6.7.74 & loo
I
\ '\I '1
SCJi
-106
‘s *7$:.=_2,,, I
I
0'
OR (nlf FIG. 5. RELATIONSHIP BETWEEN WI~OUTIN~C~ON~R
z AND DR FOR PERIODS ~6D~~~~S~~S.
-300
OR (nTf FIG. 6. ~LATION~PBE~N=AND DR DU~NG~VA~ WI~OUTIN~C~ON~R~~SELEC~DS~~.
768
A. GUFE .
. .
. . .
. ..
.
’
. .
-10
0
-50
Q f nT h-‘) FIG. 7(b). ~LA~ON~P~ 0 (nT h-‘f FIG. 7(a). RELATIONSHIPBETWEEN ADR/At ADJUSTED DR-VALUES.
AND
Q
MR
ANON-~JUS~DR-VALE AND@VALUES.
NON-
intervals of non-existing injections. Fortunately the injection for some time intervals during the recovery phase was zero. So z could be calculated dependent only on DR. The result of this calculation is shown in Fig. 5. Here the hyperbolic-like relation can also be perceived. One recognizes unambi~ously that z decreases when DR increases and vice versa. z is nearly 20 h for high ring current intensities. The relative strong scattering of the points in this figure is caused again by the different decay processes of the storms. This is seen clearly in Fig. 6 showing the relation between r and DR for four storms where during a longer time interval the injection was absent. Tinsley and Akasofu (1982) have found a z of 25 h for a time interval free from injection. With this value our estimated values of T are in good accordance. However, here we must point to the fact that the high value t of 25 h estimated for the missing injection contradicts that of 6 h for the acting injection. How can this contradiction be solved? We think it can be done by supposing that either the acting injection does not frequently reach the ring current region and therefore the ring current cannot be intensified, or Q is not the correct parameter for an energy injection into the ring current. In both cases it must be supposed that the observed effect in the magnetic horizontal intensity during the recovery phase is scarcely or not influenced by the variation of the Q-value. This leads to the question of whether the temporal variations of
DR may be controlled by Q or not. To answer this a calculation of dDR/dt values using non-balanced DR
values is necessary. These were estimated for a 5 h interval in the recovery phase as a mean value of two successive DR values DR-,, D& and DR,, . The two difference quotients follow ARJAt
= (DR,-DR_
,)/At
AR,/At = (DR, , - DR,)lAt
(3 (6)
At is 1 h.
From this it was calculated ADRjAht =
(7)
The relation between the values ADRjAt and Q is shown in Fig. 7(a). It can clearly be seen that there is no functional relation between both parameters. However, as Fig. 7(b) shows there is a linear dependence between the non-balanced DR-values and Q. In this case there hardly exists a difference to the result of the balanced DR values shown in Fig. 2. How can this be explained with regard to Fig. 7(a)? It is guessed that the linear relation between DR and Q is only virtual at the beginning of the recovery phase. The decrease of the injection shows a similar temporal behaviour as the loss process of the ring current. We believe that the decay of the ring current will not often be influenced by the decreasing injection. This will
769
The influence of the recovery phase injection on the decay of the ring current
-I March
1974
OR (nT)
November
1975
OR(nT) FIG.
8.
LEFTSIDE:TWO RING CURRENTEFFECTSWITHOUT XNJECTION IN THE FIRST PARTOF THE RECOVERY PHASE. RXGHTSIDE: RELATIONSHIP BETWEEN 2,AND DROFTHE LEFTSIDERING CURRENT EFFECTS.
clearly be shown in the following by the investigation of special events. Event investigation
In the following Q values are used which were calculated exactly after equation (3). These values were designated as Q*. For intervals with Q* > 0 the injection is zero. Besides the 5-h values of Q* using the balanced DR-values dDR/dt-values were graphically estimated at the same time moments for which Q*-values were calculated. From these values z, = -DR/dDR{dt were derived. In Fig. 8 two ring current effects are shown for which the injection suddenly disappears at the end of the main phase. Q* remains positive during nearly 24 h. Within that time the ring current decay turns out quite uniformly. This also shows the functional dependence of r, on DR at the ant-hand side of the figure. For the March 1974 event such a relation is valid until the time moment 5. Afterwards it is interrupted by a new injection enhancement. The t, values at the beginning of the
recovery phase amount to nearly 20 h. It can clearly be seen that the ring current decay and injection pass similarly during the first day of the recovery phase. Figure 9 shows ring current effects on 11 February 1969 and on 1I December 1977. Here, for these events, the injection indeed diminishes at the beginning of the recovery phase but does not disappear totally. Investigating these four storms (Figs 8 and 9) we find for all the storms, decrease of DR during the 15 h of the recovery phase taking place independently from the acting injection. This is shown in Table I. The decrease of DR is nearly the same during different injections. In the case of the storm on 11 February 1969 the decrease of DR is even greater though the injection continues. A calculation of rr (without consideration of Q*) also gives for both storms shown in Fig. 9 values of nearly 20 h at the beginning of the recovery phase. The decrease of the ring current intensity, however, is interrupted in both recovery phases. In the case of the February event a new ring current
A. GRAFE
o-
O-
I’
>-
-2oc>t3 FIG.~.LEFTSIDE :TWORINGC~~ENT EPFECTSWlTH INJJXTION IN THJiFIRST PART OF THE RECOVERY i’HASE. ~GHTSIDE:RELATIONSHIPBE~EN~, AND~ROFTHELEXTSIDERINGCURR@NTEFF!XTS. TABLE 1 Decrease of Date
11February
1969 16 March 1974 17 November I975 11 December 1977
DR @T) in 15h 75 61 59 58
-20.2 +2.6 -4.4 -48.5
increase is connected with an enhancement of injection. The temporal gradient of DR is positive and therefore negative for r. However, already at the time moment 7 the ring current decreases again without being influenced by the injection. Even the first decay phase at the storm in December 1977 turns out in the same manner as before. However, already at the time moment 3 a new intensification of the ring current begins. This, however, cannot be caused by an injection determined by Q*. It is shown in Fig. 10 how differently the relation between injection and ring current intensity can develop. On the right-hand side of this figure there are
represented two storm events (March 1969, October 1974) showing the ring current recovery phase being controlled extensively by the injection. This is much less the case for both storm events on the left-hand side (February 1967, July 1974) of Fig. 10. However, also for both storms on the right-hand side the ring current decay occurs obviously during the first hours of the recovery phase non-influenced by an existing injection. This was the case for all 23 investigated storm events. As Figs 2 and 7(b) show, a linear relation between injection and ring current intensity actually exists but this is not of correlative nature in such a way that the injection decrease controls the ring current decay. The relation between both parameters is only virtual. Calculating the decay parameter for 10 h after the beginning of the recovery phase by not considering the injection the values of Fig. 1I result. According to that for a ring current intensity of lW200 nT a mean value z, of 25 h follows. The scattering of the points in this figure is caused again by the individual development of the single storms and perhaps also by their different previous histories. It seems that for stronger sto~s(>2~n~~~~~~tol5horeventolOh.
The influence of the recovery phase injection on the decay of the ring current
771
A. GRAFE
772
I
0
I
I 200
loo DR
FIG. 11. ~A~ONS~PBE~N~~AND 10 h AFlER THE BEGINNINGOF
I
300
(nl)
DR CALCULATEDFOR THE REcWJERY PHA.SEFOR 23
STORMS.
DISCUSSION
In former calculations of the ring current decay parameter it was assumed that the energy injection from the tail into the ring current region stopped suddenly at the beginning of the recovery phase (Yacob, 1964; Grafe and Best, 1966). There was no possibility to do otherwise because inte~laneta~ parameters were unknown and therefore also input rates of injection. Due to this lack the calculated characteristic times of the ring current effect were considered as not quite suitable. The determination possibility of interplanetary parameters, however, now permits the calculation of the ring current injection rate which is a function of the inte~laneta~ electric field. The consideration of this injection has led in the past to rather contrary results (for instance Sizova and Zaitzeva, 1984; Pisarsky et al., 1986). What may be the cause? We are of the opinion that the course of the ring current decay is often not influenced by injection. We believe that this is only the case within the beginning of the recovery phase. Therefore it is not correct to always consider injection values like Q for the calculation of the ring current decay parameter r. We suppose the following cause for such a behaviour. The injection energy which drives the ring current toward the Earth diminishes at the beginning of the recovery phase. At this time the energy is too weak to reach the storm time ring current region. Therefore the ring current can decay without influence by injection. Of course sometimes a new injection may appear during the recovery phase. This is shown in Fig. 10. Then the injection energy reaches the ring current region once again. However, it is often too weak. Another investigation result is the following: for one and the same ring current effect the decay process cannot be described by a constant parameter. The
decay parameter changes with the intensity of the ring current. As a rule it increases with the decrease of the ring current intensity and vice versa. The functional relation between these parameters is hy~r~lic-like. A mean value r of 25 h was found for storms in the intensity interval of 100-200 nT. As we have already mentioned this is in good accordance with the results of Tinsley and Akasofu (1982), of Sizova and Zaitzeva (1984) and of Pudovkin et al. (1988). The values given by Pisarsky et al. (1986) are far too small. Since the previous calculations of r did not take into consideration an injection the r values are quite correct. Therefore the r values estimated by Grafe (1967) and Grafe and Best (1966) correspond rather well with those calculated here. A further result is the fact that indeed for all storms a general decay relation is valid, however, there exist remarkable quantitative differences of the ring current decay. We point out that the decay time for ring currents with the same intensity is not constant. As it is shown in Fig. 11, r can be variable from I5 to 3.5 h for a ring current. This means that each storm has its own ring current development. This is not surprising considering that the behaviour of the inner magnetosphere at the beginning of every storm is different concerning the position and intensity of the quiet-time ring current and that consequently the composition of the ring current particles will be different, due to the variability of the ionospheric source for the different storms. This results in different courses of the charge exchange process. Finally the fact that the value r of 25 h is in good accordance with the lifetime of 10 keV protons for L = 3.5 should be noted, assuming that only the charge exchange process is acting (Liemohn, 1961). This shows that protons contribute essentially to the formation of the ring current. The enhancement of the decay parameter during the recovery phase is caused by an increasing lifetime of higher energetic protons after the charge exchange process. It is believed that the observed ring current effect is the sum of many single charge exchange processes with different time constants. This was previously pointed out by Grafe and Best (1966).
REFERENCES
Angenheister, G. (1924) Die erdmagnetischen Stiirungen nach den ~obachtungen des ~rnoa-ob~~ato~~~ 1. Nachrichten der Gesellschaft der Wissenschafteen, Gdttingen., Math. Phys. Kkzsse. 1. Burton, R. K., McPherron, P. L. and Russel, C. T. (1975)
empirical relationshjp between inte~ianeta~ and Ds,. J. geophys. Res. 80,4204.
in
An conditions
The influence
of the recovery
phase injection
Feldstein, Y. I., Pisarsky, V. Y., Rudneva, N. M. and Grafe, A. (1984) Ring current simulation in connection with interplanetary space conditions. Planet. Space Sci. 32, 915. Grafe, A. (1967) Bemerkungen zur Ringstromtheorie. Jahrbuch 1965 dses Adolf-Schmidt-Observatoriums fur Erdmagnetismus in Niemegk, 185. Grafe, A. and Best, A. (1966) Bemerkungen zur Hypothese zweier Sturmzeitringstriime. PAGEOPH 64, 59. __ Liemohn, H. (1961) The lifetime of radiation belt orotons with energies between 1 keV and 1 MeV. J. geophys. Res. 66,3593. Pisarsky, V. Y., Rudneva, N. M., Feldstein, Y. I. and Grafe, A. (1986) About the ring current decay constant. Geomagnetism i Aeronomija H. 3,454.
on the decay of the ring current
713
Pudovkin, M. I., Grafe, A. Zaitzeva, S. A., Sizova, L. Z. and Usmanov, A. V. (1988) Calculating the &-variation field on the basis of solar wind parameters. Gerlands Beitrzge zur Geophysik (in press). Schmidt, A. (1925-5) Das erdmagnetische AuBenfeld. Z. J Geophysik 1, 1. Sizova, L. Z. and Zaitzeva, S. A. (1984) Growth and recovery of ring current (in Russian). Preprint ZZMIRAN 52,463. Tinsley, B. A. and Akasofu, S.-I. (1982) A note on the lifetime of the ring current particles. Planet. Space Sci. 30,733. Yacob, A. (1964) Decay rate of recovery phase of geomagnetic storms and dissipation of associated ring currents. Indian Y. Met. Geophys. 15, 579.