Slow-wave Circuit Research Articles

Traveling-wave-tube simulation: The IBC code

An interactive beam-circuit code (IBC) is presented, to run interactively on fast PCs or workstations, for purposes of first-cut design of traveling-wave tubes (TWTs) at small and large amplitudes. The new physics parts are the use of particle-in-cell methods to obtain the space-charge forces, and the following of the electron beam over the full length of the tube. The model is fully nonlinear and one-dimensional, with the transverse space-charge fields approximated by one mode. The slow-wave circuit is modeled by a transmission line. All variables are displayed continuously, such as the velocity displacement of all the particles (phase space), beam charge and current densities, space-charge field, circuit field, voltage and current, circuit power, and the location of the added loss. Some initial runs are presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Large-signal field analysis of an O-type travelling wave amplifier. Part 3: Three-dimensional electron motion

A large-signal field analysis of an O-type travelling-wave amplifier employing a practical focusing-field arrangement is presented, based on a coupled Eulerian-Lagrangian formulation of the problem. The resulting three-dimensional electron trajectories give rise to a beam that varies with the axial co-ordinate and time. It is shown that the boundary conditions on the moving (a priori unknown) beam boundary can be automatically satisfied by redefining the charge and current densities for all values of the radial co-ordinate. The key step in the analysis is a representation of the field components as functions of the electron-arrival time and the electronradial position, through a sequence of Green&apos;s functionals for the slow-wave circuit. Substitution of this representation into the electron ballistic equations reduces the latter to a fixed-point problem for a pair of operators in an appropriate function space. The fixed point, and therefore the solution for the electromagnetic field components, can be obtained by standard successive approximation techniques. Finally, it is shown that when the radial component of the focusing magnetic field vanishes and its axial component becomes constant, the electron trajectories degenerate to straight lines parallel to the tube axis.

Finite-Element Analysis of Slow-Wave Schottky Contact Printed Lines

Extensive finite-element analyses on MMIC slow-wave structures with both Iocalized and layered models are presented. Good agreement is achieved between the data presented here and other theoretical results and experiments. Higher order elements that improve accuracy are discussed. The comparative studies for Schottky contact microstrip and coplanar waveguide with Iocalized and layered models are presented. Potential applications of the Iocalized models to more general and practical slow-wave circuits are also discussed.

Comments on "Numerical analysis and design for high-performance helix traveling-wave tubes"

Tsutaki et al. recently established a new design method based on an analytical technique to consider the influences of the tape width, dielectric, and shield barrel in the helix slow-wave circuit. However, there are numerous mistakes on the equations that will make it impossible for a reader to make use of these equations for analytical tools. Here, a few obvious mistakes are pointed out so that corrections can be made to several equations.

Numerical analysis and design for high-performance helix traveling-wave tubes

A new design method has been established for helix traveling-wave tubes having higher output powers (over 100 W) and wider bandwidths (2 to over 4 GHz) and capable of stable operation at frequencies in 10 to over 20 GHz bands. It is based on an analytical technique to consider the influences of the tape width, dielectric and shield barrel in the helix slow-wave circuit simultaneously, and also on an analytical technique to solve problems in regard to backward-wave oscillations at higher output powers, matching input and output sections for wider bandwidths, and undesired coaxial modes caused at operating frequencies above 20 GHz. This method realizes practical design of overall high-performance helix traveling-wave tubes with output powers of 250 W in the 14-GHz band and 20 W in the 30-GHz band and a bandwidth of 2 GHz in the 12-GHz band.

Optimum Design of a Potentially Dispersion-Free Helical Slow-Wave Circuit of a Broad-Band TWT (Short Paper)

The results of an equivalent circuit analysis are studied for a potentially dispersion-free slow-wave circuit of a TWT which consists of a dielectric-supported helix in a metal shell provided with vanes. The optimum vane dimensions are predicted, which should be helpful in broadbanding the performance of a TWT.

Large-signal field analysis of an O-type travelling-wave amplifier. Part 1: theory

A rigorous method of analysing the large-signal behaviour of a travelling-wave amplifier is presented, starting from the Maxwell equations in the Eulerian form and the electron ballistic equation in the Lagrangian form. The key step in the method is a representation of the field components as functionals of the electron-arrival time through a Green&apos;s function sequence for the slow-wave circuit. Substitution of this functional representation for the axial electric field component into the electron ballistic equation reduces the latter to a fixed-point problem for an operator in an appropriate function space. The fixed point, and therefore the solution for the electron-arrival time and hence the solution for the electromagnetic field components, can be obtained by standard successive approximation techniques. The calculation of the TWT gain, comparison of the results of the present theory with those of the existing ones etc., on the basis of such a successive approximation solution for the field components, will be deferred to a later paper.

Dispersion and Field Analysis of a Microstrip Meander-Line Slow-Wave Structure

A structure which is important as an example of a spatially periodic medium for microwave propagation is analyzed theoretically, with rigorous consideration of its partial dielectric composition, symmetry properties; and field configuration relating to its use for electron-wave interaction in a crossed-field amplifier (CFA). The analysis is carried out in a quasi-TEM approximation, leading to determination of a complex potential function within the unit cell and the associated normal-mode parameters: effective dielectric constant, phase velocity, and characteristic impedance, as functions of phase per cell and mode symmetry. With imposition of meander-line boundary conditions, solutions of the characteristic equation for the dispersion law of the structure are computed, including the influence of the inhomogeneous dielectric-vacuum construction of microstrip. Agreement with the observed phase and stopband features of a representative structure is very good. Power distribution and group velocity are calculated, and an interaction impedance, representing the coupling between the RF field and an electron beam for estimation of CFA performance is also calculated. The method lends itself to detailed computations, including the effects of structural features of practical slow-wave circuits.

Experiments on collector potential depression of T. W. T. 's†

Abstract This paper gives the results of experiments aimed at maximizing the efficiency of high power T. W. T. 's with linear slow-wave circuits by depressing the potential of the electron collector. A device for preventing noise deterioration and high current interception on the slow-wave circuit, which usually accompanies the depression of the collector potential, is described. Experimental results are given and from these some approximate relationships are deduced to predict depressed collector performance.

A 2-kW multioctave TWT focused with samarium cobalt magnets

The most severe and fundamental performance limitation of the PPM focused TWT has been excessive thermal heating of the RF propagating structure due to some fractional interception of the electron beam. The quality of beam focusing has largely been determined by the characteristics of permanent magnets in the Alnico series. With the introduction of the cobalt-rare earth alloys, a breakthrough in the performance of PPM focused TWTs can be expected. A samarium cobalt focused TWT yielding an output power of 2 kW at 10 percent duty is described. Utilizing a conventional helix slow-wave circuit, the tube covers a multioctave frequency range from 3.5 to 10.6 GHz. Successful operation has been achieved into a load VSWR of 10:1. The magnets are fabricated from powdered cobalt-rare earth alloys by a process sequence that includes powder preparation, magnetic alignment, pressing, sintering, and magnetizing. Energy products in excess of 15×106gauss-oersteds (MGOe) have consistently been achieved for use on this tube.

A technique for measuring the dispersion characteristics in slow-wave circuits containing materials with nonreciprocal RF properties

A traveling wave technique to measure the dispersion charateristics of slow-wave circuits is described which uses a sensitive phase measurement system and negates the requirment for shorting the circuit under test. Because of the elimination of the short and because the sensitivity of the measurement does not require strong coupling to the circuit fields, errors due to the creation of spurious modes are minimized. Comparison of wavelength measurements using this system with those of previous techniques show excellent agreement.

Some aspects of circuit power dissipation in high power CW helix traveling-wave tubes, part II: Scaling laws

This paper extends the basic theory of the thermal behavior or helix-type slow wave circuits described in Part I [1] to show the effect of scaling to higher frequencies. The differences in the scaling laws which result from the alternative assumptions of constant beam voltage or constant beam perveance are discussed, and a simplified formulation permitting the thermal behavior to be described in terms of universal curves is presented.

Some aspects of circuit power dissipation in high power CW helix traveling-wave tubes, part I: General theory

This paper describes the basic theory underlying calculations of the thermal behavior of helix-type slow wave circuits used in high power traveling-wave tubes. Typically, the helix is supported by means of three ceramic rods in a metal shell with the helix brazed to the rods. At the highest power levels the support rods are also brazed to the tube shell. The results of calculations on specific structures are presented which show the use of different support rod and helix materials, of beam interception, and of brazing the support rods to the shell. Of particular interest is the conclusion that the temperature difference between the hottest and coldest parts of the helix can be significantly larger than the temperature drop across the support rods when using high thermal conductivity ceramic materials brazed to the tube shell.

The Loss Characteristics of a Semiconductor Travelling Wave Amplifier

This paper presents a theoretical analysis on the effect of space harmonics in STWA. It has been proven that even if no gain can be predicted by considering only the principal harmonic component, the total gain is obtained by the effect of the other space harmonic components. This paper also presents the considerations of (1) the effect of the gap between the fingers of the circuit, (2) the effect of the gap between the current sheet and the circuit, (3) the effect of the loss of the circuit, and (4) the advantage of using the backward type slow wave circuit.

A high-power C-band dc-operated crossed-field amplifier

A C-band, dc operated, forward wave crossed-field amplifier has been developed for phased array applications. This tube, designated the SFD-237, is a circular format, emitting sole, reentrant electron stream crossed-field amplifier utilizing a helix derived slow wave circuit. Designed specifically for phased array applications, the magnetically shielded package has a maximum transverse dimension of 10 inches and is 32 inches long. Design and construction details of the amplifier will be discussed.

Superconductive Microwave Meander Lines

This paper describes the fabrication, testing, and application of superconductive meander lines. The meander line is a slow-wave circuit which consists of a number of parallel tapes uniformly spaced and connected in series. The tape length is equal to one-quarter wavelength for the center frequency of the line. Microwave signals propagate in the form of TEM waves along the tapes. Interaction between adjacent tapes leads to a dispersion curve which is in general nonlinear, but which possesses some nearly linear regions. Thus, either linear or dispersive performance may be obtained. Meander lines find application as slow-wave elements in low-noise amplifiers such as traveling wave masers, as linear delay lines, or as dispersive delay lines in pulse-compression filters. The present investigation deals with lead meander lines fabricated by the photoetch process. Reflection from and transmission through the meander line were measured by conventional techniques at room temperature, 77°K, and 4.2°K. A striking decrease in insertion loss was noted when the line became superconductive. Insertion loss and VSWR of the superconductive line were rapidly fluctuating functions of frequency, generally increasing and decreasing together. At numerous frequencies between 4.0 and 4.5 GHz, a 30 nsec delay line had insertion loss of 0.5 dB and VSWR less than 2. (Most of this insertion loss was probably due to nonsuperconductive input lines inside the cryostat.) For a comparison, a copper meander line, identical in geometry to the superconductive line was operated at 4.2°K, and was found to have insertion loss that was as much as 20 dB greater than that of the superconductive line. Meander delay lines should readily lend themselves to operation a closed cycle refrigerator.

Traveling-Wave Amplification by Drifting Carriers in Semiconductors

The interaction of drifting carriers in semiconductors with traveling waves in an external slow-wave circuit is investigated. The electromagnetic fields are obtained in the circuit-space and in the semiconductor-space by three-dimensional analysis. A dispersion relation for this system is derived by connecting admittances in both spaces at the semiconductor surface. Characteristics of propagating waves are similar to those of ultrasonic wave amplification. Attenuation turns into gain when the drift velocity of the carriers exceeds the phase velocity of the wave. For illustrative examples, n-type InSb at 77°K and GaAs at room temperature are examined. Attainable gains are expected to be about 200 dB/mm for both materials.

Surface elastic-wave propagation and amplification

Surface elastic-wave propagation, transduction, and amplification (in a piezoelectric semiconductor) are discussed with emphasis on characteristics useful in electronic devices. Computed curves show the dependence on distance from the surface of the elastic and the electric fields associated with surface elastic-wave propagation in cadmium sulfide. The interaction impedance, relating the external electric field to power flow, is computed for propagation on the basal plane of CdS and found to be low in comparison with values characteristic of electromagnetic slow-wave circuits. Amplification with a continuous drift field in cadmium sulfide is reported, and differences between surface- and bulk-wave amplifiers are discussed. Some operating characteristics and fabrication techniques for making electrode transducers on piezoelectric crystals are given, together with experimental results on several passive surface-wave devices.

Multi-velocity Stream Effects and the Efficiency of Slow-cyclotron Wave Amplifiers†

ABSTRACT This paper discusses the efficiency of slow-cyclotron wave travelling-wave tubes and shows that contrary to the simple single velocity theory of such devices, exciting a slow-cyclotron wave on an electron beam can result in a substantial velocity spread in the electrons which is sufficient to prevent the realization of the high efficiencies predicted by the simple theory. A new multi-velocity theory is presented to explain this effect and to predict the conditions that must be imposed on the electron beam and slow-wave circuit in order to avoid damaging velocity spreads.

Cyclotron Harmonic Amplification in Beams and Plasmas†

ABSTRACT This paper concerns wave phenomena in electron beams and plasmas with internal motions, in the presence of a static magnetic field. It is known that axially-rotating beams show wave propagation when the Doppler-shifted frequency seen by the beam electrons is approximately a harmonic of the electron cyclotron frequency. Similar propagation in an infinite series of coupled modes can occur for beams and plasmas in which the electrons gyrate about the magnetic field lines, rather than the axis. Associated with each Doppler-shifted cyclotron harmonic, a slow and a fast space-charge wave are propagated along an electron beam. These sets of waves can interact with each other, with slow or fast wave circuits, or with a plasma, to yield growing waves. The nature of these interactions is discussed in the paper. It is suggested that this mechanism of wave amplification along an unneutralized electron beam may provide an explanation of the noise growth observed in electron beams from shielded guns, and in cr...