The transformer coupled plasma reactor (TCP) is a low frequency, inductively coupled plasma reactor, with a gradient electromagnetic source field, such that electrons experience a secular (time average) force-the ponderomotive force. There are two electric forces and one magnetic force, the latter of which is strongly active in the TCP. The ponderomotive force has previously been explored for confinement in fusion reactors, but has not been discussed in connection with semiconductor processing. In modeling with plasma fluid equations, there is a need to include large-scale particle kinetics. The calculation of the ponderomotive force in laboratory devices is a problem, because the form of the field is often taken as a zero-curl approximation which violates Maxwell’s equations. To clarify this issue we have analyzed the ponderomotive force field in the transverse-electric electromagnetic field of a rectangular waveguide. A specific model of the TCP is analyzed. This shows that the rf-magnetic field of the TCP coil, in the range of a few gauss, creates a significant ponderomotive force at 13 MHz, which is enhanced at lower frequencies such as 1 MHz. This force acts to protect the rf window from erosion and cancel ambipolar diffusion losses, thereby improving the density uniformity of the plasma.