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Time evolution of the westward-traveling surge on an ionospheric time scale
Planer. Printed
SpaceSci., in Great
Vol. 35, No. 2, pp. 145-151, Britain.
1987
1X)324633/87 $3.00+0.00 Pergamon Journals Ltd.
TIME EVOLUTION OF THE WESTWARD-TRAVELING SURGE ON AN IONOSPHERIC TIME SCALE L. ZHU and J. R. KAN
Geophysical Institute and Department of Physics, University of Alaska, Fairbanks, AK ~775-0800. U.S.A. (Received in final form 18 September 1986)
Abstract-A global westward traveling surge model is formulated to study the evolution of the convection pattern, the surge velocity, the meld-aligned current and the conductivity ~st~butions. The time scale of the model is governed by the recombination in the aurora1 ionosphere. The main results are as follows. (i) The Harang discontinuity is formed due to the blockage of the Hall current from diverging along field lines. (ii) The westward-traveling surge moves rapidly at the onset of a substorm and then slows down to become stationary as the substorm subsides. The average westward speed is a few kilometers per second for aurora1 electrons of a few kiloel~tronvolts energy. The speed increases with the energy of the aurora1 electrons. (iii) The sense of the field-aligned current in the post-midnight sector agrees with region I and region II current only when the Hall current is “blocked” from diverging along field lines.
1. INTRODUCTION
The westward-traveling surge (WTS) is a prominent feature of the magnetospheric substorm (Akasofu, 1986). It has gained renewed theoretical interest in recent years (Rothwell et a/., 1984; Kan and Kamide, 1985; Kan and Sun, 1985). The ionosphere is shown to play an active role in the motion of aurora1 forms in the WTS. Specifically, the motion is shown to depend (i) on the distortion of the convection pattern evolving on the Alfven transit time scale in the magnetosphere (Kan and Sun, 1985) and (ii) on the enhan~ment of ionospheric conductivity evolving on the recombination time scale in the ionosphere (Rothwell et al., 1984). In this paper, we present a global WTS model which can be viewed as an extension of the local WTS model of Rothwell et al. (1984) on the one hand, and an extension of the Hall current blockage model of Kan and Kamide (1985) to include the ionospheric recombination time scale on the other hand. The main difference between the local one-dimensional WTS model and the global two-dimensional WTS model lies in the treatment of the field-aligned currents. In the local model, the Hall current is assumed to be blocked on the poleward boundary but not on the westward boundary of the conductivity strip (Rothwell et al., 1984). This assumption is removed from the global WTS model in which the blockage of the Hall current is allowed to occur wherever the conductivity gradient is nonzero. Marklund et al. (1985) proposed a model in which both the Hall curent and Pederson current are allowed to be blocked.
The ionospheric conductivity
is time-independent
in
their mode1. 2.
~EOR~IC~
MODEL
The upward field-aligned current in the model is assumed to be carried by the precipitating aurora1 electrons (in the kilovolt energy range). The electron number density is governed by the continuity equation which can be written as g = QJ,,/e-jIn2
(1)
where Q is the average number of ions produced per incident electron per meter, e is the electronic charge, /I is the recombination coefficient, and J,, is the fieldaligned current carried by the precipitating aurora1 electrons. From the definition of the height-integrated Hall conductivity &, the rate of change of the Hall conductivity can be approximated by g,_e&&
(2)
dt N B, at
where El is the effective height of the conducting ionosphere and B,, is the ambient magnetic field in the ionosphere. From the divergence of the ionospheric current, the field-aligned current can be written as ^
J,, = - B,V * @,Ei +&B,
^
x Ei)
(3)
where & is the unit vector of the ambient magnetic 145
146
L. ZHU and
J. R. KAN 3. NUMERICAL
field pointing downward in the Northern Hemisphere and Ei is the electric field in the ionosphere. Combining (l), (2) and (3) one obtains 8% ---=
at
HQ BR
[VC, . (Ei + RB,
X
Ei) + ~,V. Ei]
o
-- B 5 e 0H
c;
(4)
where R = C,,&. For simplicity, R is assumed to be independent of the energy of the precipitating electrons. The ionospheric electric field Ei depends on whether or not the Hall current is blocked from diverging along field lines. The blockage of the Hall current is defined by Kan and Kamide (1985) V - [ZPEp + C&, x (E, + E,)] = 0
(5)
where EP( = -V&) is the polarization field produced by the blockage process and E,( = - V4,) is the external field imposed on the ionosphere. The ionospheric electric field is given by E, = E,+E,.
(6)
Evolution of the WTS on the ionospheric time scale is governed by (4), (5) and (6).
RESULTS
The ionosphere is modeled by computational grids on a plane polar coordinate system as described in Kan and Kamide (1985). The numerical procedure for solving (4), (5) and (6) is as follows. At t = 0, the external field E, is imposed on the ionosphere with a given initial conductivity XP and &,. From (5), E, is calculated and E, is obtained from (6). The Ei thus obtained is substituted into (4) to update the conductivity ZH and ZP. The updated conductivity is then used in (5) and (6) to update E, and Ei. The computational loop is repeated until a steady state is reached asymptotically in time. Figure 1 shows the input quantities of the model. Figure la shows the external potential distribution imposed on the ionosphere which describes the convection pattern at t = 0. Figure 1b shows the initial ionospheric Hall conductivity distribution. The initial conductivity on the nightside is due to the ionization produced by the diffuse aurora1 precipitation. On the dayside, the initial conductivity is due to the solar U.V. radiation which is proportional to the cosine of the solar zenith angle. The ratio Z& = 1.5 is used throughout the numerical computation. Figure 2 shows the temporal variation of the WTS for a 5.6 keV monoenergetic aurora1 electron beam with H = 7 x IO3m, Q = 7 x lo- 3 ions (e-m)- ’ (Rees, 1963) and p = lo-l3 m3 ss’ (Walls and Dunn, 1974).
(A)
(B) 12
MAX
(A) The
MAX
49.70
CONTOUR
INTERVAL
5.00
KV
15.03
CONTOUR
INTERVAL2.00
FIG. 1. THE INPUT QUANTITIES OF THE WESTWARD-TRAVELING SURGE potential distribution at t = 0. (B) The Hall conductivity distribution &/X,, = 1.5 is assumed.
MHO MODEL.
at t = 0. The ratio
147
Westward-traveling surge of magnetospheric substorm Panels (a) and (b) show the equipotential contours or the convection pattern at t = 40 s and t = 110 s. The convection pattern exhibits the characteristic Harang discontinuity which is in good agreement with observations (Heppner, 1977 ; Evans et al., 1980 ; Kamide et al., 1981; Ahn et al., 1986). Panels (c) and (d) show the corresponding height-integrated Hall conduc-
tivity. Panels (e) and (f) show the corresponding development of the westward and eastward aurora1 electrojets. Panels (g) and (h) show the field-aligned current distribution, where the dashed contours denote upward currents and the solid contours denote downward currents. The location of the maximum upward field-aligned current can be identified as the
(B) 12
(A) 12
MIN
-38.88 MAX 35.64
CONTOUR
00
00
INTERVAL 5.00
MIN -38.22 KV
MAX 35.33 CONTOUR INTERVAL 5.00
W
(D)
MIN
I
.oo
00
15.18 CONTOUR INTERVAL 2.00
00 1 .oo MAX 15.99 CONTOUR INTERVAL2.00 MIN
MAX
MHO
FIG. 2 (A to D). Caption overleaf.
MHO
L. ZHU and
148
1
0.9
AMP/M
J. R. KAN
0.9
(HI
(G)
00 -0.71 MAX 0.56 CONTOUR INTERVALO.10
AMP/M
MIN
MIN
PA/m*
00 -0.8%
0.56 MAX CONTOUR INTERV7AL0.10
PA/m*
FIG. 2. TEMPORAL EVOLUTION OF THE WESTWARD-TRAVELING SURGE UNDER THE BLOCKAGE OF THE HALL CURRENTANDTHEIONIZATIONOF~.~ keV AURORALELECTRONS. The calculated potential distributions are (A) at t = 40 s and(B) at f = 110 s. The corresponding conductivity distributions are in (C) and (D). The corresponding ionospheric currents are in (E) and (F). The corresponding field-aligned current distributions are in (G) and (H).
149
Westward-traveling surge of magnetospheric substorm
ENERGY FIG.
3. THE SPEED OF
OF ELECTRONS
(KEV)
THE WESTWARD-TRAVELING
SURGE AS A
FUNCTION OF THE AURORAL ELECTRON ENERGY.
head of the WTS where the aurora is brightest. Note that the maximum upward current position moves westward. The westward surge initially (t < 40 s) moves fairly fast and then slows down to become stationary after t > 110 s. This is in contrast to the constant velocity (for a given aurora1 energy) found in the local WTS model (Rothwell et al., 1984). Figure 3 shows the average speed of the WTS as a
function of the energy of a monoenergetic aurora1 electron beam. As the energy increases, the speed increases and the head of the WTS moves further West before stopping. The average westward speed is about 7.7 km s-’ for the 5.6 keV aurora1 electrons, which is in reasonable agreement with the observed velocities of the WTS (Akasofu, 1968 ; Pytte et al., 1976). Figure 4 shows the results obtained under the assumption that the ionospheric Hall current were allowed to diverge freely along field lines (i.e. no blockage of the Hall current). The polarization electric field E, = 0 and E, = E. for all time. The initial condition is given in Fig. 1. The ionospheric conductivity enhanced by a 5.6 keV monoenergetic aurora1 electron beam is shown in panels (a) and (b) at t = 40 s and t = 110 s, respectively. The corresponding fieldaligned current distributions are shown in panels (c) and (d). Note that the upward field-aligned currents in the post-midnight sector in Figs 4c and 4d occur on the poleward side of the downward current. This is opposite to the results in panels (g) and (h) of Fig. 2, which are consistent with the observed sense of the region I and region II field-aligned currents (Iijima and Potemra, 1976). Also note that the speed of the WTS estimated from Fig. 4 is predominantly westward at 11 km s- ’ (for 5.6 keV aurora1 electrons). A small poleward motion with a few hundred meters per second speed can be inferred with high uncertainty
(A)
t=)
MAX
15.35
CONTOUR
INTERVAL2.00
(B) t=llO
MAX
set
12
15.52
CONTOUR INTERVAL2.00 MHO FIG.4 (A and B). Caption overleaf.
MHO
L. ZHU and J. R. KAN
150
MAX 0.54 CONTOUR lNTERVALO.10
/&‘m’
MAX 0.54 CONTOUR INTERVAL 0.10
pA,'m2
Fm.4. TEMPOKALEVOLUTIONOFTHEWESTWARD-TRAVELINGSURGEWITHOUTTHEBLOCKAGEOFTHE HALL CURRENT, BUTUNDER THE IONIZATI~NOF~.~ keV AURORALELECTRONS. The potential distribution in this case is time-independent as given in Fig. 1A. The Hall conductivity distributions are (A) at t = 40 s and (B) at I = 110 s. The corresponding field-aligned current distributions are in (C) and (D). These results are to be compared with those in Fig. 2 to show the effects of the blockage of the Hall current.
from the results in Fig. 4. Poleward motion is not noticeable in Fig. 2 and thus appears to be suppressed by the blockage of the Hall current. This is qualitatively consistent with the results of Rothwell et al. (1984). From the results in Figs 2 and 4, it is clear that the blockage of the Hall current not only plays an important role in producing the Harang discontinuity in the convection pattern, but also leads to the correct sense of the region I and II field-aligned currents in the post-midnight sector.
4. SUMMARY
We have developed a global WTS model on the ionospheric time scale. The main results of the model are as follows. (i) The formation of the Harang discontinuity can be understood in terms of the blockage of the Hall current from diverging along field lines. (ii)The WTS speed is high at the onset of a substorm and then slows down to zero speed as the substorm subsides. The average westward speed increases with the energy of the precipitating aurora1 electrons. The average westward speed
ranges from 1.2 km s- ’ for a 1 keV aurora1 electron beam to 7.7 km s-’ for a 5.6 keV aurora1 electron beam. (iii) The upward field-aligned current occurs equatorward of the downward current in the postmidnight sector if the Hall current is blocked from diverging along field lines. This is consistent with the observed sense of the region I and region II field-aligned currents. Opposite sense of field-aligned current in the post-midnight sector occurs if the Hall current is allowed to diverge freely along field lines in the model. Acknowledgements-This
work was supported in part under Air Force contract F19628-85-K-0012 and by NSF grant ATM83-*7456.
REFERENCES
Ahn, B.-H., Kamide, Y. and Akasofu, S.-I. (1986) Electrical changes of the polar ionosphere during magnetospheric substorm. J. geophys. Res. 91, 5737. Akasofu, S.-I. (1986)Polar and Magnerospheric Substorms. D. Reidel, Dordrecht. Evans, J. V., Holt, J. M., Oliver, W. L. and Wand, R. H. (1980) Millstone Hill incoherent scatter observations of aurora1 convection over 60” < A < 75”, 2. Initial results. J. geophys. Res. 85, 4 1.
Westward-traveling surge of magnetospheric substorm Heppner, J. P. (1977) Empirical models of high latitude electric field. J. geophys. Res. 82, 1115. Iijima, T. and Potemra, T. A. (1976) Large-scale characteristics of field-aligned currents associated with substorms. J. geophys. Res. 81, 3999. Kamide, Y., Richmond, A. D. and Matsushita, S. (1981) Estimation of ionospheric electric fields, ionospheric currents and field-aligned currents from ground magnetic records. J. gcophys. Res. 86, 80 1. Kan, J. R. and Kamide, Y. (1985) Electrodynamics of the westward traveling surge. J. geophys. Res. 91, 7615. Kan, J. R. and Sun, W. (1985) Simulation of the westward traveling surge and Pi2 pulsations during substorms. J. geophys. Res. 90, 10911. Marklund, G. T., Raadu, M. A. and Lindqvist, P.-A. (1985)
151
Effect of Birkeland current limitation on high-latitude convection patterns. J. geophys. Res. 90, 10864. Pytte, T., McPherron, R. L. and Kokubun, S. (1976) The ground signatures of the expansion phase during multiple onset substorms. Planet. Space Sci. 24, 1115. Rees, M. H. (1963) Aurora1 ionization and excitation by incident energetic electrons. Planet. Space Sci. 11, 1209. Rothwell, P. L., Silevitch, M. B. and Block, L. R. (1984) A model for the propagation of the westward traveling surge. J. geophys. Res. 89, 8941. Walls, F. L. and Dunn, G. H. (1974) Measurement of total cross-sections for electron recombination with NO+ and 0~ using ion storage technology. J. geophys. Res. 79, 1911.
SpaceSci., in Great
Vol. 35, No. 2, pp. 145-151, Britain.
1987
1X)324633/87 $3.00+0.00 Pergamon Journals Ltd.
TIME EVOLUTION OF THE WESTWARD-TRAVELING SURGE ON AN IONOSPHERIC TIME SCALE L. ZHU and J. R. KAN
Geophysical Institute and Department of Physics, University of Alaska, Fairbanks, AK ~775-0800. U.S.A. (Received in final form 18 September 1986)
Abstract-A global westward traveling surge model is formulated to study the evolution of the convection pattern, the surge velocity, the meld-aligned current and the conductivity ~st~butions. The time scale of the model is governed by the recombination in the aurora1 ionosphere. The main results are as follows. (i) The Harang discontinuity is formed due to the blockage of the Hall current from diverging along field lines. (ii) The westward-traveling surge moves rapidly at the onset of a substorm and then slows down to become stationary as the substorm subsides. The average westward speed is a few kilometers per second for aurora1 electrons of a few kiloel~tronvolts energy. The speed increases with the energy of the aurora1 electrons. (iii) The sense of the field-aligned current in the post-midnight sector agrees with region I and region II current only when the Hall current is “blocked” from diverging along field lines.
1. INTRODUCTION
The westward-traveling surge (WTS) is a prominent feature of the magnetospheric substorm (Akasofu, 1986). It has gained renewed theoretical interest in recent years (Rothwell et a/., 1984; Kan and Kamide, 1985; Kan and Sun, 1985). The ionosphere is shown to play an active role in the motion of aurora1 forms in the WTS. Specifically, the motion is shown to depend (i) on the distortion of the convection pattern evolving on the Alfven transit time scale in the magnetosphere (Kan and Sun, 1985) and (ii) on the enhan~ment of ionospheric conductivity evolving on the recombination time scale in the ionosphere (Rothwell et al., 1984). In this paper, we present a global WTS model which can be viewed as an extension of the local WTS model of Rothwell et al. (1984) on the one hand, and an extension of the Hall current blockage model of Kan and Kamide (1985) to include the ionospheric recombination time scale on the other hand. The main difference between the local one-dimensional WTS model and the global two-dimensional WTS model lies in the treatment of the field-aligned currents. In the local model, the Hall current is assumed to be blocked on the poleward boundary but not on the westward boundary of the conductivity strip (Rothwell et al., 1984). This assumption is removed from the global WTS model in which the blockage of the Hall current is allowed to occur wherever the conductivity gradient is nonzero. Marklund et al. (1985) proposed a model in which both the Hall curent and Pederson current are allowed to be blocked.
The ionospheric conductivity
is time-independent
in
their mode1. 2.
~EOR~IC~
MODEL
The upward field-aligned current in the model is assumed to be carried by the precipitating aurora1 electrons (in the kilovolt energy range). The electron number density is governed by the continuity equation which can be written as g = QJ,,/e-jIn2
(1)
where Q is the average number of ions produced per incident electron per meter, e is the electronic charge, /I is the recombination coefficient, and J,, is the fieldaligned current carried by the precipitating aurora1 electrons. From the definition of the height-integrated Hall conductivity &, the rate of change of the Hall conductivity can be approximated by g,_e&&
(2)
dt N B, at
where El is the effective height of the conducting ionosphere and B,, is the ambient magnetic field in the ionosphere. From the divergence of the ionospheric current, the field-aligned current can be written as ^
J,, = - B,V * @,Ei +&B,
^
x Ei)
(3)
where & is the unit vector of the ambient magnetic 145
146
L. ZHU and
J. R. KAN 3. NUMERICAL
field pointing downward in the Northern Hemisphere and Ei is the electric field in the ionosphere. Combining (l), (2) and (3) one obtains 8% ---=
at
HQ BR
[VC, . (Ei + RB,
X
Ei) + ~,V. Ei]
o
-- B 5 e 0H
c;
(4)
where R = C,,&. For simplicity, R is assumed to be independent of the energy of the precipitating electrons. The ionospheric electric field Ei depends on whether or not the Hall current is blocked from diverging along field lines. The blockage of the Hall current is defined by Kan and Kamide (1985) V - [ZPEp + C&, x (E, + E,)] = 0
(5)
where EP( = -V&) is the polarization field produced by the blockage process and E,( = - V4,) is the external field imposed on the ionosphere. The ionospheric electric field is given by E, = E,+E,.
(6)
Evolution of the WTS on the ionospheric time scale is governed by (4), (5) and (6).
RESULTS
The ionosphere is modeled by computational grids on a plane polar coordinate system as described in Kan and Kamide (1985). The numerical procedure for solving (4), (5) and (6) is as follows. At t = 0, the external field E, is imposed on the ionosphere with a given initial conductivity XP and &,. From (5), E, is calculated and E, is obtained from (6). The Ei thus obtained is substituted into (4) to update the conductivity ZH and ZP. The updated conductivity is then used in (5) and (6) to update E, and Ei. The computational loop is repeated until a steady state is reached asymptotically in time. Figure 1 shows the input quantities of the model. Figure la shows the external potential distribution imposed on the ionosphere which describes the convection pattern at t = 0. Figure 1b shows the initial ionospheric Hall conductivity distribution. The initial conductivity on the nightside is due to the ionization produced by the diffuse aurora1 precipitation. On the dayside, the initial conductivity is due to the solar U.V. radiation which is proportional to the cosine of the solar zenith angle. The ratio Z& = 1.5 is used throughout the numerical computation. Figure 2 shows the temporal variation of the WTS for a 5.6 keV monoenergetic aurora1 electron beam with H = 7 x IO3m, Q = 7 x lo- 3 ions (e-m)- ’ (Rees, 1963) and p = lo-l3 m3 ss’ (Walls and Dunn, 1974).
(A)
(B) 12
MAX
(A) The
MAX
49.70
CONTOUR
INTERVAL
5.00
KV
15.03
CONTOUR
INTERVAL2.00
FIG. 1. THE INPUT QUANTITIES OF THE WESTWARD-TRAVELING SURGE potential distribution at t = 0. (B) The Hall conductivity distribution &/X,, = 1.5 is assumed.
MHO MODEL.
at t = 0. The ratio
147
Westward-traveling surge of magnetospheric substorm Panels (a) and (b) show the equipotential contours or the convection pattern at t = 40 s and t = 110 s. The convection pattern exhibits the characteristic Harang discontinuity which is in good agreement with observations (Heppner, 1977 ; Evans et al., 1980 ; Kamide et al., 1981; Ahn et al., 1986). Panels (c) and (d) show the corresponding height-integrated Hall conduc-
tivity. Panels (e) and (f) show the corresponding development of the westward and eastward aurora1 electrojets. Panels (g) and (h) show the field-aligned current distribution, where the dashed contours denote upward currents and the solid contours denote downward currents. The location of the maximum upward field-aligned current can be identified as the
(B) 12
(A) 12
MIN
-38.88 MAX 35.64
CONTOUR
00
00
INTERVAL 5.00
MIN -38.22 KV
MAX 35.33 CONTOUR INTERVAL 5.00
W
(D)
MIN
I
.oo
00
15.18 CONTOUR INTERVAL 2.00
00 1 .oo MAX 15.99 CONTOUR INTERVAL2.00 MIN
MAX
MHO
FIG. 2 (A to D). Caption overleaf.
MHO
L. ZHU and
148
1
0.9
AMP/M
J. R. KAN
0.9
(HI
(G)
00 -0.71 MAX 0.56 CONTOUR INTERVALO.10
AMP/M
MIN
MIN
PA/m*
00 -0.8%
0.56 MAX CONTOUR INTERV7AL0.10
PA/m*
FIG. 2. TEMPORAL EVOLUTION OF THE WESTWARD-TRAVELING SURGE UNDER THE BLOCKAGE OF THE HALL CURRENTANDTHEIONIZATIONOF~.~ keV AURORALELECTRONS. The calculated potential distributions are (A) at t = 40 s and(B) at f = 110 s. The corresponding conductivity distributions are in (C) and (D). The corresponding ionospheric currents are in (E) and (F). The corresponding field-aligned current distributions are in (G) and (H).
149
Westward-traveling surge of magnetospheric substorm
ENERGY FIG.
3. THE SPEED OF
OF ELECTRONS
(KEV)
THE WESTWARD-TRAVELING
SURGE AS A
FUNCTION OF THE AURORAL ELECTRON ENERGY.
head of the WTS where the aurora is brightest. Note that the maximum upward current position moves westward. The westward surge initially (t < 40 s) moves fairly fast and then slows down to become stationary after t > 110 s. This is in contrast to the constant velocity (for a given aurora1 energy) found in the local WTS model (Rothwell et al., 1984). Figure 3 shows the average speed of the WTS as a
function of the energy of a monoenergetic aurora1 electron beam. As the energy increases, the speed increases and the head of the WTS moves further West before stopping. The average westward speed is about 7.7 km s-’ for the 5.6 keV aurora1 electrons, which is in reasonable agreement with the observed velocities of the WTS (Akasofu, 1968 ; Pytte et al., 1976). Figure 4 shows the results obtained under the assumption that the ionospheric Hall current were allowed to diverge freely along field lines (i.e. no blockage of the Hall current). The polarization electric field E, = 0 and E, = E. for all time. The initial condition is given in Fig. 1. The ionospheric conductivity enhanced by a 5.6 keV monoenergetic aurora1 electron beam is shown in panels (a) and (b) at t = 40 s and t = 110 s, respectively. The corresponding fieldaligned current distributions are shown in panels (c) and (d). Note that the upward field-aligned currents in the post-midnight sector in Figs 4c and 4d occur on the poleward side of the downward current. This is opposite to the results in panels (g) and (h) of Fig. 2, which are consistent with the observed sense of the region I and region II field-aligned currents (Iijima and Potemra, 1976). Also note that the speed of the WTS estimated from Fig. 4 is predominantly westward at 11 km s- ’ (for 5.6 keV aurora1 electrons). A small poleward motion with a few hundred meters per second speed can be inferred with high uncertainty
(A)
t=)
MAX
15.35
CONTOUR
INTERVAL2.00
(B) t=llO
MAX
set
12
15.52
CONTOUR INTERVAL2.00 MHO FIG.4 (A and B). Caption overleaf.
MHO
L. ZHU and J. R. KAN
150
MAX 0.54 CONTOUR lNTERVALO.10
/&‘m’
MAX 0.54 CONTOUR INTERVAL 0.10
pA,'m2
Fm.4. TEMPOKALEVOLUTIONOFTHEWESTWARD-TRAVELINGSURGEWITHOUTTHEBLOCKAGEOFTHE HALL CURRENT, BUTUNDER THE IONIZATI~NOF~.~ keV AURORALELECTRONS. The potential distribution in this case is time-independent as given in Fig. 1A. The Hall conductivity distributions are (A) at t = 40 s and (B) at I = 110 s. The corresponding field-aligned current distributions are in (C) and (D). These results are to be compared with those in Fig. 2 to show the effects of the blockage of the Hall current.
from the results in Fig. 4. Poleward motion is not noticeable in Fig. 2 and thus appears to be suppressed by the blockage of the Hall current. This is qualitatively consistent with the results of Rothwell et al. (1984). From the results in Figs 2 and 4, it is clear that the blockage of the Hall current not only plays an important role in producing the Harang discontinuity in the convection pattern, but also leads to the correct sense of the region I and II field-aligned currents in the post-midnight sector.
4. SUMMARY
We have developed a global WTS model on the ionospheric time scale. The main results of the model are as follows. (i) The formation of the Harang discontinuity can be understood in terms of the blockage of the Hall current from diverging along field lines. (ii)The WTS speed is high at the onset of a substorm and then slows down to zero speed as the substorm subsides. The average westward speed increases with the energy of the precipitating aurora1 electrons. The average westward speed
ranges from 1.2 km s- ’ for a 1 keV aurora1 electron beam to 7.7 km s-’ for a 5.6 keV aurora1 electron beam. (iii) The upward field-aligned current occurs equatorward of the downward current in the postmidnight sector if the Hall current is blocked from diverging along field lines. This is consistent with the observed sense of the region I and region II field-aligned currents. Opposite sense of field-aligned current in the post-midnight sector occurs if the Hall current is allowed to diverge freely along field lines in the model. Acknowledgements-This
work was supported in part under Air Force contract F19628-85-K-0012 and by NSF grant ATM83-*7456.
REFERENCES
Ahn, B.-H., Kamide, Y. and Akasofu, S.-I. (1986) Electrical changes of the polar ionosphere during magnetospheric substorm. J. geophys. Res. 91, 5737. Akasofu, S.-I. (1986)Polar and Magnerospheric Substorms. D. Reidel, Dordrecht. Evans, J. V., Holt, J. M., Oliver, W. L. and Wand, R. H. (1980) Millstone Hill incoherent scatter observations of aurora1 convection over 60” < A < 75”, 2. Initial results. J. geophys. Res. 85, 4 1.
Westward-traveling surge of magnetospheric substorm Heppner, J. P. (1977) Empirical models of high latitude electric field. J. geophys. Res. 82, 1115. Iijima, T. and Potemra, T. A. (1976) Large-scale characteristics of field-aligned currents associated with substorms. J. geophys. Res. 81, 3999. Kamide, Y., Richmond, A. D. and Matsushita, S. (1981) Estimation of ionospheric electric fields, ionospheric currents and field-aligned currents from ground magnetic records. J. gcophys. Res. 86, 80 1. Kan, J. R. and Kamide, Y. (1985) Electrodynamics of the westward traveling surge. J. geophys. Res. 91, 7615. Kan, J. R. and Sun, W. (1985) Simulation of the westward traveling surge and Pi2 pulsations during substorms. J. geophys. Res. 90, 10911. Marklund, G. T., Raadu, M. A. and Lindqvist, P.-A. (1985)
151
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