Periodic Structures

  • Levi Schächter
Part of the Accelerators Physics book series (PARTICLE)


One of the conditions for distributed beam-wave interaction to occur is phase velocity smaller than c. It is possible to satisfy this condition by loading the waveguide with a dielectric material, however the problem with dielectrics is that they are susceptible to breakdown at relatively low electric fields therefore it is difficult to generate high power microwave radiation with regular materials. Another difficulty is the electric charge which accumulates on the surface and must be drained for adequate operation. Consequently, in many microwave sources metallic structures with periodic boundary are preferred as the central component which facilitates the interaction. The periodic geometry can be conceived as a set of obstacles delaying the propagation of the wave due to the multi-reflection process and, as will be shown during our discussion on Floquet’s theorem, an infinite spectrum of spatial harmonics develops. A few of these harmonics may propagate with a phase velocity larger or equal to c but the absolute majority have a smaller phase velocity.


Dispersion Relation Phase Velocity Periodic Structure Spatial Harmonic Magnetic Vector Potential 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Levi Schächter
    • 1
  1. 1.Department of Electrical EngineeringTechnion — Israel Institute of TechnologyHaifaIsrael

Personalised recommendations