A dielectric barrier discharge plasma reactor comprising: - a chamber subjected to atmospheric pressure and having at least one plasma gas inlet port and at least one outlet port for cold plasma at atmospheric pressure, wherein the chamber further comprises: - an inner tube and an outer tube, with the inner tube and the outer tube being made of dielectric material, each comprising an upper end, a lower end and a wall with an inner surface and an outer surface, the upper end of the inner tube being coupled to the plasma gas inlet port, the upper end of the outer tube being hermetically sealed and being traversed by the inner tube, the lower end of the inner tube being open and the lower end of the outer tube being coupled to the outlet port for cold plasma at atmospheric pressure, and wherein the inner tube and the outer tube are arranged so that at least a portion of the inner tube extends inside the outer tube parallel to the longitudinal axis of the outer tube and so as to define: - a diffusion space, formed inside the outer tube between the lower end of the inner tube and the lower end of the outer tube; and - an annular space, formed between the outer surface of the wall of the inner tube and the inner surface of the wall of the outer tube; wherein the chamber further comprises: - a first high-voltage electrode and a ground electrode, spaced apart by an inter-electrode gap, in which at least a first dielectric material is disposed; - a high-voltage electric power supply input port coupled to the high-voltage electrode, and adapted to be coupled to a first high-voltage power supply so as to allow an electric discharge to be generated in the inter-electrode space; and wherein: - at least a portion of the inner tube is disposed as close as possible to the high-voltage electrode and extends through the first dielectric material and the ground electrode; and - at least a portion of the outer tube extends through the ground electrode. - a chamber subjected to atmospheric pressure and having at least one plasma gas inlet port and at least one outlet port for cold plasma at atmospheric pressure, - an inner tube and an outer tube, with the inner tube and the outer tube being made of dielectric material, each comprising an upper end, a lower end and a wall with an inner surface and an outer surface, the upper end of the inner tube being coupled to the plasma gas inlet port, the upper end of the outer tube being hermetically sealed and being traversed by the inner tube, the lower end of the inner tube being open and the lower end of the outer tube being coupled to the outlet port for cold plasma at atmospheric pressure, - a diffusion space, formed inside the outer tube between the lower end of the inner tube and the lower end of the outer tube; and - an annular space, formed between the outer surface of the wall of the inner tube and the inner surface of the wall of the outer tube; - a first high-voltage electrode and a ground electrode, spaced apart by an inter-electrode gap, in which at least a first dielectric material is disposed; - a high-voltage electric power supply input port coupled to the high-voltage electrode, and adapted to be coupled to a first high-voltage power supply so as to allow an electric discharge to be generated in the inter-electrode space; - at least a portion of the inner tube is disposed as close as possible to the high-voltage electrode and extends through the first dielectric material and the ground electrode; and - at least a portion of the outer tube extends through the ground electrode.