Why doesn t the ring current injection rate saturate?

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1 Click Here for Full Article JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 114,, doi: /2008ja013141, 2009 Why doesn t the ring current injection rate saturate? R. E. Lopez, 1 J. G. Lyon, 2 E. Mitchell, 1 R. Bruntz, 1 V. G. Merkin, 3 S. Brogl, 4 F. Toffoletto, 5 and M. Wiltberger 6 Received 3 March 2008; revised 30 September 2008; accepted 5 November 2008; published 5 February [1] For low values of the solar wind electric field, the response of the polar cap potential is essentially linear, but at high values of VB s, the polar cap potential saturates and does not increase further with increasing VB s. On the other hand, the ring current injection rate does increase linearly with VB s and shows no evidence of saturating. If enhanced convection is the origin of the ring current, this poses a paradox. How can the polar cap potential, and thus convection, saturate when the ring current does not? We examine a possible explanation based on the reexamination of the Burton equation by Vasyliunas (2006). We show that this explanation is not a viable solution to the paradox since it would require a changing polar cap flux, and we demonstrate that the polar cap flux saturates (at around 1 GWb) as the polar cap potential saturates. Instead, we argue that during storms a quasi-steady reconnection region forms in the tail near the Earth. This reconnection region moves closer to the Earth for higher values of solar wind B s, although the polar cap potential, the dayside merging and nightside reconnection rates, and the amount of open flux do not change much as a function of B s once the polar cap potential has become saturated. As the neutral line moves closer, the volume per unit magnetic flux in the closed field line region is less. Flux tubes leaving the reconnection region in general have lower PV g as B s increases, and lower PV g flux tubes can penetrate deeper into the inner magnetosphere, leading to a corresponding greater injection of particles into the inner magnetosphere. Thus a reconnection region that is closer to Earth is more effective in creating a strong ring current. This leads to a continued dependence of the ring current injection rate on VB s, although the polar cap potential has saturated. Citation: Lopez, R. E., J. G. Lyon, E. Mitchell, R. Bruntz, V. G. Merkin, S. Brogl, F. Toffoletto, and M. Wiltberger (2009), Why doesn t the ring current injection rate saturate?, J. Geophys. Res., 114,, doi: /2008ja Polar Cap Potential Saturation [2] Convection in the magnetosphere is imposed by the solar wind through the viscous interaction and through merging between the solar wind magnetic field and Earth s magnetic field. The key indicator of the strength of that convection is the total potential drop imposed across the polar cap. This potential is mapped along magnetic field lines out to the magnetosphere where the plasma drifts in response to the magnetospheric electric field. [3] The major factor that determines the polar cap potential is merging with the solar wind, which allows the solar 1 Department of Physics, University of Texas, Arlington, Texas, USA. 2 Department of Physics and Astronomy, Dartmouth College, Hanover, New Hampshire, USA. 3 Department of Astronomy, Boston University, Boston, Massachusetts, USA. 4 DLR-GSOC, Oberpfaffenhofen, Munich, Germany. 5 Department of Physics and Astronomy, Rice University, Houston, Texas, USA. 6 National Center for Atmospheric Research/High-Altitude Observatory, Boulder, Colorado, USA. Copyright 2009 by the American Geophysical Union /09/2008JA013141$09.00 wind electric field to be communicated to the ionosphere. As a first approximation the solar wind electric field is VB s, where B s is southward component of the solar wind field that merges with the geomagnetic field so that the electric field along a merging line of length l is applied to the ionosphere. If that were all there is to it, the ionospheric potential would be linearly related to the solar wind electric field for southward IMF, so that if VB s doubles in magnitude so would the ionospheric potential (assuming l does not change much). For low values of VB s this is good description of the situation [e.g., Reiff and Luhmann, 1986; Boyle et al., 1997], however for large values of VB s the ionospheric response to the solar wind electric field changes. [4] When VB s reaches values around 3 mv/m, the polar cap potential reaches a value of around 200 kv and it does not increase much more, even if the solar wind electric field continues to increase [Russell et al., 2001]. This is referred to as the saturation of the polar cap potential. The saturation effect is seen in a variety of data sets [Russell et al., 2001; Shepherd et al., 2002; Hairston et al., 2003; Ober et al., 2003]. The saturation effect is also evident in global MHD models of the magnetosphere [Raeder et al., 2001; Siscoe et al., 2002a, 2002b; Merkine et al., 2003, 2005]. This can be seen in Figure 1, which shows the polar cap potential produced by the LFM code [Lyon et al., 2004] as a function 1of8

2 Figure 1. The dependence of the polar cap potential in the LFM global MHD code as a function of the magnitude of VB s (purely southward IMF) for two different fixed ionospheric conductances. The solar wind density was 5 cm 3, and the speed was 400 km/s. of VB s (although only B s was varied). In these runs the ionosphere was fixed to have a uniform Pederson conductance with zero Hall conductivity. The reader will note that the values of the potential seem high and it is known that the current LFM code produces potentials that are too large by a factor of two. Despite this, LFM produces potentials whose variation with VB s reflects the response of the real magnetosphere. [5] For values of VB s below 3 mv/m the polar cap potential responds linearly, with higher ionospheric conductivity producing lower potential. Above 3 mv/m the polar cap potential begins to become relatively insensitive to further increases in VB s. The origin of the saturation effect has been discussed by Siscoe et al. [2002a, 2002b], but for the purposes of this paper the mechanism for saturation is not important. What is important is that saturation of the polar cap potential occurs and that MHD models in general, and LFM in particular, reproduce the effect faithfully. 2. Ring Current Injection Rate and Saturation [6] The hallmark of a magnetic storm is the generation of an enhanced ring current, which is associated with extended periods (hours) of solidly southward (B z < 5 nt) IMF, and strong storms (Dst < 100 nt) have strongly southward (B z < 10 nt) IMF [Gonzalez et al., 1994]. Two main processes are credited with creating the ring current: substorms and enhanced convection [e.g., Reeves et al., 2003; Sharma et al., 2003; Clauer et al., 2003; Hori et al., 2005]. Numerous observations and simulations have examined the critical role of enhanced convection in controlling the creation and structure of the ring current [Daglis et al., 1999; Fok et al., 2001; Brandt et al., 2002; Ebihara and Ejiri, 2003; Bruntz et al., 2005]. These studies associate higher levels of convection with a stronger injection of particles into the ring current. [7] Burton et al. [1975] established that there is a connection between the solar wind electric field and the injection into the ring current, avb s ¼ Dst* ð1þ where a is a measure of geoeffectiveness, Dst* is the pressure-corrected Dst, and t (the ring current decay time) has been determined empirically by O Brien and McPherron [2000]. The original motivation for this equation was the Dessler-Parker-Sckopke relationship [Dessler and Parker, 1959; Sckopke, 1966], which proposed that the negative perturbation in the horizontal component of the equatorial magnetic field observed during magnetic storms was directly proportional to the energy content of the ring current. [8] The term on the right hand side of equation (1) is commonly referred to as the ring current injection rate, and it is zero if the magnitude of the Dst decays as an exponential with decay time t. If the ring current generates Dst, then because of the expected exponential decay of the ring current energy due to a loss of particles, anything less than exponential decay in Dst would indicate that particles and energy are being put into the ring current from some source. Something would have to drive that energy input. Equation (1) assumes that this energy source is directly related to the solar wind electric field for southward IMF because the merging field drives convection. Despite its simple form, and questions raised about the actual connection between Dst and the ring current [e.g., Vasyliunas, 2006], this equation has been remarkably successful in predicting Dst based on solar wind parameters [e.g., McPherron and O Brien, 2001]. And, despite the weak nonlinear dependence of t on VB s [O Brien and McPherron, 2000], equation (1) obviously implies that as VB s increases the ring current injection rate will increase as well. [9] This poses a problem given the conventional wisdom concerning the creation of the ring current, as first pointed out by Russell et al. [2001]. If the injection of particles into the inner magnetosphere is due (in part) to enhanced convection, then as the polar cap potential saturates, so too should large-scale magnetospheric convection, and the ring current injection rate should saturate as well. On the other hand, it is possible that the magnetospheric voltages become decoupled from the ionospheric voltages, and that the magnetospheric voltage continues to increase with VB s although the ionospheric voltage has saturated. However this would lead to field-aligned potential drops that would increase with increasing VB s. In fact, as VB s became quite large one would require hundreds of kv difference between the ionosphere and the magnetosphere in order to maintain a linear increase in the magnetospheric voltage while saturating the ionospheric voltage. There is no evidence for such large field-aligned potentials, so the magnetospheric voltages cannot be too different from the ionospheric voltages. Thus one expects that large-scale magnetospheric voltage (and convection) must saturate when ionospheric voltage does. [10] In fact, the version of the LFM code used in this study does exhibits a saturation of the magnetospheric voltage with respect to B s when the ionospheric voltage saturates (as determined by direct integration in the magnetospheric volume using CISM-DX [Wiltberger et al., 2005]). However, the saturation level of the magnetospheric voltage is about 50 kv greater than the ionospheric saturation voltage for the runs discussed later in this paper. We are currently investigating the origin of this offset. However, a constant offset in the voltage does not affect the fact that the 2of8

3 cross-tail current will grow as the lobe flux grows. This would show up in the calculation of the ring current injection rate, although it has nothing to do with the convection of plasma into the ring current. Thus the polar cap potential and magnetospheric convection could saturate, but the magnitude of the ring current injection rate could still increase if the rate of open flux addition also increased with increasing VB s. So the question is, how does the polar cap flux behave during periods when the polar cap potential is saturated? Figure 2. Magnitude of the ring current injection rate in nanotesla per hour as a function of VB s in millivolt per meter during periods when the magnetosphere is in the main phase of magnetic storms with a peak Dst < 75 nt. magnetospheric voltage in LFM saturates when the ionospheric voltage does. [11] Figure 2 shows the magnitude of the ring current injection rates calculated from the main phases of 93 storms from January 1995 through December 2004 that had a minimum Dst in excess of 75 nt, as a function of the magnitude VB s (the IMF is southward in all cases) using the 1-hr resolution OMNI data. It is obvious that there is a linear response throughout the range of VB s, as predicted by the Burton equation, and there is no evidence of saturation, although the polar cap starts to show saturation effects at 3 mv/m and the range of VB s in Figure 2 extends to 30 mv/m. So the paradox is, if the polar cap potential saturates why doesn t the ring current injection rate saturate as well? [12] Recently Vasyliunas [2006] offered a potential solution to the paradox. He reexamined the Burton equation and pointed out that a generalized form of the Dessler-Parker- Sckopke relationship upon which the Burton equation is based contains a term related to the total open flux in the magnetosphere that has not been considered (as such) in previous studies. Taking the time derivative of this term adds a negative term to the left hand side of equation (1) proportional to the time rate of change of the polar cap flux. The change in the open flux is given by the difference between the rate of dayside merging and nightside reconnection. Since the rate of dayside merging is proportional to VB s, that term and avb s could cancel out and the ring current injection rate would just be proportional to the rate of nightside reconnection. In fact, Vasyliunas [2006] suggested that the dependence of the time rate of change of Dst on VB s could be... completely accounted for by the magnetotail effect from the increase of the open flux as the result of dayside reconnection. [13] This solution to the paradox depends on an overall imbalance between dayside merging and nightside reconnection. If the open polar cap flux continues to grow there will be an increasingly negative contribution to Dst, which is obvious once one considers that there is a southward perturbation at the Earth from the cross-tail current system [Turner et al., 2000; Maltsev and Ostapenko, 2002], and the 3. Polar Cap Flux and Saturation [14] The polar cap flux is a critical quantity in magnetospheric dynamics. As discussed above, changes in the polar cap flux reflect the balance between dayside merging and nightside reconnection, which are two of the most fundamental dynamical quantities driving the magnetosphere. Thus a number of studies, using both observations and simulations, have used the polar cap size or polar cap boundary as a diagnostic of magnetospheric activity [e.g., Newell et al., 1996; Lyon et al., 1998; Lopez et al., 1999; Wiltberger et al., 2000; Milan, 2004; Milan et al., 2004]. In particular Merkin and Goodrich [2007] directly addressed the question we pose here. Using the LFM simulation, they determined that the polar cap area (hence the flux) does saturate under conditions of strongly southward IMF. However, Merkin and Goodrich [2007] did not present observational confirmation supporting the simulation result. [15] If we examine the published literature we find a number of cases where the polar cap flux has been determined from observations. Milan et al. [2004] examined an 8-hr period during which VB s at times exceeded 7 mv/m (with B z around 11 nt), well within the saturation domain. During this period the maximum polar cap flux was 0.95 GWb. Milan [2004] examined an additional 8 hour period, and again the polar cap flux maximum was below 1 GWb. Yahnin et al. [1994] studied a steady magnetospheric convection event during which VB s = 1.5 mv/m (well below the saturation level), and they determined that the polar cap flux was 0.8 GWb. Sotirelis et al. [1998] calculated the polar cap flux for 87 periods using DMSP data, and the maximum polar cap flux they found was 976 MWb. During the periods examined by Sotirelis et al. [1998] the maximum negative B z was 6.5 nt (VB s was not reported), and they reported a linear trend between B z and the polar cap flux with no obvious evidence of saturation. On the other hand, all these studies report maximum polar cap sizes around 1 GWb, and the results of Milan et al. [2004] include a period when the magnitude of negative B z was almost twice the largest value sampled by Sotirelis et al. [1998] with no large difference in maximum polar cap flux. [16] DeJong et al. [2007] have examined the behavior of the polar cap flux during substorms, sawtooth events, and steady magnetospheric convection (SMC) events, using global auroral images from IMAGE and Polar to define the size of the polar cap. The events examined represent a wide range of polar cap sizes, and the substorm and SMC events all had a maximum polar cap flux below 1 GWb. On the other hand, about 20% of the sawtooth events exceeded 1 GWb (up to 1.5 GWb in one case). However using auroral images alone can sometimes lead to larger estimates for the 3of8

4 Figure 3. OVATION plots of the estimated polar cap for the 30 May 2005 and 20 November 2003 storms. size of the polar cap since the poleward boundary of the closed field line precipitation may not always produce emissions detectable by the instrument [Lopez et al., 1992]. In any case, the superposed epoch average maximum polar cap flux for the sawtooth events was 1.07 GWb. [17] In addition to these studies, Newell et al. [2001] presented occurrence statistics for the polar cap flux, and there is a maximum value near 1 GWb, but that paper does not present the polar cap flux as a function of VB s. However, we can examine individual storm events, using the method for calculating the polar cap flux used by Sotirelis et al. [1998] and Newell et al. [2001], to see if there is a difference between large storms and super storms. We selected six storms between 1997 and 2006 where the maximum Dst exceeded 100 nt and where polar cap flux estimates are available from the OVATION site ( Aurora/ovation). All of these storms had maximum polar cap fluxes of around 1 GWb or less. [18] Figure 3 presents OVATION plots for maximum polar cap flux during two of these events, the storm of 20 November 2003, and the storm of 30 May Both have maximum polar cap fluxes of slightly over 1 GWb. For the period corresponding to the time during which the open flux was calculated for the 30 May 2005 storm, VB s in the solar wind was 6.7 mv/m and the maximum Dst was 138 nt, comparable (at least in VB s ) to the event discussed by Milan et al. [2004]. However, during the 20 November 2003 storm, VB s was 25 mv/m (B z < 40 nt) and the maximum Dst was 422 nt. So the VB s for these two events was quite different, as was Dst, yet the polar cap flux inferred from observations was about the same for both. The DMSP particle precipitation data during these two events (not shown) indicate that polar cap had a similar latitudinal extent along the dawn-dusk meridian. All of this strongly suggests saturation of the open flux at about 1 GWb. [19] It seems that the open flux saturates in both observations and simulations. The polar cap flux must saturate just beyond the range of VB s present in the Sotirelis et al. [1998] data set since there was no evidence of saturation reported in that paper. We estimate the maximum VB s in the Sotirelis et al. [1998] data set to be around 2.5 mv/m (based on Figure 9 in that paper showing polar cap flux as a function of epsilon), and the polar cap flux for that data point was just about 1 GWb. This is consistent with a 3 mv/ m threshold for saturation effects in the polar cap potential. So as VB s becomes larger, the polar cap flux (on average) increases linearly until the magnitude VB s reaches 3 mv/m and the polar cap flux reaches 1 GWb, at which point the flux does not increase much further, regardless of the value of VB s. [20] Since the polar cap flux saturates there can be no large-scale contribution to the Burton equation during magnetic storms from the open magnetic flux term discussed by Vasyliunas [2006]. This is because the time rate of change of the flux will go to zero as the open flux saturates and so there will be no contribution to the ring current injection rate from an increasing polar cap flux. This is not to say that there are no transient variations in the polar cap flux during the main phase of storms. In fact, density variations in the solar wind have been shown to change the merging and reconnection rates and affect the polar cap flux during storms [Lopez et al., 2004; Boudouridis et al., 2005]. However, the macroscale behavior of the ring current injection rate illustrated in Figure 2 cannot be explained by an accelerating increase in the rate of change of the open magnetic flux in the tail. Moreover, it also means that there 4of8

5 is a maximum contribution to Dst itself from the open flux in the tail (i.e., the tail current system). [21] The fact that Dst is more intense for storms with larger VB z with no evidence of saturation means that these more negative Dst values must be associated with larger plasma pressures and pressure gradients in the inner magnetosphere. However, the generation of larger ring current for magnetic storms with larger VB s (beyond 3 mv/m) cannot be a feature of increased global convection. This leaves us with the original paradox intact. To resolve it we must reexamine how the ring current is built up in the inner magnetosphere during storms. 4. Generation of the Ring Current and Resolution of the Paradox [22] Recent results from the Rice convection model [e.g., Toffoletto et al., 2003] have provided new perspectives on what is required in the magnetosphere to create a strong ring current. In particular, it has been shown that regular, largescale convection cannot create large ring currents. What is required is some process that creates flux tubes with low PV g, where V = R ds/b is the flux tube volume [Lemon et al., 2004; Zhang et al., 2008]. Reconnection in the midtail is the mechanism for creating these low PV g flux tubes. These flux tubes generate strong internal electric fields and ~E ~B drift deep into the inner magnetosphere in what is known as the interchange instability [e.g., Xing and Wolf, 2007]. Adiabatic acceleration of the particles in the flux tube provides the population for the ring current. Kan et al. [2007] discussed this issue and suggested that magnetic storm intensity might be related to the position of the neutral line in the tail during storm time substorms. Storm time substorms whose neutral line form closer to the Earth would produce a greater enhancement of the ring current as compared to storm time substorms whose neutral line forms further from the Earth. [23] Having determined that the LFM simulation reproduces saturation of the polar cap potential as well as saturation of the polar cap flux, let us consider what storm time driving of the code produces. Even though LFM does not produce a significant storm time ring current (lacking the energy-dependent drifts), the code has been used successfully to model many features of magnetic storms [e.g., Goodrich et al., 1998; Lopez et al., 2004]. In particular, there are two relevant features in the storm simulations that have been reported [Lopez et al., 2000, 2003] that we now discuss. [24] The first result is that the polar cap flux grows during the early part of the storm, but then it remains fairly constant, in contrast to the very large variations in the open flux observed during substorm simulations [e.g., Lyon et al., 1998; Wiltberger et al., 2000]. This is entirely consistent with our finding that the polar cap flux saturates. It also calls into question what one calls a storm time substorm. If the hallmark of a substorm is the loading and subsequent unloading of energy in the tail [e.g., Baker et al., 1996], then if the polar cap flux barely changes can we call some discrete activity a substorm? In fact, many intensifications of the electrojet, accompanied by particle flux increases at geosynchronous orbit, etc., may be due to directly driven processes during the main phase of a storm [Lopez et al., 2004]. Even though some of these increases in magnetospheric activity might involve some changes in the amount of open flux in the tail [Boudouridis et al., 2005], the loading/unloading pattern of substorms is not evident. Thus we consider the supposition of Kan et al. [2007] that the position of substorm neutral line is important to be only partially correct, since simulations of the storm time magnetotail do not show the loading-unloading behavior of substorms, and in fact the term storm time substorm may be a misnomer. Also, it is relevant to note that Bargatze et al. [1985] found that when was VB s large, the loadingunloading response in the AE data disappeared, leaving only the directly driven response. [25] This leads us to the second relevant result of the storm simulations. Instead of generating repeated substorms, with continued creation of new near-earth reconnection regions that then retreat down the tail, the magnetosphere forms a reconnection region relatively near Earth (about R E ) which persists for an extended period of time [Lopez et al., 2000]. Circumstantial evidence for the existence of this feature during the main phase of storms has been presented [Lopez et al., 2003]. The storm time reconnection region reconnects newly merged flux that has been transported to the magnetotail, so that the dayside merging rate and the nightside reconnection rate are roughly equal. The polar cap flux thus stays at a roughly constant level, which is consistent with the saturation of the polar cap flux. By forming relatively close to the Earth, the newly merged flux tubes could have small enough PV g that quasisteady convection can occur without the pressure-balance inconsistency [Erickson and Wolf, 1980]. So to modify the argument of Kan et al. [2007], the question is now, where does the quasi-stationary storm time reconnection region form, and how is it related to VB s? [26] Figure 4 presents results from five simplified physics runs. In each case the solar wind velocity was 400 km/s, the density was 5 cm 3, the sound speed was 40 km/s, and the ionosphere was a uniform with a fixed Pederson conductance of 5 mhos and no Hall conductivity, but B s was varied with B z = 7.5 nt, 10 nt, 12.5 nt, 15 nt, and 20 nt, corresponding to VB s = 3 mv/m, 4 mv/m, 5 mv/m, 6 mv/m, and 8 mv/m, respectively. The images show a single time step several hours into the runs, after the polar cap potential had reached its equilibrium, saturated value. The time stamp in each frame is slightly different because the maximum Alfvén speed in each run is slightly different, leading to small differences in the physical size of the time step. The color coding shows the magnitude of the specific entropy, PV g, in the equatorial plane (with g = 5/3). The solid black lines marks where the interpolated B z is 0 nt, which is the magnetic null at the reconnection line. [27] The exact positions of the contours do somewhat vary in time, but Figure 4 is a representative snapshot many hours after the IMF turned southward (0800 UT in simulation time). As B s increases that the average position of the magnetotail reconnection region as well as the entire boundary between open and closed field lines moves earthward. Thus the physical volume of the closed field line region decreases as B s increases. However, since the amount of open flux does not change much as B s increases past the saturation limit, the amount of closed flux must have a saturation value with respect to B s. This means that 5of8

6 6of8 the overall volume per unit magnetic flux in the closed field line region must be smaller for larger values of B s. In fact, it is evident that for larger values of B s, the specific entropy of newly reconnected flux tube just earthward of the storm reconnection region is generally smaller for larger values of B s. [28] One can also note that the inner magnetosphere has much smaller PV g, so that there is very little transport into the inner magnetosphere in the frame presented. In fact, most of the transport during this kind of driving of the simulation occurs as flow along the flanks of the magnetosphere [Goodrich et al., 2007]. However, on occasion, because of the nonsteady nature of the reconnection in the tail, there is evidence of some flow straight up the tail, and it is this kind of transport that would build up the ring current. The LFM code produces inner magnetosphere plasma pressures that is much lower than reality, so in the real magnetosphere, PV g in the inner magnetosphere is considerably larger than LFM alone produces [Toffoletto et al., 2004]. Thus in reality, we would expect such episodes of ring-current-building transport to be more prevalent since flux tubes produced at the reconnection region would be able to move into the inner magnetosphere more effectively that LFM would suggest. [29] Lower PV g flux tubes will penetrate deeper into the inner magnetosphere, where the dipole field dominates the flux tube volume so that the flux tube volume will barely change, regardless of magnetospheric activity. The flows that penetrate deeper into the inner magnetosphere will result in a greater buildup of the ring current due to greater adiabatic acceleration of the plasma in the flux tube. Thus flux tubes leaving the tail reconnection region during a storm with larger VB s will be able to penetrate deeper into the inner magnetosphere, and be more effective in accelerating ring current particles than flux tube leaving the tail reconnection region during a storm with lower VB s. [30] This seems to be the resolution to the paradox. The ring current injection rate as expressed in the Burton equation is an actual measure of the rate of injection plasma into the inner magnetosphere. The contribution to Dst from the open flux in the tail reaches a maximum as the open flux saturates at about 1 GWb. Even though the polar cap potential and hence the global measure of convection saturates, the continued reduction in the volume of the closed field line region in the magnetotail as B s increases and the lower PV g at the reconnection line produces a more effective transport of plasma into the inner magnetosphere. This results in a greater injection into the ring current. It also results in a ring current injection rate (as measured by Dst) that will continue to increase as VB s increases, despite the saturation of the polar cap potential. 5. Conclusion [31] Since the discovery that the transpolar potential saturates for large values of VB s, there has been a paradox Figure 4. Simulation results for five different values of IMF B z. The black contour marks B z = 0 nt in the equatorial plane, and the specific entropy, PV g, is color coded in units of log 10 [npa(r E /nt) 5/3 ]. The grid lines are set at 5-R E intervals.

7 in our understanding of the ring current injection rate based on the Burton equation [Russell et al., 2001]. Reconsidering the underlying fundamental assumptions behind the Burton equation, Vasyliunas [2006] provides important insights into the problem. In particular, Vasyliunas [2006] highlights the role of the rate of increase in the open flux in determining the time rate of change of Dst. However, we find that the open polar cap flux has a saturation limit of about 1 GWb, so once that limit is reached the polar cap flux cannot contribute to the change in Dst. On the other hand, reconsidering the processes most important to creating a strong ring current, and the critical role played by low PV g flux tubes in injecting and adiabatically accelerating particles into the inner magnetosphere does provide a resolution based on global MHD simulations of the storm time magnetosphere. During periods of extended, large negative B z, the magnetosphere forms a quasi-steady reconnection region that moves earthward and which produces, on average, lower PV g flux tubes as VB s increases. Lower PV g flux tubes can penetrate deeper into the inner magnetosphere, producing a more intense ring current. This mechanism preserves a link between the ring current injection rate and VB s even during periods when the polar cap potential and the polar cap flux are saturated. [32] Acknowledgments. This paper was based upon work supported by CISM, which was funded by the STC Program of the National Science Foundation under agreement ATM The authors would like to thank T. Hill, R. L. McPherron, G. Siscoe, V. Vasyliunas, and R. A. Wolf for useful conversations. We thank the World Data Center for Geomagnetism, Kyoto, for the use of the Dst data. 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