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A coupled solar wind-magnetosphere–ionosphere model for determining the ionospheric penetration electric field
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Journal of Atmospheric and Solar-Terrestrial Physics 69 (2007) 1127–1134 www.elsevier.com/locate/jastp
A coupled solar wind-magnetosphere–ionosphere model for determining the ionospheric penetration electric field P.L. Rothwell, J.R. Jasperse Space Vehicles Directorate, Air Force Research Laboratory, Hanscom Air Force Base, 29 Randolph Rd., Bedford, MA 01731, USA Received 13 April 2006; received in revised form 21 July 2006; accepted 1 August 2006 Available online 24 March 2007
Abstract The transpolar potential Fpc may be estimated from the solar wind as measured by the advanced composition explorer (ACE) satellite at the first Lagrangian point L1. In our model, the transpolar potential drives the region-1 (J1) currents through the ionosphere consistent with a solar-dependent ionospheric conductance. It is shown that the ionospheric potential may be derived from an equivalent Poisson equation, the solution of which gives the global distribution of the ionospheric electric field, including the penetration electric field near the equator. This eastward penetration electric field just past sunset, which is created by J1, is offset by a region-2 (J2) generated westward (shielding) electric field with an unknown rise time. We find that there is a correlation between storm-time potential enhancements and the presence of equatorial bubbles as measured on DMSP satellites. The magnetic storms of 6–7 April 2000 and 20–21 November 2003 are analyzed. In both cases, the observed presence of equatorial plasma bubbles showed better agreement with model predictions using a longer J2 rise time, consistent with Huang et al. [Huang, C.-S., Foster, J., Kelley, M.C., 2005. Longduration penetration of the interplanetary electric field to the low-latitude ionosphere during the main phase of magnetic storms. Journal of Geophysical Research 110(A11309), doi:10.1029/2005JA011202]. r 2007 Elsevier Ltd. All rights reserved. Keywords: Solar wind; Penetration electric fields; Shielding; Plasma bubbles
1. Introduction In this paper we assume that electric fields (Eeq) measured at equatorial latitudes during magnetic storms are primarily caused by the transpolar potential Fpc created by the solar wind. Other electric field sources, such as neutral winds and gravity waves, may also be present, but our present approach restricts us to follow only the energy flow from the solar wind to equatorial latitudes. EastCorresponding author. Tel.: +1 781 377 9664.
E-mail addresses: [email protected] (P.L. Rothwell), [email protected] (J.R. Jasperse). 1364-6826/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.jastp.2006.08.013
ward equatorial electric fields near the dusk terminator increase the upward drift of plasma, creating plasma density bubbles or plumes that contribute to radio scintillations. The time evolution of the density structure around an equatorial plasma plume has been calculated by Retterer (2005) and Retterer (1999). By knowing the strength of the penetration electric field and the response of the plasma, comparisons can be made with the Air Force Research Laboratory (AFRL) Communication and Navigation Outage Forecast System (C/NOFS) satellite (de la Beaujardie`re et al., 2006, 2004). The transpolar potential is consistent with region-1 (J1) currents that are voltage driven but current
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limited, where the currents close through the ionosphere within minutes. Following the model of Siscoe (1982), the J1 currents also partially close through the magnetosphere with a time delay, forming the ring current and associated region-2 (J2) currents. In Paper1 (Rothwell and Jasperse, 2006), equivalent time-dependent circuit equations were derived and an empirical relationship established between the solar wind data measured at L1 and the penetration electric field. The ionospheric response to J1 and J2 was modeled after Nopper and Carovillano (1978) which includes the effects of a sun-lit ionosphere and a dipole magnetic field. The conductance at the terminators used in the Rothwell–Jasperse model had a much larger conductance gradient (and hence more realistic) than that used in the Nopper–Carovillano model. In contrast to the J1 current, the presence of J2 creates a westward electric field also just past 1800 h LT which shields the J1-produced eastward (positive) electric field. Therefore, the net post-sunset electric field is the difference between the J1 and J2 components. Since these two components operate on different time scales finding the net penetration electric field Eeq(t) at any one time is difficult. 2. The model The purpose of the present report is to provide a quantitative method for electrically coupling the interplanetary medium with the equatorial ionosphere. Our method unites three methods that were independently developed. The first method was developed by Siscoe et al. (2002) based on the work of Hill et al. (1976), and extended by Ober et al. (2003). We refer to it as the Hill–Siscoe–Ober or H–S–O model. In this model, the potential across the polar ionosphere FPC and the associated J1 field-aligned currents (FACs) are determined by solar wind and interplanetary magnetic field parameters. The second model, developed by Nopper and Carovillano (1978) (the N–C model), determines the global ionospheric electric-potential distributions based on the J1 and J2 currents. The third model is the ring current circuit model (S-RC) developed by Siscoe (1982). In this model, FPC drives J2 through the ring current, which is presumed to have inductive-like electrical properties. This is consistent with the observation by Hines (1963) that magnetic-gradient drifting ions are gyro-energized by the cross-tail electric field. We join these three models to provide a
time-dependent method of estimating electric-field penetration of the solar wind to the equatorial ionosphere. First, the transpolar potential is determined from the ACE data using the H–S–O model expression as given in Paper1. FPC ðHSOÞ ¼
1=3 ½30P1=2 sw þ 57:6E sw Psw P 1=2 ½0:0187xSPP P1=6 sw þ 0:036E sw xSP þ Psw
kV: ð1Þ
Here Psw denotes the solar wind pressure in nanoPascals (nPa). The geoeffective electric field is defined by Esw ¼ |Vx| BT sin2(c/2) consistent with the magnetopause reconnection rate found by p Sonnerup (1974), BT ¼ ðBx2 þ By2 Þ, c is the ‘clock’ angle between By and Bz and Vx is the xcomponent, in GSM coordinates, of the solar wind velocity. The symbol SPP denotes the average polar cap conductance and x is a factor that takes into account the multiple paths J1 follows in closing through the ionosphere. The conductance SPP is modified as the square root of the daily F10.7 proxy for the EUV solar flux (Robinson and Vondrak, 1984). The N–C model is used to solve for the global ionospheric electric potential, denoted by F, using a Poisson-type equation that is consistent with current continuity (Vasyliunas, 1970): r ½S rF ¼ j k sin ðIÞ,
(10 )
where jJ is the specified distribution of FACs associated with J1 and J2 and I is the dipole dip angle. Here, R is the ionospheric conductance tensor. Note that jJ is equivalent to a positive charge density for downward current and a negative charge density for upward current. The Siscoe (1982) model for coupling the J1 and J2 Birkeland currents is shown in Fig. 1. The model takes as input FPC(H–S–O), as defined in Eq. (1), which drives a J1 current across the polar cap and to lower latitudes where it partially closes in the magnetosphere, forming the J2 currents. Therefore, it is necessary to assign values to the equivalent resistors shown in Fig. 1. This is done by the appropriate averaging of the ionospheric conductance model as given in Paper1. The values obtained are Rp ¼ 0.174 O, RA ¼ 0.018 O, and Rs ¼ 0.117 O. (The resistances Rcx represent charge exchange in the ring current and are not modeled in this paper.) As described in Paper1, the expressions for the J1 and J2 currents for an assumed step-like behavior in
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with J2(t0) set equal to J2(t) at the end of each 256 s interval. In Paper1 we assumed a step-like FPC which simplified the J2 response as shown in Eq. (3). The J2 rise time t is given by t¼
Fig. 1. Taken from Siscoe (1982). In this approach the region-1 (J1) and region-2 (J2) currents are coupled, being driven by the same voltage source. The three ionospheric resistances Rp, RA, and Rs are found to be Rp ¼ 0.174 O, RA ¼ 0.018 O, and Rs ¼ 0.117 O using a specified ionospheric conductance model (Rothwell and Jasperse, 2006). The above circuit forms a threeloop electronic circuit that can easily be solved for J1 and J2 in terms of FPC(H–S–O). Since FPC(H–S–O) may be found by inputting solar wind data into Eq. (1), this model gives an approximation of the ionospheric response to the solar wind. The resistances Rcx represent charge exchange in the ring current which is not treated.
FPC are as follows: 1 1 Rs þ þ J1 ¼ FPC Rp Rs þ 2RA 2RA ðRs þ 2RA Þ ti 1 exp , t J2 ¼
t FPC 1 exp . t 2RA
ð2Þ (3)
For an arbitrary time-dependent FPC(t) the equations for J1 and J2 become 1 1 Rs J1ðtÞ ¼ FPC ðtÞ þ , þ J2ðtÞ Rp Rs þ 2RA Rs þ 2RA (4) "
"Z
0 ## t t 0 FPC ðt Þ exp dt0 t t0
1 2RA t t exp , ð5Þ t where J2(t0) is the value of J2 at the beginning of a given time interval. The ACE data is broken into a continuous sequence of four time steps of 64 s each J2ðtÞ ¼ J2ðt0 Þ þ
L ; Rk
Rk ¼
2RA Rs 2RA þ Rs
(6)
(Rothwell and Jasperse, 2006). In the present treatment, the rise time t is considered as a variable parameter since the value of L is unknown. In using Eq. (10 ) (Nopper and Carovillano, 1978) we separately determine the ionospheric potential due to J1 and J2 currents that are 1 MA in magnitude. The J1 current is taken to be distributed at 721 (magnetic latitude) in a 1201 arc centered on the dawn–dusk meridian with an extent of 31 in latitude. The J2 current is taken in a similar manner but inputted at 661 magnetic latitude. The resulting Poisson equation is solved using an ionospheric conductance model consistent with a sunlit ionosphere and auroral precipitation. The model conductance near the terminator has a large azimuthal gradient, consistent with experimental observations, such that a pre-reversal enhancement in the electric field occurs just past dusk for J1 currents. The value found for the eastward electric field at the pre-reversal enhancement is Eeq1 ¼ 1.2 mV/m (J1 ¼ 1 MA). For a J2 current of 1 MA we obtain a corresponding westward electric field with a minimum value of Eeq2 ¼ 2 mV/m at the same local time. For present purposes we assume that the distribution and latitudinal location of J1 and J2 remain fixed throughout a magnetic storm, while acknowledging they usually do not. We also assume that the ionospheric conductance remains unchanged throughout the storm when, in fact, it also does not because of auroral precipitation. However, because of these simplifying assumptions one can treat the ionospheric solution as a numerical Green’s function, see Paper1. The expression for the net electric field at the pre-reversal enhancement now takes on the simple form shown in Eq. (7). E eq ðtÞ ¼ E eq1 J1ðtÞ þ E eq2 J2ðtÞ.
(7)
It is understood, consistent with the Green’s function concept, that Eeq1 and Eeq2 implicitly have the dimensions of mV/m MA, while Eeq(t) has the dimensions of mV/m. In the present treatment we assume that Eeq1 and Eeq2 are constant throughout the magnetic storm. The first term on the RHS of Eq. (7) represents the penetration electric field and is consistent with
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the recent statement of Huang et al. (2006) that: ‘‘The penetration electric field in the low-latitude ionosphere is essentially a fraction of the magnetospheric convection electric field driven by the solar wind/IMF: the nearly constant amplitude of the penetration electric field measured in the lowlatitude ionosphere during prolonged period of stable southward IMF suggests that the ratio of the solar wind motional electric field to the ionospheric equatorial electric field may remain approximately constant’’. Note that here J1(t) is proportional to FPC(t) by Eqs. (2) or (4), and FPC is approximately proportional to Esw by Eq. (1). In the present model, the approximate constancy of |Vx|BT/Eeq for prolonged (stable) southward IMF, as found by Huang et al. (2005), only applies to the dayside ionosphere where Eeq1 and Eeq2 are nearly independent of local time. See Fig. 7 of Paper1. On the nightside, on the other hand, the rapid variation of Eeq1 and Eeq2 with LT precludes a similar conclusion. Additional physical justification for the assumed time independence of Eeq1 and Eeq2 is found in Figure A3a of Rothwell and Jasperse (2006) that shows the azimuthal components of the
electric field from J1 and J2 is almost constant within 301 of the equator. This implies that the equatorial electric field may, under certain conditions, be insensitive to the latitudinal location of the J1 and J2 current sources during a magnetic storm.
3. Model results for two magnetic storms The net Eeq(t), as estimated from the present model, is found for two major storms, 6–7 April 2000 (min Dst ¼ 290 nT) and 20–21 November 2003 (min Dst ¼ 472 nT). Selected geophysical parameters acquired during the 6–7 April 2000 magnetic storm are shown in Fig. 2, with the solar wind parameters shifted in time from the L1 point by the x-component of the solar wind velocity. Panel a shows the solar wind pressure Psw, panel b the solar wind geoeffective electric field Esw, and panel d the component BT of the interplanetary magnetic field that is perpendicular to the Earth’s magnetic dipole Dst for the same period is shown in panel c which also shows the time of bubble occurrence during the storm, as measured by the
Fig. 2. Data for the magnetic storm on 6–7 April 2000. Panel a shows the dynamic pressure of the solar wind plasma at the L1 point. Panel b shows the geoeffective component of the solar wind electric field Esw ¼ |Vx| BT sin2(c/2), where c is the ‘clock’ angle between By and Bz. p Panel d shows the time history of BT ¼ ðBx2 þ By2 Þ. Finally, the ring current parameter Dst is shown in Panel c. Also shown in panel c are the times, denoted by open triangles, at which equatorial plasma depletion bubbles were observed during the magnetic storm. The solar wind variables in panels a, b, and d were all measured at the L1 point and appropriately shifted in time.
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Defense Meterological Satellite Program (DMSP) satellites. Data in Fig. 2 show that this storm period was characterized by a sudden, strong, and sustained increase in Esw, Psw and, therefore, in FPC (Esw, Psw). The sudden increase in FPC required a proportionate increase in the portion of the J1 FAC directly connected to magnetospheric boundary layers and the magnetosheath. The J2 system grows in strength over a period of hours due to a delay in plasma response in the inner magnetosphere. As noted above, the electrical equivalence of inertia is inductance, a feature used in S-RC. Fig. 3 compares the H–S–O values from Eq. (1) for the transpolar potential FPC during the 6–7 April magnetic storm with those predicted by the Weimer (Weimer, 2005) empirical model. The Weimer model is an empirical fit to thousands of polar orbital passes taken in the early 1980s on board the Dynamic Explorer 2 satellite. The H–S–O model was evaluated for two values of xSPP, 9.8 S and 13.7 S corresponding to an auroral conductance of 0 and 3 S, respectively. Note the excellent agreement between the two models. Note also the sharp initial rise of FPC consistent with the stepfunction approximation used in Eq. (3). This latter feature implies that values of Eeq(t) later in the storm should be dependent on the J2 rise time. In Fig. 4, each of the top two panels is a time history of Eeq during the 6–7 April 2000 magnetic storm for two different J2 rise times. The top panel is for t ¼ 5 h and the middle panel for t ¼ 1 h. The
Fig. 3. Compares the transpolar potential FPC from the Weimer (2005) model for the 6–7 April 2000 magnetic storm with that from the H–S–O model for zero and three Siemens auroral conductance. The inserted plot highlights peak details.
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Fig. 4. Predicted Eeq(t) for two different rise times for J2 during the 6 April 2000 magnetic storm. The solid horizontal line is a ‘benchmark’ electric field threshold for bubble creation as mentioned in the text. In the top panel, which represents a longer (5 h) rise time for J2, Eeq approaches this threshold at points A and B consistent with the presence of plasma bubbles as detected on DMSP between 18:00 and 22:00 MLT. On the other hand, the middle panel, which represents a 1 h rise time shows significant suppression of Eeq at point B which is not consistent with the presence of bubbles. J1 and J2 are in MA. Point C denotes a region of overshielding caused by a rapid decline in FPC with residual J2 present. The bottom panel shows Dst during this time period.
solid line denotes total J1 (Eq. (4)) and the dash-dot line J2 (Eq. (5)). Note that due to the negative value of Eeq2 that Eeq(t), in contrast with J1, decreases with increasing J2. The units on the right-hand axis are in MA for J1 and J2. The solid horizontal line denotes the electric field equivalent of an upward drift velocity of 50 m/s (Fejer et al., 1999; Whalen, 2001) and is considered a working threshold above which plasma bubbles are assumed to be generated. The bottom panel shows Dst for the same period. Note for the shorter rise time shown in the middle panel that Eeq(t) exceeds the bubble threshold at the beginning of the magnetic storm but is well below it throughout the rest of the storm. This is because for the latter case J2 quickly reaches its maximum value while FPC stays relatively constant, thereby, maintaining shielding. On the other hand, in the top panel one sees not only the initial excursion above the threshold line, but also the threshold line being approached during the recovery phase due to a
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slower increase in J2. This feature may explain the later set of bubbles. Fig. 5 shows the corresponding parameters for the 19–21 November 2003 magnetic storm that Fig. 2 shows for the 6–7 April 2000 magnetic storm. Although the November 2003 storm is more severe as measured by Dst, the solar wind geoeffective electric field Esw is seen to increase more gradually during the main phase of this storm. This feature is reflected in the transpolar potential as seen in Fig. 6, with the conductance factor xSPP in Eq. (1) taken to be 10 S. Note the similar overall agreement with the Weimer (2005) empirical model as was seen in Fig. 3 for the April 2000 magnetic storm. The gradual increase in FPC implies that Eq. (3) is not applicable and that Eq. (5) must be used in determining J2. Fig. 7 shows that J2 for the November 2003 magnetic storm closely follows the variations in FPC for the t ¼ 1 h case, while for the longer time scale (5 h) the rise in J2 extends longer in time because of the gradual increase in FPC as seen Fig. 6. In both cases J2 stays below the values one would expect for a step function behavior of FPC. In other words, the gradual increase in FPC tends to diminish the sensitivity of the equatorial electric field Eeq(t) to
the J2 rise time, the situation being more adiabatic in nature. Huang et al. (2005) found a good correlation between the interplanetary electric field, as derived from the ACE data, and the electric field implied from the vertical drift velocity at Jicamarca. The
Fig. 6. Compares the transpolar potential FPC from the Weimer (2005) model for the 20 November 2003 magnetic storm with that from the H–S–O model with x SPP ¼ 10 S.
Fig. 5. Relevant solar wind and Dst data for the 20 November 2003 magnetic storm. The format is the same as given in Fig. 2 for the 6 April magnetic storm. Note that in this storm the bubbles (open triangles), as in the 6 April magnetic storm, tend to cluster near minimum Dst. However, the key difference between the two storms is that in the 6 April 2000 storm geoeffective Esw increased to its maximum value in less than an hour while for the 20 November 2003 storm it took 8 h.
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Fig. 7. Predicted Eeq(t) for two different J2 rise times during the 20 November 2003 magnetic storm. The solid horizontal line is a ‘benchmark’ electric field threshold for bubble creation as mentioned in the text. In this case there is less sensitivity to the J2 rise time. This is because the rise of the transpolar potential is more gradual in the November 2003 storm in comparison with the 6–7 April 2000 magnetic storm. The bottom panel shows Dst during the same time period. In this particular case, the later bubbles are more deeply depleted.
conclusion was drawn that the shielding times for the penetration electric fields were much longer than the 30 min as predicted by Senior and Blanc (1984). Those conclusions are consistent with the results found here.
4. Summary and conclusions We have assumed that the magnetosphere–ionosphere system is coupled in a manner as shown in Fig. 1 (Siscoe, 1982). The solar wind creates a transpolar potential FPC as defined in Eq. (1) with magnetic reconnection as the electrical power source. J1 field-aligned current is drawn from the flanks of the magnetopause into the ionosphere at dawn and exit the ionosphere at dusk. The Nopper–Carovillano ionospheric model was used to determine the ionospheric response to the transpolar potential. As also schematically shown in Fig. 1, the J2 currents are coupled with the J1 currents as both are driven by a common potential. The J2 currents have a built in delay due to plasma inertia, which mimics circuit inductance. The net equatorial
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electric field from J1 and J2 currents, as defined in Eq. (7), depends on the relative strength of the currents and, therefore, the rise time of J2. We consider the magnetic superstorms of 6–7 April 2000 and 20–21 November 2003. In the first storm, FPC had a rapid initial increase, while in the second storm, FPC was characterized by a more gradual increase that lasted over 8 h. Eeq(t) was determined in each case for two different rise times of 1 h and 5 h, respectively. In both cases it was found that the presence of plasma bubbles was consistent with the Fejer–Whalen threshold, with the later bubbles being in better agreement with the longer J2 rise time. This last result is consistent with recent results of Huang et al. (2005) who found that Eeq at Jicamarca stayed enhanced with Esw much longer than 30 min. It was also determined that if the transpolar potential gradually increased with many peaks and valleys, as in the November 2003 magnetic storm, then Eeq(t) appeared less sensitive to the J2 rise time. For in this case, at any one time, J2(t) was responding to an applied voltage somewhat less than the maximum in contrast to the step-like behavior of the April 2000 magnetic storm. A direct comparison of the model results with Jicamarca data, as reported in Huang et al. (2005), may also be made. For example, on 9 November, 2004 between the hours of 1900 h and 2100 h UT, the peak value of Eeq seen at Jicamarca was 2.2 mV/m (Huang et al., 2005). The model results were 2.2 mV/m (J1 only), and with J2 present, 1.8 mV/m (t ¼ 5 h), and 1.6 mV/m (t ¼ 1 h), respectively. A peak value of 266 kV was obtained for FPC(H–S–O) during the same time period. At other times, while the time-history of the model electric field followed the measured values at Jicamarca quite well, precise amplitude agreement was difficult to obtain due to other electric field sources being present. Acknowledgments We would like to thank Dr. Daniel Weimer from ATK Mission Research of Nashua, New Hampshire for his latest potential code and Mr. Neil Grossbard for his programming help. This work was done under AFOSR Task 2311SDA3. Dst values were obtained from the World Data Center, Kyoto (http:// www.swdcwww.kugi.kyotou.ac.jp/index.html). Interplanetary environment data was obtained from the ACE web site (http://www.srl.caltech.edu/ACE/).
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References de la Beaujardie`re, O., C/NOFS Space Definition Team, 2004. C/NOFS: a mission to forecast scintillations. Journal of Atmospheric and Solar—Terrestrial Physics 66, 1573. de la Beaujardie`re, O., Retterer, J., Kelley, M., Hunton, D., Jeong, L., 2006. New satellite will forecast ionospheric disturbances. Space Weather 4, S03C05. Fejer, B.G., Scherliess, L., de Paula, E.R., 1999. Effects of the vertical plasma drift velocity on the generation and evolution of equatorial spread F. Journal of Geophysical Research 104 (A9). Hill, T.W., Dessler, A.J., Wolf, R.A., 1976. Mercury and Mars: the role of ionospheric conductance in the acceleration of magnetospheric particles. Geophysical Research Letters 3, 429. Hines, C.O., 1963. The energization of plasma in the magnetosphere: hydromagnetic and particle-drift approaches. Planetary and Space Science 10, 239. Huang, C.-S., Foster, J., Kelley, M.C., 2005. Long-duration penetration of the interplanetary electric field to the lowlatitude ionosphere during the main phase of magnetic storms. Journal of Geophysical Research 110 (A11309). Huang, C.-S., Sazykin, S., Spiro, R., Goldstein, J., Growley, G., Ruohoniemi, J., 2006. Storm-time penetration electric fields and their effects. Eos 87, 13. Nopper, R.W., Carovillano, R.L., 1978. Polar-Equatorial coupling during magnetically active periods. Geophysical Research Letters 5, 699. Ober, D.M., Maynard, N.C., Burke, W.J., 2003. Testing the Hill model of transpolar potential saturation. Journal of Geophysical Research 108 (A12). Retterer, J., 1999. Theoretical model for fast equatorial bubbles. In: Goodman, J. (Ed.), Proceedings of the 1999 Ionospheric Effects Symposium.
Retterer, J.M., 2005. Physics-based forecasts of equatorial radio scintillation for the Communication and Navigation Outage Forecasting System (C/NOFS). Space Weather 3, S12C03. Robinson, R.M., Vondrak, R.R., 1984. Measurements of E region ionization and conductivity produced by solar illumination at high latitudes. Journal of Geophysical Research 89 (A6), 3951–3956. Rothwell, P.L., Jasperse, J.R., 2006. Modeling the connection of the global ionospheric electric fields to the solar wind. Journal of Geophysical Research 111 (A03211). Senior, C., Blanc, M., 1984. On the control of magnetospheric convection by the spatial distribution of ionospheric conductivities. Journal of Geophysical Research 89 (A1), 261. Siscoe, G.L., 1982. Energy coupling between regions 1 and 2 Birkland current systems. Journal of Geophysical Research 87 (A7), 5124. Siscoe, G.L., Erickson, G.M., Sonnerup, B.U.O¨., Maynard, N.C., Shoendorf, J.A., Siebert, K.D., Weimer, D.R., White, W.W., Wilson, G.R., 2002. Hill model of transpolar potential saturation: Comparison with MHD simulations. Journal of Geophysical Research 107 (A6). Sonnerup, B.U.O., 1974. Magnetopause reconnection rate. Journal of Geophysical Research 79 (10). Vasyliunas, V.M., 1970. Mathematical models of magnetospheric convection and its coupling to the ionosphere. In: McCormac, B.M. (Ed.), Particles and Fields in the Magnetosphere. D. Reidel, Norwell, MA, pp. 60–65. Weimer, D.R., 2005. Improved electrodynamic models and application to calculating Joule heating rates. Journal of Geophysical Research 110 (A05306). Whalen, J.A., 2001. The equatorial anomaly: its quantitative relation to equatorial bubbles, bottomside spread F, and E B drift velocity during a month at solar maximum. Journal of Geophysical Research 106 (A12).
Journal of Atmospheric and Solar-Terrestrial Physics 69 (2007) 1127–1134 www.elsevier.com/locate/jastp
A coupled solar wind-magnetosphere–ionosphere model for determining the ionospheric penetration electric field P.L. Rothwell, J.R. Jasperse Space Vehicles Directorate, Air Force Research Laboratory, Hanscom Air Force Base, 29 Randolph Rd., Bedford, MA 01731, USA Received 13 April 2006; received in revised form 21 July 2006; accepted 1 August 2006 Available online 24 March 2007
Abstract The transpolar potential Fpc may be estimated from the solar wind as measured by the advanced composition explorer (ACE) satellite at the first Lagrangian point L1. In our model, the transpolar potential drives the region-1 (J1) currents through the ionosphere consistent with a solar-dependent ionospheric conductance. It is shown that the ionospheric potential may be derived from an equivalent Poisson equation, the solution of which gives the global distribution of the ionospheric electric field, including the penetration electric field near the equator. This eastward penetration electric field just past sunset, which is created by J1, is offset by a region-2 (J2) generated westward (shielding) electric field with an unknown rise time. We find that there is a correlation between storm-time potential enhancements and the presence of equatorial bubbles as measured on DMSP satellites. The magnetic storms of 6–7 April 2000 and 20–21 November 2003 are analyzed. In both cases, the observed presence of equatorial plasma bubbles showed better agreement with model predictions using a longer J2 rise time, consistent with Huang et al. [Huang, C.-S., Foster, J., Kelley, M.C., 2005. Longduration penetration of the interplanetary electric field to the low-latitude ionosphere during the main phase of magnetic storms. Journal of Geophysical Research 110(A11309), doi:10.1029/2005JA011202]. r 2007 Elsevier Ltd. All rights reserved. Keywords: Solar wind; Penetration electric fields; Shielding; Plasma bubbles
1. Introduction In this paper we assume that electric fields (Eeq) measured at equatorial latitudes during magnetic storms are primarily caused by the transpolar potential Fpc created by the solar wind. Other electric field sources, such as neutral winds and gravity waves, may also be present, but our present approach restricts us to follow only the energy flow from the solar wind to equatorial latitudes. EastCorresponding author. Tel.: +1 781 377 9664.
E-mail addresses: [email protected] (P.L. Rothwell), [email protected] (J.R. Jasperse). 1364-6826/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.jastp.2006.08.013
ward equatorial electric fields near the dusk terminator increase the upward drift of plasma, creating plasma density bubbles or plumes that contribute to radio scintillations. The time evolution of the density structure around an equatorial plasma plume has been calculated by Retterer (2005) and Retterer (1999). By knowing the strength of the penetration electric field and the response of the plasma, comparisons can be made with the Air Force Research Laboratory (AFRL) Communication and Navigation Outage Forecast System (C/NOFS) satellite (de la Beaujardie`re et al., 2006, 2004). The transpolar potential is consistent with region-1 (J1) currents that are voltage driven but current
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limited, where the currents close through the ionosphere within minutes. Following the model of Siscoe (1982), the J1 currents also partially close through the magnetosphere with a time delay, forming the ring current and associated region-2 (J2) currents. In Paper1 (Rothwell and Jasperse, 2006), equivalent time-dependent circuit equations were derived and an empirical relationship established between the solar wind data measured at L1 and the penetration electric field. The ionospheric response to J1 and J2 was modeled after Nopper and Carovillano (1978) which includes the effects of a sun-lit ionosphere and a dipole magnetic field. The conductance at the terminators used in the Rothwell–Jasperse model had a much larger conductance gradient (and hence more realistic) than that used in the Nopper–Carovillano model. In contrast to the J1 current, the presence of J2 creates a westward electric field also just past 1800 h LT which shields the J1-produced eastward (positive) electric field. Therefore, the net post-sunset electric field is the difference between the J1 and J2 components. Since these two components operate on different time scales finding the net penetration electric field Eeq(t) at any one time is difficult. 2. The model The purpose of the present report is to provide a quantitative method for electrically coupling the interplanetary medium with the equatorial ionosphere. Our method unites three methods that were independently developed. The first method was developed by Siscoe et al. (2002) based on the work of Hill et al. (1976), and extended by Ober et al. (2003). We refer to it as the Hill–Siscoe–Ober or H–S–O model. In this model, the potential across the polar ionosphere FPC and the associated J1 field-aligned currents (FACs) are determined by solar wind and interplanetary magnetic field parameters. The second model, developed by Nopper and Carovillano (1978) (the N–C model), determines the global ionospheric electric-potential distributions based on the J1 and J2 currents. The third model is the ring current circuit model (S-RC) developed by Siscoe (1982). In this model, FPC drives J2 through the ring current, which is presumed to have inductive-like electrical properties. This is consistent with the observation by Hines (1963) that magnetic-gradient drifting ions are gyro-energized by the cross-tail electric field. We join these three models to provide a
time-dependent method of estimating electric-field penetration of the solar wind to the equatorial ionosphere. First, the transpolar potential is determined from the ACE data using the H–S–O model expression as given in Paper1. FPC ðHSOÞ ¼
1=3 ½30P1=2 sw þ 57:6E sw Psw P 1=2 ½0:0187xSPP P1=6 sw þ 0:036E sw xSP þ Psw
kV: ð1Þ
Here Psw denotes the solar wind pressure in nanoPascals (nPa). The geoeffective electric field is defined by Esw ¼ |Vx| BT sin2(c/2) consistent with the magnetopause reconnection rate found by p Sonnerup (1974), BT ¼ ðBx2 þ By2 Þ, c is the ‘clock’ angle between By and Bz and Vx is the xcomponent, in GSM coordinates, of the solar wind velocity. The symbol SPP denotes the average polar cap conductance and x is a factor that takes into account the multiple paths J1 follows in closing through the ionosphere. The conductance SPP is modified as the square root of the daily F10.7 proxy for the EUV solar flux (Robinson and Vondrak, 1984). The N–C model is used to solve for the global ionospheric electric potential, denoted by F, using a Poisson-type equation that is consistent with current continuity (Vasyliunas, 1970): r ½S rF ¼ j k sin ðIÞ,
(10 )
where jJ is the specified distribution of FACs associated with J1 and J2 and I is the dipole dip angle. Here, R is the ionospheric conductance tensor. Note that jJ is equivalent to a positive charge density for downward current and a negative charge density for upward current. The Siscoe (1982) model for coupling the J1 and J2 Birkeland currents is shown in Fig. 1. The model takes as input FPC(H–S–O), as defined in Eq. (1), which drives a J1 current across the polar cap and to lower latitudes where it partially closes in the magnetosphere, forming the J2 currents. Therefore, it is necessary to assign values to the equivalent resistors shown in Fig. 1. This is done by the appropriate averaging of the ionospheric conductance model as given in Paper1. The values obtained are Rp ¼ 0.174 O, RA ¼ 0.018 O, and Rs ¼ 0.117 O. (The resistances Rcx represent charge exchange in the ring current and are not modeled in this paper.) As described in Paper1, the expressions for the J1 and J2 currents for an assumed step-like behavior in
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with J2(t0) set equal to J2(t) at the end of each 256 s interval. In Paper1 we assumed a step-like FPC which simplified the J2 response as shown in Eq. (3). The J2 rise time t is given by t¼
Fig. 1. Taken from Siscoe (1982). In this approach the region-1 (J1) and region-2 (J2) currents are coupled, being driven by the same voltage source. The three ionospheric resistances Rp, RA, and Rs are found to be Rp ¼ 0.174 O, RA ¼ 0.018 O, and Rs ¼ 0.117 O using a specified ionospheric conductance model (Rothwell and Jasperse, 2006). The above circuit forms a threeloop electronic circuit that can easily be solved for J1 and J2 in terms of FPC(H–S–O). Since FPC(H–S–O) may be found by inputting solar wind data into Eq. (1), this model gives an approximation of the ionospheric response to the solar wind. The resistances Rcx represent charge exchange in the ring current which is not treated.
FPC are as follows: 1 1 Rs þ þ J1 ¼ FPC Rp Rs þ 2RA 2RA ðRs þ 2RA Þ ti 1 exp , t J2 ¼
t FPC 1 exp . t 2RA
ð2Þ (3)
For an arbitrary time-dependent FPC(t) the equations for J1 and J2 become 1 1 Rs J1ðtÞ ¼ FPC ðtÞ þ , þ J2ðtÞ Rp Rs þ 2RA Rs þ 2RA (4) "
"Z
0 ## t t 0 FPC ðt Þ exp dt0 t t0
1 2RA t t exp , ð5Þ t where J2(t0) is the value of J2 at the beginning of a given time interval. The ACE data is broken into a continuous sequence of four time steps of 64 s each J2ðtÞ ¼ J2ðt0 Þ þ
L ; Rk
Rk ¼
2RA Rs 2RA þ Rs
(6)
(Rothwell and Jasperse, 2006). In the present treatment, the rise time t is considered as a variable parameter since the value of L is unknown. In using Eq. (10 ) (Nopper and Carovillano, 1978) we separately determine the ionospheric potential due to J1 and J2 currents that are 1 MA in magnitude. The J1 current is taken to be distributed at 721 (magnetic latitude) in a 1201 arc centered on the dawn–dusk meridian with an extent of 31 in latitude. The J2 current is taken in a similar manner but inputted at 661 magnetic latitude. The resulting Poisson equation is solved using an ionospheric conductance model consistent with a sunlit ionosphere and auroral precipitation. The model conductance near the terminator has a large azimuthal gradient, consistent with experimental observations, such that a pre-reversal enhancement in the electric field occurs just past dusk for J1 currents. The value found for the eastward electric field at the pre-reversal enhancement is Eeq1 ¼ 1.2 mV/m (J1 ¼ 1 MA). For a J2 current of 1 MA we obtain a corresponding westward electric field with a minimum value of Eeq2 ¼ 2 mV/m at the same local time. For present purposes we assume that the distribution and latitudinal location of J1 and J2 remain fixed throughout a magnetic storm, while acknowledging they usually do not. We also assume that the ionospheric conductance remains unchanged throughout the storm when, in fact, it also does not because of auroral precipitation. However, because of these simplifying assumptions one can treat the ionospheric solution as a numerical Green’s function, see Paper1. The expression for the net electric field at the pre-reversal enhancement now takes on the simple form shown in Eq. (7). E eq ðtÞ ¼ E eq1 J1ðtÞ þ E eq2 J2ðtÞ.
(7)
It is understood, consistent with the Green’s function concept, that Eeq1 and Eeq2 implicitly have the dimensions of mV/m MA, while Eeq(t) has the dimensions of mV/m. In the present treatment we assume that Eeq1 and Eeq2 are constant throughout the magnetic storm. The first term on the RHS of Eq. (7) represents the penetration electric field and is consistent with
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the recent statement of Huang et al. (2006) that: ‘‘The penetration electric field in the low-latitude ionosphere is essentially a fraction of the magnetospheric convection electric field driven by the solar wind/IMF: the nearly constant amplitude of the penetration electric field measured in the lowlatitude ionosphere during prolonged period of stable southward IMF suggests that the ratio of the solar wind motional electric field to the ionospheric equatorial electric field may remain approximately constant’’. Note that here J1(t) is proportional to FPC(t) by Eqs. (2) or (4), and FPC is approximately proportional to Esw by Eq. (1). In the present model, the approximate constancy of |Vx|BT/Eeq for prolonged (stable) southward IMF, as found by Huang et al. (2005), only applies to the dayside ionosphere where Eeq1 and Eeq2 are nearly independent of local time. See Fig. 7 of Paper1. On the nightside, on the other hand, the rapid variation of Eeq1 and Eeq2 with LT precludes a similar conclusion. Additional physical justification for the assumed time independence of Eeq1 and Eeq2 is found in Figure A3a of Rothwell and Jasperse (2006) that shows the azimuthal components of the
electric field from J1 and J2 is almost constant within 301 of the equator. This implies that the equatorial electric field may, under certain conditions, be insensitive to the latitudinal location of the J1 and J2 current sources during a magnetic storm.
3. Model results for two magnetic storms The net Eeq(t), as estimated from the present model, is found for two major storms, 6–7 April 2000 (min Dst ¼ 290 nT) and 20–21 November 2003 (min Dst ¼ 472 nT). Selected geophysical parameters acquired during the 6–7 April 2000 magnetic storm are shown in Fig. 2, with the solar wind parameters shifted in time from the L1 point by the x-component of the solar wind velocity. Panel a shows the solar wind pressure Psw, panel b the solar wind geoeffective electric field Esw, and panel d the component BT of the interplanetary magnetic field that is perpendicular to the Earth’s magnetic dipole Dst for the same period is shown in panel c which also shows the time of bubble occurrence during the storm, as measured by the
Fig. 2. Data for the magnetic storm on 6–7 April 2000. Panel a shows the dynamic pressure of the solar wind plasma at the L1 point. Panel b shows the geoeffective component of the solar wind electric field Esw ¼ |Vx| BT sin2(c/2), where c is the ‘clock’ angle between By and Bz. p Panel d shows the time history of BT ¼ ðBx2 þ By2 Þ. Finally, the ring current parameter Dst is shown in Panel c. Also shown in panel c are the times, denoted by open triangles, at which equatorial plasma depletion bubbles were observed during the magnetic storm. The solar wind variables in panels a, b, and d were all measured at the L1 point and appropriately shifted in time.
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Defense Meterological Satellite Program (DMSP) satellites. Data in Fig. 2 show that this storm period was characterized by a sudden, strong, and sustained increase in Esw, Psw and, therefore, in FPC (Esw, Psw). The sudden increase in FPC required a proportionate increase in the portion of the J1 FAC directly connected to magnetospheric boundary layers and the magnetosheath. The J2 system grows in strength over a period of hours due to a delay in plasma response in the inner magnetosphere. As noted above, the electrical equivalence of inertia is inductance, a feature used in S-RC. Fig. 3 compares the H–S–O values from Eq. (1) for the transpolar potential FPC during the 6–7 April magnetic storm with those predicted by the Weimer (Weimer, 2005) empirical model. The Weimer model is an empirical fit to thousands of polar orbital passes taken in the early 1980s on board the Dynamic Explorer 2 satellite. The H–S–O model was evaluated for two values of xSPP, 9.8 S and 13.7 S corresponding to an auroral conductance of 0 and 3 S, respectively. Note the excellent agreement between the two models. Note also the sharp initial rise of FPC consistent with the stepfunction approximation used in Eq. (3). This latter feature implies that values of Eeq(t) later in the storm should be dependent on the J2 rise time. In Fig. 4, each of the top two panels is a time history of Eeq during the 6–7 April 2000 magnetic storm for two different J2 rise times. The top panel is for t ¼ 5 h and the middle panel for t ¼ 1 h. The
Fig. 3. Compares the transpolar potential FPC from the Weimer (2005) model for the 6–7 April 2000 magnetic storm with that from the H–S–O model for zero and three Siemens auroral conductance. The inserted plot highlights peak details.
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Fig. 4. Predicted Eeq(t) for two different rise times for J2 during the 6 April 2000 magnetic storm. The solid horizontal line is a ‘benchmark’ electric field threshold for bubble creation as mentioned in the text. In the top panel, which represents a longer (5 h) rise time for J2, Eeq approaches this threshold at points A and B consistent with the presence of plasma bubbles as detected on DMSP between 18:00 and 22:00 MLT. On the other hand, the middle panel, which represents a 1 h rise time shows significant suppression of Eeq at point B which is not consistent with the presence of bubbles. J1 and J2 are in MA. Point C denotes a region of overshielding caused by a rapid decline in FPC with residual J2 present. The bottom panel shows Dst during this time period.
solid line denotes total J1 (Eq. (4)) and the dash-dot line J2 (Eq. (5)). Note that due to the negative value of Eeq2 that Eeq(t), in contrast with J1, decreases with increasing J2. The units on the right-hand axis are in MA for J1 and J2. The solid horizontal line denotes the electric field equivalent of an upward drift velocity of 50 m/s (Fejer et al., 1999; Whalen, 2001) and is considered a working threshold above which plasma bubbles are assumed to be generated. The bottom panel shows Dst for the same period. Note for the shorter rise time shown in the middle panel that Eeq(t) exceeds the bubble threshold at the beginning of the magnetic storm but is well below it throughout the rest of the storm. This is because for the latter case J2 quickly reaches its maximum value while FPC stays relatively constant, thereby, maintaining shielding. On the other hand, in the top panel one sees not only the initial excursion above the threshold line, but also the threshold line being approached during the recovery phase due to a
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slower increase in J2. This feature may explain the later set of bubbles. Fig. 5 shows the corresponding parameters for the 19–21 November 2003 magnetic storm that Fig. 2 shows for the 6–7 April 2000 magnetic storm. Although the November 2003 storm is more severe as measured by Dst, the solar wind geoeffective electric field Esw is seen to increase more gradually during the main phase of this storm. This feature is reflected in the transpolar potential as seen in Fig. 6, with the conductance factor xSPP in Eq. (1) taken to be 10 S. Note the similar overall agreement with the Weimer (2005) empirical model as was seen in Fig. 3 for the April 2000 magnetic storm. The gradual increase in FPC implies that Eq. (3) is not applicable and that Eq. (5) must be used in determining J2. Fig. 7 shows that J2 for the November 2003 magnetic storm closely follows the variations in FPC for the t ¼ 1 h case, while for the longer time scale (5 h) the rise in J2 extends longer in time because of the gradual increase in FPC as seen Fig. 6. In both cases J2 stays below the values one would expect for a step function behavior of FPC. In other words, the gradual increase in FPC tends to diminish the sensitivity of the equatorial electric field Eeq(t) to
the J2 rise time, the situation being more adiabatic in nature. Huang et al. (2005) found a good correlation between the interplanetary electric field, as derived from the ACE data, and the electric field implied from the vertical drift velocity at Jicamarca. The
Fig. 6. Compares the transpolar potential FPC from the Weimer (2005) model for the 20 November 2003 magnetic storm with that from the H–S–O model with x SPP ¼ 10 S.
Fig. 5. Relevant solar wind and Dst data for the 20 November 2003 magnetic storm. The format is the same as given in Fig. 2 for the 6 April magnetic storm. Note that in this storm the bubbles (open triangles), as in the 6 April magnetic storm, tend to cluster near minimum Dst. However, the key difference between the two storms is that in the 6 April 2000 storm geoeffective Esw increased to its maximum value in less than an hour while for the 20 November 2003 storm it took 8 h.
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Fig. 7. Predicted Eeq(t) for two different J2 rise times during the 20 November 2003 magnetic storm. The solid horizontal line is a ‘benchmark’ electric field threshold for bubble creation as mentioned in the text. In this case there is less sensitivity to the J2 rise time. This is because the rise of the transpolar potential is more gradual in the November 2003 storm in comparison with the 6–7 April 2000 magnetic storm. The bottom panel shows Dst during the same time period. In this particular case, the later bubbles are more deeply depleted.
conclusion was drawn that the shielding times for the penetration electric fields were much longer than the 30 min as predicted by Senior and Blanc (1984). Those conclusions are consistent with the results found here.
4. Summary and conclusions We have assumed that the magnetosphere–ionosphere system is coupled in a manner as shown in Fig. 1 (Siscoe, 1982). The solar wind creates a transpolar potential FPC as defined in Eq. (1) with magnetic reconnection as the electrical power source. J1 field-aligned current is drawn from the flanks of the magnetopause into the ionosphere at dawn and exit the ionosphere at dusk. The Nopper–Carovillano ionospheric model was used to determine the ionospheric response to the transpolar potential. As also schematically shown in Fig. 1, the J2 currents are coupled with the J1 currents as both are driven by a common potential. The J2 currents have a built in delay due to plasma inertia, which mimics circuit inductance. The net equatorial
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electric field from J1 and J2 currents, as defined in Eq. (7), depends on the relative strength of the currents and, therefore, the rise time of J2. We consider the magnetic superstorms of 6–7 April 2000 and 20–21 November 2003. In the first storm, FPC had a rapid initial increase, while in the second storm, FPC was characterized by a more gradual increase that lasted over 8 h. Eeq(t) was determined in each case for two different rise times of 1 h and 5 h, respectively. In both cases it was found that the presence of plasma bubbles was consistent with the Fejer–Whalen threshold, with the later bubbles being in better agreement with the longer J2 rise time. This last result is consistent with recent results of Huang et al. (2005) who found that Eeq at Jicamarca stayed enhanced with Esw much longer than 30 min. It was also determined that if the transpolar potential gradually increased with many peaks and valleys, as in the November 2003 magnetic storm, then Eeq(t) appeared less sensitive to the J2 rise time. For in this case, at any one time, J2(t) was responding to an applied voltage somewhat less than the maximum in contrast to the step-like behavior of the April 2000 magnetic storm. A direct comparison of the model results with Jicamarca data, as reported in Huang et al. (2005), may also be made. For example, on 9 November, 2004 between the hours of 1900 h and 2100 h UT, the peak value of Eeq seen at Jicamarca was 2.2 mV/m (Huang et al., 2005). The model results were 2.2 mV/m (J1 only), and with J2 present, 1.8 mV/m (t ¼ 5 h), and 1.6 mV/m (t ¼ 1 h), respectively. A peak value of 266 kV was obtained for FPC(H–S–O) during the same time period. At other times, while the time-history of the model electric field followed the measured values at Jicamarca quite well, precise amplitude agreement was difficult to obtain due to other electric field sources being present. Acknowledgments We would like to thank Dr. Daniel Weimer from ATK Mission Research of Nashua, New Hampshire for his latest potential code and Mr. Neil Grossbard for his programming help. This work was done under AFOSR Task 2311SDA3. Dst values were obtained from the World Data Center, Kyoto (http:// www.swdcwww.kugi.kyotou.ac.jp/index.html). Interplanetary environment data was obtained from the ACE web site (http://www.srl.caltech.edu/ACE/).
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