Dynamics of the region 1 Birkeland current oval derived from the Active Magnetosphere and Planetary Electrodynamics Response Experiment ( AMPERE )

[1] The region 1 (R1) and region 2 current systems typically form concentric rings of field-aligned currents in the polar ionospheres; we term the inner ring the R1 oval. We apply an automated fitting scheme to field-aligned current densities provided by the Active Magnetosphere and Planetary Electrodynamics Response Experiment (AMPERE) and identify the latitude of maximum R1 current at all magnetic local times to yield the size of the R1 oval. We investigate the dynamics of the R1 oval size in response to geomagnetic activity for two cases corresponding to: repeated substorm activations with a minimally enhanced ring current; a significant ring current enhancement with multiple substorms. During the first event the dynamics of the R1 oval size reflected an expanding-contracting polar cap: during substorm growth phase dayside reconnection added open magnetic flux to the polar cap, expanding the R1 oval equatorward. Tail reconnection during the substorm expansion phase converted open into closed magnetic flux and the polar cap contracts as reflected by the poleward retreat of the R1 oval. During the period of enhanced ring current intensity the R1 oval grew to larger sizes during each substorm growth phase than it did during the other event, consistent with the suggestion that a stronger ring current stabilizes the magnetospheric tail to the onset of magnetic reconnection. The presented methodology allows AMPERE data to be condensed into a single parameter, the R1 oval size, which reflects magnetospheric dynamics and provides a convenient measure of the instantaneous magnetospheric system state in both hemispheres.


Introduction
[2] At the dawn of the space age, using data from the early polar-orbiting Satellite 1963 38C, Zmuda et al. [1966] reported transverse magnetic disturbances in the auroral regions and interpreted these disturbances -fashionable in those days -as signatures of hydromagnetic waves.Cummings et al. [1969] pointed out that some of these transverse signatures are more likely due to currents flowing along magnetic field lines, so-called field-aligned currents (FACs).Schield et al. [1969] coined the alternative term Birkeland currents to honor the fact that it was Birkeland [1908] who introduced the concept of electric currents flowing vertically into the polar ionosphere during his discussion of observations of aurora borealis and associated magnetic perturbations made during one of his expeditions.
[3] Analyzing more than one year's worth of magnetic field data from the Triad satellite, Iijima andPotemra [1976a, 1976b] showed that transverse magnetic disturbances were a common feature of the magnetosphere, and their strength and location strongly varied with solar wind parameters.Translating the magnetic disturbances into vertical electric currents, Iijima and Potemra [1978] presented the global average structure of Birkeland currents that produce the observed magnetic perturbations.Iijima and Potemra [1978] found that the Birkeland currents consist of two concentric rings, the equatorward current flows into the ionosphere on the dusk side and out of the ionosphere on the dawn side.For the poleward ring of current the polarity is reversed, such that it flows out of the ionosphere on the dusk side and into the ionosphere on the dawn side.Iijima and Potemra [1978] also introduced the term region 1 and region 2 current to identified the poleward and equatorward ring, respectively.
[4] It was quickly realized that the magnetopause currents introduced by Chapman and Ferraro [1931a, 1931b, 1932a, 1932b] were at least partly responsible for the occurrence of the region 1 Birkeland currents at high latitudes [Atkinson, 1978].The region 2 current was found to be driven by a partial ring current, such that the global magnetospheric current system is now understood to be as depicted in Figure 1.Note that the region 1 and 2 currents close in the polar ionosphere via Pedersen currents, which have not been included in Figure 1.For further reviews of the polar Birkeland currents see also Sato and Iijima [1979], Potemra [1985Potemra [ , 1988]], and Cowley [2000].
[5] Magnetospheric dynamics and hence also the dynamics of the region 1/2 currents are governed by the Dungey magnetic convection cycle [Dungey, 1961].The cycle begins with closed terrestrial magnetic field lines located on the dayside which reconnect with solar wind magnetic field lines during periods of southward interplanetary magnetic field (IMF).Newly opened field lines are convected with the solar wind flow toward the magnetospheric tail.In this paper we will investigate how the size of the oval of maximum region 1 current changes in response to dayside and nightside reconnection.

The AMPERE Dataset
[6] The Iridium® constellation consists of 66+ commercial satellites in 780 km polar circular orbits distributed over six orbital planes to provide global satellite telephone and data service.Each satellite carries an engineering magnetometer as part of their attitude system and Anderson et al. [2000] showed that combining two hours of magnetic field perturbation data from all satellites allows one to estimate the global distribution of radial current densities [see also Anderson et al., 2002].In the polar regions, i.e. at magnetic latitudes >60 , these radial currents correspond to the Birkeland currents or field-aligned currents (FACs) commonly associated with the region 1 (R1) and region 2 (R2) current system [Iijima and Potemra, 1978;Cowley, 2000].Other authors have used this dataset to characterize the average FAC distribution during various IMF conditions [Anderson et al., 2008;Green et al., 2009], to relate FACs to auroral phenomena [Korth et al., 2004], and to estimate the global Poynting flux into the polar regions by combining the magnetic perturbation data with electric field data from the SuperDARN radars [Waters et al., 2004].All of these studies used the engineering magnetometer data which was telemetered to the ground with coarse time resolution (200 s per sample) such that the data had to be accumulated over long periods of time, about two hours, to acquire a composite sample of the magnetic signatures in the polar regions.This limitation has been resolved under the Active Magnetosphere and Planetary Electrodynamics Response Experiment (AMPERE).AMPERE is a facility funded by the National Science Foundation that increased the time resolution of the magnetic perturbation data provided by the Iridium® satellites by a factor of ten to 20 s/sample during normal mode and by a factor of 100in high-rate sampling when the resolution is increased to 2 s/sample.This allows the global radial current density to be estimated every 10 min commensurate with the inter-satellite time spacing in each orbit plane.The process of obtaining radial current densities involves least squares fitting gradients of spherical harmonic functions to the raw magnetic perturbations, and applying Ampere's Law [Waters et al., 2001].Because the potential functions that have been determined through the spherical harmonic fitting technique are continuous, the derived radial current density can in theory be calculated at any spatial resolution.The data used here was provided with a longitudinal resolution of 1 hour MLT, i.e., the resolution is double that provided by the orbit plane spacing of the spacecraft.The sampling rate limits the latitudinal resolution and in normal mode the AMPERE data are spaced by 1 in magnetic latitude; in burst mode, when the sampling rate of the raw magnetic field perturbations is higher, the latitude resolution further increases.The fitted data used in this study are publicly available from the project website at http:// ampere.jhuapl.edu.

Methodology
[7] Given a current density distribution from AMPERE, it is our goal to automatically determine the location of the R1 and R2 currents as accurately as possible.To achieve that goal, we fit, at auroral latitudes, a suitable function to all 24 observed current density profiles per time step.From the latitudinal fits we can extract the location of the R1 and R2 current at 24 local times; we then fit a truncated cosine expansion to the R1 current locations in order to estimate the size of the region enclosed by the R1 current.We will now describe in detail the steps outlined above.
[8] The current density data derived from AMPERE often shows well defined R1 and R2 current signatures, especially for southward IMF [Anderson et al., 2008].Figure 2 shows the AMPERE-derived radial current densities in the northern (Figure 2, left) and southern (Figure 2, right) hemisphere during a moderately geomagnetically active period (Kp $ 2-3) on 12 December 2010.The current densities were calculated from data accumulated over 10 min between 2124 UT and 2134 UT and are plotted in magnetic latitude/MLT coordinates; according to the convention used here downward currents are negative and colored blue, the upward direction is positive and such currents are colored red.Currents with a magnitude below 0.2 mA/m 2 are not plotted; this threshold is motivated by an analysis shown later in this paper.Although the AMPERE data shows considerable medium-and small-scale structure, the R1 currents were relatively well-defined during this interval, consisting of upward currents (colored red) on the dusk flank and downward currents (colored blue) on the dawn flank.Toward the dayside the maximum R1 current was located around 75-80 MLAT, on the nightside it was located closer to 70 MLAT.This is true for both hemispheres.Equatorward of the R1 current system, the R2 currents were well defined on the dusk side in the northern and on the dawn flank in the southern hemisphere.In the northern hemisphere the R2 current was observed between 00and 03 MLT and again around 08 MLT; however there exists a gap between the two regions.In the southern hemisphere the R2 current was only observed between 13 and 19 MLT.
[9] Note that the strong R1/R2 current system on the dusk flank in the northern hemisphere was not matched by similarly strong currents on that flank in the southern hemisphere.Instead, the R1/R2 currents were strongest on the dawn flank there.We believe that this is due to a IMF By effect; in fact, in the hours leading up to the interval shown in Figure 2, the IMF clock angle was around À120 degrees which is known to twist the magnetic configuration of the magnetospheric tail [Fairfield, 1979;Cowley, 1981].
[10] Along a meridional cut from 55 to 85 magnetic latitude at most magnetic local times, the current densities in both hemispheres are dominated by a bipolar signature that are the R1 and R2 currents.To localize the maximum of both current systems at a given local time, we fit the observed latitudinal current density profile, j(l), with a sinusoid multiplied by a Gaussian of the form where o 0 , a 0 , l 0 , w 0 , and f 0 are free parameters determined by minimizing the variance between j fit (l) and j(l).o 0 , a 0 , l 0 , and w 0 are the zero offset, amplitude, center location and width of the Gaussian, respectively; f 0 describes the phase shift of the sinusoid.The sign of the amplitude a 0 controls the polarity of the fitted currents, i.e. whether the equatorward current is downward or upward.The Gaussian described by equation ( 1) has a Full-Width-Half-Maximum (FWHM) of ffiffiffiffiffiffiffiffiffi 8ln2 p w 0 , and the sinusoid adds a bipolar signature to the fit.As equation (1) shows, the "wavelength" of the sinusoid was chosen as twice the FWHM. Figure 3 shows how the free parameters relate to the shape of the curve.
[11] The function we fit to meridional current density profiles described in equation ( 1) is of course only one of many possibilities.We have tried others, for example simply selecting the latitude of maximum/minimum current density or a superposition of two Gaussians, but we found through inspection by eye of hundreds of latitudinal profiles that on average equation (1) yields the best results, i.e., the fit selects the correct locations of the R1/R2 currents at a high success rate.
[12] Figure 4 shows j(l) (black dots) and j fit (l) (solid green line) for the data shown in Figure 2 along the 18 MLT meridian of the northern hemisphere.From j fit (l) evaluated every 0.02 we find the latitudes of the maximum and minimum current, l max and l min , which for this local time we identify as the latitudes of peak R1 and R2 current density, respectively.We repeat this procedure at each MLT hour to yield 24 latitudes for R1 and R2.We adopt a convention that the positive extremum locates R1 for 12 ≤ MLT < 24 whereas the negative extremum locates R1 for 00 ≤ MLT < 12, consistent with the known average distribution of the R1 and R2 currents [e.g., Anderson et al., 2008].
[13] In this study we are only interested in the location of the R1/R2 current systems.On occasion the ordering of positive and negative extrema does not agree with the conventional R1/R2 pattern.We therefore enforce the relative position of the currents by rejecting all fits on the dusk side where the downward (R2) current is found to be located poleward of the upward (R1) current.Similarly, on the dawn side, we reject fits when the upward (R2) current is located poleward of the downward (R1) current.
[14] The fitting algorithm provides formal confidence intervals for the five free parameters from the covariance matrix.However, none of the parameters of equation ( 1) give the location of the R1 current l R1 and R2 current l R2 directly; rather their location is determined by the value of l 0 , w 0 , and f 0 .Therefore, the errors of l 0 , w 0 , and f 0 introduce an error to l R1 and l R2 which is not analytically derivable from the parameter errors.We estimate the uncertainty in l R1 and l R2 by varying the parameters l 0 , w 0 , and f 0 systematically and simultaneously within their respective confidence intervals, finding that combination of values where l R1 and l R2 are displaced most when compared to that location found with all errors equal to zero.The maximum latitudinal offset is then taken as the uncertainty of l R1 andl R2 and used in the second fitting step.
[15] The procedure described above yields the latitudes of the strongest R1 and R2 current density, l R1 (m) and l R2 (m), respectively, and their uncertainties as functions of MLT, denoted by m.AMPERE provides global estimates of the radial current density, such that this fitting procedure is applied to data from both hemispheres to find l N, R1 (m) and l N, R2 (m) in the northern and l S, R1 (m) and l S, R2 (m) in the southern hemisphere, independently.In the next step of our procedure we fit a suitable function to the four sets of latitudes l N, R1 (m), l N, R2 (m), l S, R1 (m), and l S, R2 (m) to yield the four ovals of strongest R1/R2 current in the northern and southern hemisphere.
[16] Oval-shaped geophysical boundaries have often been approximated by use of truncated cosine series [Feldstein and Starkov, 1967;Milan et al., 2003;Boakes et al., 2009] and we choose the same approach by fitting l R1 (m) and l R2 (m) as functions of local time, m, to a cosine function of form where L 0 , a 1 and f 1 are free parameters determined by minimizing the variance between f(m) and l R1 (m) or l R2 (m).f(m) describes an oval that is displaced from the magnetic pole where L 0 is the mean latitude, a 1 is the amplitude of the displacement from L 0 and f 1 is the phase of the displacement relative to L 0 .During the fit the l R1 and l R2 locations are assigned uncertainties which were determined as described above such that errors of the best-fit values L 0 , a 1 and f 1 are also estimated.Using Gaussian error propagation the uncertainty in f(m) is then found.
[17] Figure 5 shows two examples of this procedure in the northern (Figures 5a, 5b, 5e, and 5f) and southern  (Figures 5c, 5d, 5g, and 5h) hemisphere.Figures 5a-5d show the results for the same time as Figures 2 and 4 when AMPERE observed relatively strong current densities; the median R1 current density over all MLTs during this period is around 0.6 mA/m 2 in both hemispheres.Figures 5e-5h show the result of the R1/R2 current location detection an hour later, when the currents were weaker with a median value of about 0.4 mA/m 2 .Figures 5a, 5c, 5e, and 5g show how the current locations vary with MLT as dots, their size indicating the current density amplitude at each local time; vertical lines at each data point indicate the error bar as estimated during the first fitting process.Figures 5b,  5d, 5f, and 5h show the same positions plotted on a magnetic latitude/MLT grid; for reference, the original AMPERE data are shown as solid/dashed contours for negative/positive current densities (also compare Figure 2).The solid blue and red lines in both panels shows the best fit of equation ( 2) to the data during the second step.MLTs where no points are plotted violated the condition that the R2 current always be equatorward of the R1 current, or the current density profile fit did not converge at that local time.Dashed red and blue lines in all panels give the 1-sigma confidence intervals of the fitted ovals.
[18] It can be seen from Figure 5 that when the AMPERE current densities are relatively strong, the oval fit results in an accurate determination of the R1/R2 current locations at most magnetic local times.The error of the oval determination is below 0.5 MLAT, even though the error in determining the latitudinal positions of the maximum/ minimum currents from the meridional profiles is at times significantly larger.Figures 5e-5h show that even though the AMPERE currents were weak during that interval and small in spatial extent, the fitting procedure still produced a sensible result, albeit with a larger error.Last, Figure 5 shows that the oval of R1 current contracted by about 5 MLAT during the one hour time period that lay between the two observations.
[19] Applying the above procedure to all AMPERE data between January 2010 and August 2011 we find that on average 50% of all 4 million meridional current density profiles are successfully fitted; as the R1/R2 current systems tend to be stronger on the flanks, the success rate there is about 60% whereas it is about 40% around magnetic local noon/midnight.The success rate of the oval fitting is about 95%, i.e., in only 5% of the available AMPERE current maps it is not possible to determine a location of the R1/R2 current oval.Of course, the determined current ovals are not always sensible and to get a feeling for what constitutes a good oval fit, we show Figure 6.Each black dot in Figure 6 represents one successful determination of the R1 current oval using the technique described above between January 2010 and August 2011.On the x axis we show the median current density of each oval fit, i.e. the median current density value over all MLTs where a R1/R2 current location could be determined.All median current density values were then binned into 0.05 mA/m 2 wide bins and the median of all y values in each bin was calculated and marked by a red cross in Figure 6.The vertical red lines give the range which contains 90% of the values in each bin.
[20] In Figure 6 (top) we show the fitted size of the R1 current oval L 0 (compare equation ( 2)) against the median of all current densities that went into a particular oval fit.At median current densities greater than 0.2 mA/m 2 L 0 increases with increasing median current densities.We also observe that the spread in values of L 0 decreases above 0.2 mA/m 2 .We note that there are indications that the size reaches a saturation plateau at current densities larger than about 1 mA/m 2 .As the average R1/R2 current increases with magnetospheric activity driven by the solar wind [Anderson et al., 2008] this effect might be similar to the observed saturation of the cross polar cap potential [Shepherd, 2007;Wilder et al., 2010].Figure 6 (middle) shows that the higher the median current density, the lower the median error over all MLTs in the determination of the maximum/minimum current locations from the latitudinal current density profiles.Again 0.2 mA/m 2 can be marked as that current density above which the error is small and nearly constant.The same applies when looking at the variation of the error of the R1 current oval size DL 0 with median current density; above about 0.2 mA/m 2 DL 0 is nearly constant, reaching a minimum spread in values around 0.8 mA/m 2 .In Figure 6 we only show the results for the R1 current oval determination but all observations mentioned above hold true when studying similar plots for the R2 current oval.Consequently, we will henceforth consider a R1/R2 current oval fit to be trustworthy whenever the median current density from all locations that went into that particular oval fit was above the threshold of 0.2 mA/m 2 .As can be seen from Figure 6 (bottom), this choice reduces the error in oval size on average to below 1 MLAT.
[21] The procedure described above applied to AMPERE data yields an automated identification of the location of the R1 and R2 currents in both hemispheres whenever the median current density is above 0.2 mA/m 2 .Although the fitting scheme described above identifies the location of both the R1 and R2 current system, here we focus on the R1 location, hereinafter called the R1 oval, because the R1 currents are believed to locate closer to the ionospheric projection of the open-closed field line boundary [e.g., Cowley, 2000].Again looking at all AMPERE data between January 2010 and August 2011, we find that the R1 oval can be determined with a median current density above 0.2 mA/ m 2 in about 55% of all $ 170, 000 available current density maps.Note, however, that this time span falls into a deep solar minimum and that increased solar activity is likely to produce stronger R1/R2 currents and hence should improve the availability and accuracy of the described method.In the following section we will investigate how the R1 oval responds to different phases of the substorm cycle as well as its movement associated with ring current intensification as characterized by the Sym-H index.

Observations
3.1.12 December 2010 to 14 December 2010 [22] In Figure 7 we show results for two days between 12 December 2010, 1200 UT and 14 December 2010, 1200 UT.In the first panel we plot the IMF Bz component in black; times when the Bz component is southward are marked with red shading.The gray traces show the positive and the negative of the IMF magnitude.The IMF data were taken from the OMNI dataset [King and Papitashvili, 2006] which are propagated to the nose of the Earth's bow shock.In the next panels we plot the Sym-H index, followed by the AU and AL indices.Sym-H is the magnetic perturbation measured at the Earth's equator associated with the ring current, while AU and AL are the upper and lower envelopes of magnetic perturbations associated with the auroral electrojets.In each of the bottom two panels we show three time series: the median current density of the R1 oval in blue, the size of the R1 oval L 0 as black dots, and the error of the R1 oval size DL 0 in red.These values are shown for the northern and southern hemisphere.According to the discussion in the previous section we only plot values of L 0 whenever the median current density was above 0.2 mA/m 2 .This threshold is shown as a blue dashed line in the plots of the median current densities.
[23] For the two days shown in Figure 7 Sym-H was moderate and relatively steady whereas the AL index indicates that there were multiple auroral activations marked by vertical dashed lines.The R1 oval size underwent repeated cycles of expansion and contraction corresponding to AL variations.Prior to each auroral enhancement, the R1 oval size gradually increased reaching its maximum very close to the time of maximum depression in AL.As AL recovered to values close to zero, the R1 oval shrank to a size comparable to that before the auroral enhancement.The variations in the R1 oval size correlate with the intensity and duration of the southward IMF prior to the auroral enhancement.This is most evident for the increases in R1 oval size for activations vi, vii, and viii which were progressively greater corresponding to more strongly negative IMF Bz preceding these auroral activations.This indicates more dayside reconnection and hence more magnetic flux-loading of the magnetotail before substorm onset, implying that more open magnetic flux accumulated in the polar cap, which in turn pushed the R1 oval to lower latitudes.The largest increase in R1 oval size in both hemispheres during the period shown in Figure 7 was prior to the iii auroral enhancement, when the oval size increased by 166% from 12.5 to almost 20 .This interval of R1 oval growth was also associated with a period of steady, strongly southward IMF, with Bz around À5 nT for about 3 hours.It is worth pointing out that this increase in radius means that the area enclosed by the oval more than doubled during this period.
[24] In general, the behavior of the northern and southern R1 ovals to sudden changes in the AL index are similar.Both undergo a cycle of increase prior to onset and decrease starting at the time of activation with similar values of its R1 Figure 7. Stackplot of the OMNI IMF Bz component in black with the IMF magnitude (positive and negative) in gray, the Sym-H index, the AL and AU index, the median current density, the size L 0 , and the error DL 0 of the R1 oval in the northern hemisphere followed by the median current density, the size L 0 , and the error DL 0 of the R1 oval in the southern hemisphere between 12 December 2010, 1200 UT and 14 December 2010, 1200 UT.The blue dashed line in the panels of the median current density shows the threshold of 0.2 mA/m 2 .Auroral activations are marked by vertical black dashed lines.oval size.While there are some subtle differences in size between the north and the south R1 oval, the most notable difference is in the observed median current densities as shown by the blue line above the R1 oval sizes.During the interval shown in Figure 7 the median R1 current densities were generally higher in the southern hemisphere consistent with a higher conductance in the summer hemisphere.Note however, that this does not allow one to identify the driver as a current or voltage source since the difference in current between the hemispheres follows necessarily from a difference in conductance regardless of the nature of the source dynamo.
[25] Between auroral enhancement iii and iv the R1 oval exhibited a small cycle of expansion and contraction.During the expansion phase of the R1 oval the IMF Bz component was negative, which drives dayside reconnection, the contraction however was not associated with a depression in the AL index.It is possible that a substorm occurred during this period but that it was not represented in the AL index because of the spatial spacing of the magnetometers from which the data is used to calculate the index.
[26] It can be seen from Figure 7 that phases of expanding R1 oval were also accompanied by increasing median current densities which in turn decreased the error of the R1 oval size.During the interval between 12 December 2010, 1200 UT and 14 December 2010, 1200 UT as shown in Figure 7, 27% of the total number of available current density maps failed to produce a R1 oval fit in the northern hemisphere with a median current density above 0.2 mA/m 2 .In the southern hemisphere this number was about 16%, due to the higher current densities in that hemisphere.

09 March 2011 to 14 March 2011
[27] In this section we consider a period between 09 March 2011, 0000 UT and 14 March 2011, 0000 UT during which the Sym-H index decreased to about À90 nT indicating a significant ring current enhancement.In the first panel of Figure 8 we show the IMF Bz component as a black trace and the positive and negative IMF magnitude in gray, both taken from OMNI.The second panel shows the Sym-H index, followed by the AL and AU index, and finally the median current density, size L 0 and size error DL 0 of the R1 oval in the northern and southern hemisphere for this time period.The interval can be divided into three parts: for the first day (09 March 2011) the Sym-H index was steady and small, comparable to the first event discussed above.Between 10 March 2011, 0000 UT and 11 March 2011, 0600 UT the Sym-H index declined rather steadily to À90 nT, most likely in response to the nearly uninterrupted strongly southward IMF during this period.During the following 2 1/2 days the IMF was mostly northward and small in magnitude, and over this period the Sym-H index recovered to values around À10 nT.
[28] During the interval of decreased Sym-H index, i.e. while the ring current intensity was enhanced, there occurred several strong auroral activations, as reflected by the AL index.Some of these substorms have been marked by vertical dashed lines in Figure 8 and it can be seen that associated with these the R1 oval boundary expanded and contracted.Underlying these short-term fluctuations, however, is a longer-term trend: the size to which the R1 oval expands increases as Sym-H decreases.Similarly, the contracted R1 oval size decreases as Sym-H increases.This indicates that the magnetosphere is able to accumulate more open magnetic flux during periods of an intensified ring current.
[29] As was the case during the first event discussed, the dynamics in R1 oval size in the northern and southern hemisphere were nearly identical.The magnitude of the current densities were comparable in the northern and southern hemisphere as expected close to equinox when the ionospheric conductivities are similar in both hemispheres.Between 10 March 2011, 0000 UT and 13 March 2011, 0000 UT the southward IMF ensured consistently strong R1 currents which in turn led to a near-continuous determination of the R1 oval size with small errors.

Discussion
[30] We used AMPERE radial current density data to locate the maximum R1 current in the northern and southern hemisphere at all magnetic local times and study the dynamics of R1 current location in response to geomagnetic activity.During the first event between 12 December 2010, 0000 UT and 14 December 2010, 0000 UT for which Sym-H was steady around À10 nT, we find that the motion of the R1 oval is organized by the substorm cycle: during the substorm growth phase associated with southward IMF, the size of the R1 oval increases to between 15 and 20 ; around substorm onset, some of which correspond to northward IMF turnings, the size of the R1 oval starts to decrease and continues to do so all the way through the expansion phase reaching a minimum size of 12 to 14 .
[31] The described dynamics of the R1 oval can be understood in the context of the expanding-contracting polar cap (ECPC) paradigm [Lockwood and Cowley, 1992;Cowley and Lockwood, 1992] where the expansion and contraction of the polar cap boundary (PCB) can be readily understood in terms of dayside and nightside reconnection, and ionospheric convection.A burst of dayside reconnection will perturb the equilibrium position of the PCB by adding open magnetic flux to the polar cap; equilibrium is reinstated through ionospheric convection.At the end of the dayside reconnection burst, the system returns to a state of equilibrium with a PCB that is expanded equatorward.Conversely, magnetic reconnection can occur on the nightside inside the magnetotail where open magnetic flux is closed.Once the system returns to a state of equilibrium, the magnetic flux enclosed by the PCB has decreased and the PCB has moved poleward.
[32] In this picture the loading of open magnetic flux into the magnetotail through dayside reconnection corresponds to the growth phase of magnetospheric substorms.Substorm expansion and recovery correspond to the reduction of open magnetic flux through reconnection on the nightside.Using an array of space-and ground-based instruments Milan et al. [2003] investigated the variation of the open magnetic flux during two substorm cycles.They identified the PCB using global auroral imaging and subsequently estimated the polar cap area, which also allowed them to track the movement of the PCB over a period of seven hours.Their analysis confirmed the interpretation by Cowley and Lockwood [1996]: during periods of southward IMF Bz, i.e. conditions that are associated with dayside reconnection, the polar cap expanded.Within 10 min of substorm onset they found that the polar cap area decreased.Furthermore, from the rate of change in polar cap area they estimated reconnection voltages that were consistent with radar plasma drift measurements.Milan et al. [2003] go to great length to show that the poleward boundary of the auroral oval as observed by a global imaging satellite such as IMAGE [Burch, 2000] is at all magnetic local times (MLTs) co-located with the PCB.The expansion and contraction of the R1 oval observed during the first case study qualitatively shows that the dynamics of the R1 oval size are coupled to the dynamics of the PCB.
[33] In a second case study we investigate the response of the R1 oval size during a period of ring current intensification.As the Sym-H index decreases the R1 oval size increases to about 20 , larger than occurred during the 12 to 14 December event.We attribute the increase in R1 oval size to continuous dayside reconnection driven by the large negative IMF Bz.Following the ring current intensification there are several auroral activations that correlate with local maxima in the R1 oval size.These signatures are again indicative of an expanding and contracting polar cap associated with substorms and they occur while the R1 oval size remains greater than about 20 .That the R1 oval reaches a larger size before auroral activations occur, and remains expanded throughout the southward IMF interval, suggests that some mechanism allows more magnetic flux to accumulate in the magnetospheric tail before substorm onset during this event.We suggest that the magnetic perturbation associated with a stronger ring current has a dipolarizing effect on the magnetotail and we hypothesize that this allows more open magnetic flux to accumulate in the magnetotail before the stored magnetic energy is released via substorms.In fact, Milan et al. [2009] showed, using again global auroral imaging data, that the long-term variations in polar cap area are well correlated with the Sym-H index, indicating that during times of enhanced ring current intensity the magnetosphere is able to accumulate more open magnetic flux.Superposed on these long-term variations they find smaller oscillations of the polar cap area associated with the phases of the substorm cycle.
[34] As the two case studies showed, the relationships in R1 oval size, IMF Bz, auroral activation and ring current strength all agree with the dynamics of the PCB presented by Milan et al. [2003Milan et al. [ , 2008Milan et al. [ , 2009]].This suggests that the R1 oval size reflects the dynamics of the open magnetic flux in the magnetosphere even though the R1 oval does probably not co-locate with the PCB.Ohtani et al. [2010] conducted a large statistical study of DMSP magnetometer and particle data which on the nightside relates the position of fieldaligned currents to the precipitation boundaries defined by Newell et al. [1996].They find that, statistically, on the nightside (18-06 MLT) the poleward edge of the R1 current as identified using the DMSP magnetometer data is colocated with the b5i and b5e boundary.Newell et al. [1996] defines the b5i and b5e boundary as "the poleward edge of the main auroral oval", i.e. the boundary between open and closed magnetic field lines [Milan et al., 2003].In this study we automatically locate the center of the R1 current -as opposed to the poleward edge as identified by Ohtani et al. [2010] -such that we expect the R1 oval to be offset equatorward of the PCB.Thus the slightly larger values for the magnetic flux enclosed by the R1 oval as opposed to the open magnetic flux determined from auroral images is to be expected.
[35] On the dayside the relation between Birkeland currents and the PCB is somewhat more complex but Wing et al. [2010] compare the FAC locations to measurements of the particle energy spectrum.Characteristics of the energy spectrum of both ions and electrons can then be used to infer the origin of these particles and hence, whether they originate on open or closed field lines.Wing et al. [2010] find that the boundary plasma sheet (BPS) is the source region in about 50% of the cases at the center of the R1 current.The BPS is typically located on closed magnetic field lines.However, the other 50% of the time the R1 currents are associated with particles originating from the low-latitude boundary layer (LLBL) or the mantle, both regions which are typically associated with open field lines.The analysis by Wing et al. [2010] suggests that on the dayside the location of the maximum R1 current is also most of the time close to but often slightly equatorward of the PCB.Thus, in addition to providing a convenient measure of the global Birkeland current location and intensity, we tentatively suggest that the R1 oval identified in this study might be used as a proxy for the location of the PCB, provided that one is careful to recognize that the R1 oval is probably offset slightly equatorward of the actual PCB location.We have shown that the R1 oval captures the dynamics of the polar cap boundary as previously established.

Conclusions
[36] In this paper we describe a novel approach to identify and track in data from the Active Magnetosphere and Planetary Electrodynamics Experiment (AMPERE) the locus of the region 1 Birkeland currents at all magnetic local times.We call the location of the maximum R1 currents the R1 oval which can be determined every 10 min in both hemispheres simultaneously.We study the change in size of the R1 oval in response to auroral activations observed in the AL index and in response to a decrease in the Sym-H index, i.e. during a period of enhanced ring current.We find that the R1 oval size is well ordered by the phases of individual substorms: during the growth phase the size of the R1 oval increases as more open magnetic flux is stored in the magnetotail due to enhanced dayside reconnection.Once the substorm is triggered and open magnetic flux is returned to the inner magnetosphere by tail reconnection, the R1 oval shrinks in size throughout the substorm expansion phase.We show that during times of enhanced ring current the size of the R1 oval can expand to larger sizes than during times of low ring current intensity.We attribute this to a stabilizing effect of the ring current on the magnetotail which allows more open magnetic flux to accumulate in the magnetotail before conditions develop for substorm onset.The dependence of the oval size on substorm phase tends to be superposed on the longer-term dependence on the ring current intensity.Both characteristics of the polar cap have been described before by localizing the PCB using global auroral imaging [Milan et al., 2003[Milan et al., , 2008[Milan et al., , 2009]].Although the R1 oval location is not to be mistaken for the actual location of the PCB, we are confident that the R1 oval size, which can be determined at 10-minute cadence in both hemisphere simultaneously, captures the dynamics of the polar cap boundary movement and accumulation of open magnetic flux in the magnetosphere.
[37] Acknowledgments.LBNC acknowledges funding from the National Science Foundation under grant ATM-0924919.LBNC also acknowledges funding from the Deutsches Zentrum für Luft-und Raumfahrt under grants 50OC1102 and 50OC1001.JBHB and JMR acknowledge the support of the NSF under grants ATM-0849031 and ATM-0946900.
[38] Robert Lysak thanks the reviewers for their assistance in evaluating this paper.
As magnetic field lines are continuously opened by dayside reconnection the amount of open magnetic flux inside the magnetosphere increases.On the nightside open magnetic flux accumulates until magnetic field lines reconnect in the magnetotail plasma sheet to again form closed field lines.The open magnetic flux inside the magnetosphere is thereby reduced.Newly closed magnetic field lines subsequently drift back from the tail to the dayside where they can participate in a new cycle of reconnection.From these considerations it is clear that the amount of open magnetic flux inside the magnetosphere is dependent on the rates of reconnection both on the dayside and on the nightside.It is apparent that the amount of open magnetic flux governs the location of the boundary between open and closed magnetic flux in the magnetosphere, the open-closed field line boundary (OCB).Furthermore, as the OCB moves due to changing reconnection rates, its ionospheric projection, the polar cap boundary (PCB), will also change its location.And finally, because the region 1 currents are believed to flow partly inside the boundary layer between open and closed magnetic flux, the region 1 current location in the polar ionospheres is governed by the change of the proportion of open magnetic flux inside the magnetosphere.

Figure 1 .
Figure 1.A schematic diagram of the region 1 and 2 current systems, looking onto the northern hemisphere of Earth from the tail.Currents flowing into/out of the polar ionosphere are shown in blue/red, respectively.See text for further details.Illustration adapted from Cowley [2000].

Figure 2 .
Figure 2. (left) Northern and (right) southern hemisphere radial current densities in magnetic latitude/ magnetic local time coordinates derived from AMPERE during southward IMF on 12 December 2010, 2129 UT.Negative/positive current densities colored blue/red are directed downward/upward.

Figure 3 .
Figure 3. Example of the function that is fitted to latitudinal profiles of the current density (black solid line).The gray dotted line shows only the Gaussian part of the function.The free parameters o 0 , a 0 , l 0 , w 0 , and f 0 determine the shape of the curve, compare equation (1).

Figure 4 .
Figure 4. Latitude profile of the radial current density at 18 MLT on 12 December 2010, 2129 UT in the northern hemisphere.The black dots mark the measurements of the current density by AMPERE, the green solid line shows the fit to these points; the dashed green line shows the Gaussian part of the fit.The best-fit parameters are given in the bottom right together with the quality parameter R of the fit.Vertical blue and red lines mark the location of the minimum and maximum current density, respectively.At 18 MLT, the minimum/maximum is assumed to correspond with the R2/R1 current.

Figure 5 .
Figure 5. Result of the fitting procedure in the (a, b, e, and f ) northern and (c, d, g, and h) southern hemisphere.Figures 5a-5d show the results during a period of relatively strong R1/R2 currents, and Figures 5e-5h show results of the fitting for relatively weak current densities.The locations of maximum R1/R2 current are shown as red/blue dots, respectively.Vertical lines indicate uncertainty estimates for the locations.The best-fit of the cosine expansion to the R1/R2 locations is shown as a red/blue solid line.The dashed lines indicate error boundaries of the location of the current oval determined during the fitting process.

Figure 6 .
Figure 6.(top) The R1 current oval size L 0 versus the median current density, (middle) the median error of the maximum/minimum current location versus the median current density, and (bottom) the error in R1 current oval size DL 0 versus the median current density.Each black dot represents a successfully fitted R1 current oval between January 2010 and August 2011, the red crosses give the median of the distribution within one bin and the red vertical line gives the range of values which contains 90% of all values in that bin.

Figure 8 .
Figure 8. Stackplot of the OMNI IMF Bz component in black with the IMF magnitude (positive and negative) in gray, the Sym-H index, the AL and AU the median current density, the size L 0 , and the error DL 0 of the R1 oval in the northern hemisphere followed by the median current density, the size L 0 , and the error DL 0 of the R1 oval in the southern hemisphere between 09 March 2011, 0000 UT and 14 March 2011, 0000 UT.The blue dashed line in the panels of the median current density shows the threshold of 0.2 mA/m 2 .Auroral activations are marked by vertical black dashed lines.