A new approach for the theory on electron beam-wave interactions

A new approach to the theoretical study of the electron beam-wave interaction in arbitrary RF structures is presented in this paper. In any such interaction system, there are two coordinate systems: the lab system; the rest coordinate system for the plasma, if it exists; and the moving coordinate system for the electron beam. Both the electron beam and the plasma are considered special media with different characteristics. The permittivity tensor and the permeability tensor can be found in the moving coordinate system for the beam while that for the plasma can be found in the lab coordinate system. Then, making use of the transformation of electromagnetic fields in Minkovski space and the Lorentz transformation of the 4D wave vectors, all the physics quantities in the moving coordinate system can be transferred into the lab coordinate system. Then the Maxwell's equations with the transferred constitutive tensors should be used to derive the desired dispersion equation. This new approach is a very efficient and accurate method for the study of electron beam-wave interactions.