High power microwave sources and technologies using metamaterials Metamaterials have been actively researched for well over a decade primarily by the optics and then the low power microwave communities. The high power microwave community was late to adopt them primarily because of concerns of metamaterial survivability since they are inherently highly resonant structures. In the context of this book metamaterial structures are broadly defined as periodic structures that might have halfwavelength periodicity or have sub wavelength periodicity; they may be double positive and they may be double negative. Furthermore it is shown how traditional periodic structures (used since the 1940s and 1950s) can have properties that until recently were attributed to double negative metamaterial structures Multi transmission line model for slow wave structures interacting with electron beams and multimode synchronization Ahmed F. Abdelshafy Mohamed A. K. Othman Alexander Figotin and Filippo Capolino Generalized Pierce model from the Lagrangian Alex Figotin and Guillermo Reyes Dispersion engineering for slow wave structure design Ushemadzoro Chipengo and Niru K. Nahar John L. Volakis Adrian W. Cross and Alan D.R. Phelps.