- Email: [email protected]
Dependence of the geometry of the region of open field lines on the interplanetary magnetic field
Plonel. Space Sci. Vol. 29. No. 8, pp. 803-807, Printed in Great Britain.
DEPENDENCE
0032-0633/81/080803~5$02.00/0 Pergamon Press Ltd.
1981
OF THE GEOMETRY
S.-I.AKASOFU
OF THE REGION
OF OPEN FIELD
D. N. COVEY
and
Geophysical Institute, University of Alaska, Fairbanks, AK 99701, U.S.A. and C.-I. MENG
Applied Physics Laboratory, Johns Hopkins University, Laurel, MD 20810, U.S.A. (Received 24 February 1981) Abstract-The geometry of the open flux area in the polar region is computed by superposing a uniform interplanetary magnetic field (IMF) with various orientation angles to a model of the magnetosphere. It is confirmed that the IMF BYcomponent is as important as the B, component in “opening” the magnetosphere. It is also shown that the computed area of open field lines is remarkably similar to the observed ones which were determined by using the entry of solar electrons. In particular, when the IMF vector is confined in the X-Z-plane and the B, component has a large positive value, the open area becomes crescent-shaped, coinciding approximately with the cusp region. 1. INTRODUCTION
There are now several observations which indicate or suggest that drastic changes of the geometry of the open region occur as the orientation of the interplanetary magnetic field (IMF) vector changes. These observations are based on the geometry of the area into which low-energy or high-energy solar electrons enter (Meng et al., 1977; McDiarmid et al., 1980). Meanwhile, effects of the IMF on the structure of the magnetosphere have long been studied, most recently by Stern ,_^__. ,_^__. ..^_^. (1’175), Saunders (lY’I6), Voigt (lY78), Voigt and Fuchs (1979), Leboeuf et al. (1978), and Akasofu and Covey (1980). The purpose of this paper is to examine specifically the dependence of the geometry of the open field line region of the magnetosphere on the IMF by assuming a simple linear superposition of the IMF on a model magnetospheric field. This study can also be con_:>__-> A_ Lsluereu LO oe a quaiitative test of the vaiidity of the superposition method, since one can compare the observed open region and the computed open region. It is indeed of great interest to examine whether or not this simple method can provide, as a first approximation, a topologicaliy correct configuration of the open magnetosphere, without using a full-scale plasma simulation method. In order to make the open region of the model as realistic as possible, one must carefully construct a three-dimensional model of the mag-
netosphere so as to be able to determine whether or not individual magnetospheric field lines are connected to the IMF field lines. For this purpose, one must be cautious in constructing the anti-solar end of the magnetotail. Keeping these aspects in mind, we constructed the following model [for details, see Akasofu and Covey (1980)]. Our model of the magnetosphere consists of the Earth’s dipole field (of magnetic moment ME) and an image dipole field corresponding to a dipole of moment 7.0 ME at X = 28.0 RE, plus the magnetic field of the magnetotaii (soiar-magnetospheric coordinates are used in this paper). The tail field is simulated with two sets of 77 ring currents, one set in each hemisphere, separated by 0.2 RE across the equatorial plane (the so-called “neutral sheet”). The currents flow counter-clockwise (as viewed from the Earth) in the northern ring and clockwise in the southern ring. They are distributed uniformiy over a distance of i8O RE, the nearest pair being located at X = -10 R,; thus, the successive rings are spaced uniformly by a distance of 2.37 RE. In order to generate the observed 8” flaring of the tail, the radius of the rings is made to increase linearly by 14%. Further, the current intensity in successive rings is made to decrease with distance down the tail, starting with 250,000 A at X = -10.0 R, to zero at X = -190 R,. In this way, we construct first a model of the magnetosphere in the absence of the IMF and 803
S.-I. AKASOFUet
804
determine the geometry of the magnetopause. The magnetopause consists of the magnetic field lines which “pass” through a very small area around the dayside neutral points (one in each hemisphere). Then, superposing the IMF of magnitude IBI = 10-r in the model, we trace systematically a large number of field lines in the magnetosphere. Following Saunders (1976) the open field lines are defined as magnetic field lines which reach the magnetopause. The use of a relatively large value of IBl = 10-r as the magnitude of the IMF is to examine effects of the IMF for the magnetosphere with a relatively short tail of length 200 RE.It is generally accepted that the length of the tail is significantly longer than 200 RE,so that a smaller magnitude of the IMF will have the same effects. 2. RESULTS AND WITH
COMPARISON
OBSERVATIONS
The geometry of the open field line area is determined for two sets of IMF orientations. In the first set, the IMF vector is confined in the X-Z-plane, and the angle between the Z-axis and the IMF vector is denoted by CY,being reckoned positive as the vector rotates away from the Sun. The values of cy examined here are 30”, 60”, 90” H BX-62 0
al.
and 120” and 180”, so that the B, component is always negative. In the second set, the IMF vector is confined in the X-Y-plane, and the angle between the Z-axis and the IMF vector is denoted by p, being reckoned positive as the vector rotates toward the dawn side, so that the B, component is always negative. The values of /3 examined here are also 30”, 60”, 90” and 120” and 180”. (a) (Y= 30”(Bx = -5.07, B, = O-y, B, = 8.7-y) p = 30”(B, = Oy, B, = -5.0~B, = 8.7~). Figure 1 shows the geometry of the northern open region for both (Y= 30” and p = 30” in latitude-magnetic local time (MLT) coordinates. For LY= 30”, the open region is a very small area which is located at 79” in latitude along the noon meridian. Therefore, the magnetosphere is practically closed in this situation. For p = 30”, the open region is almost confined in the evening sector in the northern hemisphere. Though it is not shown here, the open region is located in the morning sector in the southern hemisphere and its geometry is the mirror image (with respect to the noon-midnight meridian) of the northern one. The significance of this result .,* I wtu oe discussed in @j. (b) (Y= 60”(B, = -8.7n B, = Oy,B, = 5.0~) p = 6O”(Bx = Oy, B, = -8.7y, B, = 5.0~). Figure 2 shows the geometry of the northern
BY-62 17
w
BX-BZ
18
FIG. 1. THEGEOMETRYOFTHENORTHERNOPENREGIONIN INVARIANT LATITUDE-MAGNETIC LOCAL TIME (MLT) COORDINATES FOR a = 30” (& = -s.Oy, B, = 0, B, = 8.7~) AND FOR p = 30” (& = 0, B, = s.Oy, B, = 8.7~).
Note that the open area for (Y= 30” is a very small area near the center of the black square which is located at 79” in latitude along the noon meridian.
06
fl= 60' FIG. 2. THE GEOMETRY OFTHE NORTHERN OPEN REGION FOR a = 60” (B, = -8.7y, B, = 0, B, = 5.0~) AND FOR fl= 60”
(I?, = 0, B, = -8.77, B, = 5.0~). The open region for a is indicated by the black squares and the open region for p is indicated by the open octagons.
805
Geometry of region of open field tines
open region for both QI= 60” and p = 60”. One can immediately recognize a large difference of the geometry of the open region for the same value (60”) of cy and p. For LY= 60”, the magnetic field lines from a crescent-shaped region in the dayside Can reach the magnetopause. It is interesting to note in this respect that McDiarmid et al. (1980) found that high-energy solar electron fluxes have a single peak in their pitch-angle distribution in a crescentshaped area in the polar region and a double peak in the rest of the polar region when the IMF components were B, - -2Oy, B, -5~ and B, +3Oy. They suggested that the open region had a crescent shape. Their Figs. 6(a) and (b) are reproduced here as Figs. 3(a) and (b). One can see the simiIarity of the open regions in Fig. 3(a) and Fig. 2 (a. = 60”). It is interesting to note also in this connection that the dayside aurora1 arc system lies in a crescent region similar to those shown in Figs. 2 and 3(a) and remains bright even when the IMF S, component is large and positive (although the nightside arc system becomes very faint); for details, see Akasofu and Kan (1980).
For p = 60”, the open region is mainly confined in the evening sector in the northern hemisphere; in the southern hemisphere, the open region is mainly confined in the morning sector. Similar patterns were also suggested by Stern (1973) and computed by Saunders ii976j.
Agltliii,
rL^
LIlC
-^I
cum-
puted open region is similar to that suggested by McDiarmid et al. (1980) although the B, component was greater than the BY component, namely, B, = 4.3~ BY = -0.7~ and B, = 19.2~. The open area in the southern hemisphere is the mirror image (with respect to the noon-midnight meridian) of it and appears in the morning sector, if the IMF vector is directed in the opposite direction, namely B, = Oy, B, = 8.7~ and B, = 5.0~. Such an asymmetry of the entry of solar electrons with respect to the sign of the IMF B, component was noted also by Meng et al. (1977). Further, Meng et ai. (1977) showed that the situation is reversed in the southern hemisphere. Therefore, our results are qualitatively in agreement with the observations. In this connection, it is suggested that the dependence of the appearance of the mantle plasma and the lobe plasma on the IMF BY component (Schopke et al., 1974; Hardy et al., 1979) is also related to the results obtained in this paper.. (c) cr = 90”(B, = -10~ By=%, B,=Oy) 8 = 90”(B, = Oy, B, = - 10~. B, = 0~). Figure 4 shows the results for (Y=90” and p = 90”. The results for IY= 90” are similar to those for a! = 60”, except that the open areas become appreciably greater than those for CY= 60”. It is thus of great interest to examine auroras under sim=5x-82
00
Ib) FIG.~. ~~EGEOM~~TUYOF~~~OPEN
FIELDLIN~RE~IONIN. FERRED FROMTHE ENTRYOFSOLAR ELECTRONS(MCDIARMID et al., 1980). (a) 3, = -2Oy, B, = -5y, B, = 307 cb) 3, =4.3% BY = -0.7y, B, =9.2r.
FIG. 4. THE GEOMETRY OF THE NORTHERN FOR a=m" (&=-l&y, B,=O, &=o) (B, = 0, BY= -!Oy, B, = 0).
OPEN REGION AND @=90”
S.-I. AKASOFU et\al.
806
ponent in opening the magnetosphere is indeed very crucial. (d) a = 120”(&= -8.77, B, = Oy, B, = -5.0~) p = 120”(&= On B, = -8.77, B, = -5.07). Figure 5 shows results for LY= 120” and p = 120”. For both cases, the open area is close to the region enclosed by the normal size oval. This is expected because the IMF B, component is negative. Note that there is a slight asymmetry of the area with respect to the noon-midnight meridian for p = 120”. (e) (Y= p = 18O”(B, = Oy, B, = Oy, B, = -10-y). Figure 6 shows the result. The aurora1 oval is the same for both LY= 180” and p = 180”. The open area is a little greater than that of the normal size oval. F1c.5.THEGEOMETRYOFTHENORTHERNOPENREGIONFOR a = 120"(B, = - 8.77, BY = On B, = - 5.0~) AND B = 120" (Bx= Oy,B, = - 8.77, B, = - 0~).
ilar IMF conditions. Therefore, the nightside of the polar region is still essentially closed even for (Y= 90”. For p = 90”, however, the open area expands drastically and becomes similar to that enciosed by the average size aurorai ovai. This result indicates that the B, component is very important in making the nightside of the polar region open, as pointed out by Stern (1973), Gonzalez and Mozer (1974), Saunders (1976), and Akasofu and Covey (1980). For IMF polar angles of less than 90” or B, > 0, the importance of the B, com-
06
18
3. DISCUSSION
The remarkable similarity of the open regions (inferred from the impact area of solar electrons) by McDiarmid et al. (1980) and Meng et al. (1977) and the computed open regions proves the validity of the simple superposition method of the IMF on a magnetospheric field model, at least in studying the topoiogicai changes of rL_ L”t: ---__r__-l__:_ nuigue~“bpuelK structure caused by variations of the orientation of the IMF. In this connection, it is also important to note that there is a significant similarity between the results obtained by a full-scale plasma simulation method and by the simple superposition method (Leboeuf et al., 1979; Lyon et al., 1980) employed in this paper (cf. Akasofu and Covey, 1980).
Acknowledgements-We thank Dr I. B. McDiarmid for his interest in our work. The work reported here was supported in part by a contract from the USAF F1962879-C-0067 to the Geophysical Institute, University of Alaska, and grants from the National Science Foundation (ATM79-23740) to the Geophysical Institute, University of Alaska, and the Air Force Office of Scientific Research (AFOSR-79-0010) to the Johns Hopkins University. REFERENCES
ItIF=
GAMMA
00
a
= 1800
p=
180”
FIG. 6. THE GEOMETRY OF THE NORTHERN OPEN REGION FORa=B=180°(Bx=Oy,B,=Oy,B,=-10y).
Akasofu, S.-I. and Covey, D. N. (1980). Effects of the interplanetary magnetic field on the magnetotail structure: large-scale changes of the plasmasheet during magnetospheric substorms. Planet. Space Sci. 2% 757. Gonzalez, W. D. and Mozer, F. S. (1974). Quantitative model for the potential resulting from reconnection with an arbitrary interplanetary magnetic field. J. geophys. Res. 79, 4186. Hardy, D. A., Hills, H. K. and Freeman, J. W. (1979). Occurrence of the lobe plasma at lunar distance. .I. geophys. Res. 84, 72.
Geometry of region of open field lines Leboeuf, J. N., Tajima, T., Kennel, C. F. and Dawson, J. M. (1978). Global simulation of the time-dependent magnetosphere. Geophys. Res. Lett. 5, 609. Lyon, J. Cl., Brecht, S. H., Huba, .I. D., Fedder, J. A. and Palmadesso, P. J. (1980). Computer simulation of a geomagnetic substorm. EOS 61, 1072. MC=iNFd
, I. B.,
ijiiiiWWS.,
J.
R
aiid
WilSOii,
iv!.
D.
(1980). Comparison of magnetic field perturbations and solar electron profiles in the polar cap. J. geophys. Res. 85, 1163. Meng, C.-I., Akasofu, S.-I. and Anderson, K. A. (1977). Dawn-dusk gradient of the precipitation of low-energy electrons over the polar cap and its relation to the interplanetary magnetic field. J. geophys. Res. 82,527l. Saunders, R. S. (1976). The characteristics of magnetospheric electric fields as mapped onto the polar caps. Ph.D. thesis, University of Denver.
807
Schopke, N., Paschmann, G., Rosenbauer, H. and Fairfield, D. H. (1976). Influence of the interplanetary field on the occurrence and thickness of the plasma mantle. J. geophys. Res. 81, 2687. Stern, D. P. (1973). A study of the electric field in an open magnetospheric model. J. geophys. Res. 78, 7292. \rr\;“+ *“fig&,
r. U.
” ,,O-lQ\ ‘1. \17,0,.
A “t,t:, ..,“,^ f..lA IL... __._.%___._r:.._ ‘3 aL‘lL,c-3I(ILc; IICZIU-IIIIF ILL” ,111 ~:LL,“,,
model for the Earth’s magnetosphere. J. atmos. terr. Phys. 40, 355. Voigt, G. H. and Fuchs, K. (1979). A macroscopic model for field line interconnection between the magnetosphere and the interplanetary space, in Quantatiue Modelling of Magnetospheric Processes (Ed. W. P. Olson), p. 448, AGU, Washington, D. C.
DEPENDENCE
0032-0633/81/080803~5$02.00/0 Pergamon Press Ltd.
1981
OF THE GEOMETRY
S.-I.AKASOFU
OF THE REGION
OF OPEN FIELD
D. N. COVEY
and
Geophysical Institute, University of Alaska, Fairbanks, AK 99701, U.S.A. and C.-I. MENG
Applied Physics Laboratory, Johns Hopkins University, Laurel, MD 20810, U.S.A. (Received 24 February 1981) Abstract-The geometry of the open flux area in the polar region is computed by superposing a uniform interplanetary magnetic field (IMF) with various orientation angles to a model of the magnetosphere. It is confirmed that the IMF BYcomponent is as important as the B, component in “opening” the magnetosphere. It is also shown that the computed area of open field lines is remarkably similar to the observed ones which were determined by using the entry of solar electrons. In particular, when the IMF vector is confined in the X-Z-plane and the B, component has a large positive value, the open area becomes crescent-shaped, coinciding approximately with the cusp region. 1. INTRODUCTION
There are now several observations which indicate or suggest that drastic changes of the geometry of the open region occur as the orientation of the interplanetary magnetic field (IMF) vector changes. These observations are based on the geometry of the area into which low-energy or high-energy solar electrons enter (Meng et al., 1977; McDiarmid et al., 1980). Meanwhile, effects of the IMF on the structure of the magnetosphere have long been studied, most recently by Stern ,_^__. ,_^__. ..^_^. (1’175), Saunders (lY’I6), Voigt (lY78), Voigt and Fuchs (1979), Leboeuf et al. (1978), and Akasofu and Covey (1980). The purpose of this paper is to examine specifically the dependence of the geometry of the open field line region of the magnetosphere on the IMF by assuming a simple linear superposition of the IMF on a model magnetospheric field. This study can also be con_:>__-> A_ Lsluereu LO oe a quaiitative test of the vaiidity of the superposition method, since one can compare the observed open region and the computed open region. It is indeed of great interest to examine whether or not this simple method can provide, as a first approximation, a topologicaliy correct configuration of the open magnetosphere, without using a full-scale plasma simulation method. In order to make the open region of the model as realistic as possible, one must carefully construct a three-dimensional model of the mag-
netosphere so as to be able to determine whether or not individual magnetospheric field lines are connected to the IMF field lines. For this purpose, one must be cautious in constructing the anti-solar end of the magnetotail. Keeping these aspects in mind, we constructed the following model [for details, see Akasofu and Covey (1980)]. Our model of the magnetosphere consists of the Earth’s dipole field (of magnetic moment ME) and an image dipole field corresponding to a dipole of moment 7.0 ME at X = 28.0 RE, plus the magnetic field of the magnetotaii (soiar-magnetospheric coordinates are used in this paper). The tail field is simulated with two sets of 77 ring currents, one set in each hemisphere, separated by 0.2 RE across the equatorial plane (the so-called “neutral sheet”). The currents flow counter-clockwise (as viewed from the Earth) in the northern ring and clockwise in the southern ring. They are distributed uniformiy over a distance of i8O RE, the nearest pair being located at X = -10 R,; thus, the successive rings are spaced uniformly by a distance of 2.37 RE. In order to generate the observed 8” flaring of the tail, the radius of the rings is made to increase linearly by 14%. Further, the current intensity in successive rings is made to decrease with distance down the tail, starting with 250,000 A at X = -10.0 R, to zero at X = -190 R,. In this way, we construct first a model of the magnetosphere in the absence of the IMF and 803
S.-I. AKASOFUet
804
determine the geometry of the magnetopause. The magnetopause consists of the magnetic field lines which “pass” through a very small area around the dayside neutral points (one in each hemisphere). Then, superposing the IMF of magnitude IBI = 10-r in the model, we trace systematically a large number of field lines in the magnetosphere. Following Saunders (1976) the open field lines are defined as magnetic field lines which reach the magnetopause. The use of a relatively large value of IBl = 10-r as the magnitude of the IMF is to examine effects of the IMF for the magnetosphere with a relatively short tail of length 200 RE.It is generally accepted that the length of the tail is significantly longer than 200 RE,so that a smaller magnitude of the IMF will have the same effects. 2. RESULTS AND WITH
COMPARISON
OBSERVATIONS
The geometry of the open field line area is determined for two sets of IMF orientations. In the first set, the IMF vector is confined in the X-Z-plane, and the angle between the Z-axis and the IMF vector is denoted by CY,being reckoned positive as the vector rotates away from the Sun. The values of cy examined here are 30”, 60”, 90” H BX-62 0
al.
and 120” and 180”, so that the B, component is always negative. In the second set, the IMF vector is confined in the X-Y-plane, and the angle between the Z-axis and the IMF vector is denoted by p, being reckoned positive as the vector rotates toward the dawn side, so that the B, component is always negative. The values of /3 examined here are also 30”, 60”, 90” and 120” and 180”. (a) (Y= 30”(Bx = -5.07, B, = O-y, B, = 8.7-y) p = 30”(B, = Oy, B, = -5.0~B, = 8.7~). Figure 1 shows the geometry of the northern open region for both (Y= 30” and p = 30” in latitude-magnetic local time (MLT) coordinates. For LY= 30”, the open region is a very small area which is located at 79” in latitude along the noon meridian. Therefore, the magnetosphere is practically closed in this situation. For p = 30”, the open region is almost confined in the evening sector in the northern hemisphere. Though it is not shown here, the open region is located in the morning sector in the southern hemisphere and its geometry is the mirror image (with respect to the noon-midnight meridian) of the northern one. The significance of this result .,* I wtu oe discussed in @j. (b) (Y= 60”(B, = -8.7n B, = Oy,B, = 5.0~) p = 6O”(Bx = Oy, B, = -8.7y, B, = 5.0~). Figure 2 shows the geometry of the northern
BY-62 17
w
BX-BZ
18
FIG. 1. THEGEOMETRYOFTHENORTHERNOPENREGIONIN INVARIANT LATITUDE-MAGNETIC LOCAL TIME (MLT) COORDINATES FOR a = 30” (& = -s.Oy, B, = 0, B, = 8.7~) AND FOR p = 30” (& = 0, B, = s.Oy, B, = 8.7~).
Note that the open area for (Y= 30” is a very small area near the center of the black square which is located at 79” in latitude along the noon meridian.
06
fl= 60' FIG. 2. THE GEOMETRY OFTHE NORTHERN OPEN REGION FOR a = 60” (B, = -8.7y, B, = 0, B, = 5.0~) AND FOR fl= 60”
(I?, = 0, B, = -8.77, B, = 5.0~). The open region for a is indicated by the black squares and the open region for p is indicated by the open octagons.
805
Geometry of region of open field tines
open region for both QI= 60” and p = 60”. One can immediately recognize a large difference of the geometry of the open region for the same value (60”) of cy and p. For LY= 60”, the magnetic field lines from a crescent-shaped region in the dayside Can reach the magnetopause. It is interesting to note in this respect that McDiarmid et al. (1980) found that high-energy solar electron fluxes have a single peak in their pitch-angle distribution in a crescentshaped area in the polar region and a double peak in the rest of the polar region when the IMF components were B, - -2Oy, B, -5~ and B, +3Oy. They suggested that the open region had a crescent shape. Their Figs. 6(a) and (b) are reproduced here as Figs. 3(a) and (b). One can see the simiIarity of the open regions in Fig. 3(a) and Fig. 2 (a. = 60”). It is interesting to note also in this connection that the dayside aurora1 arc system lies in a crescent region similar to those shown in Figs. 2 and 3(a) and remains bright even when the IMF S, component is large and positive (although the nightside arc system becomes very faint); for details, see Akasofu and Kan (1980).
For p = 60”, the open region is mainly confined in the evening sector in the northern hemisphere; in the southern hemisphere, the open region is mainly confined in the morning sector. Similar patterns were also suggested by Stern (1973) and computed by Saunders ii976j.
Agltliii,
rL^
LIlC
-^I
cum-
puted open region is similar to that suggested by McDiarmid et al. (1980) although the B, component was greater than the BY component, namely, B, = 4.3~ BY = -0.7~ and B, = 19.2~. The open area in the southern hemisphere is the mirror image (with respect to the noon-midnight meridian) of it and appears in the morning sector, if the IMF vector is directed in the opposite direction, namely B, = Oy, B, = 8.7~ and B, = 5.0~. Such an asymmetry of the entry of solar electrons with respect to the sign of the IMF B, component was noted also by Meng et al. (1977). Further, Meng et ai. (1977) showed that the situation is reversed in the southern hemisphere. Therefore, our results are qualitatively in agreement with the observations. In this connection, it is suggested that the dependence of the appearance of the mantle plasma and the lobe plasma on the IMF BY component (Schopke et al., 1974; Hardy et al., 1979) is also related to the results obtained in this paper.. (c) cr = 90”(B, = -10~ By=%, B,=Oy) 8 = 90”(B, = Oy, B, = - 10~. B, = 0~). Figure 4 shows the results for (Y=90” and p = 90”. The results for IY= 90” are similar to those for a! = 60”, except that the open areas become appreciably greater than those for CY= 60”. It is thus of great interest to examine auroras under sim=5x-82
00
Ib) FIG.~. ~~EGEOM~~TUYOF~~~OPEN
FIELDLIN~RE~IONIN. FERRED FROMTHE ENTRYOFSOLAR ELECTRONS(MCDIARMID et al., 1980). (a) 3, = -2Oy, B, = -5y, B, = 307 cb) 3, =4.3% BY = -0.7y, B, =9.2r.
FIG. 4. THE GEOMETRY OF THE NORTHERN FOR a=m" (&=-l&y, B,=O, &=o) (B, = 0, BY= -!Oy, B, = 0).
OPEN REGION AND @=90”
S.-I. AKASOFU et\al.
806
ponent in opening the magnetosphere is indeed very crucial. (d) a = 120”(&= -8.77, B, = Oy, B, = -5.0~) p = 120”(&= On B, = -8.77, B, = -5.07). Figure 5 shows results for LY= 120” and p = 120”. For both cases, the open area is close to the region enclosed by the normal size oval. This is expected because the IMF B, component is negative. Note that there is a slight asymmetry of the area with respect to the noon-midnight meridian for p = 120”. (e) (Y= p = 18O”(B, = Oy, B, = Oy, B, = -10-y). Figure 6 shows the result. The aurora1 oval is the same for both LY= 180” and p = 180”. The open area is a little greater than that of the normal size oval. F1c.5.THEGEOMETRYOFTHENORTHERNOPENREGIONFOR a = 120"(B, = - 8.77, BY = On B, = - 5.0~) AND B = 120" (Bx= Oy,B, = - 8.77, B, = - 0~).
ilar IMF conditions. Therefore, the nightside of the polar region is still essentially closed even for (Y= 90”. For p = 90”, however, the open area expands drastically and becomes similar to that enciosed by the average size aurorai ovai. This result indicates that the B, component is very important in making the nightside of the polar region open, as pointed out by Stern (1973), Gonzalez and Mozer (1974), Saunders (1976), and Akasofu and Covey (1980). For IMF polar angles of less than 90” or B, > 0, the importance of the B, com-
06
18
3. DISCUSSION
The remarkable similarity of the open regions (inferred from the impact area of solar electrons) by McDiarmid et al. (1980) and Meng et al. (1977) and the computed open regions proves the validity of the simple superposition method of the IMF on a magnetospheric field model, at least in studying the topoiogicai changes of rL_ L”t: ---__r__-l__:_ nuigue~“bpuelK structure caused by variations of the orientation of the IMF. In this connection, it is also important to note that there is a significant similarity between the results obtained by a full-scale plasma simulation method and by the simple superposition method (Leboeuf et al., 1979; Lyon et al., 1980) employed in this paper (cf. Akasofu and Covey, 1980).
Acknowledgements-We thank Dr I. B. McDiarmid for his interest in our work. The work reported here was supported in part by a contract from the USAF F1962879-C-0067 to the Geophysical Institute, University of Alaska, and grants from the National Science Foundation (ATM79-23740) to the Geophysical Institute, University of Alaska, and the Air Force Office of Scientific Research (AFOSR-79-0010) to the Johns Hopkins University. REFERENCES
ItIF=
GAMMA
00
a
= 1800
p=
180”
FIG. 6. THE GEOMETRY OF THE NORTHERN OPEN REGION FORa=B=180°(Bx=Oy,B,=Oy,B,=-10y).
Akasofu, S.-I. and Covey, D. N. (1980). Effects of the interplanetary magnetic field on the magnetotail structure: large-scale changes of the plasmasheet during magnetospheric substorms. Planet. Space Sci. 2% 757. Gonzalez, W. D. and Mozer, F. S. (1974). Quantitative model for the potential resulting from reconnection with an arbitrary interplanetary magnetic field. J. geophys. Res. 79, 4186. Hardy, D. A., Hills, H. K. and Freeman, J. W. (1979). Occurrence of the lobe plasma at lunar distance. .I. geophys. Res. 84, 72.
Geometry of region of open field lines Leboeuf, J. N., Tajima, T., Kennel, C. F. and Dawson, J. M. (1978). Global simulation of the time-dependent magnetosphere. Geophys. Res. Lett. 5, 609. Lyon, J. Cl., Brecht, S. H., Huba, .I. D., Fedder, J. A. and Palmadesso, P. J. (1980). Computer simulation of a geomagnetic substorm. EOS 61, 1072. MC=iNFd
, I. B.,
ijiiiiWWS.,
J.
R
aiid
WilSOii,
iv!.
D.
(1980). Comparison of magnetic field perturbations and solar electron profiles in the polar cap. J. geophys. Res. 85, 1163. Meng, C.-I., Akasofu, S.-I. and Anderson, K. A. (1977). Dawn-dusk gradient of the precipitation of low-energy electrons over the polar cap and its relation to the interplanetary magnetic field. J. geophys. Res. 82,527l. Saunders, R. S. (1976). The characteristics of magnetospheric electric fields as mapped onto the polar caps. Ph.D. thesis, University of Denver.
807
Schopke, N., Paschmann, G., Rosenbauer, H. and Fairfield, D. H. (1976). Influence of the interplanetary field on the occurrence and thickness of the plasma mantle. J. geophys. Res. 81, 2687. Stern, D. P. (1973). A study of the electric field in an open magnetospheric model. J. geophys. Res. 78, 7292. \rr\;“+ *“fig&,
r. U.
” ,,O-lQ\ ‘1. \17,0,.
A “t,t:, ..,“,^ f..lA IL... __._.%___._r:.._ ‘3 aL‘lL,c-3I(ILc; IICZIU-IIIIF ILL” ,111 ~:LL,“,,
model for the Earth’s magnetosphere. J. atmos. terr. Phys. 40, 355. Voigt, G. H. and Fuchs, K. (1979). A macroscopic model for field line interconnection between the magnetosphere and the interplanetary space, in Quantatiue Modelling of Magnetospheric Processes (Ed. W. P. Olson), p. 448, AGU, Washington, D. C.