In the first section of this thesis the simple Pierce Theory for the travelling wave tube is discussed and developed. The result of this analysis is a number of equations which produce information about gain and bandwidth. The next section of the thesis is devoted to a discussion of periodic structures with particular emphasis on dielectric loaded periodic structures. Finally the Pierce Theory is applied to the dielectric slow wave structure. Results are presented of a study performed to find a correlation between the physical dimensions of the dielectric structure and the gain-bandwidth properties of a travelling wave tube employing the structure. These results, which are in graphical form, can be used to eliminate the initial exploratory design work for travelling wave tubes of this type. A sample use is made of the design curves and the results are compared to a computational check to show both the usefulness and the limitations of the curves / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate