We report the results of an investigation of the reverse convection potentials in the day side high latitude ionosphere during periods of steady northward interplanetary magnetic field (IMF). While it has been shown that the polar cap potential in the ionosphere exhibits non-linear saturation behavior when the IMF becomes increasingly southward, it has yet to be shown whether the high latitude reverse convection cells in response to increasingly northward IMF exhibit similar behavior. We use solar wind data from the ACE satellite from 1998 to 2005 to search for events in the solar wind when the IMF is northward and the interplanetary electric field is stable for more than 40 minutes. We then use bin-averaged SuperDARN convection data and apply a spherical harmonic fit to calculate the average potential pattern for each northward IMF bin. Results show that the reverse convection cells do, in fact, exhibit non-linear saturation behavior. The saturation potential is approximately 20 kV and is achieved when the electric coupling function reaches between 18 and 30 kV/RE.
 Plasma convection in the magnetosphere is driven by a combination of viscous interactions with the solar wind and magnetic merging between the geomagnetic field and the interplanetary magnetic field (IMF). These processes generate electric fields in the outer magnetosphere that map along quasi-equipotential magnetic field lines into the polar ionosphere. The electrostatic potential across the polar region, ΦPC, is often used as a measure of the strength of magnetosphere-ionosphere coupling. When the IMF is southward, a two-cell potential pattern is generated with anti-sunward convection in the center of the polar cap and sunward return convection at auroral latitudes, as in work by Dungey . During instances of strongly southward IMF, the potential as a function of solar wind electric field has an observed non-linear “saturation” effect [Siscoe et al., 2002; Shepherd et al., 2002; Russell et al., 2001].
 When the IMF is northward, two additional convection vortices appear on the dayside at high latitudes with reversed sunward convection near noon due to magnetic reconnection at the cusp [Crooker, 1992]. The typical pattern that arises is similar to those shown in Figure 3. The reverse convection cells are said to be driven by high-latitude field aligned currents termed DPZ [Friis-Christensen and Wilhjelm, 1975] or NBZ [Iijima et al., 1984]. It has yet to be determined whether the vortices driven by the NBZ currents also saturate. The purpose of this study is to determine if the potential across the reverse convection cells also exhibits non-linear behavior.
 In order to provide a measure of the energy coupling from cusp reconnection into the magnetosphere, a solar wind - magnetosphere coupling function similar to that proposed by Kan and Lee  was used. Geometric factors were modified to select strongly northward IMF and the final form is given in equation (1):
 Where ERC is the reverse convection energy coupling function, V is the anti-sunward component of the solar wind velocity, BT = is the transverse magnetic field and = cos−1 is the IMF clock angle. Figure 1 shows how ERC varies with respect to transverse IMF components. It can be seen that this form of coupling function strongly favors positive IMF, as desired. Were the original Kan-Lee function to be used, events of strong northward IMF would lead to a small value because the geometric term assumes little to no electric field coupling under northward IMF.
 Using ERC, events were found using ACE MAG and SWEPAM data from 1998 to 2005 propagated to the magnetopause using the technique developed by Weimer et al. . Events of quasi-stable ERC were then placed into bins containing a minimum and maximum ERC value. The criteria for quasi-stability was that the event stayed within the bin's maximum and minimum ERC value for a minimum of 40 minutes. The ERC range for each bin was selected to maximize the spatial coverage of Doppler measurements within each bin, but at the same time provide enough discretization in the curve in Figure 4 to see the saturation effect. Table 1 shows the range and number of events in each ERC bin, and Figure 2 shows the statistics on BZ and BY for each bin. From Figure 2, it is clear that while the value of BZ varies over the bins, the value of BY does not vary as much, demonstrating that any saturation effect measured would be influenced most by the northward pointing of the IMF.
The bin range values listed are in the units kV/RE.
 The convection patterns from which the potential of the reverse convection cells were calculated by the Super Dual Auroral Radar Network (SuperDARN) [Chisham et al., 2007]. In order to obtain average reverse convection potentials, ΦRC, for each bin, two steps were required. First, median velocity vectors for spatial bins were calculated on a spatial grid of 100km and in 10-degree increments of magnetic azimuth. This pre-processing reduces the amount of data which goes into the spherical harmonic fitter. It is also beneficial because it smoothes out large positive and negative values which cancel out in the fitter at convection reversal boundaries. Next, the APLFIT technique was applied, where an electric potential pattern is derived from the velocity vectors through a spherical harmonic expansion, as in work by Ruohoniemi and Baker . Figure 3 shows results of the spherical harmonic fit for four ERC bins. Once an ERC bin's potential pattern is determined, the reverse convection potential is measured by taking the difference between the minimum and maximum potential of the high latitude reverse cells.
Figure 3 shows four convection patterns as the IMF turns increasingly northward. Each pattern is presented in AACGM MLAT-MLT format with the magnetic pole at the center and magnetic noon directed up the page. The lowest latitude shown is 60 degrees and the contour spacing is 1kV. Color-coding shows the number of gridded SuperDARN measurements that contributed to the calculation of each pattern. The four convection patterns in Figure 3 correspond to the following bins of ERC: (a) 2–4, (b) 10–13, (c) 19–23, and (d) 32–39 kV/RE. The values of the reversed convection potential, ΦRC, are 2.85, 10.66, 17.44, and 19.36 kV respectively. The reader is invited to count the potential contours across the dayside reverse convection cells to demonstrate these potential values.
 As seen in Figure 3, as the value of ERC increases, the reversed convection cells first become more pronounced but then the reversed convection potential eventually saturates. Also note that as the value of ERC is allowed to increase the number of SuperDARN measurements available to calculate the pattern also decreases. Beyond 60 kV/RE there were too few Doppler measurements available to calculate a potential pattern.
3. Results and Discussion
Figure 4 shows a plot of the reverse convection potential for ERC values up to 60 kV/RE. The horizontal bars show the range of values used in each ERC bin used to calculate each convection pattern. For low values of ERC (i.e. 0–18 kV/RE) the reverse convection potential exhibits linear characteristics but as ERC increases the reverse potential starts to saturate, similar to what has been identified previously for southward IMF [Shepherd et al., 2002].
 It is still unclear at this time why the NBZ currents and the potential across the vortices they generate should saturate. In the case of southward IMF, there are several models that account for saturation of ΦPC. Three common models are: the strengthening of Region 1 field aligned currents to the point where their J × B force replaces the Chapman-Ferraro currents as the main counter to solar wind ram pressure; the erosion of the magnetopause magnetic field which limits reconnection; and the magnetopause becoming blunt, giving the solar wind more room to flow around the magnetosphere [Siscoe et al., 2004]. Since the NBZ currents are driven by reconnection at the cusp, it is unlikely that these models could also be applied to saturation of the reverse convection cells. One thing that hasn't been investigated is whether or not there is a limit to the amount of current the ionosphere can carry. If it is the case that the ionospheric conductivity plays a role, then it could help explain the saturation phenomenon for both the southward and northward IMF cases.
 For further study, case studies of events with even stronger ERC will be done combining high latitude radar and satellite data. Analysis of the reverse convection cell response time will also be done, as well as further analysis of the transition from linear to non-linear behavior. The Canadian high latitude PolarDARN radars, as well as the Resolute Bay incoherent scatter radar when it begins operation, will also give more coverage to the regions where reverse cells form, and at the next solar maximum, a better picture of the reverse convection potential during strong IMF will be developed. This will assist in determining as well as possible the maximum potential the reverse convection phenomena can generate. Also, comparing electric fields with the Southward IMF case and looking for seasonal asymmetries would help to determine how much current can pass through the ionosphere at a given time.
 This research is supported by the National Science Foundation through grant ATM-0728538 to the Virginia Polytechnic Institute and State University. At JHU/APL the research is supported by the National Science Foundation through grant ATM-0418101. Operation of the northern hemisphere SuperDARN radars is supported by the national funding agencies of Canada, France, Japan, the United Kingdom and the United States.