SELF-CONSISTENT FIELD THEORY OF GENERAL PERIODIC CIRCUITS FOR TRAVELING WAVE TUBES

Abstract

A general method for exact analysis of cylindrical periodic circuits for traveling wave tubes without initial assumptions of field or current distributions is described. The procedure is based on transforming the stationary periodic circuit to Fourier space, in the same manner as one does the ordinary RF fields. By this approach the circuit is represented in Fourier space by an infinite number of harmonic circuit components. The interaction, or coupling, between the field harmonics and the stationary circuit harmonics is conceptually a convolution process. The mathematical description of this process involves the intermediary of a convoluting circuit matrix formed from the harmonics of the stationary metallic circuit. For any circuit this matrix is Hermitian and therefore guaranteed a full set of orthogonal eigenvectors and corresponding real eigenvalues. This complete set of vectors serves as a basis for expansions of the RF electric and magnetic harmonic fields. Due to the general nature of the metallic circuit, with surface areas that are partly metallic and partly open, the eigenvectors separate into two distinct sets, one set having eigenvalues equal or close to unity, and the other set eigenvalues equal or close to zero. The first set is associated directly with the metallic parts of the circuit and describes localized surface modes, including surface currents on the two circuit boundaries. The second set, which essentially is a nullset, does not "see" the metallic parts of the circuit, and describes the fields in the open areas of the circuit. Similar expansions are made in the dielectric rod support system exterior to the circuit itself. The paper provides a systematic and general analysis of the entire periodic configuration, based on a conversion of the field equations to a set of first order differential equations in the tangential components of the RF electric and magnetic field harmonics. In all regions the solutions are expressed in terms of transmission matrices which combine through simple boundary conditions to form an overall homogeneous set of equations. Its numerical solution provides all relevant data for the entire periodic configuration, comprising the finite thickness circuit itself, the dielectric support rods, and the enclosing metallic shield. The paper provides explicit formulae for numerical calculations of circuit characteristics, such as omega-beta diagram, interaction impedance, loss due to finite circuit conductivity, and detailed field and current distributions. Throughout the paper emphasis is placed on generality, so that the results are applicable to any kind of periodic cylindrical circuits. Application of the theory to a tape helix circuit is discussed briefly.