A machine operating by magnetic field interactions, the machine comprising: a first machine element extensive in the direction of operation, the first machine element having a first laterally facing support surface relative to the direction of operation; a plurality of discrete first permanent magnets fixed, in spaced apart adjacent positions, to the first support surface of the first machine element extensive in a direction of operation of the machine; a second machine element extensive in the direction of operation, the second machine element defining a second laterally facing support surface relative to the direction of operation, the first support surface and the second support surface defining parallel planes; a second magnet fixed to the second support surface of the second machine element extensive in the direction of operation; a machine frame, the first machine element and the second machine element being engaged with the machine frame such that either the first machine element or the second machine element is configured to move in the direction of operation relative to the other of the machine elements; and a plurality of solenoids; characterized in that adjacent pairs of the first plurality of first permanent magnets have north and south pole faces (N, S) mutually facing across gaps; the second magnet has a linear series of grooves arrayed in the direction of operation; each of the plurality of solenoids is mounted in a respective one of the grooves of the second magnet, the plurality of solenoids being configured to be electrified in series interconnection to produce an electromagnetic field; and between pairs of said grooves, pole faces (24") of the second magnet are spaced apart from the discrete first permanent magnets; and the spacing of said gaps between the adjacent discrete first permanent magnets are non-aligned with a spacing of said grooves in the second magnet. a first machine element extensive in the direction of operation, the first machine element having a first laterally facing support surface relative to the direction of operation; a plurality of discrete first permanent magnets fixed, in spaced apart adjacent positions, to the first support surface of the first machine element extensive in a direction of operation of the machine; a second machine element extensive in the direction of operation, the second machine element defining a second laterally facing support surface relative to the direction of operation, the first support surface and the second support surface defining parallel planes; a second magnet fixed to the second support surface of the second machine element extensive in the direction of operation; a machine frame, the first machine element and the second machine element being engaged with the machine frame such that either the first machine element or the second machine element is configured to move in the direction of operation relative to the other of the machine elements; and a plurality of solenoids; characterized in that adjacent pairs of the first plurality of first permanent magnets have north and south pole faces (N, S) mutually facing across gaps; the second magnet has a linear series of grooves arrayed in the direction of operation; each of the plurality of solenoids is mounted in a respective one of the grooves of the second magnet, the plurality of solenoids being configured to be electrified in series interconnection to produce an electromagnetic field; and between pairs of said grooves, pole faces (24") of the second magnet are spaced apart from the discrete first permanent magnets; and the spacing of said gaps between the adjacent discrete first permanent magnets are non-aligned with a spacing of said grooves in the second magnet.