The recent Voyager radio astronomy measurements near Jupiter show that the Jovian decametric radiation consists of numerous discrete features called decametric arcs which are observed at all Jovian longitudes. It is generally believed that these arcs are produced by an interaction of Io with the Jovian magnetosphere. In this paper we propose that the large number of decametric arcs is caused by multiple reflections of a standing Alfven wave current system excited by Io. Estimates of the reflection coefficient at the ionosphere and other damping processes show that a large number of reflections can occur, with the Alfven wave current system possibly extending completely around Jupiter. This source geometry can account for a number of otherwise puzzling characteristics of the Jovian decametric radiation.