Reaction jacket for a photosynthetic reactor, configured to float on an expanse of water and to define a gas/liquid culture medium diphasic flow path between first and second openings of the reaction jacket, the jacket including two sheaths, outer and inner, respectively, at least partially made from a material transparent to light radiation, the inner sheath extending inside the outer sheath such that these sheaths define an inter-sheath space between them in fluid connection with the first opening of the jacket, where the outer sheath has an open proximal end and a closed distal end, and the inner sheath has an open proximal end in fluid connection with the second opening of the jacket and a distal end provided with at least one communication orifice between the inside of the inner sheath and the inter-sheath space.