Empirical polar cap potentials

DMSP satellite plasma flow data from 1987–1990 are used to derive empirical models of the polar cap potential for quasi‐steady interplanetary magnetic field (IMF) conditions. The large data set, due to the high duty cycle and nearly Sun synchronous DMSP orbits, allowed very stringent data selection criteria. The analysis indicates that a good description of the unskewed (Heppner Maynard pattern A) steady state polar cap potential is Φ A = 10 −4 v 2 +11.7 B sin 3 (θ/2) kV, where v is the solar wind velocity in kilometers per second, B is the magnitude of the interplanetary magnetic field in nanoteslas, and θ = arccos ( B z /| B |) GSM . The IMF‐dependent contribution to the cross polar cap potential does not depend significantly on solar wind pressure. Functional forms for the potential do benefit from inclusion of an IMF independent term proportional to the solar wind flow energy. Best fits to IMF‐independent contributions to the steady state polar cap potential yield ∼16 kV for v sw = 400 kilometers per second. During steady IMF the total unskewed polar cap potential drop is shown to be approximately Φ A = 16.5 + 15.5 Kp kV. The distribution of potential around the polar cap is examined as a function of magnetic local time. A sinusoidal distribution is an excellent description of the distribution, and more complex forms are not justified by this data set. Analysis of this data set shows no evidence of saturation of the polar cap potential for large |MF|. A simple unified description of the polar cap potential at all magnetic local times (MLT) and IMF, Φ(IMF, MLT) = −4.1 + 0.5 sin ((2π/24) MLT + 0.056 + 0.015 B y eff ) (1.1 × 10–4 v 2 + 11.1 B sin 3 (θ/2)) kV, is generated, where B y eff is B y (− B Y ) in the northern (southern) hemisphere. If IMF data is unavailable, the polar cap potential is well described by Φ A ( Kp , MLT) = − 4.1 + 1/2 sin ((2π/24) MLT + ϕ HM )(16.4 + 15.2 Kp ) kV, where Öϕ HM is a small phase correction of (−0.054, −0.031, 0.040) for Heppner‐Maynard convection patterns ( BC , A , DE ), respectively.