an improved synchronous tubular electrical machine comprises a radially outer member that has a substantially cylindrical inner surface and radially inner member that is substantially cylindrical and is coaxially disposed within the outer member such that it may move reciprocally relative to the outer member in the axial direction . a plurality of axially spaced circumferential armature coils are electrically insulated from one another and are formed as part of one of the outer member and the inner member . a plurality of axially spaced circumferential superconducting coils are formed as part of the other of the outer member and the inner member . during operation of the tubular machine , each superconducting coil is maintained in a superconducting state and an electrical current is supplied to each superconducting coil in such a manner that the current flowing around each coil is in the opposite direction to the current flowing around the coils adjacent to it . such tubular machines may be significantly more efficient , have higher peak - mean power ratios and be much smaller than current permanent magnet based synchronous tubular electrical machines .