[en] Previous theoretical work on JxB current drives is briefly reviewed. Two separate cases are identified. The first is one in which the travelling wave propagates perpendicular to the steady state magnetic field and the second is for the situation in which propagation is parallel to a significant component of the steady state field. For the first case, field penetration and synchronous electron motion is possible. The second case is investigated by considering in detail an m=0 type mode for tokamak parameters, ion motion being taken into account. It is found that neither synchronous motion nor field penetration occurs. Since it is this latter case which is appropriate to tokamaks, these being characterised by the major current flow being parallel to the field, it is concluded that the JxB type current drive has no application in high temperature tokamak devices. (author)