Cylindrical Circuit Research Articles

Time-Domain Multimode Analysis of a Terahertz Gyro-TWT Amplifier

High-order mode employed as the operating mode of a terahertz (THz) gyrotron traveling-wave tube (gyro-TWT) amplifier shows strong dispersion, which deteriorates the device performance in amplifying picosecond THz pulses. Theoretical investigation of a THz gyro-TWT amplifier with a lossy cylindrical circuit is carried out to study the problems, such as lossy structure design, parameters selection, frequency-domain performance, and time-domain dynamics. The robust high growth rate low-kz amplification and the broadband high-kz amplification are two preferred operation conditions. The revealed characteristics are also useful for developing THz gyro-TWTs with other kinds of over-moded circuits.

Circuits on cylinders

We consider the computational power of constant width polynomial size cylindrical circuits and nondeterministic branching programs. We show that every function computed by a π2 MOD C0 circuit can also be computed by a constant width polynomial size cylindrical nondeterministic branching program (or cylindrical circuit) and that every function computed by a constant width polynomial size cylindrical circuit belongs to ACC0.

Circuits on Cylinders

We consider the computational power of constant width polynomial size cylindrical circuits and nondeterministic branching programs. We show that every function computed by a Pi_2 o MOD o AC^0 circuit can also be computed by a constant width polynomial size cylindrical nondeterministic branching program (or cylindrical circuit) and that every function computed by a constant width polynomial size cylindrical circuit belongs to ACC^0.

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

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.

Interaction Impedance Measurements by Propagation Constant Perturbation

The perturbation in the complex propagation constant of a lossy, nonreciprocal, periodic waveguide produced by the insertion of a rod, which may be cylindrical or periodic, parallel to the waveguide axis is developed. The application to the experimental determination of the interaction impedance and electromagnetic field distribution of waveguides is presented, together with the approximations which are applicable. The perturbation formulas for three particular classes of circuit-lossless, reciprocal, cylindrical circuits; lossy, nonreciprocal, cylindrical circuits; and lossy, nonreciprocal, periodic circuits-of interest for traveling wave tubes and other extended interaction microwave tubes, are derived and the limitations discussed. Explicit interaction impedance relations for these circuits in terms of the phase constant perturbation, caused by a cylindrical or periodic rod, are given.