Recently, Kim et al.  reported that, for Bz north in the solar wind, the polar cap potential is linearly dependent on the log of ULF power in the solar wind. Figure 1 shows their main result, which was determined using fluctuations in the interplanetary magnetic field (IMF).
 The ULF power is due to either magnetohydrodynamic (MHD) turbulence in the solar wind or to Alfvén waves generated in the solar wind. Either way, these fluctuations will propagate to the polar cap on field lines connected to the solar wind as Alfvén waves. The link between the solar wind and the polar cap for Bz north is presumably due to connections between the interplanetary magnetic field (IMF) and the earth's field in the polar cusp [Kelley, 2009]. This connection has long been linked to the two polar cap convection cells. The mechanism discussed here may contribute to these cells.
 The energy flux from the solar wind to the magnetosphere has long been studied for a steady solar wind velocity and various IMF geometries and quantified by Weimer . Fluctuations in the velocity and the IMF are well-documented. The solar wind area in magnetic contact with the polar cap may act like an aperture antenna launching Alfvén waves toward the earth. This presumably occurs for any IMF geometry but during Bz south, dayside convection dominates the polar cap potential (PCP). We argue here that, for Bz north, the mechanism discussed here competes for control of the PCP equally with cusp connections and, at lower latitudes, with viscous interaction [Axford and Hines, 1961].
 There are two aurora characteristics in the Bz-north polar cap. The most well-known is the theta aurora [Frank et al., 1986]. This auroral form splits the polar cap and is collocated with an upward field-aligned current. Cumnock et al.  showed that this arc erupts out of the auroral oval and migrates across the polar cap to its theta-bar location. This was verified in a rocket experiment in which consecutive rockets crossed an arc emerging out of the oval. Leaving sunward convection equatorward of the arc [Berg et al., 1994], the arc itself propagated at a speed higher than a realistic convection speed. This is similar to the rapid poleward (apparent) motion of substorm-related aurora.
 The second type of polar cap aurora was reported by Lassen and Danielsen  and is shown in Figure 2. These multiple arcs were synthesized from all-sky camera data over many years. The more northward Bz is, the more polar cap arcs exist. But multiple arcs are seen on a given night, not just a single theta aurora [Rich et al., 1990]. Figure 3 shows an example of multiple reversals in the electric field, each one of which has a field-aligned current associated with it. In fact, since ∇ × V = Jz (upward in northern hemisphere) [Kelley, 2009], even small variations in V may have subvisual arcs.
 The reciprocal of the intrinsic impedance of the Alfvén (ηA) wave is comparable to the height-integrated Pedersen conductivity (ΣP) of the polar cap, so energy will be absorbed or reflected, depending on the season and other factors. However, when a reflected wave returns to the solar wind, again, some of the energy will be reflected back to the ionosphere. Thus, a constant source of Poynting flux exists. Using transmission line theory [Inan and Inan, 2000], the reflection coefficient is,
 Large fluctuations in the solar wind are often observed, in particular during high speed streams, as shown in Figure 3 where the fluctuations in the interplanetary electric field (IEFy) are large and the lowest frequencies penetrate to the equatorial ionosphere (panel 2) [Kelley and Dao, 2009]. In the polar cap, the fluctuations are also the order of the mean [Kelley, 2009]. The fluctuations in the winter polar cap are much larger than in the summer polar cap [Heelis and Hanson, 1980; see also Kelley, 2009, Figure 8.8b]. The high conductivity of the summer cap will reflect more solar wind energy than the winter cap. Thus, larger fluctuation electric fields are expected in winter, as observed.
 For Bz north, polar cap arcs are ubiquitous, as shown in Figure 2, and common in the winter polar cap. The tapering of the electric field from the solar wind to the ionosphere goes as (BSW/BI)1/2 [Mozer, 1970]. Using BSW = 5 nT and BI = 50,000 nT, 8 × 105 km in the solar wind becomes 80 km in the ionosphere. The vortices are even smaller than this, as shown in Figure 4, indicating vortices of 10 km in the polar cap for Bz north. We believe that 2-D turbulence theory explains vortex expansion from 10 km to the two large vortices as being due to inverse cascade, which characterizes this type of turbulence [Kraichnan, 1967].
 Earle and Kelley  pointed out that electric field data on rockets and satellites [Kelley and Kintner, 1978; Boehm et al., 1995] indicate a break in the slope of polar cap electric-field spectral density around 1 km scale with a dependence of k−5/3 at smaller k and k−3 at larger k where k denotes a wave number. These results are predicted by Kraichnan  and hence are evidence for 2-D turbulence.