The fundamental physical phenomenon upon which linear electron accelerators and traveling beam tubes depend is the fact that the phase velocity of guided TM waves can be reduced to a fraction of the velocity of light. There are various practical ways of achieving these reduced velocities, such as diaphragms or spiral grooves in the guide wall. An open helix has been used by Pierce. An accurate knowledge of the field pattern would greatly facilitate an understanding of these devices. It is of particular importance to have exact information about the field in the region in which the charge actually travels, namely, in a region located at least a considerable fraction of a wave‐length from the guide walls. Because of the complex shapes assumed by actual guide walls calculations of the field are inevitably somewhat inexact and complicated. The authors propose that, for the purposes of theory, the well‐established proposition concerning the equivalence of true and simulated dielectrics in producing a slow field be used. We propose to think of slowing down the phase velocity by lining the guide walls with a natural dielectric. The essential properties of the slow field, particularly in the important region referred to above, will not be affected by this method of obtaining it while, on the other hand, the field calculation becomes quite easy and exact. Although this procedure is intended in the main as a device to facilitate the theoretical calculation of the field, the authors believe that such a step—replacement of periodic metallic structures by dielectrics—might prove useful in some actual applications.