Theoretical Study for Folded Waveguide Traveling Wave Tube

A wideband folded waveguide traveling-wave tube (TWT) amplifier has advantages of simpler coupling structures and robust structure over the conventional helix TWT. The phase velocity of waves in folded waveguide is slowed down to the velocity of electron beam. Slow-wave interaction with the electron beam in folded waveguide is studied in a linear fashion. For a cold beam, the linear theory predicts a gain of 2 dB/cm and a bandwidth of 37% at the center frequency of 14 GHz. A closed algebraic dispersion relation for the frequency and the axial phase shift per period is obtained using an equivalent circuit model. Numerical solution calculated from the dispersion relation and three-dimensional electromagnetic code, HFSS simulations predict a mode coalescing in the folded waveguide. And a theoretical phase velocity prediction of the electromagnetic wave in this circuit is verified by HFSS simulations.     

Characteristics of Bifilar Helix Circuit

The characteristics of two kinds of bifilar helix circuit are discussed in this paper. One is alike wound bifilar helix and another is contrawound bifilar helix. Alike wound bifilar helix is often used in O-type backward wave tube (BWO). Owing to wider operating bandwidth, higher interaction impedance and large dimensions, the contrawound helix is suitable for broadband millimeter wave traveling wave tube (MMW TWT).     

Strapped bifilar helices for high-peak-power traveling-wave tubes

A method of increasing the peak-pulsed power output of broad-band traveling-wave tubes is described. The method involves the use of a modified bifilar helix for the slow-wave structure. The modification employs 1) special straps or 2) mode-selective attenuation to prevent backward-wave oscillation in the anti-symmetric mode. This results in the possibility of using helices in the symmetric mode at values of ka (circumference-to-free-space wavelength ratio) as large as 0.6 at the highest amplification frequency. This in turn makes possible an increase in peak-pulsed beam power of a factor of approximately sixteen times that possible with a single helix. Both analytical and experimental results regarding the behavior of the structures are presented showing the propagation characteristics. The experimental results include cold measurements to determine ω-β diagrams and measurements with an electron beam which yield experimental values of interaction impedance.     

Traveling-wave amplifiers and backward-wave oscillators for VHF

An important aspect of the design of traveling-wave amplifiers and backward-wave oscillators for frequencies below 500 mc is the problem of obtaining a tube of reasonably small physical dimensions. Hollow beams of greater perveance than is obtainable with solid beams offer one method of reducing the size of such tubes by permitting operation at a lower voltage and greater gain per wavelength, for a specified beam power, than is possible in a solid beam tube. Some aspects of the design of minimum size hollow-beam forward-wave amplifiers using single helix circuits and backward-wave oscillators using bifilar helix circuits are presented. Several tubes of these types for operation below 500 mc have been built. Amplifier bandwidths and oscillator tuning ranges in excess of four to one in frequency have been obtained experimentally. Amplifier efficiencies in excess of 20 per cent and oscillator efficiencies in excess of 10 per cent have been achieved.     

Field Theory of Planar Helix Traveling-Wave Tube

A pair of unidirectionally conducting screens, conducting in different directions, constitute a planar helix. The planar helix is proposed as a slow-wave structure for application in a traveling-wave tube (TWT). Field theory is applied to analyze the behavior of the planar helix in the presence of a flat electron beans present between the two screens. Results indicate the presence of three modes, with one mode having a negative attenuation constant, as in the case of the usual helix-type TWT. Curves are shown for a typical proposed planar TWT. Also, the effect of beam current is indicated.     

A coupled mode description of the backward–wave oscillator and the Kompfner dip condition

The start oscillation condition for the backward-wave oscillator and the operation of the traveling-wave tube amplifier at the Kompfner dip point are described from the point of view of the coupling of two modes of propagation. Growing waves are not involved. Two waves are sufficient when the tube is more than a half plasma wavelength long. Operation in this "large space charge" domain is inherently simpler than in the "low space charge" domain. The start oscillation condition and the Kompfner dip condition are simply expressed in terms of the coupling constant between modes, HL = (2n ± 1) π/2, where n is an integer. In addition, the uncoupled modes must have the same velocity. The result is also expressed in terms of the more familiar parameters CN and hL. The effect of loss in the circuit mode is calculated. When the two waves carry energy in opposite directions, growing waves result. This case is discussed briefly.     

Slow-Wave Characteristics of a Frame–Rod Structure Based on Micro-Fabricated Technology for THz Vacuum Electron Devices

A simple equivalent circuit analysis of the frame–rod slow-wave structure (SWS) on dielectric substrates of a traveling-wave tube (TWT) is developed, using the quasi-TEM approximation approach for the dispersion and coupling impedance characteristics of the structure. Moreover, the obtained complex dispersion equation and coupling impedance are numerically calculated. The calculation results by our theory method agree well with the results obtained by the 3D EM simulation software HFSS. It is shown that the dispersion of the frame–rod circuit is decreased; the phase velocity is reduced and the bandwidth becomes greater, while the coupling impedance decreases after filling the dielectric materials in the frame–rod SWS. In addition, a comparison of slow-wave characteristics of this structure with a rectangular helix counterpart is made. As a planar slow-wave structure, this structure has potential applications in compact TWTs based on the micro-fabrication technology, which could be scaled to millimeter wave, even to THz frequency.     

Interaction between the electron beam and the surface wave in a dielectric plate

A model of the traveling-wave tube (TWT) that includes a dielectric plate adjoining a perfectly conducting surface and a metal screen parallel to the plate is considered. The dispersion equation in the presence of a homogeneous electron beam filling the space between the plate and the screen is derived. The method of differentiation of the dispersion equation is used to obtain and calculate coefficients of the TWT characteristic equation and coupling and depression coefficients, i.e., coefficients determining the main properties of the TWT. The considered model is compared with an “impedance” comb structure and a cylindrical helix. Conclusions concerning the prospects of development of a “dielectric” TWT are drawn.     

Relativistic effects in the traveling-wave amplifier

A relativistically correct large-signal theory is developed for the analysis of high-power, axially symmetric traveling-wave amplifiers in order to investigate the physical phenomena involved in the interaction process. The nonlinear integro-differential system equations are developed from the Lorentz force equation, the one-dimensional equivalent circuit equation, the wave equation, and the continuity of charge relation. These equations are applied to two electron stream models: a ring model which permits the effects of nonlaminar flow and space-charge forces to be evaluated, and a disk-electron model in which these effects are ignored. The ring model space-charge fields are obtained from the appropriate Green's function for Poisson's equation in a moving frame of reference. Numerical solutions are presented and discussed with major emphasis on the disk-model solutions. The principal results are that the gain per unit length decreases with increasing beam velocity, the circuit phase velocity for optimum power output approaches the dc beam velocity u0, asu_{0}/capproaches unity, and the conversion efficiency is almost independent of u0for the synchronous case. The linearized one-dimensional theory of the traveling-wave tube is also discussed. Several of the large-signal results are predicted from the small-signal theory.     

A Simple Closed-form Formula for Backward-Wave Start-Oscillation Condition for Millimeter-Wave Helix TWTs

An accurate and simple closed-form formula, for backward-wave start-oscillation condition for a millimeter-wave helix traveling-wave tube amplifier was developed, using an artificial neural network (ANN) algorithm. The analysis considers the effects of circuit loss and also the variation of electron beam diameter corresponding to beam filling. The formula is simple and amenable to easy computation, even using a scientific calculator, and without resorting to exhaustive numerical iterative search followed in conventional analyses and, at the same time, without sacrificing the accuracy in results. The formula was validated against published results, and excellent accuracy was observed. The analysis has been further used for inferring some physical interpretations on the effects of beam-filling factor and circuit loss on the start-oscillation condition of a typical millimeter-wave helix traveling-wave tube.     

Theoretical analysis of log-periodic circuits in microwave amplifiers

The feasibility of applying the log-periodic concept to microwave amplifiers has been investigated. This approach, successfully utilized in antenna design, offers the potential of greater bandwidth at a given power level than attainable from existing uniform devices. Log-periodic devices analogous to klystron, traveling-wave, and hybrid amplifiers have been studied. The dimensions of each section, including the beam diameter, in a log-periodic amplifier are a constant factor times those of the preceding section. Thus the general outline of such devices is conical. These devices have been simulated on a digital computer using a model in which the coupling between periodic sections is provided by one space-charge mode and one circuit mode. The accuracy of this model has been verified by simulation of existing traveling-wave tubes. Computer results on a 100kW log-periodic "klystorn," using a backward-wave circuit with a total taper ratio of 4.6 to 1, indicate that a useful bandwidth of approximately 3 to 1 can be obtained. Increasing the mechanical taper increases the bandwidth in direct proportion. Computer results on log-periodic versions of helix traveling-wave tubes are also given.     

Wave propagation on multifilar helices

The modes of the sheath helix are shown to be related closely to the space harmonics of real helices. Multiwire helices propagate many modes, the principal space-harmonic component of each approaching more closely the appropriate sheath helix mode as the number of wires is increased. Each mode can be excited by a certain phase sequence of exciting currents for the wires in one transverse plane. Experimental verification of the theory is reported using a bifilar helix tube. Phase velocities and impedances are measured, using Kompfner's null method and the start of backward-wave oscillations for the principal forward and backward components respectively.     

The theory of twisted transverse-wave couplers

The coupled-mode theory of a class of transverse-wave couplers in which the plane of polarization of the electric field rotates along the length of the coupler is described. The synchronism conditions between the circuit wave and the beam that lead to strong interaction with one or more of the transverse beam waves are given and the case of equal interaction with the two cyclotron waves is discussed in detail. It is observed that any two transverse waves of opposite polarization can be excited equally in a twisted coupler, or that coupling to one of two waves with the same phase velocity but opposite polarizations can be achieved.     

Theory of Gyrotron Traveling-Wave Amplifiers

A unified single-mode theory is developed for the gyrotron traveling-wave amplifier (gyro-TWA) at harmonics of electron gyro frequency, both in linear and nonlinear regimes. The theory is applicable to a wide class of waveguide cross sections and waveguide modes; it can also be useful for arbitrary harmonic numbers and with the generalized electron beam model. The waveguide fields are expanded into series of multipoles about the electron guiding centers. A general dispersion equation is derived. Some numerical examples of the gain-frequency curves of gyro-TWA's with out-ridged, magnetron-type, rectangular and circular waveguides are computed by employing the results of kinetic theory.     

Orthogonal waves on electron beams

The propagation of slow electrokinetic waves on finite electron beams which fill a conducting tunnel is discussed for modes of axial symmetry. In addition to the familiar space-charge modes, a pair of modes exists which are related to the vortex frequency (omega_{upsilon} = omega_{c} - 2theta_{0}). The finite magnetic field introduces a coupling between these modes. A set of four orthogonal modes can be derived by the use of matrix transformations, thus eliminating the necessity of solving a complicated characteristic equation. For infinitely high magnetic fields, the two additional modes disappear and the four modes reduce to the fast and slow space-charge waves.     

Noise measurements on a magnetron injection gun beam

The results of noise measurements conducted on a helix-type traveling-wave amplifier containing a magnetron injection gun are described. A minimum noise figure of 15.3 dB was observed at 760 MHz with an approximate beam power of 1600 watts. The noise figure was minimized by an adjustment of the magnetic field, which determines the transit time of the electrons through a drift region. This optimizes the magnitude and phase of the standing noise waves at the helix input.     

Traveling-wave tube analysis of the Adler tube

The cyclotron waves on an electron beam in the pump field of the Adler tube are studied with respect to their circular polarization. It is found that positive and negative circularly polarized beam waves are coupled through the pump electric field. As a consequence of the coupling, the small signal traveling-wave analysis leads to the conclusion that the positive circularly polarized beam wave is comprised of the fast signal wave and all idlers of frequenciesn(omega pm omega_{p})where n is an even integer, while the negative circularly polarized wave is comprised of all idlers with odd integral values of n. This information appears to be new, and can perhaps be used to design input and output couplers which discriminate against unwanted idler waves.     

Ring-plane traveling-wave amplifier: 40 KW at 9 MM

A 9-mm traveling-wave tube (TWT) amplifier using a ring-plane circuit is described. This tube has produced a peak power of 43 kw at an efficiency of 12 per cent(2C)with a solid beam. Several guns producing solid and hollow beams have been used with comparable results at high voltages (15 to 100 kv) and low currents (0.11 to 3.8 a). A waveguide transition (special coupler) incorporating a magic tee is used to couple independently to the two modes that can exist on the slow-wave circuit. The circuits, due to their good heat dissipation capability, can be operated either pulsed or CW. Their large size (ka= 1, 2, 3 ...) with useful cross sections comparable with those of ordinary waveguides, makes them attractive for producing kilowatt powers even at much higher frequencies.     

Coupled-mode analysis for nonuniform crossed-field drift beams

Coupled-mode theory is used to describe the propagation of waves on a nonuniform crossed-field beam in a drift region. The nonuniformity considered in this paper is due to potential variation along the beam. Numercial solutions are obtained for the normal-mode amplitudes for two types of potential variation, namely, linear and exponential. It is shown that the coupling between the modes, which is due to the potential variation, can be used to reduce the noise figure of crossed-field amplifiers.     

Behavior of traveling-wave tubes near circuit cutoff

A theory is developed which explains the operation of a traveling-wave tube when operated near the cutoff frequency of the slow-wave circuit, including the effect of two circuit waves instead of the usual one. The theory is normalized in a manner analogous to that used in more conventional analyses and a first-order expansion about the cutoff frequency is used, making a relatively small number of curves applicable to a large number of cases. The relationship between this theory and the three-wave theory usually used in traveling-wave-tube analysis is shown, and they are in agreement when the system is operated far from the cutoff frequency. Numerical results are given for a range of parameters which might be useful in traveling-wave-tube design, and an excellent agreement with published experimental results is shown.