There are two ways of heating a plasma confined by a strong axial magnetic field. In the first of these the electric field is parallel to the magnetic field, the situation that obtains in ohmic heating. In the second of these, the electric field is perpendicular to the main axial magnetic field. In this paper we consider the second case only and consider the electric field to be produced by an externally imposed oscillation of the axial field. This method of heating is often called magnetic pumping. It is found that as far as the heating of the plasma is concerned, there are four characteristic times which play a fundamental role. These four times are: (1) the collision time, (2) the period of the oscillating field, (3) the time of transit of a typical ion through the heating region, and (4) the cyclotron period of an ion. If these four characteristic times are all of comparable order, the theoretical analysis is exceedingly complex. Therefore, four cases were considered in which these were taken to be of different orders. The heating mechanism differs in each of these four cases since the period of the externally produced electric field is chosen to be comparable to one of the characteristic times in the analysis. In each of the four cases configurations were found which led theoretically, at least, to efficient heating of the plasma. In those cases where the energy imparted to the plasma appears in the form of wave motion, the subsequent damping of these waves is discussed.