This paper starts from the kinetic theory to expound the method of characteristics.Influenceof the equilibrium distribution function fo upon analyzed result is fully investigated.The dispersionequation is regorously derived in a waveguide coordinate system in case of interaction between TE_(mn)field in a circular waveguide and a single-momentum ring-shaped electron beam.In the meantime,we make some critical review of previous papers and clarify their confusion and ambiguities. This paper starts from the kinetic theory to expound the method of characteristics. Influence of the equilibrium distribution function fo priori analyzed result is fully investigated.The dispersionequation is regorously derived in a waveguide coordinate system in case of interaction between TE mn field in a circular waveguide and a single-momentum ring-shaped electron beam.In the meantime, we make some critical review of previous papers and clarify their confusion and ambiguities.