On 1 April 2004 the GUVI imager onboard the TIMED spacecraft spots an isolated and elongated polar cap arc. About 20 min later, the Cluster satellites detect an isolated upflowing ion beam above the polar cap. Cluster observations show that the ions are accelerated upward by a quasi-stationary electric field. The field-aligned potential drop is estimated to about 700 V and the upflowing ions are accompanied by a tenuous population of isotropic protons with a temperature of about 500 eV. The magnetic footpoints of the ion outflows observed by Cluster are situated in the prolongation of the polar cap arc observed by TIMED GUVI. The upflowing ion beam and the polar cap arc may be different signatures of the same phenomenon, as suggested by a recent statistical study of polar cap ion beams using Cluster data. We use Cluster observations at high altitude as input to a quasi-stationary magnetosphere-ionosphere (MI) coupling model. Using a Knight-type current-voltage relationship and the current continuity at the topside ionosphere, the model computes the energy spectrum of precipitating electrons at the top of the ionosphere corresponding to the generator electric field observed by Cluster. The MI coupling model provides a field-aligned potential drop in agreement with Cluster observations of upflowing ions and a spatial scale of the polar cap arc consistent with the optical observations by TIMED. The computed energy spectrum of the precipitating electrons is used as input to the Trans4 ionospheric transport code. This 1-D model, based on Boltzmann's kinetic formalism, takes into account ionospheric processes such as photoionization and electron/proton precipitation, and computes the optical and UV emissions due to precipitating electrons. The emission rates provided by the Trans4 code are compared to the optical observations by TIMED. They are similar in size and intensity. Data and modelling results are consistent with the scenario of quasi-static acceleration of electrons that generate a polar cap arc as they precipitate in the ionosphere. The detailed observations of the acceleration region by Cluster and the large scale image of the polar cap arc provided by TIMED are two different features of the same phenomenon. Combined together, they bring new light on the configuration of the high-latitude magnetosphere during prolonged periods of Northward IMF. Possible implications of the modelling results for optical observations of polar cap arcs are also discussed.