From data of the European incoherent scatter radar EISCAT, and mainly
from its tristatic capabilities, statistical models of steady convecti
on in the auroral ionosphere were achieved for various levels of magne
tic activity. We propose here to consistently extend these models to t
he polar cap, by avoiding the use of a predefined convection pattern.
Basically, we solve the second-order differential equation governing t
he polar cap convection potential with the boundary conditions provide
d by these models. The results display the classical twin-vortex conve
ction pattern, with the cell centres around 17 MLT for the evening cel
l and largely shifted towards midnight (3-3.5 MLT) for the morning cel
l, both slightly moving equatorward with activity. For moderate magnet
ic activities, the convection flow appears approximately oriented alon
g the meridian from 10:00 MLT to 22:00 MLT, while in more active situa
tions, it enters the polar cap at prenoon times following the antisunw
ard direction, and then turns to exit around 21:00 MLT. Finally, from
these polar cap patterns combined with the auroral. statistical models
, we build analytical models of the auroral and polar convection expec
ted in steady magnetic conditions.