We show that Green's function solutions to the collisionless time-dependent Boltzmann equation can be economically used to construct a time-dependent model of auroral plasma formation by global time-dependent convection electric fields in dipolar magnetic geometry. We show that recently observed features, such as formation of field-aligned distributions, formation of injection fronts and formation of inverse dispersion signatures, can be accounted for in a global time-dependent convection model. This paper also sets forth the theoretical and presentation framework for subsequent data analytic studies of convected electron and ion distribution functions.