Abstract: A linear machine comprises a primary part and a secondary part. The primary part forms a receptacle around an axis and has a plurality of annular primary coils, which are arranged concentrically with respect to the axis, can have alternating current applied to them, and are separated by intermediate elements, in order to produce a magnetic field in the receptacle. The secondary part, which can be moved relative to the primary part by the magnetic field in the receptacle along the axis, is provided with secondary coils having superconductor windings. In order to produce a linear motor which allows high force densities, the intermediate elements are produced from non-magnetizable material and the primary coils and the secondary coils are arranged with an air-gap winding, wherein the secondary coils are manufactured from a high-temperature superconductor and direct current can be applied or is applied to them. Force densities of more than 18 N/cm2 can be achieved in the receptacle by the linear motors.