Abstract: A Lorentz actuator provides a force between a first part and a second part of the apparatus, comprising a main magnet system, attached to a first part of the apparatus and providing a first magnetic field; a subsidiary magnet system, attached to the first part and arranged in a Halbach configuration, providing a second magnetic field; and an electrically conductive element attached to a second part of the apparatus and arranged so as to produce a force between the first and second parts of the apparatus by interaction of an electric current carried by the electrically conductive element and the combination of the first and second magnetic fields.

Abstract: A positioning device comprising a first part and a second part which is displaceable relative to the first part by means of a system of Lorentz-force motors, whereby, relative to the first part, the second part is supported in a Z-direction by means of at least one gas cylinder, said gas cylinder comprising a housing having a pressure chamber, which housing is coupled to the first part; and a piston which is coupled to the second part and which can be displaced in the pressure chamber in the Z-direction, said piston being journaled relative to said housing substantially at right angles to the Z-direction.