Richard G Carter

• MA, PhD
• Professor Emeritus at Lancaster University

Cambridge Core - RF and Microwave Engineering - Microwave and RF Vacuum Electronic Power Sources - by Richard G. Carter

The design of klystrons has long been a manual process guided by experience. However, with well-defined specifications and sufficiently rapid simulation methods, it is a good candidate process for automatic optimization techniques. In this paper, such a technique is evaluated and refined using klystron specific techniques, leading to several design...

This paper reviews the main types of radio-frequency power amplifiers which are, or may be, used for high-power hadron accelerators. It covers tetrodes, inductive output tubes, klystrons and magnetrons with power outputs greater than 10 kW continuous wave or 100 kW pulsed at frequencies from 50 MHz to 30 GHz. Factors affecting the satisfactory oper...

This paper reviews the main types of r.f. power amplifiers which are, or may be, used for particle accelerators. It covers solid-state devices, tetrodes, inductive output tubes, klystrons, magnetrons, and gyrotrons with power outputs greater than 10 kW c.w. or 100 kW pulsed at frequencies from 50 MHz to 30 GHz. Factors affecting the satisfactory op...

This paper describes a method for computing the field components in a barrel open resonator from a specified electric field on the axis. It shows how the shape of the resonator can be determined from the fields and how the properties of the resonator can be calculated. The method can be applied to other, similar, problems.

The applications of magnetrons to high power proton and cw electron linacs are discussed. An experiment is described where a 2.45 GHz magnetron has been used to drive a single cell superconducting cavity. With the magnetron injection locked, a modest phase control accuracy of 0.95° rms has been demonstrated. Factors limiting performance have been i...

Particle accelerators have many important uses in scientific experiments, in industry and in medicine. This paper reviews the variety of technologies which are used to accelerate charged particles to high energies. It aims to show how the capabilities and limitations of these technologies are related to underlying physical principles. The paper emp...

A simple method for modeling the performance of an inductive output tube (IOT) is described. The model reproduces the characteristics of an IOT with good accuracy over the full dynamic range of the tube.

The use of an injection locked CW magnetron to drive a 2.45 GHz superconducting RF cavity has been successfully demonstrated. With a locking power less than -27 dB with respect to the output and with a phase control system acting on the locking signal, cavity phase was accurately controlled for hours at a time without loss of lock whilst suppressin...

Multipactor can be a limiting factor in the design on many SRF cavities, however this is often a difficult phenomena to numerically model. In order to study the reliability of various codes we have undertaken to study the simulation of multipactor in rectangular waveguides and to compare this to experimental results obtained in previous work. In th...

A crab cavity is required in the CLIC to allow effective head-on collision of bunches at the IP. A high operating frequency is preferred as the deflection voltage required for a given rotation angle and the RF phase tolerance for a crab cavity are inversely proportional to the operating frequency. The short bunch spacing of the CLIC scheme and the...

This paper describes the use of evolutionary algorithms to optimize the interaction structure of a klystron.

Advances in the control of CW magnetrons have raised the possibility of using these devices as the RF power sources for particle accelerators. This paper describes the conceptual design of a 1 MW, 175 MHz, CW magnetron and compares its performance with tetrode amplifiers.

This paper describes an extension of the method of moments to allow full solutions of a reentrant cavity for modes with azimuthal variation by coupling the TE and TM solutions at the interface between the two regions. In addition a treatment of MBK stability using wake field theory is proposed.

In a triode type electron gun the amplification factor, mu, determines how the beam current varies with time for any given gun geometry and applied voltages. A simple triode low-mu formula has regularly been used to predict IOT behaviour however, it is incapable of addressing non-uniform cathode emission resulting from modern grid geometry and smal...

This paper describes a simple method for modeling the performance of an Inductive Output Tube (IOT). The model reproduces the characteristics of an IOT with good accuracy over the full dynamic range of the tube.

A number of particle accelerators worldwide require RF crab cavities for a number of applications, including maximizing collision luminosity, production of short X- ray pulses, and diagnostics. The Cockcroft Institute has led the development crab cavities for the LHC, ELC and CLIC colliders. The design for each of these cavities is very different d...

A crab cavity is required in the CLIC to allow effective head-on collision of bunches at the IP. A high operating frequency is preferred as the deflection voltage required for a given rotation angle and the RF phase tolerance for a crab cavity are inversely proportional to the operating frequency. The short bunch spacing of the CLIC scheme and the...

The compact linear collider (CLIC) requires a crab cavity to align bunches prior to collision. The bunch structure demands tight amplitude and phase tolerances of the RF fields inside the cavity, for the minimal luminosity loss. Beam loading effects require special attention as it is one potential sources of field errors in the cavity. In order to...

Crab cavities have been proposed for a wide number of accelerators and interest in crab cavities has recently increased after the successful operation of a pair of crab cavities in KEK-B. In particular crab cavities are required for both the ILC and CLIC linear colliders for bunch alignment. Consideration of bunch structure and size constraints fav...

For the design of a high efficiency MBK the calculation of the properties of resonant cavities is critical. A method of moments can be used to find these properties quickly and to a known accuracy.

This paper describes a theoretical model for the small-signal transient behaviour of a klystron. Comparisons are made between results obtained from the model and those of experimental measurements.

This paper shows how the properties of cylindrically symmetrical klystron cavities can be computed quickly and accurately using the method of moments. The method can be used to benchmark results obtained using computer codes based on the discretisation of the volume of the cavity.

The effectiveness of positive phase velocity tapering to improve the performance of a broadband helix traveling-wave tube (TWT) has been investigated. A large-signal model of an existing 4.5-18 GHz two-section mini-TWT with uniform pitch has been validated against the experimental results, and used as a starting point to design and develop a number...

The lowest resonant frequencies of reentrant cylindrical cavity resonators are calculated using the method of moments to obtain upper and lower bounds. The accuracy and convergence of the results are investigated and the factors and shunt impedances calculated. A simple empirical assumption about the choice of basis functions leads to results that...

Random walk and genetic algorithm techniques have been implemented in a 3-D collector simulation code to automate the design optimization of multistage depressed collectors. An axisymmetric four-stage collector and an asymmetric two-stage collector have been optimized following both approaches. Procedures for the implementation of these methods in...

A simple and accurate method has been developed to optimize the performance of coaxial couplers for traveling-wave tubes using a 3-D electromagnetic field simulation code. The new technique, which is a combination of numerical and analytical procedures, is presented with a comparison with conventional practice. By using this method, a number of cou...

The ILC crab cavity will require the design of an appropriate power coupler. The beam-loading in dipole - mode cavities is considerably more variable than accelerating cavities, hence simulations have been performed to establish the required external Q. Simulations of a suitable coupler were then performed and were verified using a normal conductin...

The ILC reference design report (RDR) recommends a 14 mrad crossing angle for the positron and electron beams at the IP. A matched pair of crab cavity systems are required in the beam delivery system to align both bunches at the IP. The use of a multi-cell, 3.9 GHz dipole mode superconducting cavity is proposed, derived from the Fermilab CKM cavity...

The Slow-wave Structure (SWS) cold parameters are typically obtained by analytical methods, experimental procedure or three-dimensional (3-D) full- wave simulations. The advantages and best applicability of each method will be assessed in order to provide the tube designer with a reference for a more efficient, fast and accurate design of helical S...

It is demonstrated that the output of a 2.45-GHz magnetron operated as a current-controlled oscillator through its pushing characteristic can lock to injection signals in times of the order of 100-500 ns depending on injection power, magnetron heater power, load impedance, and frequency offset of the injection frequency from the natural frequency o...

A detailed experimental study has been made of suspected multipactor discharge in a klystron input cavity in the presence of an axial magnetic field. The existence of the discharge was detected by changes in the return loss at the input coupler. This method does not require any modification of the cavity. Discharges appeared to take place over a ra...

Accurate phase control is demonstrated for an injection locked CW `cooker' magnetron in the presence of significant disturbing influences to its natural frequency (i.e. temperature, load and supply voltage fluctuations). This was achieved by driving the magnetron as a current controlled oscillator and at the same time controlling the phase of the i...

Low-power continuous wave "cooker" magnetrons driven from industrial-quality switch-mode power supplies have been frequency locked by driving them as current-controlled oscillators in a phase-lock loop (PLL). The noise performance of these frequency-locked oscillators is reported as a function of heater power. The injection of -30- to -40dB signals...

Multipacting induced discharge in a rectangular waveguide is studied experimentally at a RF frequency of 500 MHz. The waveguide has a cross-section of 457 mm by 102 mm. The maximum forward RF power is 600 and 300 kW in traveling and standing wave mode, respectively. A continuous multipacting band structure is observed. Electron pick-up probes of an...

In this paper, spreadsheet for the calculation of re-entrant and co-axial cavities for klystron and multiple beam klystron (MBK) have been built using equivalent circuit model. The results from the spreadsheet were compared with those from MAFIA and MicrowaveStudio (MWS), and the errors are within 5% if the validation criterions are satisfied for t...

In this paper, a simple model for studying the beam-wave interaction in the output gap of a klystron was developed using MathCad. The output parameter could be obtained, with the advantage of simplicity and speed compared with traditional disc and ring model. The calculated results were compared with those from MAFIA simulation and the errors for e...

An improved two-dimensional simulator MAGFLD has been developed which is useful for the design and simulation of periodic permanent magnet (PPM) focusing system for linear beam tubes. At present, input is possible only through the input file, which is very simple and user friendly. A complete PPM circuit is generated using the coordinates of first...

The High Power Radio Frequency (HPRF) Faraday Partnership is a UK technology forum for all users, designers, developers and researchers of RF and microwave devices and systems. High power RF and microwave engineering are key enabling technologies in a wide range of industrial sectors. Formed in October 2001 and funded initially by the UK Department...

Although a rectangular waveguide coupler has the conceptual advantages of simplicity and capability of withstanding higher power, builders of modern superconducting accelerators are routinely choosing instead a coaxial coupler for its proven performance. Multipacting induced discharge has been found to be an operating mechanism that prevents a rect...

In this presentation we study how cavity and bunch parameters affect the efficiency of power transfer from the bunches to the cavity and also provide verifying data for other models. The parameters of the klystron used in the investigation were beam power 2MW, beam voltage 100KV and beam current 20A giving a saturated efficiency around 65%.

Two-dimensional package EGUN was used for the simulation of multistage collector. Based on this package a pre- and a post-processor have been developed which make the package user friendly and analyses the performance of the collector. In this article, we modelled the multistage collector for high efficiency space TWT.

This paper deals with simple model of the interaction between the output cavity of a klystron and an electron bunch has been developed using Mathcad method. The objective of this paper is to find out how to choose the klystron parameters to get the highest possible conversion efficiency under ideal conditions. The six-disc model investigates the ef...

Experimental and numerical studies of multipactor in rectangular waveguide geometries are discussed in this paper. A new section of rectangular waveguide similar to the input coupler of the CESR-type SRF cavities has been designed to experimentally verify various multipacting suppression methods. It will also show the effects on multipactor of cryo...

The extraction of ions from the plasma of a gas discharge and their formation into a beam is investigated theoretically. The results are shown to be applicable to a gridded ion gun. The results are also applicable to the design of canal extraction systems, but it is shown that in this case a simpler method exists for obtaining the necessary informa...

Research has been carried out which investigated the effect of the beam parameters on the nonlinear performance of a helix TWT across a specified broad frequency band. The beam parameters include the beam voltage (at constant DC power) and the beam radius. A large signal (1D and 2.5D) computer program was used for this purpose, which models the int...

The design of a symmetric and an asymmetric collector has been optimised using the genetic algorithm. The improvement in collector efficiency in both cases is remarkable.

The use of spectrally efficient modulation schemes in future communications systems require power amplifiers which combine high conversion efficiency with good linearity. This paper examines how the efficiency and linearity of a helix TWT depends upon the choice of the parameters of the electron beam and the helix slow-wave structure.

Techniques based on the perturbation of cavity resonators are commonly used to measure the permittivity and permeability of samples of dielectric and ferrite materials at microwave frequencies. They are also used to measure the local electric- and magnetic-field strengths in microwave structures including the shunt impedances of cavity resonators a...

The intermodulation performance of a helix TWT was computed using a large-signal disc model with two, three and eight correlated carriers and also using the program IMAL which models a generalized nonlinearity described by its single-carrier transfer characteristics. The results obtained by both methods showed good agreement. The intermodulation pe...

TWTs for space applications commonly have a helix pitch profile which incorporates a section with increased phase velocity followed by a negative phase velocity taper. A simple method is described for the initial design of a helix slow-wave structure of this kind to achieve high overall efficiency. It is shown that the use of a section with increas...

Pulsed magnetron oscillators sometimes show an instability known as "twinning" in which the spectrum shows two, or more, closely spaced peaks. This phenomenon is undesirable and can lead to problems when it occurs in magnetrons used in radars. An experimental investigation of twinning is described from which conclusions are drawn about the design p...

The computer simulation of helix travelling-wave tubes requires accurate information about the phase velocity, interaction impedance and attenuation of the helix slow wave structure at each frequency. This has received considerable attention, from the pioneering work of Pierce onwards, and it is possible to compute or measure the phase velocity wit...

A large signal model is used to analyze the stability of a high gain helix TWT against the reflected signals caused by mismatches at its input and output terminations. The stability of a section of the tube in the presence of the reflected signals is determined by making a number of passes through the section for a very low drive power. A section i...

For a coaxial window of 2450 MHz, 60 kW magnetron, there are mainly two main requirements. One of the requirements is its low reflection coefficient at 2450 MHz operating frequency, the other is its handling capacity of more than 60 kW CW power. This paper is to establish initial design methods using the transmission line theory for such a coaxial...

Several cases for different connection ways of straps and output coupling plate were simulated by MAFIA. High-order axial modes are found because the anode length is longer than 1/2 wavelength. Their frequency properties show that the effect of straps is strong enough to get a good mode separation when the four straps (or the coupling plate) have t...

An approach of designing helix SWS for achieving high beam (interaction) efficiency of the TWT, is presented. The SWS parameters are determined for a C-band 60 W TWT at beam voltage 3.0kV and beam current 75mA. The rf phase velocity of the SWS is optimised with positive taper followed by negative taper. It is shown that the positive taper in the ci...

Travelling-wave tube amplifiers, used in satellite and other broad-band communication systems, must be operated as close as possible to saturation to achieve good d.c. to r.f. conversion efficiency. The non-linearity of a tube close to saturation causes the generation of inter-modulation products whose amplitudes must be small enough to meet the sy...

A three-dimensional (3-D) package for simulation of asymmetric and crossed-field multistage depressed collectors for microwave tubes has been developed. This package is based upon the 3-D finite-difference code KOBRA3-INP. The main features of the package are a user-friendly input interface, post-processors for collector analysis and calculation of...

An important objective in the operation of low energy medical standing wave linear accelerators for medical X-ray use, is to limit the spread of energies into the low energy region in order to reduce skin dose to a minimum. This article suggests how this might be achieved by adjustment of the timing of the electron beam pulse relative to the rf pow...

The Pierce impedance of helix slow-wave structures has been measured using nonresonant perturbation techniques. Effects of space harmonics and TE fields were demonstrated using experimental results for the first time. It was found that there was an error in the derivation of the correction factor commonly used for the uniform-axial-field assumption...

The 3-dimensional finite-difference time-domain method in non-orthogonal co-ordinates (non-standard FDTD) is used to calculate the frequencies of resonators. The numerical boundary conditions of the method are presented. The influences of boundary conditions and discrete meshes on the numerical accuracy are investigated. We present the nonstandard...

A finite-difference frequency-domain algorithm has been developed in non-orthogonal curvilinear co-ordinates. The full vector Maxwell's equations are discretized on boundary-fitted meshes. Because the algorithm is formulated in a non-orthogonal co-ordinate system, it is not restricted to any a special orthogonal co-ordinate system, and can over the...

The efficiency of travelling-wave tubes (TWTs) operated under nonlinear conditions is usually enhanced by adjusting the phase velocity of the slow-wave circuit towards the output end of the tube. This technique, known as tapering, aims to maintain the optimum phase relationship between the electron bunches and the slow electromagnetic wave. The pap...

It is often necessary to introduce a sever or attenuator into the slow wave structure of a travelling wave tube (TWT) to ensure stability against feedback oscillations. These are caused by signals reflected by mismatches at the input and output of the slow-wave structure and by the inherent backward wave. The position of the sever is an important d...

A fast and accurate one-dimensional large-signal model for coupled-cavity TWTs has been developed that can be used interactively for the optimization of a TWT design. Different modeling techniques for enhancing the speed of the large-signal model with no loss in accuracy are discussed. It has been shown that the speed of the model can be increased...

Training for the role of project leader can often be haphazard or even non-existent. A one-year M.Sc. course has been developed which aims to provide the necessary knowledge and skills

In the development of computer models of coupled-cavity travelling wave tubes, it is necessary to have some means of calculating the properties of the slow-wave structure. Direct calculation is difficult because of the complexity of the shapes involved. One possible method makes use of the equivalent circuit representation of the slow-wave structur...

In the theory of microwave linear beam tubes, it has hitherto been assumed that the space charge potential for a cylindrical electron beam passing through a concentric, earthed, conducting tunnel broken by interaction gaps can be calculated by supposing that the tunnel is continuous. In this paper, the effects of the gaps are computed for both an e...

Recent developments in engineering education in Britain have concentrated on the addition of engineering applications to existing degree courses. It is suggested that this should be regarded as the first stage of a continuing development. A possible procedure for this development is discussed. It is shown that using information about the work done...

The slow-wave structures used in high-power travelling-wave tubes may be represented by equivalent circuits. It is shown that, by a suitable choice of equivalent circuit parameters, a good fit can be obtained between calculated curves and measured data points. The equivalent circuits may be used to represent the slow-wave structure in computer mode...

A proposed wave energy converter consists of an array of small floating bodies moving in surge and restrained by dampers. The hydrodynamic behaviour of one such body is studied theoretically and experimentally. Approximate agreement between theory and experiment is reported. The absorption length of individual bodies is small but it is suggested th...

A method is described for designing coil systems producing Cheb¿shev equal-ripple variation of the axial magnetic field. The off-axis fields of such systems are investigated, and they are found to have advantages over the usual systems for generating uniform fields when a field is required that is uniform within an ellipsoidal, rather than a spher...

Previous studies of an ion-beam klystron showed anomalous results when the drift space was filled by a plasma. This paper describes experiments carried out to study the ion-beam/plasma system in greater detail. Techniques have been developed for the measurement of ion and electron densities, and for the study of radiofrequency propagation character...

The design of canal ion sources is discussed taking into account the lens effect of the canal aperture, and the results summarized in a universal design curve. Experimental data available falls between this curve and one in which lens effects are neglected. The relationship between theory and experiment is considered.

Two methods can be used to suppress multipacting in a rectangular coupler waveguide. The slotted waveguide method calls for opening slots on the broad walls in the wave propagation direction that perturb the resonance and trap multipacting electrons. The DC magnetic bias method utilizes a solenoid coil wrapped around the waveguide to generate a mil...

This report describes a LLRF system developed at Lancaster University and an experiment undertaken at the STFC Daresbury Laboratory by Cockcroft Institute Staff to validate an approach to phasing the crab cavities for the International Linear Collider. The work has involved the manufacture and processing of a pair superconducting cavities, the deve...

The International Linear Collider (ILC) has a 14 mrad crossing angle in order to aid extraction of spent bunches. As a result of the bunch shape at the interaction point, this crossing angle at the collision causes a large luminosity loss which can be recovered by rotating the bunches prior to collision using a crab cavity. The ILC baseline crab ca...