Intensification of the Cowling current in the global MHD simulation

Intensification of the Cowling current in the global MHDsimulation model

B. B. Tang,1,2 C. Wang,1 Y. Q. Hu,3 and J. R. Kan4

Received 26 November 2010; revised 13 February 2011; accepted 21 March 2011; published 8 June 2011.

[1] We examine the effects of the ionospheric conductance on the intensification of thewestward electrojet current in the ionosphere based on the piecewise parabolic method witha Lagrangian remap (PPMLR) globalMHD simulation model. The ionospheric conductanceis empirically linked to the plasma pressure in the plasma sheet. The simulation resultsare consistent with observations: When the Pedersen and Hall conductances are small, theionospheric current shows a two‐cell pattern; when the conductances increase and the ratioSH /SP ≥ 2, an intense westward electrojet appears in the midnight sector. This intensewestward electrojet is the Cowling current driven by the induced southward electric field dueto the blockage of the northward Hall current from closure in the equatorial plasma sheet.The simulation shows the development of the Cowling electrojet is essential to theintensification of the westward electrojet in the ionosphere.

Citation: Tang, B. B., C. Wang, Y. Q. Hu, and J. R. Kan (2011), Intensification of the Cowling current in the global MHDsimulation model, J. Geophys. Res., 116, A06204, doi:10.1029/2010JA016320.

1. Introduction

[2] Baumjohann [1983] showed that an intense westwardelectrojet would appear in the midnight sector, and its mag-nitude is much greater than the preexisting two‐cell currents.The increasing of this westward electrojet is usually taken asa signature of the substorm expansion phase.[3] Kamide et al. [1996] pointed out that this intense

westward electrojet in the midnight and early morning regionis essentially conductance‐dominated. That is, the magnitudeof the electrojet is mainly controlled by the conductance,comparing to the electric field. The highly enhancement ofthe conductance, including the Hall conductance during thesubstorm expansion phase results in the high magnitude ofthe westward electrojet in the midnight sector. This scenariois also supported by an equivalent current model [Nakai andKamide, 2005]. In their model, the westward electrojet islargely intensified when the Pedersen and Hall conductanceincrease to 20 S and 60 S from their initial value, and 90% ofthe westward electrojet is Hall current.[4] Kan [2007] showed that the intensification of the west-

ward electrojet is caused by the blockage of the northwardHall current(INH) driven by the westward electric field. The

blockage is due to the lack of the radial current in themidnight sector of the equatorial plasma sheet. A southwardpolarization electric field is induced by the blockage of thenorthward Hall current, which drives a southward Pedersencurrent(ISP) to cancel the northward Hall current. Here, ablockage parameter(a) is defined to express the extent ofcurrent blocking:

� ¼ ISP=INH ¼ ES= EW * Rð Þ ð1Þ

where the parameter R = SH /SP is the ratio of the Hall toPedersen conductance. Thus the westward electrojet consistsof the westward Pedersen (IWP) current driven by the west-ward E field and the westward Hall current (IWH) driven bythe induced southward polarization E field, and it is usuallycalled the Cowling electrojet(IC). The resulting westwardCowling electrojet can be written as

IC ¼ IWH þ IWP ¼ SHES þ SPEW ¼ 1þ � * R2� �

* SPEW ð2Þ

From equation (2), the westward Cowling electrojet is highlysensitive to the Hall‐to‐Pedersen conductance ratio R.[5] Observations have already shown both the nightside

Pedersen and Hall conductance, and thus the ratio R, wouldchange significantly from the substorm growth phase to theexpansion phase [Lester et al., 1996; Aikio and Kaila, 1996;Gjerloev and Hoffman, 2000]. During the growth phase, SH

and SP are less than 10 S and the ratio R is close to 1. Boththe Pedersen and Hall conductances increase at the end of thegrowth phase or the onset of the expansion phase, whilethe ratio R reaches 2 or more. The typical peak value of theconductance will be tens of siemens. For example, Lesteret al. [1996] showed the maximum SP and SH are 34 S and71 S, respectively, andGjerloev and Hoffman [2000] showed

1State Key Laboratory of Space Weather, Center for Space Science andApplied Research, Chinese Academy of Sciences, Beijing, China.

2Graduate University of the Chinese Academy of Science, Beijing,China.

3School of Earth and Space Science, University of Science andTechnology of China, Hefei, China.

4Geophysical Institute, University of Alaska Fairbanks, Fairbanks,Alaska, USA.

Copyright 2011 by the American Geophysical Union.0148‐0227/11/2010JA016320

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 116, A06204, doi:10.1029/2010JA016320, 2011

A06204 1 of 8

http://dx.doi.org/10.1029/2010JA016320

∼20 S and 48 S. Now, back to equation (2), if we set a ∼ 1for a nearly complete blockage, and R ∼ 2, the westwardCowling electrojet will increase by a factor of ∼5. Thus,about 80% of the Cowling current is contributed by the Hallcurrent component.[6] Recently, global MHD simulations have been devel-

oped as a powerful tool to investigate the solar wind‐magnetosphere‐ionosphere coupling system. The ionosphericconductances are treated more and more carefully than theformer simple uniform constants. Some researchers [Raederet al., 2001a, 2001b; Fedder et al., 1995; Tanaka et al.,2010] compute the nightside conductance from the electronprecipitations [Robinson et al., 1987], while Ridley et al.[2004] directly use the field aligned current to estimate thenightside conductance. By the applications of the conduc-tance model, they studied the general features of the substormevolution or large‐scale magnetosphere characters. Mean-while Tanaka [2007] showed the configuration of Cowlingcurrent channel in the midnight ionosphere by using a real-istic ionospheric conductivity model, but how this Cowlingcurrent channel is formed still needs further analysis.

[7] Based on an empirical conductance model fromobservations, this paper focuses on the effects of the con-ductance on the formation of the westward Cowling currentin the ionosphere by using global MHD simulations. It isorganized as follows: we describe the numerical simulationmodel in section 2, present the model results in section 3,and discuss and conclude it in section 4.

2. Simulation Method

[8] In this study, we use the global MHD simulation code,developed byHu et al. [2007], on the basis of an extension ofthe Lagrangian version of the piecewise parabolic method(piecewise parabolic method with a Lagrangian remap(PPMLR)) [Collela and Woodward, 1984] to solve the idealMHD equations. The numerical mesh is a stretched cartesiancoordinate system with the Earth center at the origin and thex, y and z axes pointing to the Sun, the dawn‐dusk and thenorthward direction, respectively. The simulation box istaken to be −300 RE ≤ x ≤ 30 RE, −150 RE ≤ y, z ≤ 150 RE

with the smallest grid of 0.4 RE. An inner magnetosphereboundary is set at r = 3 RE, and an electrostatic ionosphere isput at r = 1.017 RE. Thus a magnetosphere‐ionosphere cou-pling process is considered as follows: First, field‐alignedcurrents are mapped from the inner boundary to the ionosphere,then an electrostatic equation is solved at the ionosphere

r � S � rFð Þ ¼ �Jk sin Ij j ð3Þ

whereS is the conductance tensor constructed bySP andSH,F is the ionospheric potential, Jk is the field aligned currentand I denotes the inclination angle of the dipole field. At last,the calculated ionospheric potential is mapped back to theinner boundary to get the convection velocity. It is noted thatthese two mapping processes are along magnetic dipole fieldlines.[9] The conductance model used in the simulation is a

crude first approximation from the observations, and it con-sists of two parts: the conductance distribution pattern andthe conductance value. The general conductance pattern isempirically derived from ground magnetic disturbances [Ahnet al., 1998], but a Gaussian distribution is set in latitudedirection to reduce the conductance to the background valueat the polar and subauroral region, that is, 2 S for the Hallconductance and 1 S for the Pedersen conductance. Mean-while, the oval conductance depends mainly on the plasmapressure in the near‐Earth plasma sheet. Xing et al. [2010]find that substorm expansion onset is associated with anincrease of plasma pressure in the radial distance between∼9 and 12 RE due to the particle energization, which may berelated to the enhanced earthward convection driven by thenear‐Earth reconnection in the plasma sheet. So the maxi-mum values of SP and SH are set to be ∼6 S, and thus theratio R is ∼1 without a near‐Earth X line (NEXL). OnceNEXL is formed, the maximum values of SP and SH areincreased artificially to ∼25 and 60 S in 10 min, but keep theoriginal conductance distribution pattern. Thus, the ratio Rbecomes larger than 2. Figure 1 shows the Pedersen and Hallconductance patterns in detail after the enhancement of theconductances.[10] In this study, we consider a southward turning of IMF

BZ from 5 nT to −5 nT, which would result in dynamic

Figure 1. (a) The pattern of Pedersen conductance and(b) Hall conductance.

TANG ET AL.: INTENSIFICATION OF THE COWLING CURRENT A06204A06204

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activities in the magnetotail and ionosphere, while other solarwind parameters keep constant: the solar wind speed is400 km/s in x direction, the proton number density 5 cm−3 andtemperature 106 K. T = 0 min is the time when IMF discon-tinuity encountering the bow shock.

3. Simulation Results

[11] When the IMF discontinuity reaches the magneto-pause, the magnetic flux is removed by the reconnection;thus, large‐scale earthward convection starts to transport themagnetic flux from the distant tail slowly, and the plasmasheet is getting thinner. However, if this earthward convec-tion cannot supply the magnetic flux to dayside magneto-pause timely, a new near‐Earth X line would form (in this run,it is at t = ∼56 min). Figure 2 depicts the earthward con-vection minutes before and after the formation of NEXL.The enhanced earthward convection would result in theincrease of the thermal pressure. The conductance modelused in this simulation is physically reasonable, though it isnot self‐consistent.

[12] Since the ionospheric conductance changes signifi-cantly when the NEXL is formed, the ionospheric currentevolves from the two‐cell pattern to the state of an intensewestward electrojet existing in the midnight region. Figure 3shows this two current patterns at t = 47 min and 77 min,respectively. In Figure 3a, a weak eastward electrojet appearsin the afternoon sector between 70° and 75° latitude, andmeanwhile, a westward electrojet grows at morning sector.At this time, the intensity of these two electrojet is nearlyequal which is less than 0.2A/m. The background fieldaligned current is relatively weak. When the ionosphericconductances are enhanced, the westward electrojet expandsboth latitudinally and longitudinally, and flows across themidnight region. The intensity of the electrojet increasesdramatically, which peaks at the late midnight region,

Figure 2. The convection pattern in the equatorial plane(top) before and (bottom) after the formation of NEXL. Thebackground contour is Z component of the magnetic field,and the red line indicates the location of reconnection.

Figure 3. The ionospheric current vectors at (a) t = 47 minand (b) t = 77 min. Dotted circles show latitudes of 60°, 70°,and 80°. The background contour shows the FAC distribu-tion, with warm colors for downward FAC and cool colorsfor upward FAC.


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reaching 0.8A/m. The field aligned current extends to thenightside region, and grows in intensity, too.[13] Figure 4 illustrates how the westward electrojet

intensifies in the midnight meridian which shows changesof the total region 1 field‐aligned current, the maximumPedersen and Hall conductance, the maximum electric fieldand the total westward current and its components from thetop to the bottom panels, respectively. For simplicity, the totalregion 1 field‐aligned current is integrated from all upwardcurrent in the dusk sector and the westward current is between61° and 71° latitude. The first response of the nightsideionosphere to the IMF discontinuity is at ∼12 min shownby the appearance of the westward electric field and current.The response time also accords with Yu and Ridley [2009].However, before the formation of NEXL (the vertical solidline), the southward electric field is very small, which meansthe blockage effect is not obvious. Thus the westward elec-trojet is weak and mainly consists of the Pedersen current.When the ionospheric conductance increases(the verticaldotted line), the southward electric field has to develop tocancel the northward Hall current generated by the westwardelectric field, and its value is larger than the westward electric

field. Since the Hall conductance is at least two times of thePedersen conductance, the westward Hall current becomesthe main part of the westward current. The former weakwestward current intensifies to be the Cowling current. Inthis simulation run, the total current is around 0.6 MA, andthe westward Hall current dominate the Cowling currentby contributing more than 80% of the total current. Corre-spondingly, the total amount the region 1 FAC increasesfrom ∼0.8 MA to ∼1.8 MA, which is in accordance with theresult in Figure 3.[14] The ratio of IC /IWP shown in Figure 4 is >5 when

the ionospheric conductance is increased, which indicate theblockage is noticeable according to equation (2). Figure 5shows the current blockage in details. The fact that theionospheric current in latitude direction must be blocked isdue to the lack of radial current in the midnight sector of thenear‐Earth plasma sheet from the current loop view [Kan,2007]. Figure 5a shows the average radial current in theequatorial plane, which is similar to the observational evi-dence presented by Iijima et al. [1990]. The current vectorin the midnight region is relatively small comparing withthe premidnight and postmidnight sector, and thus the cur-

Figure 4. The ionospheric physical quantities since the IMF discontinuity encounters the bow shock. Thetotal amount of region 1 FAC, the maximum value of the ionospheric conductance, the electric field and thetotal westward electrojet in the midnight ionosphere from the first panel. The solid and dotted vertical linesindicate the starting time of near‐Earth reconnection and the increasing time of ionospheric conductances,respectively.


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rent along the latitude direction in the midnight region islimited. Figure 5b shows the blockage parameter defined byequation (1). Once the conductance increases, which resultsin the intensification of the northward Hall current, theblockage effect becomes very significant. The original valueof the blockage parameter is 0.05 to 0.5, and increases to∼0.8 after the conductance enhancement. A rough estimationbased on equation (2) shows IC /IWP = (1 + a * R2) ∼ 5.5,which agrees with the result shown in Figure 4. This indicatesthe intensification of the westward electrojet at midnightregion is dominated by the enhancement of the ionosphericconductance, especially the Hall conductance, which accordswell with the observation conclusion [Kamide et al., 1996].[15] The intensification of the Cowling current can be

reflected in the ground magnetic disturbances which are

derived from equivalent current system by the Biot‐Savartlaw. The H component of ground magnetic disturbances atdifferent magnetic latitudes along the midnight meridian areplotted in Figure 6a. Before the enhancement of the iono-spheric conductance, the magnetic disturbance is relativelysmall, and then a sharp decrease of the perturbations at t =61 min shows the sudden intensification of the westwardelectrojet intensity and the largest disturbance is around 65°latitude, the location of the largest intensity of the Cowlingcurrent. Similarly, this current pattern evolution is alsospeculated by simulated AU/AL index as shown in Figure 6b:the AU/AL index retains small at the beginning, and ALindex is rapidly depressed when ionospheric conductanceis enhanced.

Figure 5. (a) The average radial current in the equatorialplane and (b) the contour of the blockage parameter in themidnight meridian in the ionosphere.

Figure 6. (a) The magnetic disturbance at 0000 MLT and(b) the simulated AU/AL index.


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[16] Meanwhile, the magnetotail is very active. The mag-netic field lines are stretched tailward and the BZ componentreduces first, which results in the formation of NEXL at t =56 min (shown in Figure 7a). Then earthward moving mag-netic flux piles up, and dipolarization occurs. It is notedthat the dipolarization front moves from X = −7.8 RE to X =−10.6 RE, indicating the moving direction is tailward. Cor-responding to this magnetic field change, the cross‐tail cur-rent first increases during the thinning process, and then it islargely disrupted at X = −10 RE. Figure 7c shows the totalamount of the cross‐tail current in the box at −13 ≤ x ≤ − 7 RE,∣z∣ ≤ 1.5 RE, and cross‐tail current undergoes an increasing‐decreasing process. During the decreasing process, the cross‐tail current reduces from 2.05 to 1.2 MA, about a 40%reduction. However, since the conductance model is notself‐consistent in our simulation, the causal relationship ofthe M‐I coupling process will not be further discussed here.

4. Discussion and Summary

[17] Using a relatively simple ionospheric conductancemodel, our MHD model successfully produces the intensifi-cation of the Cowling current in an IMF BZ southward turningcase. In this study, the formation of NEXL is taken as a sig-

nature of the enhancement of the ionospheric conductance.Figure 4 demonstrates the westward electrojet increasesslowly before the NEXL forms, and is mainly the Pedersencurrent. Once the ionospheric conductance is enhanced, thewestward electrojet rapidly intensifies into Cowling current,and over 80% of this current is composed by the Hall current.The dominance of the Hall current is caused by the blockageof current in the latitude direction, which would produce asouthward electric field, too [Kan, 2007]. The total amount ofthe Cowling current is estimated to be around 0.6 MA, pro-ducing the AE index of 500 nT. The model results are notunusual for a moderate substorm [Kamide and Akasofu, 1974]and agree well with the empirical estimations [Akasofu, 2003].[18] For a comparative study, we run another case which

retains the ionospheric conductance unchanged all the timeeven after the NEXL is formed. The result indicates theionospheric current remains the two‐cell pattern. Figure 8ashows the current pattern at t = 77 min when NEXL isformed, which is still similar to that in Figure 3a. Figure 8billustrates this westward current qualitatively in the sameformat as in Figure 4. The amount of the total westwardcurrent is no more than 0.15 MA, and it is mainly composedby the Pedersen current rather than Hall current. As would beexpected, the blockage effect is not significant. The blockage

Figure 7. The physical quantities at the magnetotail: (a) Z component of the magnetic field (the valueof the solid line has been subtracted 30 nT for the convenience of plotting); (b) the cross‐tail current density;(c) the amount of the cross‐tail current in the region −13 ≤ x ≤ − 7 RE, ∣z∣ ≤ 1.5 RE.


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parameter is less than 0.5, as shown in Figure 8c. This impliesthat the ionospheric conductance is an indispensable factorin controlling the westward electrojet, which accords withprevious observations [Kamide et al., 1996].[19] However, there are several improvements which could

be made in the future work. First, the present study sets theionospheric conductance empirically, and a self‐consistentionospheric conductance model is needed to capture themagnetosphere‐ionosphere coupling process. Second, theionospheric current dominated by ionospheric conductancesdoes not mean the electric field can be ignored. It is foundthat the ES increases significantly to 30–40 mV/m during

substorm expansion phases [Sun et al., 2008], while it is20 mV/m at most in our simulation. This may limit thetotal amount of the Cowling current. Third, the model resultshows the cross‐tail current would reduce when the west-ward electrojet intensifies into the Cowling current, but thedetailed current circuit has not been analyzed for the nonself‐consistency of the conductance.[20] In general, the enhancement of the ionospheric con-

ductance, particularly the Hall conductance results in thecurrent blockage in the midnight region, and thus it is animportant precondition for the intensification of the Cowlingcurrent. Moreover, the ionospheric conductance is linked to

Figure 8. Results from the comparative case without the enhancement of ionospheric conductances:(a) the ionospheric current at t = 77 min after near‐Earth reconnection; (b) the ionospheric physical quan-tities, which are in the same format as in Figure 4; and (c) the blockage parameter in the midnight meridian.


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the conditions in the magnetotail, and the current blockageis attributed to the lack of the radial current in the near‐Earth plasma sheet. Thus, the Cowling current intensificationshould be treated as a magnetosphere‐ionosphere couplingprocess.

[21] Acknowledgments. This work was supported by grants NNSFC40831060, 40921063, and 41031065 and in part by the Specialized ResearchFund for State Key Laboratories of China.[22] Masaki Fujimoto thanks the reviewers for their assistance in

evaluating this paper.

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Y. Q. Hu, School of Earth and Space Science, University of Science andTechnology of China, Hefei 230026, China.J. R. Kan, Geophysical Institute, University of Alaska Fairbanks, Fairbanks,

AK 99775, USA.B. B. Tang andC.Wang, State KeyLaboratory of SpaceWeather, Center for

Space Science andApplied Research, Chinese Academy of Sciences, Beijing100190, China. ([email protected]; [email protected])


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Intensification of the Cowling current in the global MHD simulation