A cooling jacket for cooling using a fluid includes an inner part, an outer jacket that extends in an axial direction and surrounds the inner part in a cross-sectional plane perpendicular to the axial direction, and a duct for holding the fluid. A first boundary of the duct an outer surface of the inner part, while a second boundary of the duct includes an inner surface of the outer jacket. The inner part is arranged inside the outer jacket, and a material property of the outer jacket is different from the material property of the inner part.