A homopolar, transverse pole rotor (14) having a central cylindrical body (24) with a set of circumferentially spaced, axially extending salient poles (28) at each end thereof, is constructed to reduce windage losses. Integral shrouds (29, 31) are placed on either side of each set of salient poles, and a relief is machined into the outer surface of each shroud to form an accentuated pole tip (64) which ensures magnetic centering of the rotor. To further minimize windage losses, the diameter of the central cylindrical body (24) can be reduced, and non-magnetic material can be secured within interpole recesses. Mechanical fasteners (66), dove tails (72) or tensioned circumferential banding (82) can be used to secure the non-magnetic interpole pieces to the rotor.