We have developed a dynamic numerical model of the plasma along an auroral field in order to provide a vehicle for studying ionosphere-magnetosphere coupling process. The model is a multimoment, multifluid approximation of a gyrotropic plasma consisting of three species (electron, hydrogen ions, oxygen ions) along a segment of auroral magnetic field line extending from an altitude of 800 km to 10 earth radii. We have performed simulations for the case of a current-free polar wind equilibrium of the field line plasma and the case in which a large upward field-aligned current is applied to the field line. In the former case, the agreement between our model and previous static results is reasonable given the difference boundary conditions inherent in the two cases. In the case of a field-aligned current, we note that the flux tube plasma responds to the current on several time scales. After an initial rapid heating of the electrons due to precipitation in a converging magnetic field, electric field coupling of the electrons to the ions causes thermal oscillations of the flux tube plasma to persist on time scales of the order of 1 hour, illustrating the complicatd nature of the response of a collisionless plasma when heat flow transport is treated in a dynamic manner.