The evaporator contains a bundle of U-tubes, where the coolant is evaporated and superheated. There are at least two separate coolant circuits. Deflection plates ensure a meandering flow path for a liquid cooling agent. The first coolant circuit comprises the outer bundle of tubes whose cross-section (5) has the shape of two circular segments facing each other, connected at the end by the outer tube bends. The individual coolant paths are regions separated horizontally. The other coolant circuit is a similar region (6) lying between the segments, again joined at the tube end by the inner tube bends.