A new model based on the generalized Lorentzian velocity distribution
function (VDF) is used to estimate the total current density J(tot) al
ong the magnetic field lines as a function of the field-aligned electr
ic potential difference V between the ionosphere and the magnetosphere
. As in the earlier kinetic models based on the Maxwellian VDF, J(tot)
is a nonlinear function of V, except for values of V between 0.1 and
10 kV, where the current-voltage relationship becomes linear. The effe
ct of an enhanced population of suprathermal particles in the tail of
the VDF is to increase the value of the applied potential for which th
e linear relationship is a valid approximation. The application of thi
s current-voltage relationship to the auroral precipitation region and
return current region is discussed.