Evaporation source, in particular for use in a sputtering process or in a vacuum arc evaporation process, preferably a cathode vacuum arc evaporation process. The evaporation source includes an inner base body which is arranged in an outer carrier body and which is arranged with respect to the outer carrier body such that a cooling space in flow communication with an inlet and an outlet is formed between the base body and the carrier body. In accordance with the invention, the cooling space includes an inflow space and an outflow space, and the inflow space is in flow communication with the outflow space via an overflow connection for the cooling of the evaporation source such that a cooling fluid can be conveyed from the inlet via the inflow space the overflow connection and the outflow space to the outlet.